Answer:
51.2
Step-by-step explanation:
To divide 2560 by 50, you can use long division. The answer is 51.
Explanation:To divide 2560 by 50, you can use long division. Here's how:
Start by dividing 25 into 256. The quotient is 10.Multiply 10 by 50, which equals 500.Subtract 500 from 2560 to get 2060.Bring down the next digit, which is 0.Divide 25 into 206, which gives you a quotient of 8.Multiply 8 by 50, which equals 400.Subtract 400 from 206 to get 60.Bring down the next digit, which is 0.Divide 25 into 600 to get a quotient of 24.Multiply 24 by 50, which equals 1200.Subtract 1200 from 600 to get 0.Therefore, 2560 divided by 50 equals 51.
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Is my answer correct???
Answer:
Line segment is part of a line bounded by two endpoints
Step-by-step explanation:
Line segment is part of a line bounded by two endpoints
A tank with 5 mg/L of phenol is mixed with a 55 gallon drum of phenol with 1536 mg/L. Mixing the two together results in a total mass of phenol in the new container that is less than that in the original two containers.
1)True
2)False
3)Not Enough Information
4)Sometimes
Answer: False
Step-by-step explanation:
The phenol would not evaporate or boil and would not reduce in quantity as it has a higher boiling point. So mixing it in different containers would not change the mass of phenol.
"When servicing a drive shaft, technician A says that its a good idea to tape the U-joint caps to prevent them from coming off. Technician B says that needle bearings are used with these type U-joints. Which technician is correct?
Answer: Both Technicians
Step-by-step explanation: A drive shaft which is also called the propeller shaft,is a major part of a the drive train/ unit of a vehicle with the role of Transmitting TORQUE POWER TO THE WHEELS,it is usually made up of STEEL.
Drive shaft is elongated,it is round and it requires needle bearing for friction reduction and taping to prevent it from falling off when the shafts are removed during servicing. Both Technicians are correct as both options are needed.
Both technicians are correct. Technician A's suggestion to tape the U-joint caps is a preventative measure to prevent loss of needle bearings. Technician B is correct that needle bearings are used with U-joints.
Explanation:Both Technician A and Technician B are correct in their assertions. Technician A's suggestion to tape the U-joint caps when servicing a drive shaft is a basic preventative measure to ensure they do not come loose and cause a problem. This is because losing a cap can lead to a loss of the needle bearings, which are crucial to U-joint function.
Technician B's statement is also correct that needle bearings are indeed used with these type of U-joints. Needle bearings allow the U-joints to rotate smoothly under the high pressure of the drive shaft. If the needle bearings were to fail or come out, it can cause the U-joint to fail.
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Dave bought a box of fruit that weighed 8 to 2/9 kilograms if he brought a second box that weighed 3 to 2/10 kilograms, what is the combined weight of two boxes
The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]
Step-by-step explanation:
We have to add the fractional weight of both boxes to find the combined weight of both boxes.
Given
Weight of Box 1: [tex]8\frac{2}{9}[/tex] kilograms
Weight of Box 2: [tex]3\frac{2}{10}[/tex] kilograms
So the total weight will be:
[tex]= 8\frac{2}{9} + 3\frac{2}{10}[/tex]
Simplifying the fractions
[tex]=\frac{74}{9} + \frac{32}{10}\\\\= \frac{74(10)+32(9)}{90}\\\\=\frac{740+288}{90}\\\\=\frac{1028}{90}\\\\=11\frac{38}{90}\\\\=11\frac{19}{45}\\[/tex]
Hence,
The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]
Keywords: Fractions, addition
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A truck skids for a distance of 25\,\text m25m25, start text, m, end text with the road pushing on its tires with force of 1500\,\text N1500N1500, start text, N, end text as its brakes are applied.
The truck, experiencing a force of 1500 N, skids a distance of 25 meters, resulting in a change in kinetic energy of 37,500 J. Now, let's break down the concept of kinetic energy and the given data:
Definition of Kinetic Energy:
Kinetic energy, in physics, is the energy possessed by a moving object.
It represents the effort required to accelerate an object of a specific mass from rest to a particular velocity.
The body retains its kinetic energy even with slight speed variations, maintaining the energy acquired during acceleration.
Kinetic Energy Conservation:
When the body decelerates from its current velocity to a state of rest, the same amount of energy is expended.
Formal Definition:
Kinetic energy is formally described as any quantity exhibiting a gradient with respect to time in the Lagrangian of a system.
Given Data:
Force (F) = 1500 N
Distance (d) = 25 m
Calculation of Change in Kinetic Energy:
Utilize the formula for change in kinetic energy: ΔK.E = F × d
Substitute the values: ΔK.E = 1500 × 25
This results in ΔK.E = 37,500 J.
Therefore, the observed change in kinetic energy for the truck, moving a distance of 25 meters with a force of 1500 N, is precisely 37,500 J.
Complete questions
A truck skids for a distance of 25 m with the road pushing on its tires with force of 1500 N as its brakes are applied. What is the change in kinetic energy for the truck? Round the answer to two significant digits.J
First, the population is subdivided by metropolitan area. Then a crime researcher uses a random number generator to select twenty-five members from each metropolitan area to study.A. CensusB. Simple Random SamplingC. Stratified SamplingD. Cluster SamplingE. Systematic SamplingF. Convenience Sampling
Answer:
C. Stratified Sampling
Step-by-step explanation:
Stratified sampling is a sampling method in which the overall population is divided into a number of smaller sub groups.
These smaller sub-groups are called as strata.
These sub-groups are formed on the basis of similar characteristics and attributes shared by the population.
It is also known as proportional random sampling.
A restaurant has fixed costs of $147.50 per day and an average unit cost of $5.75 for each meal served. If a typical meal costs $7, how many customers must eat at the restaurant each day for the owner to break even?
Answer:
The answer is 118.
Step-by-step explanation:
First we need to subtract the meal cost from average unit cost for each meal:
[tex]7-5.75=1.25[/tex]
A restaurant profits 1.25$ for each meal. If we divide fixed cost to profit for each meal:
[tex]147.5/1.25=118[/tex]
The restaurant have to sell 118 meals at least each day for the owner to break even
Kadi is starting a kayak rental company. She is going to charge $20 to rent the kayak plus $5 per hour of rental. What is the slope and what does it represent?
Answer:
slope is 5
Step-by-step explanation:
the slope represents the cost of the kayak for as many hours as the person rents it for. the y intersect is 20 because that is the cost just to rent the boat before using it.
Paul travel to the lake and back. The trip took 3 hours and the trip back took 4 hours He averaged 10 mph faster on the trip there than on the return trip. What was Paul's average speed on the outbound trip
Answer:
40 mph
Step-by-step explanation:
We assume "outbound" refers to the trip to the lake. The ratio of speeds is inversely proportional to the ratio of times, so ...
outbound speed : inbound speed = 4 : 3
These differ by one ratio unit, so that one ratio unit corresponds to the speed difference of 10 mph. Then the 4 ratio units of outbound speed will correspond to ...
4×10 mph = 40 mph
Paul's average speed on the outbound trip was 40 mph.
___
The distance to the lake was 120 mi.
Answer:Paul's average speed on the outbound trip is 40mph
Step-by-step explanation:
Let x represent Paul's outbound trip which is the trip to the lake.
The trip to the lake took 3 hours.
Distance travelled = speed × time
It means that
Distance covered on the trip to the lake would be
3 × x = 3x
the trip back took 4 hours. He averaged 10 mph faster on the trip there than on the return trip. It means that his speed would be
x - 10
Therefore, distance travelled on return trip would be
4(x - 10) = 4x - 40
Since the distance travelled is the same, it means that
3x = 4x - 40
4x - 3x = 40
x = 40
Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.
Answer:the equation relating E to H is
E = 20H
Step-by-step explanation:
Let E represent her earnings (in dollars) after tutoring for H hours.
For each hour that she tutors, she earns 20 dollars. This means that in H hours, her total earnings would be
E = 20H
To find Mai's earnings after tutoring for 17 hours, we would substitute H = 17 into the equation. It becomes
E = 20 × 17
E = $340
Mai's earnings [tex](\(E\))[/tex] after tutoring for 17 hours would be $340, calculated as [tex]\(E = 20 \times 17\).[/tex]
To relate Mai's earnings [tex](\(E\))[/tex] to the number of hours she tutors [tex](\(H\))[/tex], we can use the following equation:
[tex]\[E = 20H\][/tex]
This equation represents that Mai earns $20 for each hour she tutors. By multiplying the number of hours [tex](\(H\))[/tex] by the rate of $20 per hour, we get her total earnings [tex](\(E\))[/tex].
Now, to find Mai's earnings after tutoring for 17 hours, we can plug in [tex]\(H = 17\)[/tex] into the equation:
[tex]\[E = 20 \times 17\][/tex]
[tex]\[E = 340\][/tex]
So, Mai's earnings after tutoring for 17 hours would be $340.
Identify the equations below that are true. You may wish to watch the video Powers of 10, Part 3 for a review of operations (adding, subtracting, multiplying, dividing) with powers of 10.a. (10^5)^3=10^5×3b. 10^5÷10^3=10^5−3c. 10^5×10^3=10^5+3d. 10^5/10^3=10^5−3
The equations that are true according to the exponent rules for powers of 10 include: [tex]10^5 / 10^3 = 10^5-3, 10^5 * 10^3 = 10^5+3,[/tex] and [tex]10^5 / 10^3 = 10^5-3.[/tex]
Explanation:The subject in question deals with exponent rules for powers of 10. Here, we'll identify which equations are true based on these rules:
a. (10^5)^3 = 10^5×3. This is not correct. According to the power of a power rule, we should multiply the exponents, so the answer should be 10^15.
b. [tex]10^5 / 10^3 = 10^5-3.[/tex] This is correct. When dividing bases that are the same, we subtract the exponent of the denominator from the exponent of the numerator, hence 10^(5-3) = 10^2.
c. 10^5 × 10^3 = 10^5+3. This is correct. When multiplying bases that are the same, we add the exponents, hence 10^(5+3) = 10^8.
d. [tex]10^5 / 10^3 = 10^5-3[/tex]. This is correct, as explained in point b. The answer is 10^2.
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Final answer:
Equation c [tex](10^5*10^3 = 10^{(5+3)})[/tex] and equations b and d [tex](10^5/10^3 = 10^{(5-3)})[/tex] are correct. To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents, respectively. This method can be used to calculate without converting to standard form.
Explanation:
The equations that are true out of the ones provided are as follows:
[tex](10^5)^3 = 10^{(5*3)}[/tex]or 10^15, so option a is not correct since it incorrectly states that [tex](10^5)^3 = 10^(5+3).[/tex][tex]10^5/10^3 = 10^{(5+3) }or 10^8[/tex], so option c is correct.[tex]10^5/10^3 = 10^{(5-3)} or 10^2[/tex], so options b and d, being the same, are both correct.To evaluate (4.506 × 10^4) × (1.003 × 10^2) without entering scientific notation into your calculator, first multiply the coefficients (4.506 × 1.003) and then add the exponents for the powers of 10 (10^4 × 10^2 = 10^(4+2) or 10^6). The result is 4.514518 × 10^6.To evaluate (8.552 × 10^6) ÷ (3.129 × 10^3) without entering scientific notation into your calculator, first divide the coefficients (8.552 ÷ 3.129) and then subtract the exponents for the powers of 10 (10^6 ÷ 10^3 = 10^(6-3) or 10^3). The result is approximately 2.73189 × 10^3.
What is the total cost of a $720 ipad that is on sale at 15% off if the local sales tax is 6%
Answer:
$828
Step-by-step explanation:
15% = 0.15
0.15 x 720 = 108
total cost = $720 + $108 = $828
Final answer:
To find the total cost of an iPad that is on sale at 15% off with a 6% sales tax, calculate the discount, subtract it from the original price, determine the sales tax, and add it to the discounted price.
Explanation:
To find the total cost of the iPad:
Calculate the discount: $720 * 15% = $108 discount
Subtract the discount from the original price: $720 - $108 = $612
Calculate the sales tax: $612 * 6% = $36.72
Add the sales tax to the discounted price: $612 + $36.72 = $648.72
Which is the graph of 3x – 2y = 6? A coordinate plane with a line passing through (negative 2, 0) and (0, 3). A coordinate plane with a line passing through (0, negative 3) and (2, 0). A coordinate plane with a line passing through (0, negative 2) and (3, 0). A coordinate plane with a line passing through (negative 3, 0) and (0, 2).
Answer:
The answer to your question is A coordinate plane with a line passing through (0, -3) and (2,0)
Step-by-step explanation:
Line
3x - 2y = 6
Solve for y
-2y = -3x + 6
y = 3/2 x - 3
Find "y" when x = 0
y = 3/2(0) - 3
y = -3 Point (0, -3)
Find "x" when y = 0
0 = 3/2x - 3
3 = 3/2 x
x = 6/3
x = 2 Point (2, 0)
The graph of the equation 3x - 2y = 6 passes through the points (0, -3) and (2, 0). This conclusion is reached after rearranging the equation into the slope-intercept form and comparing the slope and the y-intercept with coordinates of the given lines.
Explanation:To find the correct graph for the equation 3x - 2y = 6, we first need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
We rearrange our equation as follows: 3x - 6 = 2y. Simplifying, we get y = 1.5x - 3.
This equation tells us that the y-intercept (where the line crosses y-axis) is -3, and the slope is 1.5, in other words, for each step in positive x-direction, y increases by 1.5 steps.
Now looking at our coordinate plane options, the graph that fits this description is the one with a line passing through the points (0, -3) and (2, 0). Hence, this is the graph of the given equation.
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You're selling snacks at a basketball game you're offering up hotdogs and fries. Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! You sold a total of 87 hotdogs and orders of fried combined. How many hotdogs were sold and how many orders of fries? (Let x=number of hotdogs and y=number of orders of fries
Answer: the number of hotdogs that were sold is 35
the number of orders of fries is 52
Step-by-step explanation:
Let x represent the number of hotdogs that were sold.
Let y represent the number of orders of fries.
You sold a total of 87 hotdogs and orders of fried combined. This means that
x + y = 87
Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! This means that
1.5x + 0.5y = 78.5 - - - - - - - - - - -1
Substituting x = 87 - y into equation 1, it becomes
1.5(87 - y) + 0.5y = 78.5
130.5 - 1.5y + 0.5y = 78.5
- 1.5y + 0.5y = 78.5 - 130.5
- y = - 52
y = 52
Substituting y = 52 into x = 87 - y, it becomes
x = 87 - 52
x = 35
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2 Monday Tuesday Wednesday Thursday
Answer:
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2
(i) Monday
(ii) Tuesday
(iii) Wednesday
(iv) Thursday
Ans
(iv)Thursday
Step-by-step explanation:
Forecast for
Monday +4 Abs |+4| = 4
Tuesday –6 Abs |-6| = 6
Wednesday +7 Abs |+7| = 7
Thursday –2 Abs |-2| = 2
The most accurate is the day closest the temperature forecast is closest to observed temperature, which is
Thursday (-2)
Answer:
it is thursday
Step-by-step explanation:
hope it helps
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is 240π240π cubic inches greater than the volume of the cylinder with height 10.
Answer:
the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10 (option B , if 60π is changed for 60/π)
Step-by-step explanation:
The volume of a cylinder is
V= π*R²*H (H=height)
since the length L of the piece of paper is L=2*π*R →R=L/(2*π) (since is rolled to form the cylinder), then:
V= π*R²*H = π*L²/(2*π)²*H = L²*H/(4*π)
with L=10 in and H= 6 in we have
V₂= L²*H/(4*π)
the other way around is changing H for L
V₁= H²*L/(4*π)
the difference between the volumes will be
V₂- V₁ = L²*H/(4*π) - H²*L/(4*π) = L*H *(L-H)/(4*π)
replacing values
V₂- V₁ = L*H *(L-H)/(4*π) = 10*6*(10-6)/(4*π) = 60/π in³
then the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising. The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising. What is (f + g)(1)? Explain.
339 calories burned while dieting for 1 hour.
339 calories burned while combining diet with 1 hour of exercise.
212 calorie calories burned when combining diet with 1 hour of exercise.
212 calories burned while exercising for 1 hour.
This means 339 calories burned while combining diet with 1 hour of exercise
Step-by-step explanation:
Given the functions as:
f(x)=2x+210
g(x)=2x+125 then
(f+g)(x) = 2x+210 +2x+125 = 4x +335
(f+g)(1) = 4(1)+335
=339
This means 339 calories burned while combining diet with 1 hour of exercise
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Step-by-step explanation:
f(1) = 2+210 = 212
g(1) = 2+125 = 127
127+212= 339
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.
Answer:
meaning it is 339 calories burned while combining diet with 1 hour of exercise.
The measures of the angles of XYZ are in the ratio 1:4:10. What are the measures of the angles?
(SHOW YOUR WORK)
Answer:the angles are 12 degrees, 48 degrees and 120 degrees.
Step-by-step explanation:
The sum of the angles in a triangle is 180 degrees.
The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes
1 + 4 + 10 = 15
Therefore, the measure of the first angle would be
1/15 × 180 = 12 degrees
Therefore, the measure of the second angle would be
4/15 × 180 = 48 degrees
Therefore, the measure of the third angle would be
10/15 × 180 = 120 degrees
Which calculation will ALWAYS give a result greater than 1? A.5 × a number less than 1 B.4/9+ a fraction less than 12 C. 1 3/4 - a fraction less than 3/4 D.7/8 × a number less than 1
Answer:
C. 1 3/4 - (a fraction less than 3/4)
Step-by-step explanation:
Your number sense should be able to help you with this one.
A. 5 × 1/10 = 1/2, not a number greater than 1
B. 4/9 + 1/3 = 7/9, not a number greater than 1
C. 1 3/4 -1/2 = 1 1/4, a number greater than 1 (see below for more explanation)
D. 7/8 × 1/2 = 7/16, not a number greater than 1.
__
More explanation
Let x represent a number less than 3/4. Then we want to make sure that ...
y = 1 3/4 - x
will be greater than 1.
Solving for x, we get ...
x = 1 3/4 - y
Applying the requirement that x < 3/4, we have ...
x < 3/4
(1 3/4 -y) < 3/4
1 3/4 < y + 3/4 . . . . . . add y
1 < y . . . . . . . . . . . . . . .subtract 3/4
We see that the condition on x makes sure that y is always greater than 1.
Amy drives her car until the gas gauge is down to 1/8 full, then she fills the tank to capacity by adding 14 gallons. What is the capacity of the gas tank?
Answer:
Amy's car tank capacity is 16 gallons.
Step-by-step explanation:
Let the capacity of the tank be 'x'
Given:
Amount of gas in the car till it is refilled = [tex]\frac{1}{8}\times x = \frac{1}{8}x \ gallons[/tex]
Amount of gas added = 14 gallons.
We need to find the capacity of the tank.
Solution:
Now we can say that
Total Capacity of the tank is equal to sum of Amount of gas in the car till it is refilled and Amount of gas added.
framing in equation form we get;
[tex]x=\frac{x}{8}+14[/tex]
Combining the like terms we get;
[tex]x-\frac{x}{8}=14[/tex]
Now making the denominators common we will use L.C.M.
[tex]\frac{8x}{8}-\frac{x\times1}{8\times1}=14\\\\\frac{8x}{8}-\frac{x}{8}=14\\\\\frac{8x-x}{8}=14\\\\\frac{7x}{8}=14[/tex]
Now multiplying both side by 8 we get;
[tex]\frac{7x}{8}\times 8=14\times8\\\\7x = 112[/tex]
Now dividing both side by 7 we get;
[tex]\frac{7x}{7}=\frac{112}{7}\\\\x=16\ gallons[/tex]
Hence Amy's car tank capacity is 16 gallons.
Evaluate 14 - 2xy when x = -6 and y = 2.
Answer: 38
Step-by-step explanation:
14 - 2xy
(substitute x and y)
14 - 2 (-6) (2)
14 + 24
38
Answer:
its 38
Step-by-step explanation:
Do xy first and you get -24 and 14-(-28) would be a double negative so you add them together.
Please help me with this problem!!!!!!
Answer:
[tex]\sqrt{29}[/tex]
Step-by-step explanation:
The complex number x + yi can be expressed in coordinate form as
x + yi → (x, y ), thus
4 + 3i → (4, 3 )
6 - 2i → (6, - 2 )
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6-4)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{2^2+(-5)^2}[/tex]
= [tex]\sqrt{4+25}[/tex]
= [tex]\sqrt{29}[/tex]
The number of bacteria in a certain culture doubled every hour. If there were 30 bacteria present in the culture initially, how many bacteria will be present at the end of the 8th hour?
Answer:
The number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
Step-by-step explanation:
Given the initially 30 bacteria present in the culture.
Also, the number of bacteria got doubled every hour.
So, using the equation
[tex]A=A_0r^{n-1}[/tex]
Where [tex]A[/tex] is number of bacteria after [tex]n[/tex] hours.
[tex]A_0[/tex] is bacteria present initially.
[tex]r[/tex] is the common ration, in our problem it is given that bacteria doubles every hour. So, [tex]r=2[/tex]
And [tex]n[/tex] is the number of hours. In our problem we need amount of bacteria at the end of [tex]8th[/tex] hours. So, [tex]n=8[/tex]
Plugging values in the formula we get,
[tex]A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840[/tex]
So, number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
The equation of line LM is 5x − y = −4. What is the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2)?
a) y = 5x + 13
b) y = negative one fifthx + seven fifths
c) y = negative one fifthx − seven fifths
d) y = 5x − 17
Answer: b) y = negative one fifthx + seven fifths
Step-by-step explanation:
Equation of a line in Slope intercept form : [tex]y=mx+c[/tex] (1)
, where m is slope and c is constant.
Given : The equation of line LM is [tex]5x - y = -4.[/tex]
Convert it into slope- intercept form, we get
[tex]y=5x+4[/tex]
Comparing it to (1) , we get
[tex]m= 5[/tex]
Let [tex]m_1[/tex] be the slope pf the line perpendicular to LM.
Since the product of slopes of two perpendicular lines is -1.
Therefore , [tex]m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}[/tex]
Equation of line passing through (-3,2) and having slope [tex]m_1=\dfrac{-1}{5}[/tex] will be :-
[tex](y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex]
Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is [tex]y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex].
Hence, the correct answer is b) y = negative one fifthx + seven fifths.
We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5
Perpendicular lines.A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:
y = (-1/a)*x + c
Now we start with the line that we know, we need to find its slope:
5x - y = -4
We need to isolate y
y = 5x + 4
Then the slope of this line is a = 5, so the perpendicular line will be:
y = (-1/5)*x + c
Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:
2 = (-1/5)*-3 + c
2 = (3/5) + c
2 - 3/5 = c
10/5 - 3/5 = c
7/5 = c
Then the equation is:
y = (-1/5)*x + 7/5
So the correct option is b.
If you want to learn more about linear equations, you can read:
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A customer wants rhombus-shaped tiles for his countertops. The height is 3 inches and the length of each side is 6.5 inches. What is the area of each tile?
Answer:
Area of each tile = 19.5 inches^2
Step-by-step explanation:
Rhombus:-
A rhombus is a type of quadrilateral whose opposite sides are parallel and equal.Also, the opposite angles of a rhombus are equal and the diagonal intersect each other perpendicularly.
To find the area of a rhombus when the measures of its height and side length are given, use the formula
A = Base X height
Area of a rhombus = 6.5 X 3
A = 19.5 inches^2
The area of each rhombus-shaped tile is 19.5 square inches for the given dimensions. Thus, each tile has an area of 19.5 square inches.
To find the area of a rhombus, you can use the formula
⇒ Area = base × height
In this case, the height is given as 3 inches and the length of each side is 6.5 inches, but the length of the sides is not needed, as we are working with the base and height directly.
So, the area can be calculated as follows:
Identify the base and height:⇒ Base = 6.5 inches
⇒ Height = 3 inches.
Use the formula for the area of a rhombus:⇒ Area = base × height.
Calculate:⇒ Area = 6.5 inches × 3 inches
= 19.5 square inches.
Therefore, the area of each rhombus-shaped tile is 19.5 square inches.
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?A. 25%B. 3313%C. 50%D. 6623%E. 75%
Answer:
[tex]66\dfrac{2}{3}\%[/tex]
Step-by-step explanation:
Given,
The number of cartons = k,
Time taken by machine a = 8 hours,
So, the number of cartons made by machine a in one hour
= [tex]\frac{\text{Cartons in 8 hours}}{8}[/tex]
= [tex]\frac{k}{8}[/tex]
Time taken by machine b = 4 hours ,
So, the number of cartons made by machine b in one hour
= [tex]\frac{k}{4}[/tex]
Total cartons made in 1 hour = [tex]\frac{k}{8}+\frac{k}{4}[/tex]
[tex]=\frac{k+2k}{8}[/tex]
[tex]=\frac{3k}{8}[/tex]
∵ for the whole number value of k,
[tex]\frac{k}{4}>\frac{k}{8}[/tex]
i.e. machine b is faster,
Also, the percent of the cartons were sealed by the machine b
[tex]=\frac{\text{Cartons made in 1 hour by machine b}}{\text{Total cartons}}\times 100[/tex]
[tex]=\frac{\frac{k}{4}}{\frac{3k}{8}}\times 100[/tex]
[tex]=\frac{2}{3}\times 100[/tex]
[tex]=\frac{200}{3}[/tex]
[tex]=66\dfrac{2}{3}\%[/tex]
Hence, OPTION D is correct.
The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
If the relationship between cost and the number of chairs produced is linear, how do I write an equation that expresses this relationship?
Answer:
Step-by-step explanation:
If the relationship between cost and the number of chairs produced is linear, we would write an equation that expresses this relationship in the slope intercept form. It is expressed as
y = mx + c
Where
m represents the slope
c = intercept.
Slope = (y2 - y1)/(x2 - 1)
y2 = final value of y = 4800
y1 = initial value of y = 2200
x2 = final value of x = 300
x1 = initial value of x = 100
Slope, m = (4800 - 2200)/(300 - 100) = 2600/200 = $13 per chair.
To determine the intercept, we will substitute y = 4800, x = 300 and m = 13 into y = mx + c. It becomes
4800 = 13×300 + c = 3900
c = 4800 - 3900 = 900
The equation becomes
y = 13x + 900
To write an equation that expresses the relationship between cost and the number of chairs produced, we need to find the slope and y-intercept of the linear equation. The equation that expresses this relationship is Cost = $26(Number of Chairs) - $400.
Explanation:We must determine the slope and y-intercept of the linear equation in order to build an equation that describes the link between the price and the quantity of chairs produced.
Slope = Change in Cost / Change in Number of Chairs
Using the given values, the slope is (4800 - 2200) / (300 - 100) = $26 per chair.
Now, let's find the y-intercept. We can use either of the given data points. Substituting the values of one data point, we have:
$2200 = $26(100) + b
b = $2200 - $2600 = -$400.
Therefore, the equation that expresses this relationship is:
Cost = $26(Number of Chairs) - $400.
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The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Compare the towns to determine which is growing at the greatest rate and by what factor? (round to nearest hundredth)
Answer:
Smallville is growing at a greater rate
Step-by-step explanation:
use the formula for percentage increase to find what percentage the population of Bigville increased.
(Increase ÷ original number) * 100 = % of increase
increase = 571,533 - 387,480 = 184,053
(184,053 ÷ 387,480) * 100 = 47.5
Bigville percent of increase is 47.5%
Smallville percent of increase is 53.67%
since, smallville has a bigger percentage, it is growing at the greater rate
QUESTION 1
Which of the following statements are mathematical statements?
A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.
A. B, F
B. B, E
C. A, C
D. E, F
E. A, B, C
F. B, D, F
Answer: B
Step-by-step explanation:
Mathematical statements are those that can be objectively proven true or false. Among the options provided, statements B and F qualify as mathematical statements. Therefore, the correct answer choice is A.
The student asks which of the following statements are mathematical statements:
A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.
Mathematical statements are statements that can be objectively proven true or false.
B: 5 = 7 - This is a mathematical statement because it can be proven false.F: If the storm is coming, then the sky is blue - This is a conditional statement that can be tested and verified within the realm of logic and mathematics.Thus, the correct answer is A. B, F
Elainas old bicycle had tires with a 12-inch diameter her new bicycle had tires with a 16-inch diameter what is the difference in the circumference of the tires use 3.14 for pie
Answer:
The difference between the circumference of the tires is 12.56 inches.
Step-by-step explanation:
Given:
Diameter of old bicycle tires = 12 inch
Diameter of new bicycle tires = 16 inch
We need to find the difference in circumference of the tires.
Solution:
First we will find the circumference of Old bicycle tires.
Circumference can be calculated by π times diameter.
Circumference of Old bicycle tire = [tex]\pi \times 12 = 37.68\ in[/tex]
Now we will find the circumference of new bicycle tire.
Circumference of New bicycle tire = [tex]\pi \times 16 = 50.24\ in[/tex]
Now to find the difference between the circumference of the tires we will subtract Circumference of New bicycle tire from Circumference of Old bicycle tire we get;
framing in equation form we get;
difference between the circumference of the tires = [tex]50.24-37.68 =12.56\ in[/tex]
Hence The difference between the circumference of the tires is 12.56 inches.