Answer:
Infinitely many
Step-by-step explanation:
Write the equation for a parabola that has x-intercepts (−4.5, 0) and (−2.8, 0) and y-intercept (0, 37.8).
Answer:
[tex]y=3(x+4.5)(x+2.8)[/tex] or [tex]y=3x^2+21.9x+37.8[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in factored form is equal to
[tex]y=a(x-x_1)(x-x_2)[/tex]
where
a is a coefficient
x_1 and x_2 are the roots or x-intercepts of the quadratic equation
In this problem we have
[tex]x_1=-4.5\\x_2=-2.8[/tex]
substitute
[tex]y=a(x+4.5)(x+2.8)[/tex]
Find the value of a
we have the y-intercept (0,37.8)
substitute the value of x and the value of y of the y-intercept in the equation and solve for a
[tex]37.8=a(0+4.5)(0+2.8)[/tex]
[tex]a=37.8/12.6\\a=3[/tex]
so
[tex]y=3(x+4.5)(x+2.8)[/tex]
Convert to expanded form
[tex]y=3(x^2+2.8x+4.5x+12.6)[/tex]
[tex]y=3x^2+21.9x+37.8[/tex]
Answer:
Go to the link below :)
Step-by-step explanation:
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Which shows the expression below in simplified form? (7 × 10-3) - (2.3 × 10-6) A. 6.9977 × 10-3 B. 6.99977 × 10-3 C. 6.9977 × 10-4 D. 6.977 × 10-3
Option A
[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = 6.9977 \times 10^{-3}[/tex]
Solution:
Given expression is:
[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6})[/tex]
To evaluate the expression, let us make the exponent of 10 same
[tex]2.3 \times 10^{-6} = 0.0023 \times 10^{-6+3} = 0.0023 \times 10^{-3}[/tex]
[ Here, decimal point is moved three times left, so add 3 ]
Therefore,
[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = (7 \times 10^{-3}) - (0.0023 \times 10^{-3})[/tex]
[tex]\text{Take the } 10^{-3} \text{ as common }[/tex]
[tex](7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3}(7-0.0023)\\\\\text{ Solve for terms inside the bracket }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3} \times 6.9977\\\\\text{Therefore, the simplified expression is: }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 6.9977 \times 10^{-3}[/tex]
Thus Option A is correct
Suppose p represents the amount of air pressure in a tire and t, the time it takes for the tire to go flat, equals −8. What is the value of p, if the quotient of
p
t
is −4?
p = 32
Solution:
Given p represents the amount of air pressure in a tire.
t represents the time it takes for the tire to go flat and t = –8.
To find the value of p, if [tex]\frac{p}{t}=-4[/tex].
⇒ [tex]\frac{p}{t}=-4[/tex]
Substitute t = –8 in the above equation.
⇒ [tex]\frac{p}{-8}=-4[/tex]
Do cross multiply, we get
⇒ p = (–8) × (– 4)
⇒ p = 32
Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.
Suppose that 2 people exercising in an enclosed room are each generating about 2,400 BTUs of body heat per hour. If the room is 20 ft × 12 ft × 10 ft, how many BTUs per cubic foot do they produce in 1 hour?
Answer:
2 BTUs/cubic foot.
Step-by-step explanation:
Suppose that 2 people exercising in an enclosed room are each generating about 2,400 BTUs of body heat per hour.
So, 2 people will produce (2400 × 2) = 4800 BTUs for 1 hour.
Now, the volume of the room with dimensions (20 ft by 12 ft by 10 ft) will be (20 × 12 × 10) = 2400 cubic feet.
Therefore, the number of BTUs per cubic foot will be produced by [tex]\frac{4800}{2400} = 2[/tex] BTUs/cubic foot. (Answer)
WHat is the property for 5x+10=24-2x
Final answer:
The correct solution to the equation 5x+10=24-2x is x=2, which is verified by substitution and results in an identity, confirming the solution is accurate.
Explanation:
The equation 5x+10=24-2x is a simple linear equation that can be solved by collecting like terms and isolating the variable x. Begin by adding 2x to both sides to get 7x + 10 = 24, then subtract 10 from both sides to obtain 7x = 14. Dividing both sides by 7 yields x = 2, which is the sole solution to the equation. Checking the solution, 24 - 2(2) does indeed equal 5(2) + 10, giving an identity of 20 = 20. This illustrates the solution is correct and verifies our process.
what is the quotient of m^6/5 divided by 5/m^2
Answer:
[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]
Step-by-step explanation:
[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]
Jacksonville to Atlanta: 4 routes Atlanta to Knoxville: 3 routes Knoxville to Indianapolis: 2 routes Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis. He can choose from several different routes. How many different routes can Sammy take on his trip? A) 9 B) 11 C) 12 D) 24
Answer:
D) 24.
Step-by-step explanation:
The solution is 24 routes. To determine the number of different routes we multiply the routes for each part of the trip. 4(3)(2) = 24 routes.
He can take 24 different routes for his trip
The correct option is option D)
What is permutation and combination?
an arrangement of objects in a definite order is known as permutation. The members or elements of sets are arranged here in a sequence. a combination is a selection of items from a set which has distinct members, and the order of selection does not matter. even though the terms are used together they are different and formula for calculating them is also different
We are given that,
Jacksonville to Atlanta: 4 routes
Atlanta to Knoxville: 3 routes
Knoxville to Indianapolis: 2 routes
Also Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis
To find the different routes sammy can take can be computed as
4*3*2=24ways
Hence Sammy can take 24 routes
The correct option is option D)
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What is 2 2/3 + 3 2/3 equal
Answer:
[tex]6\frac{1}{3}[/tex]Step-by-step explanation:
[tex]2\frac{2}{3} + 3\frac{2}{3}[/tex]Convert into improper fractions
[tex]\frac{8}{3} + \frac{11}{3}[/tex]Add numerators and denominators
[tex]\frac{19}{3}[/tex]Simplify
[tex]6\frac{1}{3}[/tex]Hope this helps :)
OK it has 5 g Of sugar per serving. A banana has 15 g of sugar per serving.
1/3 banana hgfdsedcrtvfybgunhimjnyhtbgvfdcvfbgnhmij,omhnbvdcrmjytgvg
You are planning your cousin’s birthday party. He wants to invite at least 250 adults and children combined. Each adult will be allowed 3 cups of juice and each child will be allowed 2 cups of juice. The caterer will provide only 800 cups of juice total. Write a system of linear inequalities for the party invitees. Use A to represent the number of adults and C the number of children.
The system of inequalities is x+y≥250 and 3x+2y≤800.
Step-by-step explanation:
Given,
People to invite = at least 250
At least 250 means that the number can increase from 250.
Cups to be provided = only 800
It means the number cannot exceed 800.
Number of adults = A
Number of children = C
According to given statement;
x+y≥250
3x+2y≤800
The system of inequalities is x+y≥250 and 3x+2y≤800.
Keywords: linear inequalities, addition
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M=7,r=8, t=2 ; mr/t = what
Answer:
28
Step-by-step explanation:
Plug in the corresponding numbers to the corresponding variables. Note that:
m = 7
r = 8
t = 2
mr/t = (7 * 8)/2
(7 * (8/2)) = 7 * 4 = 28
28 is your answer.
~
The sum of the digits of a two-digit number is 10 when the digits are reversed the new number is 18 less than the original number find the original number check your answer
The original number is 64
Step-by-step explanation:
The given is:
The sum of the digits of a two-digit number is 10When the digits are reversed the new number is 18 less than the original numberWe need to find the original number
Assume that the unit digit of the number is x and the ten digit is y
∵ The unite digit of the number is x
∵ The ten digit of the number is y
∵ The sum of the two digits is 10
- Add x and y, then equate the sum by 10
∴ x + y = 10 ⇒ (1)
∵ The value of the number is x + 10y
- Reverse the digits means y will be the unit digit and x will
be the ten digit
∴ The new number is y + 10x
∵ The new number is 18 less than the original number
- That means their difference is 18, (the original number minus
the new number = 18)
∴ (x + 10y) - (y + 10x) = 18
- Simplify the left hand side
∴ x + 10y - y - 10x = 18
- Add the like terms in the left hand side
∴ -9x + 9y = 18
- Divide both sides by 9
∴ -x + y = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equation (1) and (2) to eliminate x
∴ 2y = 12
- Divide both sides by 2
∴ y = 6
- Substitute the value of y in equation (1) to find x
∵ x + 6 = 10
- Subtract 6 from both sides
∴ x = 4
∵ The original number is x + 10y
∵ x = 4 and y = 6
∴ The original number = 4 + 10(6) = 4 + 60 = 64
The original number is 64
To check the answer reverse the digits of the number
∵ The new number is y + 10x
∴ The new number = 6 + 10(4) = 6 + 40 = 46
∵ The original number is 64
∵ The new number is 46
∵ 64 - 46 = 18
∴ The new number is less than the original number by 18
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Answer:
The original number is 64.
A big ship drops its anchor.The variable l models the anchor's elevation (in meters) relative to the water's surface t seconds after the ship drops its anchor.l=−2.4t+75What is the initial height of the anchor?
Answer:
Step-by-step explanation:
l = -2.4t + 75
what this equation is saying is that the initial height of the anchor is 75 meters (thats also ur y intercept), and it drops at a rate of 2.4 meters per second.
another way u could look at it is the initial height is before u drop the anchor....0 seconds...meaning sub in 0 for t
l = 2.4(0) + 75
l = 0 + 75
l = 75 meters <=====
What is the value of. X in this equation
1.54x+6.814=8.2
Answer:
x=0.9
Step-by-step explanation:
1. You first have to isolate the x term so you subtract 6.814 from both sides which makes the equation 1.54x=1.386
2. Then, to isolate "x", you divide 1.54 on both sides to get rid of the 1.54 which makes x=.9
1 9/10, 1 7/10, blank, 1 3/10, 1 1/10 what is the blank
Answer:15/10
Step-by-step explanation:
You subtract the top of the fraction by 2
Answer:
1 5/10 or 1 1/2
Step-by-step explanation:
You seem to have an arithmetic sequence, with each term 2/10 less than the one before.
2/10 less than 1 7/10 is 1 5/10. The fraction can be reduced to 1 1/2, but you may not want to.
A flock of geese landed landed in a dog park. All the dogs ran to investigate. Alex counted
22 animals 64 legs. How many many geese and how many dogs did he count?
Answer:
12 geese
10 dogs
Step-by-step explanation:
We are given;
Total number of animals (dogs and geese) is 22 Total number of legs of animals is 64We are required to determine the number of geese and dogs that Alex counted;
We need to know that;
a dog has 4 legs while, a geese has 2 legs Therefore;Assuming he counted x number of geese and y number of dogs;
Then;
x + y = 22, and
2x + 4y = 64
Thus, solving the equation simultaneously;
we can multiply the first equation by 2, to get
2x + 2y = 44
2x + 4y = 64
Eliminating x (by subtracting the second eqn from the first eqn), we get;
-2y = -20
y = 10
Solving for x;
x = 22 - y
= 22 - 10
x = 12
Therefore; he counted 12 geese and 10 dogs
Please help!
Susan and Abe shared comic books of 3 to 5. If Abe had 14 more comic books than Susan, how many comic books did they have in all?
Answer:
The number of comic books did they have in all = 56
Step-by-step explanation:
The ratio of comics with Susan : Abe = 3 : 5
Let us assume the common factor on this ratio = m
So, the number of comics Susan has = 3 m
The number of comics Abe has = 5 m
Also, given: Abe had 14 more comic books than Susan
So, the number of comics Abe had = 14 + 3 m
⇒ 5 m = 3 m + 14
or, 2 m = 14, or m = 7
So, the number of books Susan has = 3 m = 3 x 7 = 21 books
The number of books Abe has = 5 m = 5 x 7 = 35
So, the book they have in all = 21 + 35 = 56
At the football game, 4 hamburgers and 6 soft drinks cost $34, and 4 hamburgers and 3 soft drinks cost $25. Which two equations can be used to determine the price of a hamburger and the price of a soft drink? Let x represent the cost of a hamburger and y represent the cost of a soft drink.
Answer:
[tex]4x+6y=34\\\\4x+3y=25[/tex]
Step-by-step explanation:
Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.
The cost of 4 hamburguers can be represented with this expression:
[tex]4x[/tex]
And the cost of 6 soft drinks can be represented with this expression:
[tex]6y[/tex]
Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:
[tex]4x+6y=34[/tex] [Equation 1]
The following expression represents the the cost of 3 soft drinks:
[tex]3y[/tex]
According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:
[tex]4x+3y=25[/tex] [Equation 2]
Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink
The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room . The yellow and blue rectangles extend the length of their respective sides. Where these two rectangles overlap, there is a green rectangle.
What is the area of the portion of the room shown in gray? _____ sq. ft.
The area of the gray portion in the room, after subtracting the area of the central linoleum from the total area of the room, is 112 sq. ft.
Explanation:To calculate the area of the gray portion in the room, first subtract the area of the linoleum from the total area of the room. The area of the room is given as 12 x 16 sq. ft. and the linoleum is 8 x 10 sq. ft.. To find the total area of the room, multiply the length by the width (12 x 16 = 192 sq. ft.). Then do the same for the linoleum (8 x 10 = 80 sq. ft.). Subtracting the area of the linoleum from the total area of the room gives us the gray area (192 - 80 = 112 sq. ft.). Hence, the area of the gray portion is 112 sq. ft.
Passes through (3,-7), m=-2
If you are trying to find the equation of a line:
The equation of a line is y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]
Since you have m = -2, plug it into the equation
y = mx + b
y = -2x + b To find b, plug in the point they gave you (3, -7)
-7 = -2(3) + b
-7 = -6 + b Add 6 on both sides
-1 = b Now that you have b, plug it into the equation
y = -2x - 1
What are the opposites of 8, −3.5, 1.15, and 9 1/4? Enter the answers in respective order, each separated by a comma.
-8, 3.5, -1.15. -9 1/4
I hope this helped!
2 3/4x-5/6(x-8 2/5)
Simplify
Answer:
23/12x+7
Step-by-step explanation:
2 3/4=11/4
8 2/5=42/5
----------------
11/4x-5/6(x-42/5)
11/4x-5/6x+210/30
11/4x-5/6x+7
33/12x-10/12x+7
23/12x+7
Which dimensions cannot create a triangle?
three angles measuring 10°, 25, and 145º
three sides measuring 9 m, 15 m, and 9 m
three angles measuring 40°, 70°, and 65
three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
Step-by-step explanation:
three angles measuring 40°, 70°, and 65 cannot create a triangle because sum of all the angles should be 180
If set A={2, 3, 4, 5}, Set B ={0, 1, 6, 7, 5}, then these sets are a) Disjoint b) Supersets c) overlapping d) None
Answer
overlapping
explanation:
This is overlapping set because at least one common element (5) is present in both set.
Daniel went on his bike 45 miles in four hours, what was his speed?
Answer:
11.25 miles/hour
Step-by-step explanation:
Recall, speed = Distance ÷ Time
We are given :
Distance = 45 miles
Time = 4 hours
Hence,
Speed = Distance ÷ Time
= 45 miles ÷ 4 hours
= 11.25 miles/hour
A sound system has a regular price of $249. Find the total cost of it is on sale for 40% off and the sales tax is 6.25%
Answer:
$158.74
Step-by-step explanation:
A sound system has a regular price of $249. Now, we have to find the total cost of it if there is a sale for 40% off and the sales tax is 6.25%.
Now, if there is 40% off on price $249, then the discounted price will be
[tex]249(1 - \frac{40}{100}) = 149.4[/tex] dollars.
Then the after-tax value of the sound system at the rate of 6.25% will be [tex]149.4(1 + \frac{6.25}{100}) = 158.74[/tex] dollars (Approximate)
(Answer)
Lucas says his twin baby brothers have a total weight of 15 and one eighth pounds. jackson 6 and one fourth pounds and jeremy weighs 8 and seven eighths pounds. explain how you can use estemation to tell if the total weight is reasonable
By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.
Explanation:Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.
Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.
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Sequence #2 2, 6, 18, 54, 162,___ whats next?
Sequence #3 800, 400, 200,100,50,__ Whats next?
Sequence #4 1, 4, 9, 16, __ Whats next?
Sequence #5 .001 L 1 L 1000 L _____L HELP A.S.A.P HELP TvT
Answer:
#2 486
#3 25
#4 25
#5 1,000,000
Step-by-step explanation:
Sequences like this always have some rule that determines the next number, a pattern that needs to be followed. Sometimes the pattern is easy to find, sometimes really hard.
#2 One of the first things to check is the ratio of adjacent numbers. Here we have 2 then 6 then 18 then 54 etc.
The most prominent feature of these numbers is that the next number is always three times bigger than the previous. It's safe to assume that the missing number will be 162 • 3 = 486.
#3 Of course numbers can be arranged in the decreasing order as well. However, that does not change their ratio. In this example, carefully examining, we can see that each number in the sequence is exactly twice smaller than the previous:
800 -> 400 -> 200 -> 100 etc.
Following this pattern, we can say that the next number will be 50 / 2 = 25.
#4 Of course, ratio is not the only way to help us find the pattern. One of the very often used methods is also the difference between adjacent numbers. Let's subtract each adjacent pair:
4 - 1 = 3
9 - 4 =5
16 - 9 = 7
Longer the sequence is, greater are the chances to see the pattern, but from this we could conclude that the difference between adjacent numbers is always an odd number (3, 5, 7). We could say that the next odd number is 9, so the missing number is 16 + 9 = 25
There is another pattern that could be found. This sequence could also represent the sequence of squared numbers:
1^2, 2°2, 3°2, 4^2
In this case, the next number would be 5^2 which is also 25.
#5 Again, we can find a pattern established on the ratio of numbers, but this time with repetitive symbol L. After every L, the number is a thousand times bigger than the previous number:
0.001 -> 1 -> 1000
So, following this pattern, the missing number would be 1000 • 1000 which equals to 1000000 (a million).
A pair of sunglasses has 2 lenses. Each lenses has a radius of 3.5 inches.
How much space or area do BOTH lenses take up?
Use your formula sheet for the area formula for a circle.
A 12.25:inches
B 73.5:inches
C: 10.99\:inches
D 38.47\:inches
Answer:
Area = π×(3.5)^2+ π×(3.5)^2
=76,96902001295 inch²
Miranda was asked to solve the problem 1300 divided by 26.How can she use multiplication to solve this problem
The expression of multiplication used will be 26x = 1300.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Miranda was asked to solve the problem 1300 divided by 26. The expression will be written as,
26x = 1300
x = 1300 / 26
x = 50
Hence, the expression of multiplication used will be 26x = 1300.
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Miranda can solve 1300 divided by 26 by using multiplication – specifically, by finding what number multiplies with 26 to result in 1300. She can break down the number 26 into smaller factors for easier estimation, using inverse operations to eventually find that 50 is the correct answer.
Explanation:Using Multiplication to Solve Division Problems
Miranda was asked to solve the problem 1300 divided by 26. To use multiplication to solve this division problem, she can apply the reciprocal approach. Essentially, she can multiply 1300 by the reciprocal (the inverse) of 26. The reciprocal of a number 'a' is 1/a, so the reciprocal of 26 is 1/26. However, finding the reciprocal of 26 directly can be challenging, so we can use intuitive steps that simplify the problem.
For example, we could productively think about what number, when multiplied by 26, gives us 1300. This is a form of inverse operations. One way to approach this is to break down 26 into factors like 2 and 13, which might lead to simpler multiples to work with. She may start by estimating and refining her estimations by multiplying different numbers by 26 and seeing how close she gets to 1300. It’s a trial and error process, but eventually, she will find the correct answer of 50, as 26 multiplied by 50 equals 1300.