A spring stretches in relation to the weight hanging from it according to the weight hanging from it according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the length of the spring in inches.
How to graph the equation including axis labels
How to interpret the slope and the y-intercept of the line
Answers
y= spring length = 0.75x + 0.25 (measured in inches).
First, let x=0. y will then be 0.75(0) + 0.25. This is your "vertical intercept."
Now position your pencil on that point (0,0.25). Move your pencil point 1.00 unit to the right from (0,0.25) and then up 0.75 unit. This is what the "slope" means: rise over run. Here the rise is 0.75 and the run is 1.00.
The slope, 0.75, tells us by how much more the spring stretches as 1 more lb of weight is added to the weight already hanging from the spring.
Answer and Explanation:
Given : A spring stretches in relation to the weight hanging from it according to the equation [tex]y = 0.75x + 0.25[/tex] where x is the weight in pounds and y is the length of the spring in inches.
To find :
1) How to graph the equation including axis labels ?
2) How to interpret the slope and the y-intercept of the line?
Solution :
Linear equation [tex]y = 0.75x + 0.25[/tex]
1) To draw the graph we find the x and y-intercept of the line,
x- intercept i.e. y=0
[tex]0.75x + 0.25=0[/tex]
[tex]0.75x=-0.25[/tex]
[tex]x=-\frac{0.25}{0.75}[/tex]
[tex]x=-0.33[/tex]
y- intercept i.e. x=0
[tex]y=0.75(0) + 0.25[/tex]
[tex]y=0.25[/tex]
Plotting these two points (-0.33,0) and (0,0.25).
Refer the attached figure below.
2) The general form of line is [tex]y=mx+c[/tex]
where, m is the slope and b is the y-intercept of the line.
Comparing with given line [tex]y = 0.75x + 0.25[/tex]
The slope of the line is m=0.75
and the y-intercept of the line is b=0.25.
Related Questions
Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?
7.98 × 45.67 = 3,644.466
12.3 × 3.8 = 467.4
0.45 × 2.3 = 1.035
14.22 × 2.8 = 398.16
Answers
Answer:
Option 3 - [tex]0.45\times2.3= 1.035[/tex]
Step-by-step explanation:
To find : Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?
Solution :
The correct placement of decimal in product is based on the number of digits after decimals as the number of digits after decimal of one number added to number of digits after decimal of second number is the required place in the result a decimal place.
1) [tex]7.98\times 45.67 = 3,644.466[/tex]
Not correct, decimals are 4 so place after 4 numbers.
2) [tex]12.3\times3.8= 467.4[/tex]
Not correct, decimals are 2 so place after 2 numbers.
3) [tex]0.45\times2.3= 1.035[/tex]
Correct, decimals are 3 so place after 3 numbers.
4) [tex]14.22\times2.8= 398.16[/tex]
Not correct, decimals are 3 so place after 3 numbers.
Therefore, option 3 is correct.
Spence Ferris, a sales representative, drove 4 1/2 hours on the first day of his business trip, 8 3/4 hours on the second day, 6 2/3 hours on the third day, and 5 1/6 hours on the fourth day. If he must drive a total of 30 hours in five days, how much hours must Spence drive on the fifth day.
Answers
Solve -2 (x+5)=1/4(x-10)
Answers
-8(x+5)=x-10
-8x-40=x-10
-9x=30
x=-10/3
-10
x= ------
3
Consider the solid shaped like an ice cream cone that is bounded by the functions z=x2+y2‾‾‾‾‾‾‾√ and z=50−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√. set up an integral in polar coordinates to find the volume of this ice cream cone.
Answers
To calculate the volume of a solid bounded by two functions, set up an integral in polar coordinates. The volume is found by integrating the difference of the two volumes described by the functions (50 - sqrt(x²+y²) - sqrt(x²+y²)) over r, θ, and z within their appropriate limits.
Explanation:The subject of the question is mathematics, more specifically, integral calculus in spherical or polar coordinates. Calculating the volume of a solid bounded by two functions can be done by taking the difference of the two function volumes.
The integrals, using polar coordinates (r and θ), are set up as follows:
Volume = ∫∫∫(50 - sqrt(x²+y²) - sqrt(x²+y²)) r dr dθ dz,
where the limits for r are [0, sqrt(50)], for θ are [0, 2π], and for z are [0, 50]. Also, note that 'x²+y²' is replaced with 'r²' because in polar coordinates, 'r' represents the square root of x^2 plus y^2.
This integral, when solved, gives the volume of the ice cream cone-shaped solid.
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The volume of the ice cream shaped solid can be found by converting the limits of the cone to polar coordinates and performing a double integral. The limits of the cone are represented by the expressions z = r and z = sqrt(50 - r^2). The volume integral will be ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ.
Explanation:To evaluate the volume of the solid resembling an ice cream cone, we can use the method of double integration in polar coordinates. Because we're dealing with a cone, polar coordinates are suitable as they're related to circular symmetry.
The limits of the cone are given by the functions z = sqrt(x^2 + y^2) and z = sqrt(50 - x^2 - y^2). In polar coordinates these become z = r and z = sqrt(50 - r^2).
To evaluate the volume of the cone, we need to subtract the volume of the lower cone (given by z = r) from the volume of the upper cone (given by z = sqrt(50 - r^2)). We convert the values to polar coordinates and use double integration as follows:
V = ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ
This integral, once solved, will give the volume of the ice cream shaped solid.
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A large dinosaur was 89 feet long. Convert the length to meters. (Use 1 yd≈0.9144 m.)
Answers
1 foot = 0.305 meter
89 feet = 27.127 meters.
I really hope this helped you! c:
1 yd = 0.9144 m....so 29.67 yds = (29.67 * 0.9144) = 27.13 meters
Help please!! 20 points and brainliest!!
solve the system of linear equations. separate the x- and y- values with a coma. -9x+6y=-30
-12x+9y=-30
Answers
-9x+6y=-30
-12x+9y=-30
Although we might really want to say -9x+6y=-12x+9y, we can't do it that way. We have to get rid of a variable and go from there. Solving for y, we get
-9x+6y=-30
Divide both sides by 3
-3x+2y=-10
Add 3x to both sides
2y=-10+3x
Divide both sides by 2
y=(-10+3x)/2
-12x+9y=-30
Divide both sides by 3
-4x+3y=-10
Add 4x to both sides
-10+4x=3y
Divide both sides by 3
(-10+4x)/3=y
Since we have
(-10+4x)/3=y and y=(-10+3x)/2 , we have
(-10+4x)/3=(-10+3x)/2
Since 3*2=6, we can multiply both sides by 6
-20+8x=-30+9x
Add 30 to both sides
10+8x=9x
Subtract 8x from both sides
x=10
Plug that in to any equation,and you should have your answer! Good luck, and ask if you have any questions!
One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. (a) use differentials to estimate the error in computing the length of the hypotenuse. (round your answer to two decimal places.)
Answers
To estimate the error in the hypotenuse length of a right triangle using differentials, we use the trigonometric identity sin(θ) = opposite/hypotenuse, finding the derivative, and then apply the angle error to get an error estimate of
±0.31 cm in the hypotenuse length.
The question asks to use differentials to estimate the error in computing the length of the hypotenuse of a right triangle when one side is 9 cm and the opposite angle is 30° with a possible error of ±1°. To calculate the hypotenuse (c) when dealing with problems involving right triangles, you can use the trigonometric identity sin(θ) = opposite/hypotenuse, which can be rearranged to c = opposite/sin(θ). The differential of c with respect to θ is dc/dθ = -opposite * cos(θ)/sin2(θ). Given that the opposite side is 9 cm and the angle θ is 30°, we can find dc/dθ and then multiply by the possible angle error of ±1° to estimate the error in the hypotenuse length.
Plugging in the given values and converting the angle to radians (since the derivative is taken with respect to radians), we find
dc/dθ ≈ -9 cm × cos(30°)/sin2(30°) ≈ -18 cm.
The possible change in angle is ±1°, which in radians is approximately ±0.0175 radians, thus
Estimated error in hypotenuse ≈ -18 cm × ±0.0175 ≈ ±0.315 cm.
Therefore, the estimated error in the length of the hypotenuse, rounded to two decimal places, is ±0.31 cm.
What is the like term for 4m+(-3n)+n? What is the like term for c+2c+c-5c+1
Answers
a) The three terms have variables m, n, n. The two like terms are the last two terms, which both have variable n: -3n, n.
b) The 5 terms have variables c, c, c, c, -. The like terms are the first four, which all have variable c: c, 2c, c, -5c.
If 0.5 lb of Starbucks Coffee costs $6.48, what is the unit price for Starbucks Coffee? Hint: this involves decimal division.
Answers
The unit price of Starbucks Coffee, when 0.5 lb costs $6.48, is calculated by dividing the total cost by the pounds, resulting in $12.96 per pound.
Explanation:If 0.5 lb of Starbucks Coffee costs $6.48, to find the unit price for Starbucks Coffee, we perform a simple division. You want to know how much 1 lb would cost, given that 0.5 lb costs $6.48. To do this, you divide the total cost by the number of pounds.
$6.48 ÷ 0.5 = $12.96 per pound
This means that the unit price of Starbucks Coffee, when given a price of $6.48 for a half-pound, is $12.96 per pound. This calculation is crucial in understanding how to break down costs into more manageable, standard units, making price comparisons easier and more straightforward.
Where does the graph of the linear equation, y = 1/2 x - 3, cross the y-axis?
Answers
negative 2 is where it crosses
y = 0,5x-3 = 0,5*0-3= -3
Graph parallelogram ABCD on a coordinate plane with vertices A(3,4) B(6,1) C(0,-2) and D(-3,1).
Find the slope of each side.
What do you notice about the slopes?
Answers
AB = (1 - 4) / (6 - 3) = -3 / 3 = -1
BC = (-2 - 1) / (0 - 6) = -3 / -6 = 1/2
CD = (1 - (-2)) / (-3 - 0) = 3 / -3 = -1
DA = (4 - 1) / (3 - (-3)) = 3 / 6 = 1/2
EXPLANATION
Every line has one side parallel to it and I know this because the slope is equal.
A parallelogram, the opposite sides have equal slopes.
To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.
Here are the steps to find the slope of each side:
Plot the Points:
Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.
Connect the Points:
Connect the points in order (A to B to C to D to A) to form the parallelogram.
Find the Slope:
The slope of a line passing through two points
(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1
Calculate the slope for each pair of consecutive points:
Slope of AB: mAB = 1−4/6−3
Slope of BC: mBC = −2−1/0−6
Slope of CD: mCD = 1−(−2)/−3−0
Slope of DA: mDA = 4−1/ 3−(−3)
Now, observe the slopes:
mAB and mCD
are the slopes of opposite sides. They should be equal for a parallelogram.
mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.
So, for a parallelogram, the opposite sides have equal slopes.
Sue uses the expression ( 8 x 3,000) + ( 8 x 200) + (8 x 9) to help solve a multiplucation problem what is Sue's multiplucation problem?
Answers
Answer:
Sues problem would be - 8×3,209 :8×3,209
What is the value of the expression
–180
–5
5
24
Answers
answer
–5
because (-5) x (-6) = 30
Is (-2,5) a solution to the inequality y<-3x+4 show steps
Answers
What is the equation of the line tangent to the curve xy=4 at (2,2)?
Answers
x(dy/dx) + y(dx/dx) = 0. Then x(dy/dx) = -y, and (dy/dx) = -y/x.
At (2,2), this slope is -2/2, or -1.
Then the eqn of the TL to the curve xy=4 is y-2 = -1(x-2) = -x+2
Thus, y = 2 - x + 2, or y = -x + 4 (answer)
For commission as a realtor, Michelle earns $349 plus 3% of the purchase price for each home she helps buy or sell. If she earned $8,965 in commission on a certain home, find its purchase price.
ANSWER:
$8965- $349= $8616
3/100x= 8616
8616 x 100/ 3= $287,200.
I'm posting this because somebody inboxed me asking for help and before I even got to help them, they deleted the inbox and i couldn't remember their name. I hope you see this and benefit from it, sorry!
Answers
Well, let us solve this step by step.
We know that Michelle earns 349 plus 3% of the Purchase price. Let us call the Purchase price as P, so that:
Earnings, E = 349 + 0.03 P
So if she earns 8,965 (E = 8,965) so we can find P:
8,965 = 349 + 0.03 P
0.03 P = 8,616
P = $287,200
Michelle's total commission from a house sale was $8,965, from which $349 is a fixed commission. The rest, $8616, represents the 3% of the selling price of the house. By solving the simple equation $8616 = 0.03 * X, we find that the home price is $287,200.
Explanation:This problem is a simple, but common, practice in the world of linear equations. The first step is to understand that the base commission of $349 is a constant that Michelle earns every time, whilst the remaining part of her commission comes from the 3% percentage of the sale price. After subtracting the base commission from the total commission, we get a value of: $8965 - $349 = $8616. This value is equal to 3% of the house price.
We can express this as: 8616 = 0.03 * X, where X is the value of the house. By isolating X (the house price), we divide both sides by 0.03 to get the house price. Therefore, the home price would be $8616 / 0.03 = $287,200.
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on monday 2/3 of the team practiced tuesday 7/8 wednesday 1/2 and thurday 3/4 on which day were the most team memebers present at practice
Answers
Tuesday: 7/8
Wednesday: 1/2
Thursday: 3/4
You have to compare the fractions:
There are several methods to compare fractions. I will use the conversion to a common denominator.
This is how you convert all the fractions to an equivalent form with common denominator.
The least common denominator is: 3 * 2^3 = 24
Original fraction equivalent fraction
2/3 2*8 / 3*8 = 16 / 24
7/8 7*3 / 8*3 = 21 / 24
1/2 1*12 / 2* 12 = 12 / 24
3/4 3*6 / 4*6 = 18 / 24
Now you can compare the fractions: 12/24 < 16/24 < 18/24 < 21/24.
So, you see that the greatest fraction is 21 /24, i.e. 7/8, and the answer is the day when 7/8 of the team practiced.
Answer: Tuesday.
Hour truck can carry a 3/4 ton load. Each brick weighs 4 lbs and 14 oz. How many bricks can the truck carry
Answers
The radius of a circle is increasing at a rate of 3 cm per minute. find the rate of change of the area when
Answers
Two triangles have side lengths 3, 4, 5 and 6, 8, 10, respectively. The triangles are similar to each other.
Answers
The missing side length of the second triangle is 8.
To find the missing side length of the second triangle, we can use the property that similar triangles have proportional side lengths.
Given:
First triangle: ( 3, 4, 5 )
Second triangle: ( 6, x, 10 )
Since the triangles are similar, the ratios of corresponding sides are equal:
[tex]\[ \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \][/tex]
From the first ratio, [tex]\( \frac{6}{3} = \frac{x}{4} \)[/tex], cross multiply:
[tex]\[ 6 \times 4 = 3 \times x \][/tex]
[tex]\[ 24 = 3x \][/tex]
Divide both sides by 3 to solve for ( x ):
[tex]\[ x = \frac{24}{3} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the missing side length of the second triangle is 8.
Here's a detailed calculation step-by-step:
1. Set up the ratios of corresponding sides: [tex]\( \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \).[/tex]
2. Use the first ratio to find [tex]\( x \): \( 6 \times 4 = 3 \times x \)[/tex].
3. Solve for [tex]\( x \): \( 24 = 3x \)[/tex].
4. Divide both sides by 3: [tex]\( x = \frac{24}{3} = 8 \)[/tex].
5. Therefore, the missing side length of the second triangle is 8.
Complete Question:
Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other. Find the missing side of the triangle.
Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each corner, in order to create a box with the largest possible volume?
A. 0.5 inches
B. 1 inch
C. 1.5 inches
D. 2 inches
Answers
length: 10 inches
width: 8 inches
2) dimensions of the squares cut
length: x
width: x
3) dimensions of the box:
length of the base = 10 - 2x
width of the base = 8 - 2x
height = x
4) Volume of the box
V = (10 - 2x) (8 - 2x) x = x [80 - 20x - 16x + 4x^2] = x [ 80 - 36x + 4x^2 ] =
V = 80x - 36x^2 + 4x^3
5) Maximum volume => derivative of V, V' = 0
V' = 80 - 72x + 12x^2 = 0
6) Solve the equation
Divide by 4 => 3x^2 - 18x + 20 = 0
Use the quadratic formula: x = 1.47 and x = 4.53 (this is not valid)
So, the answer is the option C. 1.5 inches.
there are 36 female preformers in a dance recital.the ratio of men to women is 2:9 how many men are in the dance recital.
Answers
2:9 means for every 2 men there are 9 women
36/9 =4
4*2 = 8
there are 8 men
jody has 2 red marbles 6 blue marbles and yellow marbles what is the ratio to red to blue
Answers
is the answer because 2/6 simplifies to 1/2 which would be the ratio of 1:2.
URGENT PLEASE HELP!!! I want to know HOW to solve this as well.
What is the solution to the equation?
4(3 + 7) = 4 · x + 4 · 7
A.
x = 3
B.
x = 4
C.
x = 7
D.
x = 10
Answers
A is your anwser. Hope this Helps
Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $20 on food. Rides at the fair cost $2.00 per ride. Which function can be used to determine how much money he has left over after x rides?
Answers
i hope that correct
christie decided to make bracelets for her class. two-fifths of the bracelets were done on Monday and three-sevenths were done on Tuesday what part of the bracelets are finished?
Answers
90,175,087,309 in expanded form
Answers
+ 0
+ 100,000,000
+ 70,000,000
+ 5,000,000
+ 0
+ 80,000
+ 7,000
+ 300
+ 0
+ 9
Expanded Factors Form:
9 × 10,000,000,000
+ 0 × 1,000,000,000
+ 1 × 100,000,000
+ 7 × 10,000,000
+ 5 × 1,000,000
+ 0 × 100,000
+ 8 × 10,000
+ 7 × 1,000
+ 3 × 100
+ 0 × 10
+ 9 × 1
Expanded Exponential Form:
9 × 1010
+ 0 × 109
+ 1 × 108
+ 7 × 107
+ 5 × 106
+ 0 × 105
+ 8 × 104
+ 7 × 103
+ 3 × 102
+ 0 × 101
+ 9 × 100
Word Form:
ninety billion, one hundred seventy-five million, eighty-seven thousand, three hundred nine
It's the holiday season and you are working for a packing company that specializes in holiday fruit cakes. For Christmas this year, the number of clients requesting fruit cakes has more than tripled and orders need to be shipped prior to the New Year. Your supervisor has asked you to work 15 hours more than a normal 40 hour work week, including Christmas day, which falls on a Friday. Therefore, one of your regular 8 hour days will be paid at the holiday rate. You get paid $10.00 per hour plus you get time and a half for overtime and double pay for the holidays. What will your gross base pay be for the week?
Answers
Normal rate: $10/hr
Time and a half= $15/hr
Double pay: $20/hr
Hours to be paid at $10/hr =32 hours
$10/hr x 32hrs= $320
$20/hr x 8hrs= $160
$15/hr x 15hrs=$225
Total gross pay: $705
To calculate your gross base pay for the week working extra hours including a holiday, you need to consider regular pay, overtime pay, and holiday pay. The gross base pay for the week will be $785.00.
Explanation:To calculate your gross base pay for the week, you need to consider your regular hours, overtime hours, and holiday pay. Here's how you can calculate it:
Calculate your regular pay for the 40 hours of work at the regular rate: $10.00 per hour x 40 hours = $400.00.Calculate your overtime pay for the 15 additional hours of work at time and a half: $10.00 per hour x 1.5 = $15.00 per hour. $15.00 per hour x 15 hours = $225.00.Calculate your holiday pay for the 8-hour day at double the regular rate: $10.00 per hour x 2 = $20.00 per hour. $20.00 per hour x 8 hours = $160.00.Add up your regular pay, overtime pay, and holiday pay: $400.00 + $225.00 + $160.00 = $785.00.Therefore, your gross base pay for the week will be $785.00.
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Approximate to pi 13.0909091
Answers
3.14159265359 x 4 = 12.5663706144
so 13.0909091 is not approximate to pi
Find all the second partial derivatives. v = e5xey
Answers
Final answer:
The second partial derivatives of v = e⁵x * ey are ∂²v/∂x² = 25e⁵x * ey and ∂²v/∂x² = 5e⁵x * e^y.
Explanation:
To find the second partial derivatives of the function v = e⁵x * ey, we need to differentiate twice with respect to x and y. Let's start with the first partial derivative with respect to x:
∂v/∂x = ∂(e⁵x * ey)/∂x
= 5e⁵x * ey
Next, we differentiate the first partial derivative with respect to x to find the second partial derivative with respect to x:
∂²v/∂x² = ∂(5e⁵x * ey)/∂x
= 25e⁵x * ey
Similarly, the second partial derivative with respect to y is:
∂²v/∂x² = ∂(5e⁵x * ey)/∂y
= 5e⁵x * e^y