17 The table below shows the distance a car has traveled.
50
20
f
40
Minutes
Distance
Traveled
(in miles)
What is the meaning of the slope of the linear model for the data?
60
100
a) The car travels 5 miles every minute.
b) The car travels 4 miles every minute.
c) The car travels 4 miles every 5 minutes.
d) The car travels 5 miles every 4 minutes.
125
80
100

Answer:

\(16(3a-2b)(4a^2+3ab+2b)\)

Step-by-step explanation:

We will be able to fill the glass up to the amount of water possible to hold in the glass, minus the amount in the cube. This means it will be able to hold \(216a^3-64b^3=(6a)^3-(4b)^3\)cubic cm of water.

Using the difference of cubes formula(you can prove this by expanding back out again), we get that \((6a^3)-(4b)^3=(6a-4b)((6a)^2+(6a)(4b)+(4b)^2)=(6a-4b)(36a^2+24ab+16b)=8(6a-4b)(4a^2+3ab+2b)=16(3a-2b)(4a^2+3ab+2b)\)

Therefore, the answer is \(\boxed{16(3a-2b)(4a^2+3ab+2b)}\) cubic centimeters and we're done!

Answer:

B and D

Step-by-step explanation:

"Sliding": moving a shape without rotating or flipping it.

The shape still looks exactly the same, just in a different place.

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The volume of the solid is 4π(\(\frac{19}{6}\)) and the integral of the f(x) , the line 2y=x, and x=2 is 3(\(e^{4}\) -1).

What is integral ?

An integral is a mathematical concept that is used to calculate the area under a curve or the total amount of change in a variable over a certain interval.

1)The first step is to find the intersection of the lines 2y=x and x=2. They will intersect at (2,1).

The second step is to find the intersection of the lines 2y=x and x=0. They will intersect at (0,0).

The third step is to find the integral over the region.

∫∫ (6e^(x^2))dxdy = ∫[0,2] (6e^(x^2))dx ∫[0,x/2] dy = ∫[0,2] (6e^(x^2))dx (x/2) = [3e^(x^2)] at [0,2] = 3e^(4) - 3e^(0) = 3(e^4 -1).

2)To find the volume of this solid, we can use the method of cylindrical shells.

we can find the function of the surface (1/3)x+(1/2)y+(1/4)z=1

by using cylindrical coordinates:

x = rcosθ , y = rsinθ , z = z

and substitute them in the equation (1/3)x+(1/2)y+(1/4)z=1

(1/3)rcosθ+(1/2)rsinθ+(1/4)z=1

(1/3)r(cosθ+2sinθ)+(1/4)z=1

z = 4(1-(1/3)r(cosθ+2sinθ))

V = ∫∫∫ 4(1-(1/3)r(cosθ+2sinθ)) rdrdθdz = 4π ∫[0,3] (1-(1/3)r(cosθ+2sinθ)) r^2 dr = 4π ∫[0,3] (1-r+(2/3)r^2) dr = 4π(3 - (3/2) + (2/3)) = 4π(19/6).

Hence , The volume of the solid is 4π(\(\frac{19}{6}\)) and the integral of the f(x) , the line 2y=x, and x=2 is 3(\(e^{4}\) -1).

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The length is 6.8 meters and the width is 8.2 meters.

Represent the length and the width with x and y

So, we have:

y = 1.2x

P = 2(x + y)

The perimeter is 30.

So, we have:

2(x + y) = 30

Divide by 2

x + y = 15

Substitute y = 1.2x

x + 1.2x = 15

This gives

2.2x = 15

Divide by 2.2

x = 6.8

Substitute x = 6.8 in y = 1.2x

y = 1.2 * 6.8

Evaluate

y = 8.2

Hence, the length is 6.8 meters and the width is 8.2 meters.

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Answer:

X+4

Step-by-step explanation:

Length is 4 more than width.

X+4= length

First box is 8

Second box is 13

Third box is 20

Answer:

14.

Length:

4+4= 8

9+4= 13

Width:

24-4= 20

Expression:

W=L-4

L=W+4

The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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Answer:

2879.4m

Step-by-step explanation:

the angle = 90 - 10 = 80°

cos(80°) = 500/x

x = 500/cos(80°) = 500/0.17365 = 2879.4

Answer:

If Mrs. Chua wants to buy 25 cupcakes, she can take advantage of the "buy 2 and get 1 free" offer.

This means that for every 3 cupcakes, she only pays the price of 2 cupcakes.

So, the total number of cupcake sets that she needs to buy is 25 divided by 3, which gives 8 with a remainder of 1.

Therefore, she needs to pay for 8 sets of cupcakes, and she will get 2 cupcakes for free since she gets 1 free cupcake for every 2 cupcakes.

So the total number of cupcakes she paid for is 8 x 2 + 2 = 18.

The cost of one cupcake is $m, so the total cost of 18 cupcakes is 18 x $m = $18m.

Therefore, Mrs. Chua paid $18m for 25 cupcakes.

If Mrs Chua wants to buy 25 cupcakes, we can take advantage of the "Buy 2 and Get 1 Free" promotion and divide the cupcakes into groups of 3. For every 3 cupcakes that she buys, she only pays for 2, which means she gets 1 cupcake for free. This means that for every group of 3 cupcakes, she only pays for 2 cupcakes, or $\frac{2}{3}$ of the total price.

Let's first find out how many groups of 3 cupcakes she needs to buy in order to get 25 cupcakes. We can divide 25 by 3 to get:

\(\begin{align}\frac{25}{3} &= 8 \frac{1}{3}

\end{align}\)

This means that she needs to buy 8 groups of 3 cupcakes and 1 extra cupcake.

To minimize the amount of money that Mrs Chua spends, we want to take advantage of the "Buy 2 and Get 1 Free" promotion as much as possible. So we want to make sure that we only pay full price for the last cupcake.

Therefore, Mrs Chua should buy 8 groups of 3 cupcakes (i.e., 24 cupcakes) and then pay full price for the last cupcake. This means that she pays for 16 cupcakes, but gets 8 cupcakes for free (because of the "Buy 2 and Get 1 Free" promotion).

So the total cost for the 25 cupcakes is:

\(\begin{align}\text{Total cost} &= \text{Cost of 16 cupcakes} + \text{Cost of 1 cupcake}\ &= \left(\frac{2}{3} \times 16\right)m + 1m\ &= \frac{32}{3}m + 1m\ &= \frac{35}{3}m\end{align}\)

Therefore, Mrs Chua pays $\frac{35}{3}m$ to buy 25 cupcakes using the "Buy 2 and Get 1 Free" promotion.

The equation is rewritten in slope-intercept form as y = -3x + 5.

Slope = -3; y-intercept = 5.

The equation of any given line, when written in the slope-intercept form is expressed as y = mx + b, where:

Given the equation in standard form as 6x + 2y = 10, rewrite the equation in slope-intercept form as explained in the steps below:

6x + 2y = 10

2y = -6x + 10 [subtraction property of equality]

Divide both sides by 2

2y/2 = -6x/2 + 10/2

y = -3x + 5

The equation is y = -3x + 5, Destinee didn't rewrite the equation correctly because he subtracted 2y from both sides rather.

The slope of y = -3x + 5 is -3.

The y-intercept of the equation is 5.

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Answer:

21

Step-by-step explanation:

3^2=9

9+12=21

Keep it up

Based on the given information, Jenna used approximately 67% of the 6 noodles for her project.

Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.

Here,

Each noodle is 1 foot long, so 6 noodles make a total of 6 feet of noodles.

From the diagram, it appears that Jenna used approximately 4 feet of noodles.

So, Jenna used 4/6 = 2/3 of the total amount of noodles.

Converting 2/3 to a percentage gives approximately 66.7%, which rounds to 67% when rounding to the nearest percent.

Therefore, Jenna used approximately 67% of the 6 noodles for her project.

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

\(y-y_1=m(x-x_1)\)

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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Answer:

b. donations using text message

d. donations using email

Step-by-step explanation:

From the question, it is clear that the people who received these requests were assigned to two groups and these 2 were assigned treatments of if they make donations after either receiving email or text messages after which their respective proportions p1 and p2 are determined.

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

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Answer: Answer is 15 hours

Step-by-step explanation:Given 6 men dig 5 holes in 25 hours

Therefore 10 men will take to dig 5 holes is

workers(1) × time(1) = workers(2)×time(2)

(This formula is used when Total work is same)

where workers(1)= 6 men

Time (1) = 25 hours

workers (2) = 10 men

We have find out Time(2)=T(2)

by applying above formula

6×25=10×T2

after simplify

T2= 15 hours

Answer:

The answer is in the picture below.

Step-by-step explanation:

Answer:

There are 256 pairs in all.

\(\text {Hey! Let's Solve this Problem!}\)

\(\text {\underline {The First Step is to Simplify the Equation}}\)

\(\text {Before: -5(x-10)=-35}\)

\(\text {After: -5x+50=-35}\)

\(\text {\underline {The Next Step is to Subtract 50}}\)

\(\text {-5x+50-50=-35-50}\)

\(\text {Your New Problem Is: -5x=-85}\)

\(\text {\underline {The Final Step is to Divide -5}}\)

\(\text {-5x/-5=-85/-5}\)

\(\text {Your Answer Would Be:}\)

\(\fbox {x=17}\)

\(\text {Best of Luck!}\)

Answer:

17

Step-by-step explanation:

-5 (x - 10) = -35

-5x + 50 = -35

-5x = -35 - 50

-5x = -85

x = 17

Hopefully this answer helps you :)

Answer:

  y = 6x -4

Step-by-step explanation:

The slope can be found from the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (14 -(-10))/(3 -(-1)) = 24/4 = 6

The y-intercept can be found from the formula ...

  b = y1 -m·x1

  b = -10 -6·(-1) = -4

The slope-intercept equation for this table is ...

  y = mx +b . . . . . line with slope m and y-intercept b

  y = 6x -4

Answer:

18 mugs

Step-by-step explanation:

first let's convert 6 3/4 into eights. 6 3/4 as an improper fraction is 27/4, which we multiply by 2 to get 54/8. now we do 54 divided by 3, since we can now ignore the denominator. 54 divided by 3 = 18. This is divided evenly so the "including mugs that are partially filled" is a red herring.

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6.11/104