Triangle ABC is graphed on a coordinate grid with vertices at A (-2, -4), B (2, -4) and C (0, 2). Triangle ABC is dilated by a scale factor of x with the origin as the center of dilation to create triangle A’B’C with the vertices A’ (-1, -2), B’(1, -2), C’ (0, 1).

Which rule best represents the dilation that was applied to Triangle ABC to create A’B’C’?

(x, y) (2x, 2y)

(x, y) (0.2x, 0.2y)

(x, y) (12x, 12y)

(x, y) (14x, 14y)

Answer:

2x(7x - 3)(7x +3)

Step-by-step explanation:

Find common factors between the 2 numbers:

98x^3 - 18x

2x(49x^2 - 9)

now find what numbers multiplied together is 49, and find what numbers added together equals 0 and the product is 3, 7 times 7 is 49 and 3(-3) = 9 while 3 - 3 = 0 so:

2x(7x - 3)(7x +3)

Answer:

35.6%

Step-by-step explanation:

31/87(100)

3100/87

35.6%

Answer:

35,6%

Step-by-step explanation:

31/87 = 0,35632184

As a percentage: 35,632184%

Rounded to one deciman place: 35,6%

Answer:

Who has that name?

Step-by-step explanation:

What's the question i'm really curious lol

Answer:

35/48

Step-by-step explanation:

35/48

Answer:

35/48

Step-by-step explanation:

It is already in it's simplest form.

Answer:

⅛ cups per waffle

Step-by-step explanation:

Maybe you missed to add the complete question. After a little research I was able to find the complete question which is as follows:

''The cost y(in dollars) to provide food for guests at a dinner party is proportional to the number x of guests attending the party. It costs $30 to provide food for 4 guests. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to provide food for 10 guests?''

So, I am solving based on this complete question.

Answer:

Please check the explanation.

Step-by-step explanation:

a. Write an equation that represents the situation.

As the cost and the number of guests are proportional.

So the equation of the form

[tex]y = mx[/tex]

Plug in the values y = 30 and x = 4 to find m

[tex]y = mx[/tex]

30 = m (4)

m = 30/4

    = 7.5

Now, substituting m = 7.5 in the equation y=mx

[tex]y = mx[/tex]

[tex]y = 7.5x[/tex]

b) Interpreting Slope

Given that the units for y are dollars, and the units for x are guests.

Thus, the slope 7.5 means it costs $7.5 per guest.

c) How much does it cost to provide food for 10 guests?''

We know the equation

[tex]y = 7.5x[/tex]

put x = 10

y = 7.5(10)

y = $75

Thus, it costs 75 dollars for 10 guests.

Answer:

The area is 12x^2

Step-by-step explanation:

Answer:

[tex]\sqrt[5]{x^2}[/tex] and [tex](\sqrt[5]{x} )^2[/tex]

Step-by-step explanation:

They are both correct.

Answer:

A, and B

Step-by-step explanation:

The reason why is because, 2 is still on x. Therefore, while 5 represents the division it stays up in the top left corner.

Answer:

96

Step-by-step explanation:

Hope this helps

Answer:3

3(4x+3)

Step-by-step explanation:

Answer:4 and a half

Step-by-step explanation:

4 and a half

Answer:

The answer is 3 Hope this help :)

Step-by-step explanation:(6,7) (4,1)

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{1-7}{4-6}[/tex]

[tex]\frac{-6}{-2}[/tex]

x=3

Answer:

The number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.

Step-by-step explanation:

Note: This question is not properly structured/written. The question is therefore rewritten properly before answering the question as follows:

To manufacture scooters, the manufacturer has a fixed cost of $34,400 plus a variable cost of $100 per scooter. Find n, the number of scooters, that need to be produced so that the average cost per scooter is $180.

The explanation of the answer is now provided as follows:

The number of scooters can be calculated as follows:

Variable cost per scooter = $100

n = number of scooter = ?

Total variable cost = Variable cost per scooter * n = $100 * n = $100n

Total cost = Fixed cost + Total variable cost = $34,400 + $100n

Average cost per scooter = Total cost / n = $180 ................ (1)

Substituting the value for Total cost into equation (1) and solve for n, we have:

($34,400 + $100n) / n = $180

$34,400 + $100n = $180n

$34,400 = $180n - $100n

$34,400 = $80n

n = $34,400 / $80

n = 430

Therefore, the number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.

Answer:

The arc length s = 44 inches

Step-by-step explanation:

We are given:

r = 4 in

Ф = 11 radians

We need to find s

The formula used is: [tex]s=r\theta[/tex]

where s represents arc length, r is radius and Ф is angle in radians

Putting values and finding s

[tex]s=r\theta[/tex]

Put r = 4 and Ф = 11

[tex]s=4\times 11\\s=44[/tex]

So, the arc length s = 44 inches

Answer:

a) [tex]-16t^{2}+64t\geq40[/tex]

b)[tex][2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}][/tex]

(see attached picture for the number line)

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) [tex]h_{max}=64ft[/tex]

d) t=2s

Step-by-step explanation:

a)

Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:

[tex]-16t^{2}+64t\geq40[/tex]

this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.

b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:

[tex]-16t^{2}+64t =40[/tex]

we can move the 40 to the other side of the equation so we get:

[tex]-16t^{2}+64t-40=0[/tex]

we can factor the equation so it's easier to solve, so we get:

[tex]-8(2t^{2}-8t+5) =0[/tex]

which simplifies to:

[tex]2t^{2}-8t+5=0[/tex]

and we can use the quadratic formula to solve this equation, so we get:

[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]

so we get:

[tex]t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}[/tex]

which yields:

[tex]2\pm \frac{\sqrt{6}}{2}[/tex]

and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:

[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex]  for a test value of 0

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1

[tex][2+\frac{\sqrt{6}}{2},\infty)[/tex] for a test value of 4

so next we test each of the values in the original inequality and see if the inequality is true:

[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex] for a test value of 0

[tex]-16(0)^{2}+64(0)\geq40[/tex]

[tex]0\geq40[/tex] false

so this is not an answer.

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1

[tex]-16(1)^{2}+64(1)\geq40[/tex]

[tex]48\geq40[/tex]

true, so this is an answer.

[tex][2+\frac{\sqrt{6}}{2}, \infty)[/tex] for a test value of 4

[tex]-16(4)^{2}+64(4)\geq40[/tex]

[tex]-16(16)+64(4)\geq40[/tex]

[tex]-256+256\geq40[/tex]

[tex]0\geq40[/tex]

false, so this is no answer.

So the answer is the interval:

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex]

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)

so we can use the following formula to find the t-value for this maximum height:

[tex]t=-\frac{b}{2a}[/tex]

so we substitute the corresponding values:

[tex]t=-\frac{64}{2(-16)}[/tex]

which yields:

t=2s

next, we can substitute this time into the original function to find the maximum height, so we get:

[tex]h=-16(2)^{2}+64(2)[/tex]

which yields:

h=64 ft

d) We found the answer for d on the previous part where we got that t=2s

Answer:

13

Step-by-step explanation:

3(7)-4x

3(7)-4(2)

21-8

=13

Answer:

[tex]y = \frac{x}{3} - 4[/tex]  

I hope this helps!

Answer:

They will at the same height of 80cm at 12 months.

Step-by-step explanation:

Sapling A:

y = 10/3x + 40

Sapling B:

y = 5x + 20

Set the equations to equal each other.

10/3x + 40 = 5x + 20

10/3x - 5x = 20 - 40

10x - 15x = 60 - 120

-5x = -60

x = 12

Sub x = 12 into one of the two equations (It doesn't matter which one you choose)

y = 5(12) + 20

y = 80

Answer:

$2656

Step-by-step explanation:

6.25% of $10,624 is $664, so that is the amount of interest every year.

$664 times 4 is $2656, so after 4 years $2656 will have been paid.

Answer:

The value of [tex]k[/tex] is -9.

Step-by-step explanation:

If [tex]A(x,y) = (-1,-6)[/tex], [tex]B(x,y) =(3, -12)[/tex] and [tex]C(x,y) = (k,6)[/tex], then [tex]\overrightarrow{BC} = \alpha\cdot \overrightarrow{BA}[/tex]. By vectors sum, we find each vector below:

[tex]\overrightarrow{BA} = A(x,y)-B(x,y)[/tex] (1)

[tex]\overrightarrow{BA} = (-1,-6)-(3,-12)[/tex]

[tex]\overrightarrow{BA} = (-4, 6)[/tex]

[tex]\overrightarrow{BC} = C(x,y)-B(x,y)[/tex] (2)

[tex]\overrightarrow{BC} = (k,6)-(3,-12)[/tex]

[tex]\overrightarrow{BC} = (k-3, 18)[/tex]

By substituting in the equation defined at the begining of this answer:

[tex](k-3, 18) =\alpha\cdot (-4, 6)[/tex]

[tex](k-3, 18) = (-4\cdot \alpha, 6\cdot \alpha)[/tex] (3)

The value of [tex]\alpha[/tex] is:

[tex]6\cdot \alpha = 18[/tex] (3a)

[tex]\alpha = 3[/tex]

If we know that [tex]\alpha = 3[/tex], then the value of [tex]k[/tex] is:

[tex]k-3 = -4\cdot \alpha[/tex]

[tex]k = 3-4\cdot \alpha[/tex]

[tex]k = 3-4\cdot (3)[/tex]

[tex]k = 3-12[/tex]

[tex]k = -9[/tex]

Then, the value of [tex]k[/tex] is -9.

Answer:

8 I believe

step-by-step explanation:

Answer:

b and m or known the y-intercept and slope

Step-by-step explanation:

you first place your point of y-intercept which is b in the equation its always got a x value of 0 paired with it.

then from there you place points using the m in the equation which is you rise over run for all your folling points on the graph.

hope that helps

Answer:

do you want us to make a metaphor ?

Answer:

(45,60,75)

Step-by-step explanation:

Because 45^2 + 60^2 = 75^2

                  5625 = 5625

Answer:

5x+4

Step-by-step explanation: