Amelia is 5 feet tall and casts a 4-foot shadow. A tree next to her casts a 12-foot shadow. The two triangles formed are similar because the angle to the sun is the same. Choose two equations that can be used to find the height, h, of the tree.

Answer:

slope = -2

y-intercept = 5

Step-by-step explanation:

1) Find slope:

[tex]\frac{3-9}{1-(-2)}[/tex] =  [tex]\frac{-6}{3}[/tex] = -2

-2 = slope

2) Find y intercept trough point slope and slope-intercept forms

y - y1 = m (x - x1)

y - 9 = -2 (x + 2)

y - 9 = -2x -4

  + 9         + 9

y = -2x + 5

y = mx + b with b being the y-intercept

5 = y-intercept

Answer:

put the examples on the test or assignment so i can answer it

Answer:

[tex]\huge\color{Black}\boxed{\colorbox{pink}{Answer♡}}[/tex]

[tex]p(x) = ax {}^{3} + 8x {}^{2} + bx + 5 ...(1)[/tex]

on dividing polynomial p(x) by ( x + 2 ) , we obtain ( -25 ) as a remainder.

Therefore , putting the value of x as ( x = -2 )

[tex]p( - 2) = a( - 2) {}^{3} + 8( - 2)^{2} + b( -2) + 5[/tex]

[tex]p( - 2) = - 8a + 32 - 2b + 5 = - 25 \\ = > - 8a - 2b + 37 = - 25 \\ = > - (8a + 2b) = - (25 + 37) \\ cancelling \: negative \: sign \: at \: both \: sides \\ 8a + 2b = 52 \\ dividing \:both \: sides \: by \: 2 \\ 4a + b = 26...(2)[/tex]

also given that..

when the polynomial p(x) is divided by 2x-1 , it gives 0 as the remainder , i.e. , 2x-1 is a root of p(x)

putting value of x = 1/2 in equation (1)

[tex]p( \frac{1}{2} ) = a( \frac{1}{2}) {}^{3} + 8( \frac{1}{2} ) {}^{2} + b( \frac{1}{2} ) + 5 = 0 \\ = > \frac{a}{8} + \frac{8}{4} + \frac{b}{2} + 5 = 0 \\ = >taking \: LCM \\ = > \frac{a + 16 + 4b + 40}{8} = 0 \\ = > \frac{a + 4b + 56}{8} = 0 \\ = > a + 4b = - 56...(3)[/tex]

4a + b = 26... (2)

a + 4b = -56... (3)

16a + 4b = 104...(4)

a ‎ ‎ ‎ ‎ ‎+ 4b = -56

16a + 4b = 104

solving these equations we get,

-15a = -160

a = -160/-15

a = 32/3

[tex]4a + b = 23 \\ 4( \frac{32}{3} ) + b = 23 \\ \frac{128}{3} + b = 23 \\ b = 23 - \frac{128}{3} \\ taking \: LCM \\ b = \frac{69 - 128}{3} \\ = > b = \frac{ -59}{3}[/tex]

hope helpful~

Answer:

Step-by-step explanation:

The spinner should land on whatever color 25% of the time.

25% of 20 = 25/100 * 20 = 500/100 = 5

So the correct answer is the number of times the spinner lands on a color 5 times. Only white does that. All the other colors either go above 5 or below it.

Answer:

White

Step-by-step explanation:

to find the theoretical probability, you just divide the number of times you spin it, which is 20, by how many equal sides the spinner has which is 4.

So therefore you'll do:

20 ÷ 4 = 5

So since that is the same probability as white, the answer is white.

Answer: y = -2x + 8

Step-by-step explanation:

gradient = change in y/ change in x = 8/-4 = -2

y = -2x + c

substitute values in

8 = 0 + c

c = 8

y = -2x + 8

The graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

The line is the distance between two points. The equation of a line in slope-intercept form is y = mx + b

Slope = -8/4
Slope = -2

Determine the y-intercept

Since the y-intercept is the point where the line cross the y-axis, hence b = 8.

FInd the required equation

y = -2x + 8

Hence if the graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

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Answer:

for every 1000 people, the maximum noise level goes up by 1.5

Answer:

42inches

Step-by-step explanation:

Perimeter = 4s

where s is length of each side

when s is 10.5

Perimeter = 4 × 10.5

= 42

Answer:The inverse tangent of 14 is θ=14.03624346° θ = 14.03624346 ° . This is the result of the conversion to polar coordinates in (r,θ) form.

Step-by-step explanation: i think this may help you

Answer:

3:15 pm

Step-by-step explanation:

You can imagine that they go in a circle (we can do whatever we want in theoretical math and physics). By doing so we know we can obtain a cosinusoidal wave by projecting the motion on a plane. Each one of the buses has a period (minimum time after what they're in the same point again). For the first one it's 15 minutes, for the second one it's 20 minutes. We have to take the least common multiple of the periods, that is 75 minutes. So They'll meet every 75 minutes. Add 75 minutes (1h and 15 minutes) to 2pm and there you go.

Answer:

30

Step-by-step explanation:

A + B = 5C

A + B + C = 180

since A + B is 5C we can rewrite with 5C

5C + C = 180

6C = 180

c = 30

Answer:

a) 2

b) -2

c) -2

d) 1/2

Step-by-step explanation:

1) f(-4) means that x=-4 and you must locate the y value on the graph

2) f(2) means that x=2 and you must locate the y value on the graph

3) f(x)=4 means that y=4 and you must locate the x value on the graph

4) f(x)=-1 means that y=-1 and you must locate the x value on the graph

Answer:

d

Step-by-step explanation:

Answer:

Which claim most accurately describes the energy transformation taking place while he practices his guitar?

Sound energy is converted into elastic energy.

Kinetic energy is converted into thermal energy.

Mechanical energy is converted into sound energy.

Electrical energy is converted into mechanical energy.

Step-by-step explanation:

Answer:

C. 4,500

Step-by-step explanation:

Answer:

y = -2/5x - 2

Step-by-step explanation:

Answer:

y = 2/5x -2 or y = 0.4x -2

Explanation:

Step 1: Calculating Slope (m).

m =   [tex]\frac{y2-y1}{x2-x1}[/tex]

m =    [tex]\frac{0-(-2)}{5-0}[/tex]

m =  [tex]\frac{2}{5}[/tex]  

m = 0.4

Now putting value of m in equation (i)

y = 0.4x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (0,-2) for calculating y-intercept:

y = mx + b

-2 = 0.4(0) + b

-2 = 0 + b

-2 = b

b = -2

Now put the value of b in equation (ii)

y = 0.4x + -2

Answer:

3.7

Step-by-step explanation:

39.5 - 35.8 is 3.7

[tex]39.51=40\\ 35.78=36\\\\ 40-36=16 more seconds more than Bailey.[/tex]

if its any number from 5 and larger, you can round it up to a whole.  

Answer:

in my opinion they do not.

Step-by-step explanation:

Answer: Total compensation is everything the company provides an employee in exchange for working. It includes base salary, bonuses, benefits, perks and on-site amenities.Total compensation indicates that an employee is making two or three times his base salary.

Answer:

+8

Step-by-step explanation:

Answer:

x = 12.81

Step-by-step explanation:

AB=EF

ABEF=ABF+AEF

NOW CONTINUES THE SOLUTION

The average speed of the airplane which travels the given distance and time is 400mph.

Speed is simply defined as distance traveled per unit of time. It is the change of position of a moving object per unit of time.

It is expressed as;

s = distance / time = d / t

Given the data in the question;

To determine the average speed of the airplane, we substitute our given values into the expression above.

s = d / t

s = 1000mi / 2.5hrs

s = 400mph

Therefore, the average speed of the airplane which travels the given distance and time is 400mph.

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Answer:

I believe the answer is 17 ft and 8 inches

Step-by-step explanation:

correct me If im wrong

Answer:

x = 1

x= -2.5

Step-by-step explanation:

we can use perfect square method quadratic method or solve it using a calculator directly

Answer:

number 2

Step-by-step explanation:

Answer:

Cy-Cx=10,000 this is the best answer ever

Answer:

  2 bottles

Step-by-step explanation:

The 15 trees will need ...

  (15 trees)×(10.5 fl oz/tree) = 157.5 fl oz

This is about ...

  (157.5 fl oz)/(33.814 fl oz/L) ≈ 4.66 L

This is just slightly more than the quantity available in 1 bottle. It amounts to ...

  4.66 L/(4.1 L/bottle) ≈ 1.14 bottles

We assume that only whole bottles can be purchased, and that we do not have an inventory of fertilizer on hand.

2 bottles are needed to fertilize 15 trees

The Van would catch up with the truck at 6:00 pm

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let us say the van catch up with the truck after t hours at a distance d.

For the truck:

45 = d/t

d = 45t

For the Van:

54 = d / (t - 2)

d = 54t - 108

45t = 54t - 108

9t = 108

t = 12 hours

The Van would catch up with the truck at 6:00 pm

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Answer:

The Van would catch up with the truck at 6:00 pm

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let us say the van catch up with the truck after t hours at a distance d.

For the truck:

45 = d/t

d = 45t

For the Van:

54 = d / (t - 2)

d = 54t - 108

45t = 54t - 108

9t = 108

t = 12 hours

The Van would catch up with the truck at 6:00 pm