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Answer:

A. Please find attached the drawing of the reflector showing the location of the focus created with Microsoft Excel

B. The width of the beam of light projected from the headlight's reflector is approximately 6.93 inches

Step-by-step explanation:

The given equation representing the cross section of the headlight reflector is y² = 6·x

The shape of the reflector = Parabolic

The general equation of a parabola is (y - k)² = 4·p·(x - h)

The focus of the parabola, Focus = (h + p, k)

By comparison to the general equation of a parabola, from the equation of the reflector, we have;

k = 0, h = 0, 4·p = 6

∴ p = 6/4 = 3/2 = 1.5

∴ The focus of the parabola = (1.5, 0)

A. Please find attached the graph of the equation of the cross-section of the reflector, showing the filament at the focus, created with Microsoft Excel

B. The depth of the reflector is x = 2 inches

A vertical or horizontal parabola has two x-values for a given y-value or two y-values for a given x-value respectively

For the given horizontal parabola, the width of a parabola at a point is the difference between the two y-values at the point

At x = 2, we have;

y² = 6 × x = 6 × 2 = 12

∴ y = ±√(12)

The two y-values at x = 2 are y₁ = √(12) and y₂ = -√(12)

The width of the parabola, w = y₁ - y₂

The width of the parabola at x = 2, w = √(12) - (-√(12))

∴ w = √(12) +√(12) = 4·√3

The width of the parabola at x = 2, w = 4·√3 inches

The width of the parabola at x = 2 = The width of the beam of light projected from the headlight's reflector = 4·√3 inches

By giving the answer as a decimal and rounded to the hundredths place, we have;

The width of the beam of light projected from the headlight's reflector ≈ 6.93 inches.

Answer:

ab=4c

Step-by-step explanation:

Since a and b are being multiplied, we can just right ab. Since 4 and c are being multiplied, we ca just right 4c.

Answer:

ab=4c

Step-by-step explanation:

Basically, if you see any variables that are together like that or numbers side by side with letters, it means it's just being multiplied! This doesn't however, work with numbers next to numbers. So for example:

Say you have a x b = 5 x 5c

It would be ab = 5 x 5c Because only letters get put next to each other. That's really the only way I know how to explain it. Have a great day and good luck!

Answer:

Hey! do not go to brainly for this, sometimes brainly can be no help and people will scam for points, or maybe try to hack you (pt virus) with those links saying the answers there.. I am not saying this for points but go to https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-distance-between-clock-hands for that

Step-by-step explanation:

So don't waste your time on brainly finding answers, you can run out of points fast, some people wont answer at all.

Answer:

Step-by-step explanation:

i dont know

Answer:

y = -1/2x+5

Step-by-step explanation:

South Street: y = 2x-4

Perpendicular slope to 2 is -1/2

Find any point on new street: (2,4)

4 = -1/2(2) + b

4= -1 + b

5 = b

Answer:

W = t + 200

Step-by-step explanation:

Number of words typed in the first letter = 200

The relationship between the total words typed, W and the number of seconds, t spent on the second letter :

W = number of words typed in first letter + t

W = 200 + t

Choosing any pair of values from the table :

W = 245 ; t = 45

W = 200 + 45

W = 245

Therefore, the number of words, W typed today can be represented as

W = 200 + t

Answer:

I am pretty sure it's A and I am very sorry if I'm wrong

Step-by-step explanation:

The way I would think about this question is this: because Jordan only wants to work a maximum of 40 hours, he can work 40 hours or less. Which is described as an equation in the top equation of letter A. And because he also wants to make $250 or more, the bottom equation in A would work as well.

I hope that makes sense! Please ask me in the comments if you want more explanation on it

Answer:

infinite number of solutions

The given histogram is unimodal skewed.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

This histogram is unimodal skewed.

There are two parts to this answer. The first part has to do with the number of modes.

This would be the item that is occurring the most frequently. In this case the mode is only 4.

It is occurring more than any other.

The second part of this has to do with the distribution of the data as it is displayed on the histogram.

There are 4 pieces of data that are only occurimg one time on the right of the histogram. We call this skewing the data.

When both sides looks almost the same we say it is symmetric.

Hence, the given histogram is unimodal skewed.

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1. a. The image's dilated side lengths on each side:

AB = CD = 45cm.

BD = AC = 24cm.

2. a. Equal ratios exist between the lengths of matching sides. The ratio is the same as the dilation's scale factor.

b. The image is a dilation of the original image.

c. The scale factor = 4.

3. a. The image is a dilation of the original image.

b. The scale factor = 2.

A scale factor, often referred to as a conversion factor, is a numerical value that is used to alter a figure's size without altering its shape. The scale factor can be calculated if both the dimensions of the original and the dilated (increased or lowered) figure are known. The basic formula for calculating a figure's scale factor is given as,

Scale factor is equal to the division between the dimensions of the new and old shapes.

In the first figure, the sides are given as:

AB = 15cm

BD = 8cm

Scale factor = 3

Now, using the scale factor formula:

Scale factor = New dimensions/Old dimensions

⇒ 3 = New dimension/15

⇒ New dimension of AB = 45cm.

Similarly, new dimension of BD = 24cm.

In the second figure, as the lengths of corresponding sides have equal ratios. Both the figures are similar. The image is the dilation of the original figure as the lengths of corresponding sides have equal ratios. The ratio is the same as the dilation's scale factor. So, the scaler factor here is 4.

Now in the last figure we can see that the coordinates of A', B', C' and D' are exactly half of that of the coordinates of A, B, C and D.

The ratio of the coordinates is 2:1.

Therefore, the scale factor = 2.

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Answer:

254.34

Step-by-step explanation:

Area of a circle = pi*r² So the radius is diameter/2 which is 9, so the area is pi*81 which is 254.34

14. 254.47

EXPLANIACTION

A=(3.14/4) * 18^2

Answer:

1.5 inches thick

Step-by-step explanation:

Answer:

c) Step 3

Step-by-step explanation:

Answer:

Its D

Step-by-step explanation:

the person above me is wrong :)

Step-by-step explanation:

I think you will get x this way:

x=180°-140°

x=40°

b)3.65(500/m)

Hope this helps

Answer:

distance is estimated 11

Answer:

NO it isnt.

Step-by-step explanation:

Go right of the decimal and throught the different place values. Since the number just right of the decimal is the highest place value, whichever number is greater, holds the greater value.

Answer:

54 cm2

Step-by-step explanation:

A = l * b

A = 6 * 9

A = 54

Answer:

h = 125

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is

h = 63 + 62 = 125

Answer:

If the radius is 4, then:

Volume = 1/2(4/3)(π)(r³) = 1/2(4/3)(3.14)(4³) = 134.0 ft³

Answer:

x>28

Step-by-step explanation:

x>7

4x>28

Answer:

is there an image of the story?

Answer:

A. Memory uses general knowledge

I deeply apologize if it's wrong but that's just what I think.

Also, I just took the test with this question and I'm pretty sure I got it correct.

Answer:

Problem 27: 35

Step-by-step explanation:

This is because 7 times (Multiplied) by 9-4 is 35. We get here by doing 9-4=5. This problem then turns into 7(5)

Answer:

height = 5.4 units

Step-by-step explanation:

r = 4.5/2 = 2.25

B = πr² = 3.14(2.25²) = 15.90

V = 1/3Bh

28.63 =1/3(15.90)h

85.89 = 15.90h

h = 5.40 units

Answer:

A

Step-by-step explanation: Rreminder be happy and stay confident <3

The percentage of Theo's clients are on the varsity team will be 27%

It is given in the question that

clients, 40% play football

clients, 60% play Baseball

Of the students who play football, 30% are on the varsity team,

50% of Theo's baseball clients are on the varsity team.

So clients who play football and are on the varsity team will be

[tex]0.4\times 0.3=0.12[/tex] = 12%

And clients who play baseball and are on the varsity team will be

[tex]0.6\times 0.5=0.15[/tex]=15%

The total percent of the varsity team will be =12+15=27%

Thus the percentage of Theo's clients are on the varsity team will be 27%

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Answer:

A: 6x^2 + 19x + 3

Step-by-step explanation:

6x + 1 (x +3)

use the foil method so first do 6x(x) and you get 6x^2 then 6x(3) + x(1) and you get the 19x then you just do 3(1) and you get your answer which as stated above is 6z^2 + 19x + 3

Answer:

76.6

Step-by-step explanation:

so the nearest tenth is 76.57143

Answer:76.6

Explanation:

Answer:

12

Step-by-step explanation: each side is 3, and there are 4 sides so 3*4=12