5
The histogram shows the number of miles driven by a sample
of automobiles in New York City. What is the class width?
40
3
Frequency
20
10
10.000
40,000
20,000 30,000
Number of Miles
50,000
10,000
10
5,000

Answer:

The value of [tex]gf\left(-2\right)[/tex] will be:

Step-by-step explanation:

Given the functions

[tex]f(n) = n^2 - 4n + 3[/tex]

[tex]g\left(n\right)\:=\:2n\:-\:1[/tex]

[tex]f\left(-2\right)\:=\:\left(-2\right)^2\:-\:4\left(-2\right)\:+\:3[/tex]

           [tex]=\left(-2\right)^2+4\cdot \:2+3[/tex]

           [tex]=2^2+4\cdot \:2+3[/tex]

            [tex]=2^2+8+3[/tex]

            [tex]=4+11[/tex]

            [tex]=15[/tex]

so

[tex]gf\left(-2\right)=g\left(15\right)[/tex]

             [tex]=2n-1=2\left(15\right)-1=30-1=29[/tex]

Therefore,

Step-by-step explanation:

y=0

7x-3*0=42

7x=42

x=42/7=6

x=0

7*0-3*y=42

-3y=42

y=-42/3=-14

Answer:

y=-14, x= 6

Step-by-step explanation:

Answer:

Its d i took the class

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If you use rise over run, you should get to. From one point to the other, the rise is 2 and the run to the right is 1. So, you do 2 divided by 1, which is 2. So, the slope would be 2.

A) y intercept is (0,3)

C) Axis of symmetry is x = -1

D) Vertex is (-1, 4)

So basically everything but choice B is true.

========================================

Explanation:

Choice A is true because plugging in x = 0 leads to y = 3. Effectively, anything with an x goes away when x = 0 leaving that 3 behind. So finding the y intercept in this form is fairly fast.

-------------------

To check choices B through D, let's convert the equation into vertex form.

y = -1x^2 - 2x + 3 is in the form y = ax^2 + bx + c where

a = -1

b = -2

c = 3

The vertex is located at (h,k) such that h = -b/(2a)

Plug the values of 'a' and 'b' into the equation below

h = -b/(2a)

h = -(-2)/(2*(-1))

h = 2/(-2)

h = -1

The x coordinate of the vertex is x = -1

Then use this to find the y coordinate of the vertex

y = -1x^2 - 2x + 3

y = -1(-1)^2 - 2(-1) + 3

y = 4

The y coordinate of the vertex is 4, meaning k = 4

The vertex overall is (h,k) = (-1, 4)

This shows choice D is true, meaning choice B has to be false.

Choice C is true because the axis of symmetry is the x coordinate of the vertex. This is the vertical line that cuts the parabola into two mirrored halves. This vertical line always goes through the vertex.

Answer:

Step-by-step explanation:

x is positive and y is negative

Answer:

(x,-y)

Step-by-step explanation:

Answer:

A belt costs $15 and a wallet costs $27.

Step-by-step explanation:

Let's mark price of a belt with x and price of the wallet with y. That leaves is with a system of equations:

x + y = $42

7x + 4y = $213

The goal when solving this system is to get rid of one of the variables. We can do that by multiplying first equation with -4:

-4x - 4y = -168

7x + 4y = 213

Now, we simply add these two equations up:

-4x - 4y + 7x + 4y = -168 + 213

3x = 45

x = $15

Now, we plug in x into any of the two starting equations to find y:

x+y=42

15 + y = 42

y = $27

Answer:

I think the answer would be A

Answer:

A

Step-by-step explanation:

Answer:

The answer is A only i. (0)

Answer:

D

Step-by-step explanation:

Given

x(x + 3)(x - 1)(2x + 1) = 0

Equate each factor to zero and solve for x

x = 0

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

Thus

x = 0, x = - 3, x = 1, x = - [tex]\frac{1}{2}[/tex] are the roots

Hence

111 x = - 1 and iv x = [tex]\frac{1}{2}[/tex] are NOT roots → D

Answer:

D.

Step-by-step explanation:

to prove congruency of two triangles, you need two congruent sides and one congruent angle

in this case we are given exactly that, 2 sides and one angle that is congruent

we would also need to make sure that the given sides and angles are actually congruent, and not mismatched

we can do this by looking at the positions of the letters in each congruency statement

for example, the letters LO and MA are the first two letters in each triangle's name, this means that they are congruent and properly matched

if you do this with every statement that you are give, you can see that the triangles can be proven by SAS

Answer:

you can look up these online it will give u the diagram and u can put it in on calculators I used to do that

A ≈ 452.39

Hope you get a good grade

Answer:

The perimeter of the new TV is approximately  95.32 inches

Step-by-step explanation:

The diagonal dimension of the original TV = 32 inches

The perimeter of the original TV = 87.16 inches

The diagonal dimension of the new TV = 70 inches

The perimeter of the new TV = 87.16 inches

For the original TV, we have;

Let w be the width of the original TV and l be the length of the original TV, we have;

2·w + 2·l = 87.16

√(w² + l²) = 32

Therefore, we have;

32² = w² + l²

w = (87.16 - 2·l)/2

w = 43.58 - l

32² = l² + (43.58 - l)²

l² + (43.58 - l)² - 32² = 0

l² + 43.58² - 2 × 43.85 × l + l² - 32² = 0

2·l² - 87.16·l + 875.2164 = 0

By the quadratic formula, we have;

l = (87.16 ± √((-87.16)² - 4×2 × 875.2164))/(2 × 2)

Therefore, l = 27.89 inches or l = 15.69

Therefore, w = (87.16 - 2·l)/2 = (87.16 - 2× 27.89)/2 = 15.69

or w = (87.16 - 2× 15.69)/2 = 27.89

Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;

15.69/27.89

w₂/l₂ for the new TV = 15.69/27.89

∴ w₂ = l₂ × 15.69/27.89

w₂² + l₂² = 70²

∴ (l₂ × 15.69/27.89)² + l₂² = 70²

l₂² × (15.69/27.89)² + l₂² = 70²

l₂²((15.69/27.89)² + 1) = 70²

l₂² = 70²/((15.69/27.89)² + 1) = 3722.04

l₂ = √(3722.04) ≈ 61.0

w₂ = l₂ × 15.69/27.89 = 61 × 15.69/27.89 ≈ 34.32

Therefore;

The perimeter of the new TV = 34.32 + 61 = 95.32 inches.

In this exercise we have to use the knowledge and information given to calculate the perimeter that will correspond to:

The perimeter of the new TV is approximately  95.32 inches

So the data for this exercise is from:

Let w be the width of the original TV and l be the length of the original TV, we have;

[tex]2*(w) + 2*(l) = 87.16\\\sqrt{(w^2 + l^2)} = 32[/tex]

Therefore, we have:

[tex]32^2 = w^2 + l^2\\w = (87.16 - 2*l)/2\\w = 43.58 - l\\32^2 = l^2 + (43.58 - l)^2\\l^2 + (43.58 - l)^2 - 32^2 = 0\\l^2 + 43.58^2 - (2 * 43.85 * l)+ l^2 - 32^2 = 0\\(2)*(l)^2 - 87.16*l + 875.2164 = 0[/tex]

By the quadratic formula, we have;

[tex]l = (87.16 +/- \sqrt{((-87.16)^2 - 4*2 * 875.2164))/(2 * 2)} )[/tex]

Therefore:

[tex]w = (87.16 - (2)*(l))/2 = (87.16 - 2* 27.89)/2 = 15.69\\w = (87.16 - 2* 15.69)/2 = 27.89[/tex]

Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;

w₂/l₂ for the new TV = [tex]15.69/27.89[/tex]

[tex]w_2 = (l_2)* (15.69/27.89)\\w_2^2 + l_2^2 = 70^2\\(l_2 *15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2 * (15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2((15.69/27.89)^2 + 1) = 70^2\\l^2_2 = 70^2/((15.69/27.89)^2 + 1) = 3722.04\\l_2 = \sqrt{(3722.04)} = 61.0\\w_2= l_2 * 15.69/27.89 = 61 * 15.69/27.89 = 34.32\\[/tex]  

The perimeter of the new TV :

[tex]P = 34.32 + 61 = 95.32[/tex]

See more about perimeter at brainly.com/question/6465134

Answer:

girls: 16

boys: 40

Step-by-step explanation:

girls : boys

2 : 5

let the total number of people be (2+5)x.

2x + 5x = 56

7x = 56

x = 8

therefore, no. of girls = 2 x 8 = 16

no. of boys = 5 x 8 = 40

This is a question on ratio and proportions + forming and solving equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer:

5q+74

Step-by-step explanation:

84-94 first which equals -10

then add that by 84 which equals 74

lastly just bring the 5q and 74 together making your expression

Answer:

1.2

Step-by-step explanation:

apex leaning and I don't know why they want me to write 20 characters long or something like that before posting this‍

Answer:

Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.

Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation.

Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation

Step-by-step explanation:

Answer:

The drift angle is approximately 7.65° towards the East from the plane's heading

Step-by-step explanation:

The speed of the plane = 350 mph

The direction in which the plane flies N 40° E = 50° counterclockwise from the eastern direction

The speed of the wind = 40 mph

The direction of the wind = S 70° E = 20° clockwise from the eastern direction

The component velocities of the plane are;

[tex]R_{Plane}[/tex] = (350 × cos 50)·i + (350 × sin 50)·j

[tex]R_{Wind}[/tex] = (40 + cos 20)·i - (40 × sin 40)·j

The resultant speed of the plane = [tex]R_{Plane}[/tex] + [tex]R_{Wind}[/tex] = 265.915·i +242.404·j

The direction the plane is heading = tan⁻¹(242.404/265.915) ≈ 42.35°

Therefore, the drift angle = Actual Angle - Direction of the plane = 50 - 42.35 ≈ 7.65° towards the East

Answer: A. 5.89

Step-by-step explanation:

edge2020

Tell us the value of the variable to solve

The graph is attached btw

Answer:

Bet.

Step-by-step explanation:

Answer:

Do you need the result of the end?

Step-by-step explanation:

5*3=15

15-3=12

Answer: it’s A

Step-by-step explanation: I got it right, hope it helps ✨

The value of the expression  [tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k}[/tex] when a = 5 and k = -2 is [tex]\frac{25}{9}[/tex]

The expression is as follows:

[tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k}[/tex]

using law of indices

Hence,

when a = 5, k = -2

[tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k} = (\frac{9(5^{-2} )}{3(5^{-1} )})^{-2}[/tex]

Then,

[tex](\frac{9(5^{-2} )}{3(5^{-1} )})^{-2}=(\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}[/tex]

[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}=(\frac{9}{25} (\frac{5}{3}))^{-2}[/tex]

[tex](\frac{9}{25} (\frac{5}{3}))^{-2}=(\frac{3}{5})^{-2}[/tex]

[tex](\frac{3}{5})^{-2}=\frac{25}{9}[/tex]

Therefore, the value of the expression is 25 / 9

learn more on expression here:https://brainly.com/question/12879207

#SPJ5

Answer:

I am sorry what are you showing

Answer:

x=-6

Step-by-step explanation:

Move all terms that don't contain x to the right and solve using the elimination process.

Answer:

1) Step 3: S = $136.49 - $3.0625 × 1/4

2) By completing the operations within the parenthesis in Step 2, before multiplying the result by 1/4

Step-by-step explanation:

1) From the given information, we have;

The amount amount Maria earns as a pet sitter = $32.75

The number of weeks Maria worked as a pet sitter = 2 weeks

The amount Mariah previously saved = $70.99

The amount Maria spent = $12.25

The amount Mariah put in her savings account = 1/4 of the remaining (balance) money

Therefore, we have;

The amount placed in Mariah's savings account, S, is given as follows;

Step 1: S = [($32.75 × 2) + $70.99 - $12.25] × 1/4

Step 2: S = [($65.5 × 2) + $70.99 - $12.25] × 1/4

Step 3: S = [($136.49) - $12.25] × 1/4

Step 4: S = $124.24 × 1/4

Step 5: S = $31.06

The amount Mariah puts in her saving's account = $31.06 and the step Mariah first makes an error is Step 3 where what she put down was as follows;

Step 3: S = $136.49 - $3.0625 × 1/4

2) She can correct the error by completing the calculation of the operation within the parenthesis in Step 2, before multiplying by the factor 1/4.

Answer:

a) The four inequalities are;

1) x ≤ 2

2) y ≥ 4

3) x + y ≥ 6

4) 0.5 × x + 0.25 × y ≤ 2

b) The limits of the combinations of fruits that are opened to her, derived using the Chart function on Microsoft Excel are;

1) (0, 8) which is 0 melons and 8 oranges

2) (0, 6) which is 0 melons and 6 oranges

3) (2, 4) which is 2 melons and 4 oranges

Step-by-step explanation:

The price per Melon = 50c = $0.5

The price per orange = 25c = $0.25

The amount she has to spend = $2

The number of melons she must buy ≤ 2

The number of oranges she must buy ≥ 4

The total number of fruits she should ≥ 6

Let x be the number of melons

Let y be the number of oranges

a) The four inequalities are;

1) x ≤ 2

2) y ≥ 4

3) x + y ≥ 6

4) 0.5 × x + 0.25 × y ≤ 2

b) Please find attached the required graph of the combination of fruits the girl buys created with Microsoft Excel

The combinations of the vertices of the feasible combinations that are opened to her, obtained from the creation of the combined graph, using Microsoft Excel are;

1) (0, 8) which is 0 melons and 8 oranges

2) (0, 6) which is 0 melons and 6 oranges

3) (2, 4) which is 2 melons and 4 oranges

Answer:

nile blue should be the correct answer

Step-by-step explanation:

Answer:

A line that slants down from left to right has a negative slope. Horizontal and vertical lines also have a slope.

Step-by-step explanation: