Graph the function f(x)= 2x -4

Answer: Choice B

A horizontal shift of 4 to the right.

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

Reason:

Replacing x with x-4 basically means we're decreasing each input by 4 units.

What this does is move the xy axis 4 units to the left. If we held the function curve fixed in place as the xy axis moved like this, then it would give the illusion the function is moving 4 units to the right.

Visual confirmation is shown below.

The airplane reaches its maximum height of 95 feet after 10 seconds

The maximum height of an object the point where the velocity of the object is zero.

Given the function that represents the height of the airplane is expressed as h(t) = -(t-10)² + 95

The maximum height is the point where h'(t) = 0

h'(t) = -2(t-10)

0 = -2t + 10

2t = 10

t = 5secs

Substitute t =10 into the function

h(5) = -(10-10)² + 95

h(5) = -0 + 95
h(5) = 95feet

Hence the airplane reaches its maximum height of 95 feet after 10 seconds

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Considering the given graph, the number of solutions for the system of equations is given by:

b.) one

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In a graph, the number of solutions is given by the number of times the lines intersect. Hence, in this problem, the system has one solution, and option b is correct.

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Answer:

Tabled Function

Step-by-step explanation:

To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  -5 ≤ x ≤ 3

Therefore, a = -5  and  b = 3

[tex]f(3)=7[/tex]

[tex]f(-5)=-17[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]

[tex]f(3)=(3)^2-2=7[/tex]

[tex]f(-5)=(-5)^2-2=23[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]

From inspection of the graph:

[tex]f(3)\approx8[/tex]

[tex]f(-5) \approx 0[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]

Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.

Using an exponential function, it is found that you would have an amount of $64,060 in 45 years.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, considering the initial value of A(0) = 2000, with a growth rate of r = 0.26 each 3 years, the equation is given by:

[tex]A(t) = 2000(1.26)^{\frac{t}{3}}[/tex]

In 45 years, the amount will be given by:

[tex]A(45) = 2000(1.26)^{\frac{45}{3}} = 64060[/tex]

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Answer:

For the first triangle:

[tex]2.75 units^{2}[/tex]

For the second triangle:

[tex]3.98 units^{2}[/tex]

Step-by-step explanation:

To find area of right triangles:

[tex]A=\frac{ab}{2}[/tex]

And you are good to go!

Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!

Have a great day!

:)

The right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40.

In setting the  vertical axis of a Bar Chart, note that it is vital for the categories to be natural as possible.

That is, the vertical axis should always begin with the number zero (0) and the scale values for the x axis must range from the lowest value on the left hand side to highest on the right hand side.

Therefore, due to the explanation given, the right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40 as it range from 0 to the highest value.

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Answer:

A

Step-by-step explanation:

i think i can be wrong

Answer:

a^4

a^2×a^3= a^5(a^2+3)

a^5/a= a^4(a^5-1)

Answer:

X= 2.667  or X= -2.5

Step-by-step explanation:

sorry if this isn't correct </3

Answer:

x=5 .........................................

Answer:

The answer is the first bullet. (number 1)

Answer:

No

Step-by-step explanation:

If you draw a line, it will not go through the origin and there isn't a constant rate of change.

Answer:

140°

205°

Step-by-step explanation:

For A

The bearing of D from C is the angle at the line joining D and C while coming from the north pole in a clockwise direction.

from the diagram, the answer is = 140°

For B

The bearing of D from C is obtained same as A

so the answer is = 205°

The equation in the form (x + a)² = b is (x + 2)² = 16

The equation is given as:

x² + 4x = 12​

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)² = 4

Add this result to both sides of x² + 4x = 12​

x² + 4x + 4 = 12​ + 4

Evaluate the sum

x² + 4x + 4 = 16

Express as a perfect square

(x + 2)² = 16

Hence, the equation in the form (x + a)² = b is (x + 2)² = 16

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Answer:

see the attachment photo!

In the 3rd quarter of year 5, the approximate total sales in the coastal region is; $7 million

The image of the graph showing the quarterly sales has been attached. From the graph, the red lines indicates the coastal region, the blue lines indicates the northern region, and the green lines indicates the southern region.

From the graph, in the third quarter, we can trace the total sales on the y-axis to be approximately $7 million dollars.

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Coordinates after 270 clockwise rotation is (-6,-2), (-3,-5) and  (-8, -5).

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

Given coordinates are: (-2,6) , (-5, 3) and (-5, 8)

For 270° clockwise about the origin, we have the following rule:

(x, y)= (-y, x)

So,

coordinates  (-2,6) change into (-6,-2)

coordinates   (-5, 3) change into (-3,-5)

coordinates  (-5, 8) change into (-8, -5).

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Answer:

B.80

Step-by-step explanation:

a straight line adds up to 180 degrees. you already have 100. 180-100=80

The factor of the function from the given option is d. x+4

The function is a type of relation, or rule, that maps one input to specific single output.

The solutions of the cubic function f(x) are -4, 5/3, and 1. WE need to  identify a factor of this function.

So, the solution are

x = -4

Factor;

x + 4

now,

x = 5/3

Factor;

x - 5/3 = 0

3x - 5 = 0

also,

x = 1

Factor;

x - 1= 0

Therefore, the factor of the function from the given option is d. x+4

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Answer:

x2

Step-by-step explanation:

bcs yeah

Answer:

C, D, and E

Step-by-step explanation:

85-20=65

t>65

This means all the numbers greater than 65.

Do not include 65 because it is not a greater than or equal to symbol.

Hope this helps!

If not, I am sorry.

Answer:

290 take away 2 zeros wuxbeucheuxuejx

Using an exponential function, it is found that it will take 24 years for the current population of 4800 deer to reduce to 600.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, considering the initial value of 4800, and that the population halves every 8 years, the equation is given by:

[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

The population will be of 600 when A(t) = 600, hence:

[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

[tex]600 = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{600}{4800}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{1}{8}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \left(\frac{1}{2}\right)^3[/tex]

Hence:

t/8 = 3.

t = 24.

It will take 24 years for the current population of 4800 deer to reduce to 600.

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Answer:

x = 6

Step-by-step explanation:

Add the system of equations together:
2x - 3y = 12

4x + 3y = 24

you get

6x = 36

divide by the coefficient

6x/6 = 1

36/6 = 6

x = 6

Not sure if you need the y, but if so, let me know!

Hope this helps!

Answer:

Simplest form = -4√44p

Step-by-step explanation:

● -2√2p × 2√22

⇒ (-2)(2)(√2p)(√22)

⇒ -4√44p ...Answer...

hope that helps...