A child grew 3 1/4 inches one year and 4 3/4 inches the next year. How many inches did the child grow over the two years?

Answer:

g(x) = 2ˣ⁻¹ + 3

Step-by-step explanation:

f(x) = 2ˣ

Translated 1 unit right

Translated 3 units up

Answer:

Well if its a translation on the x-axis  the formula would be g(x) = -2×

Although Functions are not my strong suit

I hope i got this right!

So values are

The rule is

Explicit formula

Equation here is

Answer:

[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.

Step-by-step explanation:

Given table:

[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]

First Differences in y-values:

[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]

Second Differences in y-values:

[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]

As the second differences are the same, the function is quadratic.

The coefficient of [tex]x^2[/tex] is always half of the second difference.

Therefore, the quadratic function is:

[tex]f(x)=3x^2[/tex]

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]

Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]

An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3  is [tex]f(x)=4^x[/tex]

[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]

As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.

By using the Pythagorean theorem, we conclude that side x measures (5/2)*√3 units.

In the image, we can see that the equilateral triangle can be divided into two right triangles.

If each side of the equilateral triangle measures 5 units, then for the right triangles we will have that the hypotenuse measures 5 units, and the bottom side measures half of that: 2.5 units.

Now remember the Pythagorean theorem. It says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.  Then we will have:

[tex]x^2 + 2.5^2 = 5^2[/tex]

[tex]x = \sqrt{5^2 - 2.5^2} = \frac{5}{2}\sqrt{3}[/tex]

Then we conclude that side x measures (5/2)*√3 units.

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The label on the cone that represents the diameter of the cone is the letter C

From the figure in the complete question, the line C divides the base circle into two equal segments

The above is the same as the definition of the diameter

Hence, the label that represents the diameter of the cone is the letter C

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Answer:

C is the correct Answer

Step-by-step explanation:

I believe it is 312, hope this helps, sorry if it doesn't!:)

Answer:

6x+54 should be the answer

Step-by-step explanation:

A percentage is a way to describe a part of a whole. The percentage increase in the number of tigers is 21.56%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The percentage change is given by the formula,

Percentage change = |(Intial Value - Final value)|/Initial Value × 100%

Percentage Change = |3200-3890|/3200 × 100% = 21.56%

Hence, the percentage increase in the number of tigers is 21.56%.

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Yes

Step-by-step explanation:

Because the sides of this triangle follow the Pythagorean Theorem.

i.e.

[tex]52^{2} = {20}^{2} + {48}^{2} [/tex]

[tex]\boxed{\textbf{Therefore it IS a right triangle}} [/tex]

The correct values to replace will be 2, 6, 0, and − 8 and the quotient is x³ + 3x² − 4. Then the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

P(x) = x⁴ + x³ − 6x² − 4x + 8

P(x) = 1x⁴ + 1x³ − 6x² − 4x + 8

By the synthetic division, we have

2    ║        1               1               − 6             − 4                8

                                2                6                0               − 8

                1              3                0                − 4                0

                x³           3x²                                − 4                  

By the synthetic division, the correct values to replace will be 2, 6, 0, and − 8 and the quotient is x³ + 3x² − 4. Then the correct option is B.

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Answer:

y = -x – 2

Step-by-step explanation:

Slope is ΔY/ΔX =  -1

plug this into the equation:

1=-(-3) +b

= -2=b

so we get; y = -x – 2

Answer: y = -x - 2

Step-by-step explanation:

     I will be writing this equation in slope-intercept form.

     First, we will find our m value, also known as the slope.

        [tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]

     Now, we will find our b value, or the y-intercept.

-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.

     Lastly, we will write our equation.

y = mx + b

y = -x - 2

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Answer:

G its G

Step-by-step explanation:

Answer: 10+17

Step-by-step explanation:

Distribute:

3(2+6)+4−1

6+18+4−1

Subtract the numbers:

6+18+4−1

6+17+4

Combine like terms:

6+17+4

10+17

solution:

10+17

Answer:

s-(t+r)

Step-by-step explanation:

Answer:

(-3, 13)

Step-by-step explanation:

The transformation that moves a point 4 left and 8 up is ...

 (x, y) ⇒ (x -4, y +8)

The transformation that reflects a point across the y-axis is ...

 (x, y) ⇒ (-x, y)

Applied after the translation, the transformation of ∆ABC becomes ...

 (x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)

Then point A gets moved to ...

 A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)

Answer:

1120^2

Step-by-step explanation:

25x17=425

425+(8x25)=625

625+(8x15)=745

745+(15x25)=1120

Answer:

You find the volume of a cylinder with the formula of π × r² × h

Answer:

more than what i have

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )

[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]

(b)

the angle between a tangent and a radius at the point of contact is 90°

given a line with slope m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]

(c)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{2}[/tex] , then

y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

to find c substitute A (- 5, 2 ) into the partial equation

2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]

y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent

Answer:

Step-by-step explanation:

The area of a square is 49 cm2. What is the perimeter, in cm, of the square?

first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)

or you can use an expression

4 * √49 = 28

Answer:

13.125

Step-by-step explanation:

Answer:

The answer would be C, Both I and II.

Step-by-step explanation:

You can find an attached file which shows the scenarios incase your confused.

The information about the how to open a comic book store should be included in the b. organizational plan.

An organizational plan serves as a way that can be used to plan for the future events to achieve the desire goals of the institution.

Therefore, option B is correct, because with the organizational plan, Korey can note all information required for the business and how the business will grow.

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Given the radius r and the tangent line AB, the length of the line OA is 24 units

The radius r and the tangent line AB meet at a right angle.

By Pythagoras theorem, we have:

AB² = OA² + r²

So, we have:

24² = OA² + 7²

Rewrite as:

OA² = 24² - 7²

Evaluate

OA² = 527

Take the square root of both sides

OA = 23

Hence, the length of OA is 24 units

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Answer:

its A

Step-by-step explanation:

Answer:

[tex]7 \frac{2}{9} [/tex]

Step-by-step explanation:

here is your answer

Calculation steps:

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = (14 - 4) + ( \frac{6}{9} - \frac{4}{9} )[/tex]

[tex] = 7 + \frac{6 - 4}{9} [/tex]

[tex] = 7 + \frac{2}{9} [/tex]

[tex]7 \frac{2}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = \frac{35}{3} - \frac{40}{9} [/tex]

[tex] = \frac{(35 \times 9) - (40 \times 30)}{3 \times 9} [/tex]

[tex] = \frac{315 - 120}{27} [/tex]

[tex] = \frac{195}{27} [/tex]

[tex] = 7 \frac{2}{9} [/tex]