If f(x) = x2 + x and g(x) = x − 3, find f(g(7)).

Answer:

26

Step-by-step explanation:

7(4)+-2

28-2=26

Step-by-step explanation:

y = 4 and z = -2

[tex] = 7y + z[/tex]

[tex] = 7 \times 4 + ( - 2)[/tex]

[tex] = 28 - 2[/tex]

[tex] = 26...[/tex]

Answer:

100

Step-by-step explanation:

10^2 is 100 therefore it is 100

Answer:

Step-by-step explanation:

y = mx + b is the formula to figure out your question

Now, the equation ( y = 28x + 8)

Already shows the m and b

m = 28

b = 8

Hope this helps! :)

If not ask me in the comments about your question and I’ll answer

if the perimeter=s+s+s+s

=x+x+x+x

A function assigns the value. The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x)=9x²+1 and g(x)=√(2x³). Therefore, the value of f(g(x)) will be,

[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

            = 9(2x³) + 1

           = 18x³ + 1

The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.

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Answer:

36

Explanation:

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64,...

Multiples of 18 are:

18, 36, 54, 72, 90, 108, 126, 144,...

The least common multiple of 4 and 18 is 36.

Answer:

Whats the question then?

Step-by-step explanation:

Answer: -10x+1.5

Step-by-step explanation:

[tex]-2(5x-0.75)=-10x+1.5[/tex]

Answer:

12

Step-by-step explanation:

because it digit havbeen given ad k

Sam paid $ 124.032 as tax deduction each week.

An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.

It is given that

weekly earnings of Sam is $912

Tax deduction is 13.6 %

Let the amount of Tax deduction is represented by $x

Then the equation formed is

x = 13.6 % 912

x = 13.6 *912 /100

x = $ 124.032

Therefore Sam paid $ 124.032 as tax deduction each week.

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Answer:

  $7800

Step-by-step explanation:

The total interest earned can be found by summing the earnings from each of the investments.

Let x represent the total amount invested. Then Jessica's earnings are ...

  (x/2)(0.07) +(x/2)(0.13) = 780

Simplifying the equation gives ...

  (x/2)(0.07 +0.13) = 780

  0.10x = 780

  x = 7800 . . . . . . . . divide by 0.10

Jessica has $7800 invested.

The equation that can be used for finding the lengths in the Pythagoras theorem include:

b² = c² - a²

a² = c² - b²

c² = a² + b²

It should be noted that a Pythagoras theorem is simply the theorem that's used in finding the missing length of a right angled triangle.

In this case, the equation that can be used to find the sides in a Pythagoras theorem has been given.

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Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.

En esta situación, Julio debe pagar por 29 fotocopias de los apuntes de un  compañero suyo. El monto a pagar es el producto del número de copias y el coste unitario de cada fotocopia, es decir:

x = (0.30 PEN) · (29)

x = 8.70 PEN

Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.

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Hello,

if :

[tex] \frac{16}{4(3 - 1)} = \frac{16}{4 \times 2} = \frac{16}{8} = 2[/tex]

if :

[tex] \frac{16}{4} \times (3 - 1) = 4(3 - 1) = 4 \times 2 = 8[/tex]

Answer:

Hello! The answer is c) 8.

Step-by-step explanation:

To solve this question, we need to follow the order of operations. This can be done through PEMDAS - parentheses, exponents, multiplication, division, addition, and subtraction.

First, we need to solve what's in the parentheses:

[tex]\frac{16}{4} * 2[/tex]

Now we can multiply and we get:

[tex]\frac{32}{4}[/tex]

This can be further simplified by doing 32 ÷ 4 to get 8.

Therefore, the answer is c) 8

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

x−3y=9;−x+3y=−9

x−3y=9

−x+3y=−9

Add these equations to eliminate x:

0=0

Answer:

Infinitely many solutions.

Answer:

x-intercepts:  (-1, 0) and (2, 0)

x-intercept:  (-3, 0)

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=-4x^2+4x+8[/tex]

The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0

Therefore, to find the x-intercepts of the given function, set the function to zero:

[tex]\implies -4x^2+4x+8=0[/tex]

Factor out -4:

[tex]\implies -4(x^2-x-2)=0[/tex]

Divide both sides by -4

[tex]\implies x^2-x-2=0[/tex]

Rewrite the middle term as -2x + x:

[tex]\implies x^2-2x+x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-2)+1(x-2)=0[/tex]

Factor out the common term (x - 2):

[tex]\implies (x+1)(x-2)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}[/tex]

Therefore, the x-intercepts are (-1, 0) and (2, 0).

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

Given quadratic equation:

[tex]-9 = x^2 + 6x[/tex]

Add 9 to both sides:

[tex]\implies x^2+6x+9=0[/tex]

Rewrite the middle term as 3x + 3x:

[tex]\implies x^2+3x+3x+9[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+3)+3(x+3)=0[/tex]

Factor out the common term (x + 3):

[tex]\implies (x+3)(x+3)=0[/tex]

[tex]\implies (x+3)^2=0[/tex]

Square root both sides:

[tex]\implies (x+3)=0[/tex]

Solve for x:

[tex]\implies x=-3[/tex]

Therefore, the x-intercept is (-3, 0).

As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.  

Answer:

2,734,500

Step-by-step explanation:

27,345 × 113 - 27,345 × 13 ← factor out 27,345 from each term

= 27,345(113 - 13)

= 27,345 × 100

= 2,734,500

Event A and Event B are events that do not overlap. This statement is false.

Two events overlap if there is a chance that both events occur together. A spade has a number 2. Thus, it is possible to pick a spade that has the number 2 on it. Thus, these events are dependent events.

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An equation is formed of two equal expressions. The sum of all possible values of x is 16.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

3x + 2y = 21

3x = 21 - 2y

x = (21-2y)/3

Since the value of x is needed to be positive, the value of 2y must not exceed 21. Also, the value of (21-2y) must be a multiple of two.

Now, the values of y that will satisfy the given condition in the equation are 0, 3, 6, and 9.

Further, the sum of the possible values of x are,

Sum = 7 + 5 + 3 + 1 = 16

Hence, the sum of all possible values of x is 16.

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Answer:

3081.24 cm³ (nearest hundredth)

Step-by-step explanation:

Formulas

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If a rectangular piece of paper is rolled along its length to form a cylinder:

To calculate the volume of the formed cylinder, determine the radius by using the circumference formula:

[tex]\implies \sf 2 \pi r = 44[/tex]

[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]

[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]

Substitute the round radius into the formula for Volume and solve for V:

[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]

[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]

[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]

[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]

[tex]\implies \sf V=3081.239698...cm^3[/tex]

Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).

All the options are incorrect. the required average is (3x-9)/2.

Thermometer A reads xº.
Thermometer B reads 2° below the reading on thermometer A = x-2
Thermometers C and D each read 4° less than twice the reading on thermometer  = 2(x-2)-4

Average of the values is the ratio of total sum of values to the number of values.

As per question,
A=x
B = x-2
C.D = 2(x-2)-4= 2x-8
Average = A + B + C + D /4
= x+x-2+2x-8+2x-8/4
= 6x-18/4
= 3x-9/2

Thus, the required average of temperature = 3x-9/2.

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The sample standard deviation is 2.45.

Standard deviation measures the spread of a dataset around its mean. The variance measures the average degree to which each data point differs from the mean.

The standard deviation is the square root of the variance.

Standard deviation = √6 = 2.45

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Answer: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

The last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.

A few fundamental principles apply to density curves:

Following the rules above, we can see from graph B that the curve is above the horizontal axis. That shows that the probabilities are positive which is a necessity. Moreover, the area under the curve must also be 1. That is also satisfied.

Hence, the last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.

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The future value of the annuity after the end of 5 years is $552.56.

Given that, r =5%= 0.05, 5 years  = 5 yearly payments, so n = 5, and P = $100.

The formula to find the annuity formula [tex]FV=\frac{P \times ((1+r)^{n}-1 )}{r}[/tex].

Now, [tex]FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}[/tex]

⇒FV = 100 × 55.256

⇒FV = $552.56

Therefore, the future value of the annuity after the end of 5 years is $552.56.

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