Find (f•g)(x)=x^2-7x+12 and g(x)=3/x^2-16

The answer is C. [1, ∞] on edge

Final answer:

The statement that the product of (a − b)(a − b) equals [tex]a^2 - b^2[/tex] is never true; the correct product is always [tex]a^2 - 2ab + b^2[/tex], representing the square of a difference formula.

Explanation:

The statement "The product of (a − b)(a − b) is  [tex]a^2 - b^2[/tex]." is never true. Instead, using the distributive property to expand the expression (a − b)(a − b) yields a different result, as each term in the first binomial must be multiplied by each term in the second binomial.

The correct expansion is:

Thus, the product of (a − b)(a − b) is always  [tex]a^2 - 2ab + b^2[/tex], which is the square of a difference formula, not  [tex]a^2 - b^2[/tex] which is the difference of squares formula. The latter is applicable to the product (a + b)(a - b).

The mechanic's hourly rate is $55.

Understanding Labor Costs in a Repair Shop

To determine the hourly rate a repair shop charges for labor, we must analyze the information given and apply simple arithmetic operations. According to the examples provided, an auto mechanic charges a flat fee and an hourly rate for labor. For instance, a mechanic charging a flat fee of $75 per car, plus an hourly rate of $55 can be represented by the linear equation y = 75 + 55x, where 'y' is the total labor charge, and 'x' is the number of hours worked.

Example Calculation

Using the equation above, if the job takes 3.5 hours, the labor charge (y) would be calculated as $75 + ($55  imes 3.5) = $75 + $192.50 = $267.50. Hence, we can infer that the mechanic's hourly rate is $55.

Answer:

The correct option is B.

Step-by-step explanation:

The slope of a line is constant.

If a line passes through two points then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the line passes through (-2,7) and (a,2).

Using the above formula the slope of the line is

[tex]m=\frac{2-7}{a-(-2)}[/tex]

[tex]m=\frac{-5}{a+2}[/tex]

It is given that the slope of the line is -5. Substitute m=-5 in the above equation.

[tex]-5=\frac{-5}{a+2}[/tex]

On cross multiplication we get

[tex]-5(a+2)=-5[/tex]

Divide both sides by -5.

[tex]a+2=1[/tex]

Subtract 2 from both the sides.

[tex]a=1-2[/tex]

[tex]a=-1[/tex]

The value of a is -1. Therefore the correct option is B.

Answer:

The answer is B.

Step-by-step explanation:

When the Federal Reserve decreases the reserve rate from 7% to 5%, the amount of money resulting from fraction-reserve banking increases. In this case, an initial deposit of $30,000 would result in $28,500 due to the change in reserve rate.

When the Federal Reserve decreases the reserve rate from 7% to 5%, it means that banks are required to hold a smaller percentage of deposits as reserves. This change allows banks to lend out a larger portion of the initial deposit. In this case, if the initial deposit into a bank is $30,000, the amount that would result from fraction-reserve banking would increase because the bank can now lend out a greater percentage of the deposit.

To calculate the new amount that would result from fraction-reserve banking, we need to calculate the reserve amount and the loan amount.

Therefore, the amount that would result from fraction-reserve banking from an initial deposit of $30,000 would be $28,500.

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To determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(rt) for t. Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.

To solve this problem, we can use the equation P = P0e^(rt), where P is the population at a given time, P0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.

In this case, the population has doubled in 7 years, so we can write the equation as 2P0 = P0e^(r*7). We need to solve for r.

Dividing both sides of the equation by P0 gives us 2 = e^(7r). Taking the natural logarithm of both sides gives us ln(2) = 7r. Solving for r, we find that r ≈ ln(2)/7.

Now, to determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(r*t) for t. Substituting the value of r we found, we get 3 = e^((ln(2)/7)*t). Taking the natural logarithm of both sides to solve for t, we have ln(3) = (ln(2)/7)*t. Solving for t, we find that t ≈ 7 * ln(3)/ln(2). Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.

It takes approximately 11.1 years for the population to triple.

The population growth can be modeled by the exponential function [tex]P(t)=P_0 \times e^{k t}[/tex], where [tex]P_0[/tex] is the initial population, k is the growth rate, and t is time.

In this case, since the population doubles in 7 years, we have the relationship P(7) = 2 x [tex]P_0[/tex].

[tex]P(7)=P_0 \times e^{7 k}[/tex]

[tex]2 \times P_0=P_0 \times e^{7 k}[/tex]

Divide both sides by [tex]P_0[/tex].

[tex]2=e^{7 k}[/tex]

Take the natural logarithm (ln) of both sides to solve for k:

ln(2) = 7k

[tex]k=\frac{\ln (2)}{7}[/tex]

Now that we have the growth rate k, we can use it to find the time it takes for the population to triple.

[tex]P(t)=P_0 \times e^{k t}[/tex]

For tripling, [tex]P(t)=3 \times P_0[/tex].

[tex]3 \times P_0=P_0 \times e^{k t}[/tex]

[tex]3=e^{k t}[/tex]

Take the natural logarithm again:

ln(3) = kt

[tex]t=\frac{\ln (3)}{k}[/tex]

Substitute the value of k we found earlier:

[tex]t=\frac{\ln (3)}{\frac{\ln (2)}{7}}[/tex]

Using natural logarithm values:

[tex]t \approx \frac{1.0986}{\frac{0.6931}{7}}[/tex]

[tex]t \approx \frac{1.0986}{0.0990}[/tex]

t ≈ 11.09

Answer:

Answer in pic

Step-by-step explanation:

hello :
the parabola's equation is : f(x) = a(x+2)²+1

but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1

In geometry, three points are used to name an angle when there are multiple angles that share the same vertex. If CP bisects angle DPB, angle CPB is divided into two equal angles, and the measure of angle CPB is half of the measure of angle DPB.

In geometry, it is necessary to use three points to name an angle when there are multiple angles that share the same vertex. By using three points, we can clearly identify which angle we are referring to. In this case, if CP bisects angle DPB, it means that angle CPB is divided into two equal angles, and CP is one of the dividing lines. Therefore, the measure of angle CPB is half of the measure of angle DPB.

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before the bet Rob had 7 out of 11 ( 4+7)

280/7 = 40

after bet Rob had 3

3*40 = 120

 he has $120