Ken, Justin, and Tiff have read a total of 90
books from the library. Justin read 3 times
as many books as Ken and Tiff read 2
times as many as Justin. How many books
did Justin read?

Answer:

4 songs

Step-by-step explanation:

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex].

The area of the shaded region is the sum of the areas of the two circles of same radius, each of them represented by the following formula:

[tex]A_{r} = \pi\cdot r^{2}[/tex] (1)

Where:

Then, the formula for the shaded area is:

[tex]f(r) = 2\cdot A_{r}[/tex]

[tex]f(r) = 2\pi\cdot r^{2}[/tex] (2)

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex]. [tex]\blacksquare[/tex]

The figure is missing and the statement present mistakes. Correct statement is shown below:

Two circle are inscribed inside squares. Write a function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region. Leave your answer in terms of π.

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Final answer:

To find the slope of the line given by 3x + 4y = -11, the equation is rearranged into the slope-intercept form, yielding a slope (m) of -3/4.

Explanation:

The question asks: What is the slope of the line 3x + 4y = -11?

To find the slope of the line, we first need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the given equation

We isolate y on one side by first moving 3x to the right side of the equation, and then dividing everything by 4:

Now, in the form of y = mx + b, it's clear that the slope (m) of the line is -3/4.

The measure of one angle in an octagon is 135.625 degrees.

Let's denote the measure of one angle as x.

Since there are eight angles in an octagon,

the sum of all the angles in the octagon is 180(x) + 7(2x) = 180x + 14x = 194x.

We know that the sum of the angles in any polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon.

Therefore, 194x = (8-2) × 180. Solving this equation,

we find that x = 135.625. So, the measure of each angle is 135.625 degrees.

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The length of rectangular outdoor patio is 17 feet and the width is 13 feet.

Given that, the perimeter of a rectangular outdoor patio is 60 ft.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let the width of the rectangular outdoor patio be x.

Then, the length is 4 ft greater than the width = x+4

Now, perimeter = 2(x+x+4)

⇒ 2(2x+4) = 60

⇒ 4x+8=60

⇒ 4x=52

⇒ x=13

Length = x+4 = 17

Therefore, the length of rectangular outdoor patio is 17 feet and the width is 13 feet.

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The graph of f(x) = x2 is shifted left 3 units.

To find the height of the parallelogram, set up the equation (3x + 24) x = 384 using the formula for the area of a parallelogram. Solve the resulting quadratic equation to find that x, representing the height, is 8 inche

The student is trying to find the height of a parallelogram when the base is 24 inches longer than three times the height and the area is 384 square inches. Let the height of the parallelogram be represented by x inches. According to the problem, the base (b) is 3x + 24 inches. Using the formula Base x Height = Area of parallelogram, we can set up the equation:

(3x + 24) x= 384

Now solve for x using the distributive property:

3x^2 + 24x = 384

Next, set the equation to zero:

3x^2 + 24x - 384 = 0

Divide the entire equation by 3 to simplify:

x^2 + 8x - 128 = 0

Factor the quadratic equation:

(x + 16)(x - 8) = 0

Set each factor equal to zero:

x + 16 = 0 or x - 8 = 0

Since the height cannot be negative, x = 8 is the solution. Therefore, the height of the parallelogram is 8 inches.

♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.

Dawson is 42, with a 20 year premium coverage, which will amount to $13.68 per $1000. Multiply $13.68 with 180 (because there are 180 $10,000)

13.68 x 180 = $2462.40

annual premium = $2462.40

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To solve the next one, Rachel bought a 20 year life insurance, which amounts to $17.56 per $1000

$63.14 is your answer

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hope this helps

After 8 years, there will be approximately 10,260 owls remaining in the wild. This calculation is based on an initial population of 20,000 owls decreasing by 8% annually, yielding a final population using the formula for exponential decay.

To find out how many owls will remain after 8 years, we can use the formula for exponential decay:

[tex]\[ \text{Final population} = \text{Initial population} \times (1 - \text{Rate of decrease})^{\text{Number of years}} \][/tex]

Given:

Initial population (P) = 20,000 owls

Rate of decrease (r) = 8% = 0.08

Number of years (t) = 8

Plugging in the values:

[tex]\[ \text{Final population} = 20,000 \times (1 - 0.08)^8 \][/tex]

[tex]\[ \text{Final population} = 20,000 \times (0.92)^8 \][/tex]

[tex]\[ \text{Final population} \approx 20,000 \times 0.513 \][/tex]

[tex]\[ \text{Final population} \approx 10,260 \][/tex]

So, after 8 years, there will be approximately 10,260 owls remaining in the wild.

To find the area of a rectangle, multiply the length by the width. For a rectangle that is 1/3 yards long and 2/3 yards wide, the area is 2/9 square yards, which is the answer in simplest form.

The question asks us to calculate the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to compute the area of a rectangle is length  imes width.

First, multiply the length and the width:

Length: 1/3 yards

Width: 2/3 yards

Area = (1/3) times (2/3) yards sq

Area = 2/9 square yards

This is the simplest form of the fraction, so this is the final answer: The area of the rectangle is 2/9 square yards.

Answer:

{ 2,-2}

Step-by-step explanation:

In order to solve this set we just have to first clear the "q":

[tex]7q^{2} -28=0\\7q^{2} -28+28=+28\\7q^{2} =28\\\frac{7q^{2}}{7}  =\frac{28}{7} \\q^{2}=4\\\sqrt{q^{2}} =\sqrt{4} \\q= 2, -2[/tex]

So as we know the solution for a square root is always a negative and positive number, so the solutions ser for 7q2-28=0 is 2 and -2

The general form of the equation of a circle with centre at [tex]\((a, b)\)[/tex] and radius [tex]\(m\)[/tex] is: [tex]\[ x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \][/tex].

The general form of the equation of a circle is [tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex], where [tex]\((h, k)\)[/tex] represents the centre of the circle and [tex]\(r\)[/tex] represents the radius.

If we expand and rearrange this equation, we get [tex]\( x^2 + y^2 - 2hx - 2ky + (h^2 + k^2 - r^2) = 0 \)[/tex].

Comparing this with the given options, we see that [tex]\( h = a \), \( k = b \), and \( r = m \)[/tex].

Substituting these values into the general form, we get [tex]\( x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \)[/tex], which matches the correct option.

Complete Correct Question:

What is the general form of the equation of a circle with center at (a, b) and radius of length m?

a. x2 + y2 - 2ax - 2by + (a2 + b2 - m2) = 0.

b. x2 + y2 + 2ax + 2by + (a2 + b2 - m2) = 0.

c. x2 + y2 - 2ax - 2by + (a2 + b2 + m2) = 0.

d. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.

Final answer:

There are no real number solutions for the given equation.

Explanation:

The given equation is 2x² + 8x + 8 = 0. To find the number of real number solutions for this equation, we can use the discriminant of the quadratic equation. The discriminant is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 2, b = 8, and c = 8. Substituting these values into the formula, we get D = 8² - 4(2)(8) = 16 - 64 = -48.

Since the discriminant is negative (-48), there are no real number solutions for the equation. Therefore, the answer is 0.