If F(x)=x-5 and G(x)=x^2, what is F(F(x))?

Using exponential function concepts, it is found that it represents growth of 4%.

An exponential function is modeled by:

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

In which:

In this problem, the equation is:

[tex]y = 8700(1.04)^t[/tex]

Hence:

[tex]1 + r = 1.04[/tex]

[tex]r = 0.04[/tex]

Since r = 0.04 is positive, it represents a growth of 4%.

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Final answer:

The function y = 8700(1.04)^4 represents an exponential growth with a rate of increase of 4% per time period over four periods.

Explanation:

The given function is y = 8700(1.04)^4. This represents an exponential growth because the base of the exponent, 1.04, is greater than 1. To determine the percentage rate of increase, we observe that the base, 1.04, when written as a percentage, is 104%. This means that the amount increases by 4% over each time periodperiod. Since the exponent is 4, this growth occurs over four time periods. However, the overall increase is not simply 4% multiplied by 4, as exponential growth compounds wicompoundsth each time period.

What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]

Let us find the value of cos([tex] \frac{3\pi}{4} [/tex]) and [tex] sin(\frac{7\pi}{6} ) [/tex]

[tex] cos(\frac{3\pi}{4} )=cos(\pi -\frac{\pi}{4} ) [/tex]

The angle [tex] \pi -\frac{\pi}{4} [/tex] lies in second quadrant.

So, [tex] cos(\frac{3\pi}{4} )=-cos(\frac{\pi}{4} ) =-\frac{1}{\sqrt{2}} [/tex]

[tex] So, cos(\frac{3\pi}{4} )=-\frac{1}{\sqrt{2}} [/tex]

Now, Let us find the value of [tex] sin(\frac{7\pi}{6} ) [/tex]

[tex] sin(\frac{7\pi}{6} ) =sin(\pi +\frac{\pi}{6} )=-sin(\frac{\pi}{6} ) =\frac{-1}{2} [/tex]

[tex] sin(\frac{7\pi}{6} ) =\frac{-1}{2} [/tex]

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]=2*[tex] \frac{-1}{\sqrt{2}} [/tex]-4*[tex] \frac{-1}{2} [/tex]

=[tex] \frac{-2}{\sqrt{2}} +\frac{4}{2} [/tex]

=[tex] \frac{-2\sqrt{2}}{2} +\frac{4}{2} [/tex]

=[tex] \frac{-1\sqrt{2}}{1} +\frac{2}{1} [/tex]

=[tex] -\sqrt{2} +2 [/tex]

=[tex] 2-\sqrt{2} [/tex]

[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6})=2-\sqrt{2} [/tex]

relative minimum is -2 when x is -3

option: c.   graph of line going through (1, 4) and (3, 10)

It is given that:

Margo has a coin collection.

She was given 1 coin as a gift, and she adds 3 coins per year.

i.e. she started with a initial of one coin and add 3 coins each year.

That is this situation can be represented with the help of a function:

C(t) which represents the number of coins she has in 't' years.

Now,

C(0)=1

Also,

C(t)=3t+1-------------(A)

Hence, we will check each of the given functions whether at the value of t they passes through that point or not.

a)

it is given that:

Graph passes through (1,2) and (3,4)

i.e. when t=1   C(t)=2

and when t=3 C(t)=4

but on putting the value of t in equation (A) it does not hold true.

same could be done for option (b) and option (d).

But in option (c)

It hold true.

         Since,

          when t=1

            C(t)=3×1+1=4

         when t=3

            C(t)=3×3+1=10

Hence, the correct answer is:

c.)   graph of line going through 1, 4 and 3, 10

Answer:

480cm². Verified by correct test results.

Answer:

C 9 inches

Step-by-step explanation:

Answer:

125 feet

Step-by-step explanation:

Given :

On a softball field, home plate is 43 feet from the pitcher’s mound.

A ball is hit at an angle of 27° east of the pitcher’s mound.

The ball travels 162 feet before it is caught by an outfielder.

To Find : Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Solution:

Law of cosines: [tex]a^2 = b^2 + c^2 -2bc cos A[/tex]

∠A = 27°

b = 43

c = 162

Substitute the given values

[tex]a^2 = 43^2 + 162^2 -2(43)(162) cos 27^{\circ}[/tex]

[tex]a^2 = 15679.497105[/tex]

[tex]a = \sqrt{15679.497105}[/tex]

[tex]a =125.21[/tex]

The outfielder must throw the ball 125 feet to return it to the pitcher.

Answer:

Just took the test Its C

Answer:

[tex]b = \frac{v}{h}[/tex]

Step-by-step explanation:

The formula v =bh means that the volume of a prism is equal to its base area times its height.

WE need to solve for b, we need to get 'b' alone

v=bh

to get 'b' alone we need to eliminate 'h'

To eliminate any variable we always do opposite operation.'

bh mean b times h

the opposite of multiplication is division

so to eliminate 'h' we divide by 'h' on both sides

[tex]\frac{v}{h} = \frac{bh}{h}[/tex]

[tex]b = \frac{v}{h}[/tex]

The formula for the base area (b) of a prism is b = v/h.

To solve the formula v = bh for b (the base area), to isolate b on one side of the equation. Follow these steps:

Divide both sides of the equation by h:

v/h = b

The base area (b) is now isolated on one side of the equation.

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Answer:

360°/d = kn.

Step-by-step explanation:

To know if a regular polygon can tessellate, we divide 360 by the interior angle of the polygon and the result needs to be an integer, but not in all cases you get the number of sides of the polygon, you get a multiple of the number of sides. So, none of the options are correct, the correct would be

360/d = kn, where k is an integer.

Answer:

The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.

Step-by-step explanation:

The measures of given sides are 6, 12, [tex]6\sqrt{3}[/tex].

According to the Law of Cosine:

[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}[/tex]

Using Law of Cosine, we get

[tex]\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}[/tex]

[tex]\cos A=\frac{216}{144\sqrt{3}}[/tex]

[tex]\cos A=\frac{3}{2\sqrt{3}}[/tex]

[tex]\cos A=\frac{\sqrt{3}{2}[/tex]

[tex]A=30^{\circ}[/tex]

Similarly,

[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}[/tex]

[tex]\cos B=\frac{0}{36\sqrt{3}}[/tex]

[tex]\cos B=0[/tex]

[tex]B=90^{\circ}[/tex]

Therefore, measure of angle A is 30 degree and measure of angle B is 90 degree.

According to angle sum property, the sum of interior angles of a triangle is 180 degree.

[tex]A+B+C=180^{\circ}[/tex]

[tex]30^{\circ}+90^{\circ}+C=180^{\circ}[/tex]

[tex]C=60^{\circ}[/tex]

Therefore the measure of angle C is 60 degree.

The triangle with sides 6, 12, and 6√3 has angles of 30 degrees, 60 degrees, and 90 degrees.

Given a triangle with sides 6, 12, and 6√3, we can find the angles using the Law of Cosines.

First, we use the formula for the Law of Cosines,
c² = a² + b² - 2ab * cos(C).

Let a = 6, b = 6√3, and c = 12.
We substitute these values into the formula to find angle C,

cos(C) = (6² + (6√3)² - 12²) / (2 * 6 * 6√3)

Compute the values inside the formula:

6² = 36

(6√3)² = 108

12² = 144

cos(C) = (36 + 108 - 144) / 72

cos(C) = 0

Therefore, angle C = 90 degrees.

To find the other angles, we use the Law of Sines,
(sin A / a) = (sin B / b) = (sin C / c).

We already know C = 90°, so (sin C / 12) = 1/12.

For angle A,

sin(A) / 6 = 1/12

sin(A) = 6/12 = 1/2

A = 30 degrees

For angle B:

B = 180° - 90° - 30° = 60 degrees

Therefore, the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees.

Answer:

Step-by-step explanation:

Final answer:

Javier has 4 juice boxes, 3 of which are grape flavored. The fraction representing grape juice boxes is 3/4, with equivalent fractions being 6/8 and 9/12.

Explanation:

Javier has 4 juice boxes and three are grape flavored. To describe the part of the juice boxes that is grape in the form of a fraction, we would use the total number of juice boxes as the denominator and the number of grape juice boxes as the numerator. So, the fraction representing the grape juice boxes is 3/4 (three out of four).

To write two equivalent fractions, we can multiply the numerator and the denominator by the same number. If we multiply both by 2, we get 6/8, which is equivalent to 3/4. Similarly, multiplying both by 3 gives us 9/12, which is also equivalent to 3/4.

We are given 158 books to place them on three different shelves like A, B, and C.

It says that shelf A has eight fewer books than shelf B and five more books than shelf C.

Mathematically, it can be written as (A = B - 8) and (A = C + 5).

Or we can write it as (B = A + 8) and (C = A - 5).

If we consider there are 'x' books in shelf A, then shelf B would have 'x+8' books and shelf C would have 'x-5' books.

We know that Total books are 158, so its sum must be equal to total books.

A + B + C = 158

x + (x+8) + (x-5) = 158

3x + 3 = 158

3x + 3 - 3 = 158 - 3

3x = 155

[tex] \frac{3x}{3} =\frac{155}{3} [/tex]

x = 51.667 books

But 'x' must be an integer value because number of books can not be a decimal form.

Hence, this arrangement is "NOT possible" for this question.

Answer:

it is NOT possible

Step-by-step explanation: