Solve for x. 2^x-1 = 31, give your rounded answer to four decimal places.

Answer:

see explanation

Step-by-step explanation:

using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]

Then

(a)

[tex]5^{4}[/tex] × [tex]5^{5}[/tex] = [tex]5^{(4+5)}[/tex] = [tex]5^{9}[/tex]

(b)

[tex]2^{7}[/tex] × 2 = [tex]2^{(7+1)}[/tex] = [tex]2^{8}[/tex]

(c)

[tex]6^{5}[/tex] ÷ 6² = [tex]6^{(5-2)}[/tex] = 6³

(d)

[tex]9^{7}[/tex] ÷ [tex]9^{6}[/tex] = [tex]9^{(7-6)}[/tex] = [tex]9^{1}[/tex] = 9

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

(a)

3² × [tex]3^{4}[/tex] = [tex]3^{(2+4)}[/tex] = [tex]3^{6}[/tex]

(b)

[tex]5^{7}[/tex] × 5³ = [tex]5^{(7+3)}[/tex] = [tex]5^{10}[/tex]

(c)

[tex]6^{7}[/tex] ÷ 6² = [tex]6^{(7-2)}[/tex] = [tex]6^{5}[/tex]

(d)

[tex]9^{4}[/tex] ÷ 9³ = [tex]9^{(4-3)}[/tex] = [tex]9^{1}[/tex] = 9

Answer:

period pi and amplitude 5

The total area of the given composite figure is; 84.8 ft²

We are given;

Area of triangle = 5.6 ft²

Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²

Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)

Area of rectangles = 14.4 + 16 + 43.2

Area of rectangles = 73.6 ft²

Total Area of composite figure = 73.6 ft² + 11.2 ft²

Total Area of composite figure = 84.8 ft²

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The height of the tree to the nearest hundredth is 122.49 feet

These are used to determine the sides and angle of a right triangle

Given

Angle of elevation= 54 degrees

Base distance = 89 feet

Required

Height of tree

Using the SOH CAH TOA

tan 54 = H/89

H = 89tan54

H = 122.49

Hence the height of the tree to the nearest hundredth is 122.49 feet

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Answer:

8%

Step-by-step explanation:

Divide ( 32.40 / 30 ). This outputs the answer 1.08, or 108%. This means that the outcome is 108% of the original, or 8% greater.

The simple interest in which Casho invests money was 8%.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, p = 30, SI = (32.40 - 30) = $2.40 and t = 1.

Therefore, 2.40 = (30×r×1)/100.

240 = 30r.

r = 240/30.

r = 24/3.

r = 8.

So, The rate of simple interest is 8%.

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Answer:

second term: 10

third term: 50

Step-by-step explanation:

The equation for any geometric sequence is [tex]a_{n} = a_{1} *r^{n-1}[/tex] where n is the term number you want to find, [tex]a_{1}[/tex] is the first term in the sequence, and [tex]r[/tex] is the common ratio. The equation for this sequence specifically uses 5 as its common ratio, so the equation is [tex]a_{n} =2*5^{n-1}[/tex]

[tex]a_{1} = 2*5^{1-1}=2*5^{0} =2*1=2[/tex]

[tex]a_{2} = 2*5^{2-1}=2*5^{1} =2*5=10[/tex]

[tex]a_{3} = 2*5^{3-1}=2*5^{2} =2*25=50[/tex]

[tex]a_{4} = 2*5^{4-1}=2*5^{3} =2*125=250[/tex]

Answer:

3^4

Step-by-step explanation:

when both constants have equal base then powers are added

Answer:

2.9 meters.

Step-by-step explanation:

First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier).  Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.

Answer:

i think its 21.83 i may be wrong but im pretty sure its 21.83

Step-by-step explanation:

The initial amount of the water is 15 gallons

These are functions that has a leading degree of 1. Given the equation that represents the amount of water remaining after x minutes;

y - 12 = -3(x- 1)

y -12 = -3x + 3

y = -3x +3 + 12

y = -3x + 15

In order to determine the initial amount of water, we will substitute x =0 into the function

y = -3(0) + 15

y = 15

Hence the initial amount of the water is 15 gallons

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Answer:

15

Step-by-step explanation:

The correct answer for the Function in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

A function can be defined as  a set of outputs that its varying is dependent on the inputs.

In this case the functions given have a designated outputs.

(f+g)(x) = f(x) + g(x)  - because its held by an addition

(f+g)(x) = [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

In conclusion, The correct answer for the question in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

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Answer:

See below

Step-by-step explanation:

Think about what happens when you rotate around a circle [tex]-\frac{3\pi}{4}[/tex] radians. This means that you are going clockwise [tex]-\frac{3\pi}{4}[/tex] radians.

Likewise, if you went [tex]\frac{5\pi}{4}[/tex] radians counterclockwise, you'd end up in the same place, so the cosine values must be the same.

A correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.

A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.

The general form of the equation of a circle is given as:-

( x - h )² + ( y - k )² = r²

By comparing the given equation we can see the following results:-

x² + (y – 3)² = 36

( x - ( 0 ))² + ( y - 3 )² = 6²

We can see that the coordinate of the center are ( 0, 3 ) and the radius is 6 so the diameter is 12.

Therefore the correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.

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Answer:

A and E (first and last, ending in "=36")

x2 + (y – 3)2 = 36

x2 + (y + 8)2 = 36

Step-by-step explanation:

just took the quiz

Answer:

y = (x+8)(x+3)

Step-by-step explanation:

If you multiply

(x+8)(x+3),

you get x^2 + 3x + 8x + 24

This simplifies to x^2 + 11x + 24, same as the original question.

The graph of y=x² + 11x + 24 is equivalent to the y=(x+8)(x+3).

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.

We have Graph whose equation is

y=x² + 11x + 24

Now, factories the above equation using splitting the middle term

y=x² + 11x + 24

y=x² + 8x + 3x + 24

y = x(x+8) + 3(x+8)

y= (x+3)(x+8)

Thus, the factors are (x + 3)(x+8).

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Answer:

I am sorry if you feel mad but I do not know this question I am very sorry . . . . . . . . . .

Answer:

9

Step-by-step explanation:

[tex]\text{Given that}~ x = -7\\\\\dfrac{(x-2)(x+14)}{x(x+8)}\\\\\\=\dfrac{(-7-2)(-7+14)}{-7(-7+8)}\\\\\\=\dfrac{(-9)(7)}{-7(1)}\\\\\\=\dfrac{-63}{-7}\\\\\\=9[/tex]

By completing squares, we will see that the radius is 12 units and the center is (-8, 1).

The circle of center (x₁, y₁) and radius r is written as:

(x - x₁)² + (y - y₁)² = r²

Now we go to our equation:

x² + 16x + 64 + y² - 2y + 1 = 144

Now we need to complete squares:

(a + b)² = a² + 2ab + b²

Then we can rewrite:

(x² + 2*8*x + 8*8) + (y² - 2y + 1) = 12²

(x + 8)² + (y - 1)² = 12²

So the center is the point (-8, 1) and the radius is 12 units.

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Answer:

2 miles

Step-by-step explanation:

Peter takes 7 minutes and 30 seconds per mile.

7 times 2 is 14 minutes.

30 seconds times 2 is 1 minute.

If you add these 2 values together you get 15 minutes.

So we need to times the miles by 2 to get 2 miles.

I hope this helps, have a lovely day.

Answer:

144 apples 72 pears

Step-by-step explanation:

Apples 120 + 20% = 144

Pears 120 - 40% = 72

Hope This Helped

The indicated side of the right triangle is [tex]44\sqrt{2} =\frac{88}{\sqrt{2} }[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says:[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:

[tex]sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\[/tex]

The question asks to find one of the legs (y). Then, you can find y applying the trigonometric ratio (sin 45°).

[tex]sin(45\°)=\frac{y}{88}[/tex]

Like sin45° is equal to [tex]\frac{\sqrt{2} }{2}[/tex], you have

[tex]\frac{\sqrt{2} }{2} =\frac{y}{88}\\ \\ 2y=88\sqrt{2} \\ \\ y=44\sqrt{2} \\ \\ Thus\\ \\ y=\frac{88}{\sqrt{2}}[/tex]

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Answer: 88[tex]\sqrt{2}[/tex]

Step-by-step explanation:

hope it helps

Using a geometric sequence, it is found that the approximate value of the car at the end of the 10th year will be given by:

A. $6,974.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the first term and the common ratio are given, respectively, by:

[tex]a_1 = 18000, q = \frac{16200}{18000} = 0.9[/tex]

Hence the equation is:

[tex]a_n = 18000(0.9)^{n-1}[/tex]

At the end of the 10th year, the value will be of:

[tex]a_{10} = 18000(0.9)^{10-1} = 6974[/tex]

Hence option A is correct.

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The correct numbers to get to the media or mean are 10, 33, 3, and 2.

The media is obtained by organizing the values given and selecting the one that is in the middle; while the mean is obtained by adding all values and dividing the total by the number of values.

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Step-by-step explanation:

. In Figure 5.144, of ΔABC, where

m(∠C) = 30, m(∠ABD) = 5x,

m(∠A) = 4x. Find m(∠ABC) in

degrees.

In this specific case, the initial term (a) is 5 and the common ratio (r) is -2

Henceforth, after determining what a and r are, we use the formula for the nth term. Which is:

[tex]a_n = a \times r^{n-1} [/tex]

Therefore, the 14th term is :

[tex]\implies 5 \times { (- 2)}^{14 - 1} \\\implies 5 \times {( - 2)}^{13} \\ =\boxed { -40,960} [/tex]

Hope it helps!

Answer:

[tex] \frac{x}{12} = - 4[/tex]

[tex] \frac{x}{12} = \frac { - 4}{1} [/tex]

[tex]x \times 1 = 12 \times - 4[/tex]

[tex]x = - 48[/tex]

value of x is -48

Answer:

x=-48.

Step-by-step explanation:

To find x we should multiply both sides, by 12:

[tex]\sf \cfrac{x}{12}\times12=\-4\times12[/tex]

                                       ↪

The 12s cancel on the left:

[tex]x=-4\times12[/tex]

After multiplying we obtain [tex]\sf x=-48[/tex]. Which is our answer.

Hope that this helped you! Have a good day ahead.

Best Wishes!

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Answer:

v=2

Step-by-step explanation:

Answer:

Step-by-step explanation: