Work out the value of 2⁰

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 answer to each question in the image is given below:

An equivalent equation can be defined as an equation that has the same meaning and also has the same answer with another equation or with an equation it is said to be equivalent with.

The above equation are equivalent to each other meaning they can be used to derive each other.

In conclusion, the list above is the right pairs of equivalent equations.

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Answer:

1.65 N

Step-by-step explanation:

Step 1: convert cm^2 to m^2

1 cm^2 = 0.0001 m^2

750 cm^2 = 0.075 m^2

Step 2: multiply pressure by area

F = P*A = 22 N/m^2 * 0.075 m^2 = 1.65 N

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]

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

Answer:

x^32

Step-by-step explanation:

A fraction bar is a division symbol. When you are dividing, you can subtract the exponents.

x^56 / x^24

= x ^ (56-24)

= x^32

Answer:

x^32

Step-by-step explanation:

a^m/a^n = a^(m-n)

so, x^56/x^24 = x^(56-24) = x^32

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:

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:

Step-by-step explanation:

Answer:

period pi and amplitude 5

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.

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.

Answer:

v=2

Step-by-step explanation:

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:

bacteria and fungi

Step-by-step explanation:

Single organism makes an exact copy of itself

Bacteria, some plants and fungi, few animals (sponges)

Offspring are identical to parent

Answer:

1.1x= 132

Step-by-step explanation:

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:

how many hours a week the employees are working?

Step-by-step explanation:

I could be wrong but that's my fault if it's wrong sorry

Answer:

0.05

explanation

value means total value

so it's 5*0.01

=0.05

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:

[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!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

◆◆-Greetings!-◈◈

--

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:

Answer:

B. 4^8

Step-by-step explanation:

The indices of the base 4 can be added while multiplying i.e. 3+5=8 but the base remains the same.

Answer:

B

Step-by-step explanation:

Because in powers we just add so it will be 4^3+5

=4^8

Answer:

-4z

Step-by-step explanation:

Hi student! Let me help you out.

_____________________

Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us [tex]\mathrm{-4z}[/tex].

[tex]\mathrm{-3z-z=-4z}[/tex]. -4z is our final answer.

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

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star[/tex]

◈◈-Greetings!-◆◆

___________________

Answer:

-4z

Step-by-step explanation:

-3z-z

On combining like terms,

= -4z

Answer:

Step-by-step explanation:

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: