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The polynomial-like expression is satisfied by the real value x = 1.

In this question we must apply the concepts of logarithms and algebra properties to solve the entire expression. Initially, we expand the right part of the expression:

[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (4^{x}+2^{x}-6)^{3}[/tex]

[tex](2^{x}-4)^{3} + (4^{x}-2)^{3} = [(2^{x}-4)+(4^{x}-2)]^{3}[/tex]

[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (2^{x}-4)^{3}+3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2}+(4^{x}-2)^{3}[/tex]

[tex]3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2} = 0[/tex]

[tex]2^{x}-4 + 4^{x}-2 = 0[/tex]

[tex]2^{x}\cdot 2^{x} + 2^{x}-6 = 0[/tex]

[tex]u^{2}+u - 6 = 0[/tex]

[tex](u+3)\cdot (u-2) = 0[/tex]

Hence, the roots of the pseudopolynomial are [tex]u_{1} = -3[/tex] and [tex]u_{2} = 2[/tex]. Only the second one have a real value of x. Hence, we have the following solution:

[tex]2^{x} = 2[/tex]

[tex]x\cdot \log 2 = \log 2[/tex]

[tex]x = 1[/tex]

The polynomial-like expression is satisfied by the real value x = 1. [tex]\blacksquare[/tex]

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Answer:

that would be A. 360.

Step-by-step explanation:

when you think about it, a 360 is doing a full circle which is the only option here, because the point stays the same.

Answer:

7/350 7 to 350

Step-by-step explanation:

there are 3 ways to write a ratio

:

to

/

Answer:

A) 54.5g, B) 1.4g

Step-by-step explanation:

Find the lower bound of 55 and the upper bound of the cubed root of 1. the cubed root of 1 is 1 and the upper bound of that is 1.4

The amount that the credit union will finance is $24169.60

We have given that the cost of the car is $22,346. 16

and the credit union required 10% down payment

and sale tax=7.6%

The license and title charges are $125. 13.

We have to determine that the  amount that the credit union will

finance Now  we have sale tax 7.6% for $22,346. 16

Therefore, we get

[tex]\frac{7.6}{100} \times 22,346. 16=1698.31[/tex]

credit union finance=cost of car+sales tax+the license and title  charges.

[tex]=22346.16+1698.31+12.13\\=24169.60[/tex]

Therefore, the amount that the credit union will finance is $24169.60

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Answer:

A) 72w

Step-by-step explanation:

Answer: 3:2 and 2:3

Step-by-step explanation:

Scale factor is image/preimage.

So from A to B, the image is B and the preimage is A, so the scale factor is 6/4 = 3/2.

Similarly, from B to A, the scale factor is 4/6=2/3

The solution of the given complex fraction will be;

[tex]=\dfrac{2(y-4x)}{-5x+3y}[/tex]

The complex fraction is defined as the fraction whose numerator and denominator contains fractions in it.

The given complex fraction is

[tex]\dfrac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}[/tex]

Now by taking LCM the equation will become

[tex]\dfrac{\frac{2y-4x}{xy}}{\frac{-5x+3y}{xy}}[/tex]

Now the final expression will be

[tex]=\dfrac{2(y-4x)}{-5x+3y}[/tex]

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Answer:

The population of 75 hours from now would be 40,000.

Step-by-step explanation:

The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.

Answer:

4

Step-by-step explanation:

Here are the Numbers: 1,2,4,6,41,2,4,6,41,2,4,6,4

First we order from least to greatest;

1,2,2,2,4,4,4,4,6,6,6,41,41

Since the amount of numbers are odd, we just take the middle number:4

Answer: acute angle

Step-by-step explanation: acute angle is the smallest starting from 0 to 90 DDegrees .

Answer:

  13 and three-fourths inches

Step-by-step explanation:

The map distance can be found using a proportion with the map scale.

__

  map distance / (1100 mi) = (1 in) / (80 mi)

  map distance = (1100×1)/80 in = 13 3/4 in . . . multiply by 1100 mi; cancel mi

The trip will be about 13 3/4 inches on the map.

Answer:

i believe its B

Step-by-step explanation:

Answer:

The Answer is B. $11.59

Step-by-step explanation:

Edge 2022

Answer:

1) There were 120 customers per night when the restaurant opened

2) y = -2x + 24

Step-by-step explanation:

1) x represents the # of months since a restaurant opened, and y represents the average number of nightly customers.

y=mx+b

120 is b in this situation, which is the y-intercept of the line. This means that 120 is the starting number of customers when the restaurant first opened.

Answer:

C. 5%

Step-by-step explanation:

if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent

The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let x represent the number of wheat acres and y represent the number of corn acres, hence:

150x + 350 y ≤ 250000     (1)

Also:

x + y < 1200     (2)

The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200

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Answer:

160 000

Step-by-step explanation:

400 000 - 240 000 = 160 000

Answer:

25h+12

Step-by-step explanation:

Add the numbers :

21h-10h + 16-9 + 14h+ 5

21h-10h + 12 + 14h

Combine like terms:

25h + 12

Answer:6.80

Step-by-step explanation:

The amount of interest Ryan would earn at the end of 30 years given the interest rate is $69,250.27.

When an account earns an interest that is compounded bimonthly, it means that it earns an interest every 2 months.

The formula that can be used to determine the interest earned is:

Future value - amount deposited

FV = P (1 + r)^nm

FV = 160,000(1.002^180) = $229,250.27

Interest = $229,250.27 -  $160,000 = $69,250.27

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Exponential functions are used to represent growth or decay of a substance. The amount that will be left after 12 hours is 17.42mg

The standard form of an exponential equation is given as:

[tex]y=a(1-r)^t[/tex]

where;

Given the following parameters

a = 550mg

r = 0.25

t = 12

Substitute into the formula

[tex]y=550(1-0.25)^{12}\\y = 550(0.75)^{12}\\y=17.42mg[/tex]

Hence the amount that will be left after 12 hours is 17.42mg

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Answer: 4/6

Step-by-step explanation: This because most dice have a  6 sides on them and others have more and if you roll a 6-sided dice you will get 4/6 of a probabilty that you will role a 4.

Answer:

1080÷9=120

hope it helps!

Answer:

72 degrees

Step-by-step explanation:

all triangles have angles adding up to 180

that does not look like a right triangle

only possible answer is 72

Answer:

angle U = 72°

Step-by-step explanation:

The sum of the internal angles in a pentagon is 540°

[tex]x^{o} +(2x)^{o} +(2x)^{o} +90^{o}+90^{o} =540^{o}[/tex]

[tex](5x)^{o} =540^{o} -180^{o}[/tex]

[tex]x^{o} =\frac{360^{o} }{5} =72^{o}[/tex]

Hope this helps

Applying the formula for volume of a rectangular prism and volume of a cube, we would have:

a. 6/125 cm³

b. 8/125 cm³

c. 1/125 cm³

d. 36/125 cm³

a. Volume of rectangular prism = length × width × height = (1/5) × (2/5) × (3/5)

Volume of rectangular prism = 6/125 cm³

b. Volume of cube = (side length)³ = (2/5)³

Volume of cube = 8/125 cm³

c. Volume of cube = (side length)³ = (1/5)³

Volume of cube = 1/125 cm³

d. Volume of rectangular prism = length × width × height = (3/5) × (4/5) × (3/5)

Volume of rectangular prism = 36/125 cm³

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Answer:

Your answer would be:

57.75 or 57 3/4

(I will show how many of each length of twine that is on the graph)

Point 2 1/4:

2

Point 2 3/4:

4

Point 3:

1

Point 3 1/2:

2

Point 3 3/4:

3

Point 4:

1

Point 4 1/4:

4

We can show how much length in total Stevie used with the following equation:

(2 1/4 x 2) + (2 3/4 x 4) + ( 3 x 1 ) + ( 3 1/2 x 2 ) + (3 3/4 x 3 ) + (4 x 1 ) + (4 1/4 x 4)

Each smaller equation in paraphrases shows how much of each length of twine at each point with x's on the number line. Altogether it would equal 57.75 or 57 3/4.

Step-by-step explanation:

Have a great rest of your day

#TheWizzer

Answer:

8a-9=7a+1 (inscribed angle are equal standing on the arc)

8a-7a=1+9

a=10

Answer:

The range of [tex]f(x)[/tex] is [tex]f(x)\in[0,3][/tex]

[tex]f^{-1}(x)=-\sqrt{-x^2+9}[/tex] with a domain [tex]x\in[0,3][/tex]

Step-by-step explanation:

Domain: set of input values (x-values)

Range: set of output values (y-values)

Given function:

[tex]f(x)=\sqrt{9-x^2}\quad(x\in[-3,0])[/tex]

Therefore, as the original function has a restricted domain, its range is also restricted:

[tex]f(-3)=\sqrt{9-(-3)^2}=0[/tex]

[tex]f(0)=\sqrt{9-0}=3[/tex]

[tex]\therefore\textsf{Range}\:f(x)\in[0,3][/tex]

To determine the inverse of a function

Change [tex]x[/tex] to [tex]y[/tex]:

[tex]\implies x=\sqrt{9-y^2}[/tex]

Square both sides:

[tex]\implies x^2=9-y^2[/tex]

Switch sides:

[tex]\implies 9-y^2=x^2[/tex]

Subtract 9 from both sides:

[tex]\implies -y^2=x^2-9[/tex]

Divide both sides by -1:

[tex]\implies y^2=-x^2+9[/tex]

Therefore:

[tex]\implies y=\sqrt{-x^2+9}\textsf{ and }y=-\sqrt{-x^2+9}[/tex]

As the range of the inverse function is the same as the domain of the original function:

[tex]\implies f^{-1}(x)=-\sqrt{-x^2+9}[/tex] only as the range is [-3, 0]

The domain of the inverse function is the same as the range of the original function.

[tex]\therefore\textsf{Domain of}\:f^{-1}(x):x \in [0,3][/tex]

The inverse of a function is ordinarily the reflection of the original function in the line [tex]y=x[/tex].  

**Please see attached graph**