Find two nontrivial functions f(x) and g(x) so that f(g(x)) = (-6-3x)^6

Answer:

[tex]x = - 5[/tex]

or

[tex]x = 2[/tex]

Step-by-step explanation:

We want to solve ;

[tex] {12}^{ {x}^{2} + 5x - 4} = {12}^{2x + 6} [/tex]

We equate the exponents, because is the same on both sides.

[tex] {x}^{2} + 5x - 4 = 2x + 6[/tex]

We group and rewrite in standard form to get:

[tex] {x}^{2} + 5x - 2x - 4 - 6 = 0[/tex]

[tex]{x}^{2} + 3x- 10= 0[/tex]

[tex] {x}^{2} - 2x + 5x - 10 = 0[/tex]

[tex]x(x - 2) + 5(x - 2) = 0[/tex]

[tex](x + 5)(x - 2) = 0[/tex]

[tex]x = - 5 \: or \: x = 2[/tex]

The solutions are x = 2 and x = -5.

To solve the equation [tex]12^{x^{2} +5x-4}[/tex] = [tex]12^{2x+6}[/tex], we first note that since the bases are the same, we can equate the exponents:

⇒ x² + 5x - 4 = 2x + 6.

Next, we move all terms to one side to form a quadratic equation:

⇒ x² + 5x - 4 - 2x - 6 = 0

Simplifying this gives us:

⇒ x² + 3x - 10 = 0

We can now solve this quadratic equation using the quadratic formula, which is defined as:

⇒ x = (-b ± √(b² - 4ac)) ÷ 2a

For our equation, a = 1, b = 3, and c = -10. Substituting these values into the quadratic formula:

⇒ x = (-3 ± √(3² - 4 × 1 × (-10))) ÷2 × 1

⇒ x = (-3 ± √(9 + 40)) ÷ 2

⇒ x = (-3 ± √49) ÷ 2

⇒ x = (-3 ± 7) ÷ 2

This gives us two solutions:

⇒ x = (4) ÷ 2 = 2

⇒ x = (-10) ÷ 2 = -5

So, the solutions are x = 2 and x = -5.

Answer:

c

Step-by-step explanation:

i got it right

Answer:

C.

Step-by-step explanation:

I'm too lazy to do it here for an explanation.

I did it in my notebook and I got it right.

Answer:

Cool

Step-by-step explanation:

Answer:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

2 x 2 x 2 x 2 + 3 x 3  

4 x 2 x 2 + 3 x 3

8 x 2 + 3 x 3

16 + 3 x 3

16 + 9

25

Answer:

25

Step-by-step explanation:

2^4+3^2

2^4=2*2*2*2=16

3^2=3*3=9

16+9=25

Answer:+5 or just 5

Step-by-step explanation:

Answer:

2,500 pounds

Step-by-step explanation:

one ton = 2000 pounds

1.25*2000= 2,500

Answer: 200

Step-by-step explanation:

120 divided by 3/5 is the same thing as 120 times 5/3.

So 120 x 5 = 600

And 600 divided by 3 is 200

The result of the division 120 divided by 3/5 is : 200.

Here, we have,

given that,

What is 120 divided by 3/5

we know that,

120 divided by 3/5 is the same thing as 120 times 5/3.

i.e. 120 ÷ 3/5

=> 120 × 5/3

now, we know that,

So 120 x 5 = 600

=> 600/3

And 600 divided by 3 is 200.

so, we get,

Hence, The result of the division 120 divided by 3/5 is : 200.

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2 x 3-5

= 6-5

= 1

1 is the answer

Step-by-step explanation:

3/5+4/7

= 41/35

that's the answer

Answer:

C:x=30:both angles measure 114 degrees

Step-by-step explanation:

in 2 parallel lines with a transversal, the marked angles are alternate exterior angles, which means that both angles are congruent(equal)

ur equation is: 2x+54=4x-6

60=2x

x=30

we have now eliminated options a and b

CHECK:

2*30+54=60+54=114

4*30-6=120-6=114

114=114

Answer:

4200

Step-by-step explanation:

Final answer:

To find the total number of heartbeats in an hour, multiply the heartbeats per minute by 60. For Judy, her heart beats around 4200 times in an hour.

Explanation:

Judy's heart beats 70 times a minute. To calculate how many times her heart beats in an hour, you can use the following formula:

Heartbeats per hour = Heartbeats per minute x 60 minutes

Heartbeats per hour = 70 x 60 = 4200 times

It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.

Step-by-step explanation:

Given,

Distance covered = [tex]30\frac{1}{3}[/tex] = [tex]\frac{91}{3}[/tex] miles

Time taken =[tex]\frac{1}{3}[/tex] hour

We know that;

Distance = Speed * Time

[tex]\frac{91}{3} = Speed*\frac{1}{3}[/tex]

Multiplying both sides by 3

[tex]3*\frac{91}{3} = Speed*\frac{1}{3}*3[/tex]

91 = Speed

Bob was driving at 91 miles per hour.

Now,

Distance to cover = 100 miles

Time required = x

Distance = Speed * Time

[tex]100=91x\\91x=100[/tex]

Dividing both sides by 91

[tex]\frac{91x}{91}=\frac{100}{91}\\x=1\frac{9}{91}[/tex]

It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.

Keywords: fraction, distance

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The solution to the equation 2.4y=13.75 is found by isolating the variable y, which gives us y = 5.729167.

The question asks for the solution to the equation 2.4y =13.75. To solve this equation, we simply need to isolate the variable y. This can be done by dividing both sides of the equation by 2.4.

So, now the equation becomes y =13.75 ÷ 2.4.

After performing the division, you get y = 5.729167. Thus, y=5.729167 is the solution to the equation 2.4y=13.75.

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Answer:

The given expression simplifies to 84x - 16y - 35

Step-by-step explanation:

The given equation is 2 ( 14x - 3y + 28x - 5y - 17.5)

The given equation simplifies to

28x - 6y + 56x - 10y  - 35

which is equal to

84x - 16y - 35

The expression 2 (14x - 3y + 28x + 12.2 - 5y - 17.5) simplifies to 84x - 16y - 10.6.

The expression that is equivalent to 2 (14x - 3y + 28x + 12.2 - 5y - 17.5) can be simplified using the distributive property and combining like terms.

First, distribute the 2 to each term inside the parentheses:

2(14x - 3y + 28x + 12.2 - 5y - 17.5) = 28x - 6y + 56x + 24.4 - 10y - 35

Next, combine like terms:

28x + 56x = 84x

-6y - 10y = -16y

24.4 - 35 = -10.6

So, the simplified expression is 84x - 16y - 10.6.

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Answer:

Step-by-step explanation:

true dat

Answer:

9.84 times

Step-by-step explanation:

246÷25= 9.84

Answer:

9, or more specifically, 9.84

Step-by-step explanation:

25 x 9 = 225.

25 x 10 = 250, which is too much.

Hope this helps!

Answer: you can get 8 gum balls

Step-by-step explanation:

Answer: C.

Step-by-step explanation: if you count the you can see that G = (2, -1).

Final answer:

To find the radius of the volleyball given its surface area, use the formula for the surface area of a sphere (4πr²) and solve for r. The approximate radius of the volleyball would be 4.25 inches based on a surface area of 227 square inches.

Explanation:

The surface area of a sphere formula is 4πr², where r is the radius. Given that the volleyball's surface area is about 227 square inches, we can find the radius by rearranging the formula as follows:

Answer:

22.50

Step-by-step explanation:

the ratio is 2:5 so if julie got 45 then pat would get half of what julie got

45 divided by 2

Answer: C. 5

Step-by-step explanation:

Answer:

c.5

Step-by-step explanation:

16 = 4x -4

Collect like terms

16 + 4 = 4x

20 = 4x

Divide both sides by 4

20/4 = x

Therefore x = 5

Answer:

[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]

Step-by-step explanation:

Given the geometric sequence

[tex]a_1=\dfrac{2}{3}\\ \\a_n=3a_{n-1},[/tex]

then

[tex]a_1=\dfrac{2}{3}\\ \\a_2=3a_1=3\cdot \dfrac{2}{3}=2\\ \\a_3=3a_2=3\cdot 2=6\\ \\a_4=3a_3=3\cdot 6=18\\ \\a_5=3a_4=3\cdot 18=54\\ \\...[/tex]

Hence,

[tex]b_1=a_1=\dfrac{2}{3}\\ \\b_2=a_3=6=\dfrac{2}{3}\cdot 9\\ \\b_3=a_5=54=\dfrac{2}{3}\cdot 9^2\\ \\...[/tex]

Thus, the explicit formula is

[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]

Yo sup??

To solve the 31st one just imagine and add all the cubes.

Start from the left side and keep on counting in your mind.

You will end with 25 cubes

For the 32nd one you can just draw a chart to know it.

Since this man has no bro or sis he is a single child.

The man in the picture is himself.

He is pointing to his picture and saying that 'that guys dad is my dad' and since he's a single child therefore its him itself.

So the answer is that man itself.

For the last one again try to draw a chart and connect the dots with the information.

So Lakisha had a bull dog. Since she has a bull dog she can't have Paul as her brother because paul is the brother of that girl who has her pet as horse.

This means paul is the brother of either Angela or Jessica. But its given that the brother of Angela is Ken therefore Paul is the brother of Jessica.

So the relations are

Lakisha-Bull dog, Stephen

Angela-Ken,XXXXX

Jessica-horse,Paul

Hope this helps.

Answer:

Therefore, the constant multiple of liters in jug to the weight in kilogram is 0.62(approx)

Step-by-step explanation:

Given, Madison is carrying a 11.3 liter jug of sport drink that weights  7 kg.

Let the constant term be x

According to the problem,

11.3 × x = 7

⇔[tex]x =\frac{7}{11.3}[/tex]

⇔x = 0.62

Therefore, the constant multiple of liters in jug to the weight in kilogram is 0.62(approx)

Answer:12.2%

Step-by-step explanation:

Her total paycheck minus her salary = the commission amount

So

6500 - 1000 = 5500

So....her commission as a percentage of sales  = 5500/ 45000 = about 12.2%

Answer: 8

Step-by-step explanation:

32/2 (50%)  = 16

32/4 (25%)  = 8

Add these together and you'll get 24. Subtract that from the initial amount and you'll have 8.

Answer:

The polygon that is formed is a rectangle. Because all sides are horizontal or vertical line segments, she can count to find the distance. She should find the distance of each side and add them together. The total distance around the rectangle is 18 units.

Step-by-step explanation:

The calculation of the distance between the points is simplified, given

that the points are on the same perpendicular or horizontal line.

Correct response:

The given points can be presented as follows;

A(-2, 2), D(-2, -2), B(3, 2), and C(3, -2)

By observation, given that there are two pairs of points that have the

same x-coordinates, and two pair of points have the same y-coordinates,

we have;

The distance between two points is given by the difference between the variables that are not the same as follows;

Distance between point (-2, 2), and (-2, -2), AD = 2 - (-2) = 4

Distance between points (3, 2), and (3, -2), BC = 2 - (-2) = 4

Distance between points (-2, -2), and (3, -2), CD  = 3 - (-2) = 5

Distance between points (-2, 2), and (3, 2), AD = 3 - (-2) = 5

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Answer:

- 3a + 6

Step-by-step explanation:

subtract and add like items together like

- 4a + a = -3a

b-b= 0

and

9-3 = 6

so the answer is

-3a +6

Answer:

18,354 - 4,672= 13,682

Step-by-step explanation:

I'm not sure what you meant but above is the answer of what I think you were asking.

The difference between 22,456 and 5,893 is 16,563.

Subtracting 5,893 from 22,456 involves determining the quantity that, when added to 5,893, yields 22,456.

To find the difference, we can follow these steps:

Subtract the numbers:

22,456 - 5,893 = 16,563

Therefore, the difference between 22,456 and 5,893 is 16,563.

Complete question:

Find the difference between 22,456 and 5,893.