Mathematics High School

What are the values of a and b in the equation (4x^a)^b = 256/x^8

Answers

Answer 1

b = 4 and a = -2

(4x^-2)^4
= 4^4 x^-8
= 4^4 / x^8
= 256/x^8

Answer 2

Answer:

The value of a is -2 and the value of b is 4.

Step-by-step explanation:

Given expression is,

[tex](4x^a)^b = \frac{256}{x^8}[/tex]

Using [tex](ab)^m=a^m.b^n[/tex] on left side,

[tex]4^b(x)^{ab}=\frac{4^4}{x^8}[/tex] ( [tex]4^4 = 256[/tex] )

Using [tex]a^m=\frac{1}{a^{-m}}[/tex],

[tex]4^b(x)^{ab}=4^4 (x)^{-8}[/tex]

By comparing both sides,

We get,

b = 4 and ab = -8

⇒ a = -2

Hence, the value of a is -2 and the value of b is 4.

Related Questions

What is the solution of the equation x2 + 10x + 75 = 0?

Answers

[tex]x = - \frac{77}{10} [/tex]
alternative form
[tex]x = - 7 \frac{7}{10} \: \: x = - 7.7[/tex]

There isn't one unless you know what complex numbers are. If you do then use the quadratic formula to get the answer.
x = [- b +/- sqrt( b^2 - 4ac ) ] / 2a
a = 1
b = 10
c = 75

x = [ -10 +/- sqrt(-200)]/2
x = [ -10 +/- 10 sqrt(2) / 2
x = - 5 + / - 5 sqrt(2) and that's your answer.

PLEASE HELP ME ON THIS QUESTION

THX~ BRANiLiEST AVAILABLE

PLZ EXPLAIN IF U COULD

Answers

The answer is NOT A nor B, because they're both decreasing.
D's answer shows that the graph is only increasing by 1/2, and C shows that the graph will increase at a normal rate.

The answer is C.

The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?

Answers

area of a triangle= 1/2 base times height
substitute

40=1/2*10*x
40=5x
x=8

the height is 8 inches

Answer:

Step-by-step explanation: 8 inches

In the right triangle shown, AC = BC = 7? What is AB?

Answers

Solve the right triangle shown in the figure
BC=2.7cm, AC=1.1cm, B wrong

so AB is the hypotenuse. It's an isocelels right traingle meaning the other two angles are 45 degrees. So AB = 7[tex] \sqrt{2} [/tex]. We know this because 45 45 is a special right triangle.

PLEASE GET THIS RIGHT!!!!!!!! The difference between 3.6 and a number is 2.95, as shown below. What number should go in the box to complete the subtraction problem?

Answers

The number that should go in the box is 6.

3.60
- 0.65
---------------
2. 9 5

Please help! I'm very confused. 20 points.

Answers

1) Use the distributive property to eliminate parentheses.
.. 3(6x) -3(5) -7(3x) -7(10) = 0
.. 18x -15 -21x -70 = 0 . . . . . . finish multiplying terms
.. -3x -85 = 0 . . . . . . . . . . . . . collect like terms
.. -85 = 3x . . . . . . . . . . . . . . . .add 3x
.. -85/3 = x . . . . . . . . . . . . . . .divide by 3
.. -28 1/3 = x . . . . . . . . . . . . . write as mixed number

2) 5 -(6 +9x) = 9 -(4x -1)
.. 5 -6 -9x = 9 -4x +1 . . . . . eliminate parentheses using the distributive property
.. -1 -9x = 10 -4x . . . . . . . . . collect like terms
.. -1 = 10 +5x . . . . . . . . . . . . add 9x
.. -11 = 5x . . . . . . . . . . . . . . . subtract 10
.. -11/5 = x . . . . . . . . . . . . . . divide by 5
.. -2 1/5 = x . . . . . . . . . . . . . write as mixed number

Spaceship Earth, a major tourist attraction, is a sphere whose diameter is approximately 50 m. What is the volume of Spaceship Earth? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest hundredth.

Answers

we know that
volume of a sphere=(4/3)*pi*r³
diameter= 50 m--------------> r=D/2--------> r=25 m

Volume=(4/3)*pi*25³------------> volume=65416.666 m³

the answer is 65416.67 m³

1/3 math questions. pls help! 20 pts!

Answers

Since one cm on the map represents 2 km on the trail, we can use unit rates and proportions to solve this.

8 × 1 = 8
8 × 2 = 16

The actual length of the trail is 16km.

Hope this helps!

Someone help me ASAP!!!!!!

Answers

C looks the most similar to what I have.
The points are (7.5, 0) and (0, -5)

If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.

Answers

The first derivative is found from
.. 10x +4y^3*dy/dx = 0
.. dy/dx = -5x/(2y^3)

Then
.. d^2y/dx^2 = d(dy/dx)/dx = (-5/2)(y^-3 -3xy^-4*dy/dx)

Evaluated at x=2, y=1
.. dy/dx = -5(2)/(2*1^3) = -5
.. d^2y/dx^2 = (-5/2)*(1^-3 -3*2*1^-4*(-5))
.. = (-5/2)(1 +30)
.. = -155/2 = -77.50

d^2y/dx^2 = -77.50 at the specified point.

A ball is thrown straight up with a initial velocity of 56 feet per second . The height , h , of the ball t seconds after it is thrown is given by the formula h(t)=56t-16t^2 . What is the maximum height of the ball?

Answers

Formula: H(t) = 56t – 16t^2

H(t) = - 16t^2 + 56t

A. What is the height of the ball after 1 second? H (1) = 56(1) – 16(1) ^2 = 40 pt.

B. What is the maximum height? X = - (56)/2(- 16) = 1.75 sec h (1.75) = 56(1.75) – 16(1.75) ^2 h (1.75) = 49ft.

C. After how many seconds will it return to the ground? – 16t^2 + 56t = 0 - 8t =0 t = 0

- 8t (2 + - 7) = 0 2t – 7 = 0 t = 7/2 Ans: 3.5 seconds

The maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.

What is time dependent function?

The time dependent function is the function whose values vary with change in time. For example - f(t) = 3t + 5.

Given is a ball is thrown straight up with a initial velocity of 56 ft/s. The height (h) , of the ball (t) seconds after it is thrown is given by the formula h(t) = 56t - 16t²

The given function is -

h[t] = 56t - 16t²

Now, for maximum height -

dh/dt = 0

d/dt ( 56t - 16t²) = 0

d/dt (56t) - d/dt (16t²) = 0

56 - 16 d/dt (t²) = 0

56 - 16 x 2t = 0

56 = 32t

t = 56/32

t = 7/4 seconds

Now, at t = 7/4 seconds, the height is maximum. Substituting the value

t = 7/4 seconds, we get -

h(7/4) = 56 x 7/4 - 16 x 49/16

h(7/4) = 14 x 7 - 49

h(7/4) = 98 - 49

h(7/4) = 49 meters

Therefore, the maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.

To solve more questions on Kinematics, visit the link below-

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help please!!!
In Angle ABC, C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
a = 3, c = 19

A. M B. M C. M D M

Answers

we know that In right angle triangle c^2 = a^2 + b^2.
19^2 = 3^2 + b^2
b = (361 - 9)^1/2 = 18.761663039294
Now for angles
sin(A) = a/c = 3/19
A = sin{-1}(3/19) = 9.0847202873911
A = 9.0847202873911
sin(B) = b/c = 18.761663039294 / 19
B = sin{-1}(18.761663039294 / 19) = 80.915279712614
B = 80.915279712614

There are three consecutive odd integers. Three times the largest is seven times the smallest. What are the integers?

Answers

Hello there!

This is how I would map out this problem...

First I would represent the smallest integer with the variable x. Since they are consecutive odd integers, add 2 to the middle integer and add 4 to the largest.

smallest: x
middle: x+2
largest: x+4

Now we need to find a way to solve for x. Since 3 times the largest is 7 times the smallest, we can set up an equation like this...
3(x+4)=7x

Now solve it!
3(x+4)=7x
3x+12=7x
12=4x
x=3

Now let's go back to our original data...
smallest: x
•Since the smallest is x, that means the smallest is going to be 3.
middle: x+2
•since the middle one is x+2, plug in 3 for x and we get 5.
largest: x+4
•since the largest is x+4, plug in 3 for x and we get 7.

This means the answer is...
Smallest: 3
Middle: 5
Largest: 7

I really hope this helps!
Best wishes :)

How use zero product property to solve equations

Answers

The zero product property says that A*B = 0, then A = 0 or B = 0
In words: if two numbers multiply to 0, then one (or both) of the values must be zero.

So in terms of algebra, if we had
-0.2*(x-1.9)*(x-3.5) = 0
then
x-1.9 = 0 or x-3.5 = 0

Now solve each individual equation for x
x-1.9 = 0
x-1.9+1.9 = 0+1.9 ... adding 1.9 to both sides
x = 1.9

x-3.5 = 0
x-3.5+3.5 = 0+3.5 .... adding 3.5 to both sides
x = 3.5

The two solutions are x = 1.9 or x = 3.5

These two x values, when plugged into f(x), will make f(x) = 0
These are the x intercepts because this is where the graph crosses the x axis.
Note: "root" is another term for "x intercept"

Porters family ordered 4 pizzas. They ate 2 3/8 of pizza how much pizza is left?

Answers

1 and 5/8 i would guess but is the pizza in 12th or is it just 8th's

Dimension of triangle A are three times the dimensions of triangle
b. The area of triangle A is 252 cm squared. What is the area of triangle B?

Answers

Answer:

28 cm2

Step-by-step explanation:

I did this question

explanation and answer

Answers

18)
h/4 = 12/h
h^2 = 48
h = 6.93

19)
x/ 12 = 3/x
x^2 = 36
x = 6

y^2 = 144 - 36
y^2 = 108
y = 10.39

Deeside weather the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17? Yes or no.

Simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x² + 8x

Answers

Yes 8 is a solution to the equation. The simplest answer is 6x.

the square root of 2.25 is _____. 15 1.5 0.15 irrational

Answers

1.5 if you put 2.25 in the calculator and hit the check mark looking symbol it will tell u its 1.5

Answer:

The square root of 2.25 is 1.5.

Step-by-step explanation:

We have been given an incomplete sentence. We are asked to bill in the given for our given sentence and complete it.

The square root of 2.25 is _____.

Let us find [tex]\sqrt{2.25}[/tex].

[tex]\sqrt{2.25}=1.5[/tex]

Therefore, the square root of 2.25 is 1.5 and option B is the correct choice.

Using complete sentences, explain the key features of the graph of the sine function.

Answers

check the picture below.

A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball’s height always decreasing?

A. 48 B.0 C.2.5 D.146

Answers

the answer should be C, 2.5<x<5.5

2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.

What is time interval?

" Time interval is the division of time into small equal intervals to have a proper observation of any data."

According to the given graph,

x represents time in seconds along x-axis

y represents height in foot of the ball along y-axis

As per observation,

Height of the ball increasing from 48 to 146 in the time interval

0< x < 2.5.

Height of the ball decreasing from 146 to 0 in the time interval 2.5< x < 5.5.

Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.

Learn more about time interval here

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Two competing cable companies have recently restructured their payment plans. Clear TV requires a $30 activation fee and charges $75 per month for their basic plan. Link TV requires no activation fee and charges $82.50 per month for their basic plan. When will the two plans be equal in cost?

Answers

Clear TV:
Activation fee = $30
Monthly charge = $7

Link TV:
Activation fee = $0
Monthly Charge = $82.50

Let x be the number of month that the two cost will be equal

30 + 75x = 82.5x
82.5x - 75x = 30
7.5x = 30
x = 30 ÷ 7.5 = 4 months

The two plans will be of equal cost after 4 months.

PLEASE HELP ME WITH THIS QUESTION AND DON'T FORGET TO EXPLAIN

Answers

when n=0, d(n)=690. This is the y-intercept
All the functions given in the options are linear functions in the form y=mx+b, then we must find a function with independent term (y-intercept) b=690
The functions with b=690 are the first and third option.

For the slope (m), we can calculate it with 2 points of the table:
n1=0, d(n1)=690
n2=2, d(n2)=560

m=[d(n2)-d(n1)] / (n2-n1)
m=(560-690) / (2-0)
m= (-130) / 2
m=-65

Then the function must be:
d(n)=mn+b, m=-65, b=690
d(n)=-65n+690

Answer: Third option d(n)=-65n+690

One angle of atriangle measures 12 degrees. the second angle's measurements is five times the third. what is the measure of the third angle

Answers

28 degrees. This is because the first angle is 12 degrees, the third is x degrees and the second is 5x. You know that in a triangle the angles add up to 180 degrees so 12 + 5x + x = 180. Then you get 6x =168 and x =28 degrees. (**x being the thrid angle**)

The measure of the third angle is; 28 degrees.

How does an angle form?

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.

Let the third angle be x

Given that One angle of a triangle measures 12 degrees. the second angle's measurements is five times the third.

We know that in a triangle the angles add up to 180 degrees.

so, 12 + 5x + x = 180.

Then we get

6x =168

x =28 degrees.

Learn more about angles here:

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Two angle measures in a scaled Triangle are 77 and 62 what is the measure of the third angle

Answers

Hey there :)

We know that the sum of all 3 angles in a triangle is 180°

Two angles are given to be 77° and 62°

We can find the 3rd angle by:
77 + 62 + x = 180 ( x is the angle to be found, you can use any variable, if not given)
180 - ( 77 + 62 ) = x
180 - 138 = x
41°

Roasting meats at high temperatures makes them moist and tender.

True False

Answers

The answer is false

Answer:

False

Step-by-step explanation:

Just did the Culinary Quiz 2021

Plz click the Thanks button!

<Jayla>

Find the length of the side labeled x round to the nearest 10th

Answers

Trig problem here. We have 2 right triangles, the one on the left and on the right. They share one side. To find the length of this side, look at the left triangle. The hypotenuse is 44 and theta is 25, and since cos(theta)=adjacent/hypotenuse, cos(25)=adjacent/44 therefore the sidelength is 44cos(25). We are looking for x and now have an angle and a side for the righthand side right triangle so because tan(theta)=opposite/adjacent, tan(34)=opposite/(44cos(25)) therefore the opposite side is 44*cos(25)*tan(34)

You can solve for x by using trigonometry. However, only the angle opposite to x has been given. In order to get another length, find the altitude of the triangle. Use the length of the left side given to set up an equation like this. Let "y" equal the altitude temporarily.
Cos. 25 = y/44
Cos. 25 x 44 = y
0.9063 x 44 = y
39.8772 = y

Now that we have the altitude you can set up another equation for x.
Tan. 34 = x/39.8772
Tan. 34 x 39.8772 = x
0.6745 x 39.8772 = x
26.8971714 = x

Final Answer: x is approximately 26.9

Which trigonometric function is equivalent to sec(-270) ? a. sec(-120) c. sec(-30) b. sec(60) d. sec(90)

Answers

The equivalent of sec (-270) will be found as follows:
we add our angle to 360°
-270+360
=90
But sec(-270) is a positive value, this implies that the angle that will give us the same answer as sec (-270) should also give us the positive value. This means that 90 is our answer since it will give us the positive sec value.
The answer is d. sec(90)

Answer: d

Step-by-step explanation: edge 2021

what is the solution of this equation x + 6 =24

Answers

If you are looking for x then it is X = 18

the answer is 18 because you had to subtract 6 by 24 and you get 18.

x=18

John let out 50 foot of kite string when he observes that his kite is directly above a point on the ground 30 feet away from him, how high is the kite ?

Answers

70 feet i believe confuseing to me

Answer:

the answer is 40 i had it on USATestPrep

Step-by-step explanation:

ion need one lml

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