(ar^b) ^4 = 16r^20 where a and b are positive integers work our a and b​

Answers

Answer 1

Answer:

a = 2

b = 5

Step-by-step explanation:

Given :

(ar^b)^4 = 16r^20 ; a and b are positive integers :

Opening the bracket :

a^4r^4b = 16r^20

a^4 = 16 - - - - - (1)

r^4b = r^20 - - - (2)

a^4 = 16

Take the 4th root of both sides :

(a^4)^(1/4) = 16^1/4

a = 2

From (2)

r^4b = r^20

4b = 20

Divide both sides by 4

4b/4 = 20/4

b = 5

Hence ;

a = 2

b = 5


Related Questions

The work of a student to solve a set of equations is shown:

Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z


Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3


In which step did the student first make an error?
Step1
Step 2
Step 3
Step 4

Answers

Step 2

−2y = 15 − 2z

should be

−2y = -30 + 4a

the student made a error in step 2.

Find the length of side
x
x in simplest radical form with a rational denominator.

Thanks In advance.

Answers

Answer:

Sorry I dont really understand wish I could help:(

Step-by-step explanation:

Answer:

[tex]\sqrt{10}[/tex]

[tex]\sqrt{5 } ^{2} + \sqrt{5 } ^{2} = x^{2}[/tex]

[tex]x^{2} =10[/tex]

Step-by-step explanation:

If there are12 books on a rack,a person has to choose 5books.
In how many ways can he choose if one particular book is always selected?​

Answers

Answer:

330

11 choose 4

[tex]=\frac{11!}{4!\left(11-4\right)!}\\= 330[/tex]

Step-by-step explanation:

How tall is the table?

Answers

Answer:

too complex:<

Step-by-step explanation:

120cm+120cm=240cm (2 squirrels + 2 air spaces)

90cm+90cm=180cm (2 rats + 2 air spaces)

240cm-180cm=(2 squirrels + 2 air spaces) - (2 rats + 2 air spaces)

                       =2 squirrels + 2 air spaces - 2 rats - 2 air spaces

                       =2 squirrels - 2 rats

                       =60cm

1 squirrel - 1 rat = 60cm divided by 2

                         = 30cm

120cm + 90cm = squirrel + air space + rat + air space

                        = 210cm

I've no idea!! This qn is too challenging!!

But i hope the above workings might help you in a way or another:>

The table is 105cm tall.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let the table is x

Squirrel is y

Rat is z

From 1st diagram

x+y-z=120...(1)

From 2nd diagram

x+z-y=90...(2)

Add 1 and 2

x+y-z+x+z-y=120+90

2x=210

Divide both sides by 2

x=105

Hence, the table is 105cm tall.

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t 0 2 4 6 8 10
P(t) 0 36 43 47 52 60
Kunyu's family has an above ground swimming pool in the shape of a cylinder, with a radius of 10 feet and a height of 5 feet. The pool contains 1000 cubic feet of water at time t=0. During the time interval 0≤t≤10 hours, water is pumped into the pool at the rate () cubic feet per hour. The table above gives values of () for selected values of . During the same time interval, water is leaking from the pool at the rate of () cubic feet per hour, where ()=18−0.04.

(Note: The volume V of a cylinder with radius r and height h is given by =2ℎ .)

Find the rate at which the volume of water in the pool is increasing at time t=6 hours. How fast is the water level in the pool rising at t=6 hours? Indicate units of measure in both answers.

Answers

Answer:

a. 24.12 ft³/hr b. 0.0768 ft/hr

Step-by-step explanation:

a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.

The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out

Since volume flow rate in = P(t) and volume flow rate out = R(t),

dV/dt = P(t) - R(t)

[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]

We need to find the rate of change of volume when t = 6.

From the table when t = 6, P(6) = 47 ft³/hr

Also, substituting t = 6 into R(t), we have R(6)

[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]

[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]

dV/dt ≅ 24.12 ft³/hr

So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr

b. How fast is the water level in the pool rising at t=6 hours?

Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet

dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.

So, dV/dt = πr²dh/dt

dh/dt = dV/dt ÷ πr²

Since dV/dt = 24.12 ft³/hr and r = 10 ft,

Substituting the values of the variables into the equation, we have that

dh/dt = dV/dt ÷ πr²

dh/dt = 24.12 ft³/hr ÷ π(10 ft)²

dh/dt = 24.12 ft³/hr ÷ 100π ft²

dh/dt = 0.2412 ft³/hr ÷ π ft²

dh/dt = 0.2412 ft³/hr

dh/dt = 0.0768 ft/hr

So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr

Write the ratio 4 L : 5.6 L as a fraction in the simplest form with whole numbers in the numerator and denominator

Answers

Answer:

Step-by-step explanation:

It's 5/7

You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25

4 * 1.25 = 5

5.6 * 1.25 = 7

I need to know how to find the area and to simplify it

Answers

Area of parallelogram = b × h

Base = x + 7

Height = x + 3

ATQ

Area = (x + 7) ( x + 3)

x² + 3x + 7x + 21

x² + 10x + 21

Answered by Gauthmath must click thanks and mark brainliest

A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips vary in size, it is difficult to fill the bags to the exact weight desired. However, the bags pass inspection so long as the standard deviation of their weights is no more than 3 grams. A quality control inspector wished to test the claim that one batch of bags has a standard deviation of more than 3 grams, and thus does not pass inspection. If a sample of 21 bags of potato chips is taken and the standard deviation is found to be 4.1 grams, does this evidence, at the 0.025 level of significance, support the claim that the bags should fail inspection

Answers

When we take data at work, we always do it over a period of time. To me, just one sample set does not show enough data to come to that conclusion. Also it is one batch of bags. I think you would need to have an average of data from different batches & samples to prove your data is accurate and support your claim.

Following this pattern, type a number to show how many bags of wheat there will be on the sixth square.

Will pay 14 points

Answers

The number of bags of wheat that will be on the sixth square is 32wheats

The amount of wheat in each square are expressed in geometric sequence as shown.

1, 2, 4, 8, 16,....

Geometric sequence is a sequence where the ratio of the succeeding and the preceding term is equal to a common ratio.

The nth term is expressed as

Tn = ar^{n-1}

a is the first term

r is the common quantity

n is the number of terms

a = 1

n = 6 (sixth square)

r = 4/2 = 2/1 = 2

Substitute the given values into the formula

T6 = 1(2)^{6-1}

T6 = 2^5

T6 = 32

Hence the number of bags of wheat that will be on the sixth square is 32wheats

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Answer:

32

Step-by-step explanation:

https://www.yutube.com/watch?v=U3vLXdNdTJ8

link is broken add an o to yutube

Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christian’s grade would probably rate the test something other than easy?
A.
27
B.
78
C.
84
D.
126

Answers

Answer:

C.

84

Step-by-step explanation:

This question is solved using proportions.

From the sample:

11 + 3 = 14 out of 13 + 11 + 3 = 27 would rate the test something other than easy.

Out of 162:

Applying the rule of three:

14 - 27

x - 162

Applying cross multiplication:

[tex]27x = 14*162[/tex]

[tex]x = \frac{14*162}{27}[/tex]

[tex]x = 84[/tex]

Thus the correct answer is given by option C.

Answer:

I hope this helps

Step-by-step explanation:

An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?


50
55
75
100

Answers

There are 50 different possible debating teams that could be selected as obtained using COMBINATION.

Since there are EQUAL number of juniors and seniors ;

Then we have 5 of each.

Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION

since the team MUST contain 4 SENIORS and 2 JUNIORS

4 Seniors from 5  = 5C4 = 5

2 Juniors from 5 = 5C2 = 10

Hence, (5C4 * 5C2) = 5 * 10 = 50

Hence, there are 50 different possible debating teams that could be selected.

Learn more about COMBINATION :

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Please solve the problem

Answers

Answer:

does this have to do with graphs

which decimal is equivalent to 6×100+7×10+4×1/10+8×1/1,000​

Answers

The answer is 670.408, because 6x100=600, 7x10=70, 4x1/10 as a decimal is 0.4, 8x1/1,000 as a decimal is 0.008. Then, you add all of those [tex]600+70+0.4+0.008=670.408[/tex].

the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age?​

Answers

Answer:

sadia is 32

Step-by-step explanation:

sadia : father : total

3          6          9

Divide 96 by 9

96/9 = 32/3

Multiply each by 32/3

sadia :     father : total

3*32/3    6*32/3  9*32/3

32                 64          96

I want to know how to solve this equation

Answers

Answer:

one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.

The answer would then be D

Find x (round to the nearest tenth)

Answers

9514 1404 393

Answer:

  x = 8

Step-by-step explanation:

By AA similarity, ΔABD ~ ΔCDE. So, corresponding sides are proportional.

  AB/BD = CD/DE

  x/12 = 4/6

  x = 12(4/6)

  x = 8

Which type of triangle will always have at least 1-fold reflectional symmetry?

right triangle
obtuse triangle
acute triangle
isosceles triangle

Answers

Answer:

D. isosceles triangle

Step-by-step explanation:

Ed22

A triangle with at least 1-fold reflectional symmetry is isosceles triangle, option D is correct.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

An isosceles triangle will always have at least 1-fold reflectional symmetry.

This is because an isosceles triangle has two congruent sides and two congruent angles.

If we draw a perpendicular bisector of the base (the side that is not congruent), it will bisect the base and the angle opposite to the base.

This means that the triangle is symmetric with respect to this line of reflection, which is the line of symmetry.

Therefore, the correct answer is isosceles triangle.

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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Chapter 11 part 3:

Of the three functions {f(x), g(x), h(x)} featured on the graph below (on the following page), rank the functions in order of greatest rate to least.

Answers

9514 1404 393

Answer:

  f, h, g

Step-by-step explanation:

You can look at the slope of the tangent lines to the graphs at any given x-value. At x=5, we see that g(x) is the flattest curve and f(x) is the steepest.

In order from greatest to least growth rate, the functions are ...

  f(x), h(x), g(x)

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and
standard deviation of 1.7 years.
The 10% of items with the shortest lifespan will last less than how many years?
Round your answer to one decimal place.

Answers

Answer:

Less than 3.6 years.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.8 years, and  standard deviation of 1.7 years.

This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]

The 10% of items with the shortest lifespan will last less than how many years?

Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]

[tex]X - 5.8 = -1.28*1.7[/tex]

[tex]X = 3.6[/tex]

Less than 3.6 years.

A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?

Answers

Length=48inBreadth=36in

[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]

[tex]\\ \sf\longmapsto Area=48(36)[/tex]

[tex]\\ \sf\longmapsto Area=1728in^2[/tex]

[tex]\\ \sf\longmapsto Area=144ft^2[/tex]

[tex]\\ \sf\longmapsto Area=48yard^2[/tex]

answer this now please :)

Answers

9514 1404 393

Answer:

  E.  384 cu ft

Step-by-step explanation:

The sum of length and width is half the perimeter, so the width is ...

  (40/2) -12 = 8 . . . feet

The depth is half that, so is 8/2 = 4 feet.

The volume is ...

  V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³

The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120

Answers

9514 1404 393

Answer:

  10 and 24

Step-by-step explanation:

We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).

These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).

For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)

The side lengths are 10 and 24.

__

Check

For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.

__

In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...

  x² +y² = (x+2)²   ⇒   y² = (x² +4x +4) -x²   ⇒   y² = 4x +4 = 4(x +1)

_____

Additional comment

The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.

Using the third equation in the attachment to write an expression for y, we have ...

  y = 58 -2x

Substituting that into the second equation gives ...

  (x(58 -2x)/2 = 120

  29x -x² = 120

  x² -29x +120 = 0

  (x -5)(x -24) = 0 . . . . x = 5 or 24.

The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.

Find the radius of the circle containing 18
degree arc of a circle whose length is 15 Pi meters

Answers

9514 1404 393

Answer:

  150 m

Step-by-step explanation:

The relationship between arc length (s), radius (r), and central angle (θ) is ...

  s = rθ

Dividing by θ gives the formula for r:

  r = s/θ = (15π m)/(18°(π/180°))

  r = 150 m . . . . the radius of the circle

Which of the following is true because of the Associative Law of Addition?
A. 1000 + 2000 + 6 = 3006

B. (1000) + 2000 + 6 = 1000 + (2000) + 6

C. 1000 + 2000 + 6 = 2000 + 1000 + 6

D. 1000 + (2000 + 6) = (1000 + 2000) + 6

Answers

Answer:

d part is correct because in associative property the brackets and the numbers CAN be shifted

I really need help with this one

Answers

Hi, I hope this helps:

FG + GH = FH
3x + 4x = 14
7x = 14
14/7 = 2
x= 2

ANSWER THE QUESTIONS PLEASE IT IS ON BEARING

Answers

9514 1404 393

Answer:

  (i) x° = 70°, y° = 20°

  (ii) ∠BAC ≈ 50.2°

  (iii) 120

  (iv) 300

Step-by-step explanation:

(i) Angle x° is congruent with the one marked 70°, as they are "alternate interior angles" with respect to the parallel north-south lines and transversal AB.

  x = 70

The angle marked y° is the supplement to the one marked 160°.

  y = 20

__

(ii) The triangle interior angle at B is x° +y° = 70° +20° = 90°, so triangle ABC is a right triangle. With respect to angle BAC, side BA is adjacent, and side BC is opposite. Then ...

  tan(∠BAC) = BC/BA = 120/100 = 1.2

  ∠BAC = arctan(1.2) ≈ 50.2°

__

(iii) The bearing of C from A is the sum of the bearing of B from A and angle BAC.

  bearing of C = 70° +50.2° = 120.2°

The three-digit bearing of C from A is 120.

__

(iv) The bearing of A from C is 180 added to the bearing of C from A:

  120 +180 = 300

The three-digit bearing of A from C is 300.

Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.

Answers

Answer:

1. Degree = 1, monomial

2. Degree = 2, monomial

3. degree = 2, trinomial

4. Degree = 2, binomial

5. Degree  = 2, binomial

Step-by-step explanation:


Use the graphing calculator to graph the function f(x) = Vx. Which table of values contains points that lie on the
graph of the function?

Answers

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Assuming your Vx means √x, the values in the f(x) column will be the square root of the values in the x column. That is the case for the first table shown (also attached).

Bob wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 6 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window?

Answers

ANSWER: The glass window will cost $252.00 for window replacement.

EXPLANATION:

The area of a square is given by the formula:

s^2

where s is the side length.

If we were to replace the glass window, and it will cost $7.00 per square foot, the total price will be:

FIND AREA OF THE GLASS WINDOW:

6^2 = 36 square feet

$7 per square foot so:

36 x 7 = 252

Therefore it will cost $252.00 to replace the glass window.

What does -3/8 > -1 indicate about the positions of -3/8 and -1 on the number line?!

Answers

Answer:

-3/8 is located on the right of -1

Step-by-step explanation:

-3/8 is left of -1 because -3/8 is larger than -1.

Other Questions
If f(x) = x+1 and g(x) =x^2, then gf(2) = If the federal government ordered a United States citizen to invest his or her money in a certain way, which founding constitutional principlewould that violate?OA federalismOB. separation of powersOC. limited governmentOD. republicanism 6 students were asked the age of their oldest sibling:21, 31, 26, 24, 28, 26. Arrange the scores from lowest to highest.Find the following. LABEL you answers. Q1, Q2, Q3, IQR, and Range. Q1= Q2 (median)=Q3= IQR= Q3- Q1 IQR= Range: Max score - Min scoreRange = HELP ASAP PLEASE What has been the main role of thetwelve Federal Reserve Banks?A. To help commercial banksB. To giveprivate home loansC. To regulate personal income and taxesD. To help individuals who file for bankruptcy Zero-coupon risk-free bonds are available with the following maturities and yield rates (effective, annual): Maturity(in years) Yield % 1 62 6.53 7You need to buy corn for producing ethanol. You want to purchase 10,000 bushels one year from now, 15,000 bushels two years from now, and 20,000 bushels three years from now. The current forward prices, per bushel, are $3.89, $4.11, and $4.16 for one, two, and three years respectively. You want to enter into a commodity swap to lock in these prices. Which of the following sequences of payments at times one, two, and three will NOT be acceptable to you and to the corn supplier? a. $38,900; $61,650; $83,200 b. $39,083; $61,650; $82,039c. $40,777; $61,166; $81,554 d. $41,892; $62,340; $78,997 e. $60,184; $60,184; $60,184 73.2 Iron reacts with copper (I) sulfate to produce copper and iron (II) sulfate. If 4.32x10^25particles of copper (I) sulfate react, how many moles of copper will be produced?Fe + Cu2504 --> FeSO4 + 2Cu Come I to speak in Caesar's funeral. He was my friend, faithful and just to me: But Brutus says he was ambitious; And Brutus is an honourable man. He hath brought many captives home to Rome Whose ransoms did the general coffers fill: Did this in Caesar seem ambitious? Which phrase from the mark antony's speech best shows that he's using ethos O A. He was my friend, faithful and just to me. B. Brutus says he was ambitious O C. He hath brought many captives home to Rome D. Did this in Caesar seem ambitious? In the nephron, the highest concentration of salt is found surrounding the Select one: a. loop of Henle.b. Bowman's capsule.c. distal convoluted tubule.d. proximal convoluted tubule. In 1906, the publication of The Jungle, written by Upton Sinclair, led Congress toenact stronger prohibition lawssupport the national conservation movementestablish a system of meat inspectionlegalize strikes and boycotts by labor unions in a standard deck of 52 cards what is the probability of drawing 2 jacks i need help asap ! Which is a barrier to leading a substance-free lifestyle?emotional stabilityfear of judgmentdecreased spendingfewer legal problems Find the equivalent expression using thesame bases.(98.41) por qu hay espacios en los peridicos y revistas? 1An astronaut weighs 202 lb. What is his weight in newtons? Evolution can be best defined as ________. Evolution can be best defined as ________. always taking a very long time to occur change in the gene pool of a population the production of new species change in the composition of populations Two blocks in contact with each other are pushed to the right across a rough horizontal surface by the two forces shown. If the coefficient of kinetic friction between each of the blocks and the surface is 0.30, determine the magnitude of the force exerted on the 2.0-kg block by the 3.0-kg block. Find the slope between the points (3,5) and (10,-5) . Enter DNE if the slope between the points is undefined. The Tuskegee Airmen was a group ofspecial fighting forces that werecomprised of which nationality?A. Native AmericansB. Japanese-AmericansC. African-Americans At what depth will the pressure exerted on a man be twice that of the pressure at the surface if water? The zone of convergence between sub-tropical and polar air masses, and where frequent traveling storms take place, is along the: