What is the value of x?

Answer:

r=2

Step-by-step explanation:

y = k x^r  is the formula for a direct variation

y = k x^ -r is the formula for a indirect variation

20= 5 (1/2)^ -r

Divide each side by 5

4 = (1/2) ^ -r

Rewriting

2^2 = 2^ -1 ^ -r

2^2 = 2 ^ r

The bases are the same so

2 =r

Answer:

r=-2

Step-by-step explanation:

because i had this questiion and i got it right

Answer:

19.87301587

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ok, so you would use PEMDAS, which is the correct order in which you would need to solve an equation. The idea is that the operations that come first would have to be solved first.

If you don't know it, PEMDAS is:

Parentheses

Exponents

Multiplication/division

Addition/subtraction

In this case, you would need to solve the parentheses. (7x9) is 63.

It would be rewritten as 4x5-8/63

There are no exponents, so you can skip the next operation.

Then you would do multiplication next, which would be 4x5 = 20

The equation would be rewritten as 20-8/63

-0.126984127 is -8/63

Lastly, 19.8730159 is the result of 20-0.126984127

Hope this helps!

Answer: The 1st one is 1 soultion the 2nd one is 1 soultion the 3rd one is multiple soultion and the last one is multiple solution

Step-by-step explanation: hope I am right?

1=one 2=multiple 3=one 4=multiple

The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

Answer:

8 mm

Step-by-step explanation:

Answer:

Answer is the explanation below

Step-by-step explanation:

The exponent is negative because, as a positive exponent means to multiply, a negative exponent means to divide.

\(k \begin{bmatrix} 2&3\\5&6 \end{bmatrix}~~ = ~~ \begin{bmatrix} 6&9\\15&18 \end{bmatrix}\implies \begin{bmatrix} 2k&3k\\5k&6k \end{bmatrix}~~ = ~~ \begin{bmatrix} 6&9\\15&18 \end{bmatrix} \\\\\\ 2k=6\implies k=\cfrac{6}{2}\implies k=3\)

Answer:

40    

12%

Step-by-step explanation:

25:10

100:40

12% of 100 is 12

If you want to check yourself then

40·25%         =10

100·12%        =12

Answer:

17.6%

Step-by-step explanation:

50×8%=4

75×24%=18

4+18=22

50+75=125

22÷125=17.6%

Answer:

14.4 percent increase

Step-by-step explanation:

Answer:

Length: 5 ft; width: 4 ft.

Step-by-step explanation:

A = LW     formula for area of rectangle

(2x + 1)(2x) = 20      substitute length, width, and area into formula

4x² + 2x - 20 = 0      use the distributive property to multiply out left side

2x² + x - 10 = 0         divide both sides of equation by 2

(2x + 5)(x - 2) = 0        factor out trinomial

2x + 5 = 0  or  x - 2 = 0        use zero product rule to solve for x

2x = -5  or x = 2       subtract 5 from both sides; add 2 to both sides

x = -5/2  or  x = 2

We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.

Length: 2x + 1 = 2(2) + 1 = 5

Width: 2x = 2(2) = 4

Length: 5 ft; width: 4 ft.

Answer:

4/992 = 0.00403225806

Step-by-step explanation:

I hope this helps!!

Answer: (-0.5, 4)

Step-by-step explanation:

Midpoint formula: \((\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\)

(x1, x2)=(2, -3)

(y1, y2)=(2, 6)

-----------------------------------------------

 \((\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\)

=\((\frac{2-3}{2} ,\frac{2+6}{2} )\)

=\((\frac{-1}{2} ,\frac{8}{2} )\)

=\((-0.5, 4)\)

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

\(M=(-\frac{1}{2},4)\)

Step-by-step explanation:

The midpoint formula is given by:

\(M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Let (2,2) be x₁ and y₁ and let (-3,6) be x₂ and y₂. Therefore:

\(M=(\frac{2+-3}{2},\frac{2+6}{2})\)

Simplify:

\(M=(-\frac{1}{2},\frac{8}{2})\\M=(-\frac{1}{2},4)\)

since: b_n = (-1)^{n+2}/(n+3)(n+2) => b_{n+1}/b_n = -1/(n+4) which is less than 1, and so {b_n} is decreasing and converges to zero. Therefore, we can conclude that the series b_n = (-1)^{n+2}/(n+3)(n+2) converges.

Given bn = (-1)^{n+2}/(n+3)(n+2) and to state the theorem that allows us to determine whether the series converges or diverges using this result. Thus, to obtain the answer, we will solve the two parts of the question.

Part 1: Use induction to show that bn = (-1)^{n+2}/(n+3)(n+2)To prove that bn = (-1)^{n+2}/(n+3)(n+2), we will make use of the mathematical principle of induction.

Induction is a mathematical method of proof used to establish the validity of a proposition or theorem for all positive integers (in this case, n).

Inductive step: We assume that bn = (-1)^{n+2}/(n+3)(n+2) is true for some positive integer k, which means: bk = (-1)^{k+2}/(k+3)(k+2)

Now, we need to show that this holds for k+1, that is, we need to show that b_{k+1} = (-1)^{k+3}/(k+4)(k+3)

.So, we start by calculating b_{k+1} as follows: b_{k+1} = (-1)^{k+3}/(k+4)(k+3) = (-1)(-1)^{k+2}/(k+4)(k+3) = -(-1)^{k+2}/(k+4)(k+3) = (-1)^{k+2}/(k+3)(k+4)

Thus, we have shown that b_{k+1} = (-1)^{k+3}/(k+4)(k+3) is true whenever b_{k} = (-1)^{k+2}/(k+3)(k+2) is true.

Hence, by the principle of mathematical induction, we can conclude that bn = (-1)^{n+2}/(n+3)(n+2) holds for all positive integers n.

Part 2: State the theorem that allows you to determine whether the series converges or diverges using this result.

The theorem that allows us to determine whether the series converges or diverges is the alternating series test.

The alternating series test states that if a series is of the form: \sum_{n=1}^{\infty} (-1)^n b_nwhere {b_n} is a decreasing sequence of positive terms that converges to zero, then the series converges. Furthermore, the error in approximating the sum of the series by any partial sum is less than the absolute value of the first neglected term.

In this case, the series b_n = (-1)^{n+2}/(n+3)(n+2) satisfies the conditions of the alternating series test because:{b_n} is a decreasing sequence of positive terms that converges to zero, since: b_n = (-1)^{n+2}/(n+3)(n+2) => b_{n+1}/b_n = -1/(n+4) which is less than 1, and so {b_n} is decreasing and converges to zero.

Therefore, we can conclude that the series b_n = (-1)^{n+2}/(n+3)(n+2) converges.

Learn more about mathematical induction here:

https://brainly.com/question/29503103

#SPJ11

A possible practical domain for the function is T > 12500

The domain are the input values for which a function exist.

Given the function relating the metal bar is L cm long when its temperature is T◦C as:

L(T) = 0.002T + 25

The domain of the expression is the point where 0.002T + 25 is greater than zero.

0.002T + 25 > 0

0.002T > -25
T > 12,500

Hence  a possible practical domain for the function is T > 12500

Learn more on domain here: https://brainly.com/question/26098895

Answer:

140°

........

.......

........

SOLUTION

(a) What percentage of adults exercise

percent adult that exercise becomes

Hence the answer is 42%

(b) Vegetarians is 39 + 21 = 60

percentage of the adults are vegetarian is

Hence the answer is 40%

(c) Adults who are vegetarian that exercise is 39

The percentage of adults who are vegetarian that exercise becomes

Hence the answer is 26%

(d)

Answer:

\(2 - \frac{y}{4}\)

Step-by-step explanation:

Given equation:

                          \(\frac{40 - 5y}{20}\)

Problem;

Simplify the equation;

Solution:

         \(\frac{40 - 5y}{20}\) can be expressed as;

  = \(\frac{40}{20}\)  - \(\frac{5y}{20}\)

       dividing by 20 gives;

 = 2 - \(\frac{y}{4}\)

The equation simplified is;

  = \(2 - \frac{y}{4}\)

Answer:

33

Step-by-step explanation:

3x-1+x-1=134

4x-2=134

4x=136

x=34

34-1=33

Answer:

Step-by-step explanation:

3x - 1 + x - 1 = 134

4x - 2 = 134

4x = 136

x = 34

Answer:

-5/6

Step-by-step explanation:

\(x+\frac{2}{3} = \frac{-1}{6}\)

By transposing 2/3 towards the RHS we get,

\(x=\frac{-1}{6} -\frac{2}{3}\)

\(x=-\frac{1}{6} -\frac{2X2}{3X2} =-\frac{1}{6} -\frac{4}{6} =\frac{-5}{6}\)

Hello! :)

First, Simplify both sides of the equation

x + 2/3= -1/6

Next, Subtract 2/3 from both sides

x + 2/3 - 2/3 = -1/6 - 2/3

x= -5/6 (ANSWER)

Hope this helped you!

THEDIPER

The initial flounder population in millions is 1 million. The derivative of the population function at t = 10 is 1.4000 million flounder per year.

(a) To find the initial flounder population, we substitute t = 0 into the population function P(t). Given that t is measured in years, we have:

P(0) = 7(0) + 5 - 0.2(0^2) + 1 = 0 + 5 - 0 + 1 = 6 million flounder.

Therefore, the initial flounder population is 6 million.

(b) To determine P'(10), we need to find the derivative of the population function P(t) and evaluate it at t = 10. Taking the derivative of P(t) with respect to t, we have:

P'(t) = 7 + 0.4t.

Now, substituting t = 10 into the derivative equation:

P'(10) = 7 + 0.4(10) = 7 + 4 = 11 million flounder per year.

Rounded to four decimal places, P'(10) is approximately 11.0000 million flounder per year.

Learn more about decimal here:

https://brainly.com/question/30958821

#SPJ11

Answer:

13*12 is greater than 11*14 by 2 meters^2

Step-by-step explanation:

\(A=wl=13*12=156m^2\\A=wl=11*14=154m^2\)

Goodluck

Answer:

Jenny's room has a great area.

Step-by-step explanation:

Jenny's room

\(area = l \times b \\ = 13 \times 12 \\ = 156 {ft}^{2} \)

Ruth's room

\(area = l \times b \\ = 14 \times 11 \\ = 154 {ft}^{2} \)

so,

\(156 > 154\)

So ,Jenny's room has a great area than Ruth's room.

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

The sum of all exterior angles of any regular polygon is 360°.

= \(\frac{360}{57} \\\\= 120/19\\or\:6.315\)

The number of sides should be a natural number not in fraction or decimal

The correct option is (2)  \(\frac{8}{5}\) and (3)  \(\frac{1}{6}\).

The factor of equation  f(x) = 60\(x^{4}\) +  86\(x^{3}\) – 46\(x^{2}\) – 43\(x\) + 8 are \(\frac{8}{5}\) and \(\frac{1}{6}\).

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

\($$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.\)

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   \(\frac{8}{5}\) and \(\frac{1}{6}\) can be written in the form:  

\(\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}\)

Therefore, the rational roots of polynomial f(x) = 60\(x^{4}\) +  86\(x^{3}\) – 46\(x^{2}\) – 43\(x\) + 8 are \(\frac{8}{5}\) and \(\frac{1}{6}\).

To know more about Rational Root Theorem, here

https://brainly.com/question/10937559

#SPJ4

The complete question is-

Which is a factor of f(x) = 60\(x^{4}\) +  86\(x^{3}\) – 46\(x^{2}\) – 43\(x\) + 8? use the rational root theorem to help you find your answer.

Answer:18.4

Step-by-step explanation:add

Answer:

x = 80 degrees

angle CBD and EFB are supplementary meaning they add up to 180 degrees, and given that angle CBD is 100 we would need to find the missing angle which would add up to 180 degrees.

So we would set up an equation of

X + 100 = 180

-100     -100

x = 80

i) The counting numbers which are multiples of 5 and less than 50 can be represented using the roster method as:

{5, 10, 15, 20, 25, 30, 35, 40, 45}

ii) The set of all-natural numbers x for which x+6 is greater than 10 can be represented as:

{5, 6, 7, 8, 9, 10, 11, 12, 13, ...}

iii) The set of all integers x for which 30/x is a natural number can be represented as:

{-30, -15, -10, -6, -5, -3, -2, -1, 1, 2, 3, 5, 6, 10, 15, 30}

Note that in the third set, we include both positive and negative integers that satisfy the condition.

Learn more about all-natural numbers here: brainly.com/question/32386180

#SPJ11

Answer:

44

Step-by-step explanation:

Answer:

Step-by-step explanation:

237.82÷22.5=10.5697(7 is repeating)

or you can do keep change flip

237.82       2     475.64

    1           45        45

=10.5697(7 is repeating)

about 10.57 dollars earned each hour

10.57·35=369.95 dollars earned after 35 hours

The test statistic is at α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

What is p-value?

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, presuming that the null hypothesis is true.

As given,

State the hypothesis,

Ha: μ = 132

Ha: μ ≠ 132 (two failed test)

Test satisfies:

As σ is unknown we will use t-test satisfies

t = (x - μ)/(s/√n)

Substitute values,

t = (137 - 132)/(14.2/√20)

t = 1.57

t satisfies is 1.57.

Critical values,

P(t < tc) = P(t < tc) = 0.05

using t table at df = 19

tc = ±1.729

So value is tc = (-1.729, 1.729)

P-value:

P(t > ItstatI) = p-value

P(t > I1.57I) = p-value

Using t-table

p-value = 0.1329

given

α = 0.10

So, p-value < α

Do not reject Null hypothesis.

Conclusion:

At α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

To learn more about Null hypothesis from the given link.

https://brainly.com/question/4436370

#SPJ4