If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?

Answers

Answer 1

The value of x in the direct and indirect varoation is calculated as: x = 2.

What is Direct and Indirect Variation?

If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.

With the information stated, we would have the following:

z = kx/y³

Find k, by plugging in the values of x, y, and z:

12 = k(8/2³)

12 = k(8/8)

12 = k

k = 12

Find x when y = 1 and z = 24:

24 = 12(x)/1³

24 = 12x

24/12 = x

x = 2.

Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.

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Related Questions

What is the range of this data set?

36.6, 39.8, 33.3, 34.8, 35.8, 39.6, 36.7, 36.9, 37.5, 32.2, 33.1, 33.3

Answers

Answer:

Step-by-step explanation:

39.8 - 32.2 = 7.6

Range is subtracting the highest and lowest numbers by each other .

Based on the calculations, the range for this data set is equal to 7.6.

What is a range?

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, range is calculated by using this formula;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 39.8.Lowest number = 32.2.

Substituting the given parameters into the formula, we have;

Range = 39.8 - 32.2

Range = 7.6.

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Use the distributive property to write the following expressions in expanded form. 4(x +y)

Answers

Answer:

4x+4y

Step-by-step explanation:

Answer:

4x + 4y

Step-by-step explanation:

To do this you need to know that the number (or variable) on the outside of the parenthesis must be multiplied to all of the numbers/variables on the inside of the parenthesis.

So here, you want to multiply x by 4:

4x

Then multiply y by 4:

4y

And because the expression is adding the x and y, it comes out as:

4x + 4y

Write the rate in lowest terms.
During a bad storm there was 2 in of rain in 4 hr.
The rate in lowest terms is_____?

Answers

Answer:

1/2 in/hr

Step-by-step explanation:

2 in / 4h   =   1/2 inch per hour

Let x and b be positive real numbers so that log_b(x^2) = 10. Find log_3sqrtb (1/x)

Answers

The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex]  where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.

How to analyze and solve logarithmic expressions

Logarithms are trascendental functions, that is, functions that cannot be described algebraically.

In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:

[tex]\log_{b} x^{2} = 10[/tex]

[tex]2\cdot \log_{b} x = 10[/tex]

[tex]\log_{b} x = 5[/tex]

x = b⁵

Then, the value of the latter logarithm is:

log₃ (x⁻¹)[tex]^{1/b}[/tex]  

- b⁻¹ · log₃ x

- b⁻¹ · log₃ b⁵

- 5 · b⁻¹ · log₃ b

The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex]  where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]

Remark

The statement is poorly formated, correct form is described below:

Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].

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-0.5(14a - 22) = ? this for my work, please help me.

Answers

Answer:

-7a+11

Step-by-step explanation:

CAN SOMEONE HELP PLS?? I rlly dont get this.

Answers

The little square on the angle means that the entire angle is 90 degrees

The larger angle is made up of two angles of measure 'x - 18' and 'x'

Let's put that into an equation form:

     (x - 18) + (x) = 90

        2x - 18 = 90

           2x = 108

            x  = 54

So x = 54

Hope that helps!

Please help i wan't a good grade but I can't figure this out.

Answers

Answer:

angle DCE

Angle DEC

Angle ABF

Step-by-step explanation:

you had the wrong order

Which of the binomials below is a factor of this trinomial?

x^2 + 8x + 16

A. x + 4

B. x - 4

C. x + 8

D. x - 8

Answers

The answer is A.

Pick A.

Good luck

How do you solve this?
2sinXcosX=sinX

Answers

Answer: X=60°
2sinXcosX = sinX
Divide through by 2sinX
cosX = 1/2
X = cos-1(1/2)
X= 60°

A 22° B 54° С What is the measure of AD? O 108° 0 27° 126 54°​

Answers

Answer:

A. 108

sorry if im wrong but if u am I'm so sorry

help me please mark U as BRAINLIEST​

Answers

Hope this helps. Good luck

i need help with this problem

Answers

Answer:

Disagree

Step-by-step explanation:

because it looks like less than 45

Each of students reported the number of movies they saw in the past year. Here is what they reported.
11,6 ,9 ,16 ,12 ,18 ,14
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.

Answers

Answer:

18+16+14+12+11+9+6=8686÷7=12.2812.28=13

Answer:

12.3

Step-by-step explanation:

11+6 +9 +16 +12 +18 +14 =86

86/7 = 12.28571

Tenths is the place value of the digit that appears after the decimal. It represents the 1/10 position of the digit

          (12.3) rounded  to the nearest tenth.

 

Which expression is equivalent to the following complex fraction?

Answers

Consider the fraction first ;

[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]

Hence, Option B) is required answer

A car travels 80 miles on 3 gallons of gas. At the same rate (in miles per gallon) l, how many miles will the car be expected to travel on 5 gallons of gas?

A. 48

B. 130

C. 133 1/5

D. 160

Answers

Answer:

C

Step-by-step explanation:

Which number is a common multiple of 3 and 4?
A) 8
B) 14
C) 32
D) 48

Answers

Answer:

LCM of 3 and 4 is 12

Step-by-step explanation:

This is your answer

Answer:

The answer is D.

Step-by-step explanation:

To find the common multiple you would divide each answer choice by both numbers & if the are whole numbers then there is your answer. If it is a number with a decimal somewhere then that is not the answer.

Larger is 32 ounces and sells for 2.99 and smaller is 18 ounce and sells for 1.59
What is the better buy

Answers

Divide price by size of each and compare the u it price:


2.99/32 = 0.0934 per ounce


1.59/18 = 0.0883 per ounce


The 18 ounce do $1.59 has a lower cost per ounce so is the better buy

A store sells a workout outfit that consists of a jacket, a t-shirt, and a pair of shorts. The store purchases the jacket for $34, the t-shirt for $9, and the shorts for $12. The percent of markup is 28%. Find the selling price of the outfit.

PS: include show work please I have to submit this in like 3 hours thankyou

Answers

Answer:

The Outfit costs $70.4.

Step-by-step explanation:

Add the selling price together

34 + 9 + 12 = 55

Multiply by the markup (Profit)

100% = 1

28% = 0.28

55 x 1.28 = 70.4

A very slow man walks

20 cm.in 0.5 left, what his

velocity in meter per second?

Answers

Displacement(d)=0.2m
Time taken(t)= 30 s(1min=60 s)
Velocity (v)=?
We know that,
Velocity (v) = d/t
=0.0067

A data set is normally distributed with a mean of 8.1 and a standard deviation of 3.8.
What percentage of the data is above 8.6?
Enter your answer as a number to the nearest whole percentage, like this: 42%

Answers

Answer:

  45%

Step-by-step explanation:

Your graphing calculator, statistics app, or spreadsheet can tell you that 45% of the normally-distributed data is above 8.6 when the mean is 8.1 and the standard deviation is 3.8.

Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1

Answers

Answer:

Step-by-step explanation:

Arithmetic sequaence:

[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]

[tex]a_2 = -3*4^2-1\\[/tex]

    = -3*16 -1

     = -48 - 1

    = -49

difference = second term - first term

                 = -49 -(-13)

                = -49 + 13

             d = -36

[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]

[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]

= 5*(-135)

= -675

What’s the difference between 4, 7/9 and 2 1/2

Answers

[tex]\huge \mathbb \orange{ANSWER} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]

[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]

[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]

[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]

Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.

Answers

Answer:

  k = 3

Step-by-step explanation:

The value of k is the amount by which the function f(x) is translated upward to give the function g(x). We can compare y-intercepts to see that the y-intercept of g(x) is 5 -2 = 3 units more than the y-intercept of f(x). This means ...

  g(x) = f(x) +3

Comparing to ...

  g(x) = f(x) +k

we see that k = 3.

Find the simple interest on the loan of $2500 for 2 years at 5%.
$
(Simplify your answer. Round to the nearest cent as needed.)

Answers

Answer:

Step-by-step explanation:

simple interest=prt

p=principle amount

r=rate

t=time

here p=$2500

r=5 %=0.05

t=2 years

simple interest=2500×2×0.05=$250

The simple interest on the loan of $2500 for 2 years at 5% is $250

How to determine the value?

The formula for calculating simple interest is expressed as;

I = PRT/100

Such that the parameters of the formula are;

P is the principal amountI is the simple interestR is the interest rateT is the time

Now, substitute the values, we get;

Simple interest = 2500 × 5 × 2/100

Multiply the values

Simple interest =25, 000/100

Simple interest =$250

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#SPJ2

Does anyone know the answers? Need help!!

Answers

Answer:

nice handwriting

Step-by-step explanation:

Which of the following is true of the numbers 4 and 10?

A. The greatest common factor is
B. The least common multiple is
C. The greatest common factor is 20.
D. The least common multiple is 40.​

Answers

Answer:

None

Step-by-step explanation:

Answer is isn't there

the gcf = 2

the LCM = 20

NEED HELP ASAP The salaries of Nathan and Trisha are in the ratio of 5:9. Trisha's salary is £16800 more than Nathan's. Find Nathan's salary.​

Answers

Answer:

From the ratio

The difference is 9 - 5 = 4

Hence Trisha has 4 units more than Nathan and this resulted to 16800

Therefore 1 unit will be

16800 / 4 = 4200


Nathan’s salary is 5 units

5 * 4200 = 21000

What angles are acute GFE mlk dbc dba

Answers

Answer:

d and a

Step-by-step explanation:

an acute is an angle less than 90 degrees. a 90 degree angle is a right angle (klm) the only 2 angles smaller than (klm) are (gfe) and (dba)

112 is 80% of what number?

A. 140

B. 896

C. 1,400

D. 8,960

Answers

Answer:

A

Step-by-step explanation:

112/0.8 = 140

Answer:

A

Step-by-step explanation:

I am not sure about the answer

What is a2+b2+c2? Thank you for your help.

Answers

Answer:

Pythagoras theorem

Step-by-step explanation:

dhebbd

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