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Answer:

B

Step-by-step explanation:

given that x and y vary inversely then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y is 24 when x is 8 , then

24 = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 to clear the fraction )

192 = k

y = [tex]\frac{192}{x}[/tex] ← equation of variation

when y = 18 , then

18 = [tex]\frac{192}{x}[/tex] ( multiply both sides by x )

18x = 192 ( divide both sides by 18 )

x = [tex]\frac{192}{18}[/tex] = [tex]\frac{32}{3}[/tex]

Answer:

Step-by-step explanation:

Write the inverse variation

y = k/x

Solve for k

y = 24

x = 8

y = k/x           Substitute the givens into this equation

24 = k/8        Multiply both sides by 8

8*24 = k

k = 192

Solve for x  when y = 18

y = k/x            Multiply both sides by x

xy = k             Divide by y

x = k/y

x = 192/18

x = 10 2/3       The answer is given as an improper fraction.

x = (10*3 + 2)/3

Answer: x = 32/3

Answer:

So, there are seven choices, etc, so the equation is

7x6x7x2

because there are multiple ways

so, 588

Here Allie mistook the x and y axis completely oppositely.

→ First should be the x axis and then the y axis, (x, y)

Answer:

Step-by-step explanation:

Coordinates of a point are usually represented by (x, y) where x describes the horizontal distance from the y-axis and y describes the vertical distance from the x-axis.

Point A

4 units from the y-axis ⇒ x = 4

6 units from the x-axis ⇒ y = 6

A = (4, 6)

Point B

2 units from the y-axis ⇒ x = 2

9 units from the x-axis ⇒ y = 9

B = (2, 9)

Point C

0 units from the y-axis ⇒ x = 0

4 units from the x-axis ⇒ y = 4

C = (0, 4)

Point D

Allie has mixed up the x and y coordinates of D.

7 units from the y-axis ⇒ x = 7

3 units from the x-axis ⇒ y = 3

D = (7, 3)

Answer:

D

Step-by-step explanation:

because in D one input value (3) has 2 different assigned output values (0 and -4).

that violates the definition of a function, where every input value must have exactly 1 assigned output value (but the output values themselves don't have to be different for different input values, so, e.g. A is still a function).

Answer:

k is 23876

Step-by-step explanation:

you have to multiply 254 and 94 by eachothe then that's your answer!

4/3 of a number is more than 3/4 of its number by 1 . find the number .

According to question 4/3 of a number is equal to :

[tex] \longmapsto \: \frac{4}{3} \times x[/tex]

Which means ,

[tex]\longmapsto \: \frac{4x}{3} [/tex]

According to question 3/4 of a number is equal to :

[tex]\longmapsto \: \frac{3}{4} \times x[/tex]

Which means ,

[tex]\longmapsto \: \frac{3x}{4} [/tex]

Now , forming equation :

As the question says that 4/3 of a number is more than 3/4 of its number by 1 . So :

[tex]\longmapsto \: \frac{4x}{3} = \frac{3x}{4} + 1[/tex]

Now , transposing 3x/4 to left hand side :

[tex]\longmapsto \frac{4x}{3} - \frac{3x}{4} = 1[/tex]

Now , taking L.C.M :

[tex]\longmapsto \: \frac{4(4x) - 3(3x)}{12} = 1[/tex]

Now by calculating :

[tex]\longmapsto \: \frac{16x - 9x}{12} = 1[/tex]

Now Subtracting 16x with 9x and transposing 12 to right hand side :

[tex]\longmapsto \: 7x = 12[/tex]

So ,

[tex]\longmapsto \: \boxed{ \bold{ x = \frac{12}{7} }}[/tex]

Applying a subtraction operation, it is found that his new ERA was of 3.17.

ERA is a baseball concept, but understanding of baseball is not relevant to this question.

One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:

ERA = 3.91 - 0.74 = 3.17.

His new ERA was of 3.17.

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Answer: 37

Step-by-step explanation:

            range = max - min

max = maximum value in a data set

min = minimum value in a data set

         Maximum value: 57

         Minimum value:   20

                       Range: 37

Answer:

37

Step-by-step explanation:

First of all, let's define what range is. The range is the highest value of a set of numbers minus the lowest value of the same set. In this case, your highest value is 57 and your lowest value is 20. The sum would be 57 - 20 which would equal 37 and that is your answer.

Hope I helped you out :)

Answer:

Step-by-step explanation:

Answer:

29 i

Step-by-step explanation:

As the expression given in the question.

= (2 - 5i) (p + q)i

Simplify the above

= (2 - 5i) (pi + qi)

= 2pi + 2qi - 5pi²- 5qi²

As i² = -1

Put in the above

= 2pi + 2qi + 5p +5q

= 2i × 2 + 2i × 5i + 5 × 2 + 5 × 5i

= 4i + 10i² + 10 + 25i

As i² = -1

= 4i - 10 + 10 + 25i

= 29i

Thus the value of the (2 – 5i)(p + q)i is 29i .

The milk can is in the shape of a cylinder.

The surface area of cylinder is defined as the sum of curved surface and the two circular bases of the cylinder;

‎ㅤ‎ㅤ‎ㅤ➙ (curved surface ) + 2(base area )

‎ㅤ‎ㅤ‎ㅤ➙ 2πrh + 2πr²

‎ㅤ‎ㅤ‎ㅤ➙ 2πr( h + r )

Here, in this question we have;

Therefore, Surface Area ( S.A ) :

➝ S.A = 2πr( r + h )

➝ S.A = 2 × π × 1 ( 1 + 6 )

➝ S.A = 2π ( 7 )

➝ S.A = 2 × 3.14 × 7

➝ S.A = 14 × 3.14

➝ S.A = 43.96cm²

Answer:

Surface area of cylindrical milk can is 43.96cm²

Step-by-step explanation:

Given :-

To find:-

Solution:-

formula for surface area cylindrical milk can :-

2πr(h+r)

putting the known values ,

2 × 3.14 × 1 (6+1) cm²

Surface area :- 43.96 cm²

Answer:

4502

Step-by-step explanation:

6884+78=6962

6962-2460=4502

Answer:

a is less than 0

Step-by-step explanation:

The value of a in this function is a is less than 0 .

A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x.

According to the question

Radical function that can be written in the form

[tex]f(x)=a(x+k)^{1/n} +c.[/tex] ------------------------(1)

By solving this equation we will get value of a and c

differentiating the equation

[tex]f'(x)=\frac{1}{n}* (a(x+k)^{1/n-1})[/tex]

therefore

[tex]((x+k)^{1/n-1}) > 0[/tex]

As graph is decreasing monotonically  

[tex]\frac{a}{n} < 0[/tex]

as n will be always n>0 ,

so a < 0

Now taking value of f(x)= 0 in equation (1)

[tex]f(x)=a(x+k)^{1/n} +c[/tex]

[tex]0 =-a(x_{0} + k)^{1/n} +c[/tex]   as (a < 0)

[tex]0=-a(k)^{1/n} +c[/tex]

[tex]-c =-a(k)^{1/n}[/tex]  multiplying (-1) both side

[tex]c =a(k)^{1/n}[/tex]  

i.e

c > 0

Hence, the value of a in this function is a is less than 0 .

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Answer:

∠5 = 90°

∠3 =90

Step-by-step explanation:

∠4 + ∠5 = 180   {Linear pair}

90 +∠5 = 180

      ∠5 = 180 - 90

∠5 = 90°

∠3 = ∠4   {Verically opposite angles}

∠3 = 90°

Answer:

Lines can be divided in smaller segments by using ratios

The coordinates of B are:

The given parameters are:

The coordinate of B is calculated using:

So, we have:

Simplify fraction

Hence, the coordinates of B are:

Step-by-step explanation:

Answer:

positive interger.....

Check the picture below.

so, let's get the volume of the prism.

then let's get the volume of the smaller cube.

then let's see how many times the volume of the cube goes into the prism's volume, so in short a division.

[tex]\stackrel{\textit{prism's volume}}{\left( \frac{5}{2} \right)(2)(1)\implies 5~cm^3}~\hfill \stackrel{\textit{cube's volume}}{\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies \frac{1}{8}~cm^3} \\\\[-0.35em] ~\dotfill\\\\ 5\div \cfrac{1}{8}\implies \cfrac{5}{1}\div \cfrac{1}{8}\implies \cfrac{5}{1}\cdot \cfrac{8}{1}\implies 40~~cubes[/tex]

Answer:

[tex]\frac{1}{28}[/tex]

__________________________________________________________

When doing problems like this where you have to divide fractions by whole numbers, you can try skip counting or multiplying.

So:

[tex]\frac{1/4}{7} = 28[/tex]because it skip counts 28 times.

28 as a fraction is [tex]\frac{28}{1}[/tex], which we have to flip to make [tex]\frac{1}{28}[/tex] as our answer.

__________________________________________________________

Ask in the comments box.

Step-by-step explanation:

hope it will help you

thank you

Answer:

Step-by-step explanation:

The line y = 3 is a horizontal line.

*View the attached graph*

Hope this helps!

Answer:

= - 9/8

Step-by-step explanation:

(-13/5) * x = 117/40    multiply both sides by  - 5/13

     x =  117 / 40  *  - 5/13  = - 9/8

The name of the shape depicted in the graph below is rose, so the answer is A.

A rose is a flat curve resembling a symbolic image of a flower. Geometrically, it is the algebraic or transcendent curve whose graph is characterized by a series of windings around a central point.

In the best known cases, these windings produce figures in the shape of a rose window, from which its name derives from.

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In monthly sales would mr. gonzalez need to have $100000

Mr. Gonzalez earns his living as a salary plus commission employee, then his annual earnings can be represented by

Monthly earnings=a+bx

Where a =his annual salary (fixed),

b = the percentage of sales commission and

X =represents the volume of sales made each year.

Therefore When  Mr. Gonzalez annual salary is $18,000 and makes a commission of 4%, his annual sales that will enable him earn an annual salary of $60,000 will be equal to

$60000 = $18000 + 0.04X

$60000 - $18000 = 0.04X

$48000 = 0.04X

0.04X = $1200000

X = $48000/0.04=12000000

X=$12000000

Therefore, his monthly sales is given by his  earnings divided evenly each month is equal to

$1200000/12=$100000

So the option c is correct.

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Answer:c

Step-by-step explanation:

Answer:

30[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The triangle given is a special right triangle with angle measures as follows:

45-45-90

The side lengths for this special triangle is represented with a-a[tex]\sqrt{2}[/tex]-a[tex]\sqrt{2}[/tex]

a represents the side length that sees hypotenuse and it is 30 so x and y

30[tex]\sqrt{2}[/tex]

Answer:

rhe base a for u

Step-by-step explanation:

kk

Answer:

520/9 = 57.77....8

Step-by-step explanation:

4x 10/3 x 13/3= 130/9 x4=520/9

Answer:

57 7/9

Step-by-step explanation:

4*4 1/3*4 1/3 = 57 7/9

Answer:

irrational

Step-by-step explanation:

Use the Pythagorean theorem.

5² + 6² = c²

25 + 36 = c²

c² = 61

7² = 49

6² = 64

61 is between 7² and 8², so it is not rational.