The volume of the cube is given as V= x³, where x is the side length of the cube. Find the domain of the volume of
the cube.

Answer:

  (a)  x = 12

Step-by-step explanation:

The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.

__

  [tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]

_____

Additional comment

You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.

Answer:

For 60 gallons of fuel, the airplane would weigh 2430 gallons.

Step-by-step explanation:

Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.

[tex]\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}[/tex]

Let this be the equation of straight line.

We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.

[tex]\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430[/tex]

So, the airplane weight is 2430 gallons.

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Answer:

(x=4, y=-11) (x=-6, y=29)

Step-by-step explanation:

The solution is in the picture above...

Answer:

D) 20

Step-by-step explanation:

Hope It Helps!!!

[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]

[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]

Answer:

a²​(a²​-a+2)

Step-by-step explanation:

Solution Given:

a⁴-a³+2a²​

first taking common a²​

we get

a²​(a²​-a+2) which is a required answer.

1. 6 km ≈ 3.73 mi

2. 2.5 L ≈ .66 gal

3. 90 lb ≈ 40.82 kg

The value of y if x is equal to 5 is 75 and the value of y when x = 7 is 8/7

Variations shows the relationship between variables.

4) If y varies directly as x², hence;

y = kx²

27 = 9k
k = 3

In order to determine y if x = 5

y = 3(5*5)
Y = 75

Hence the value of y if x is equal to 5 is 75

5) If y varies inversely as x, hence;

y = k/x
k = xy
k = 16(1/2)

k = 8

If x = 7, the value of y will be;

y = 8/7

Hence the value of y when x = 7 is 8/7

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Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:

n = 600/5 = 120.

The proportion of gold bars is given by:

p = 13/(13 + 17) = 13/30

Hence, out of 120 bars, the number of gold bars is given by:

nG = 120 x 13/30 = 4 x 13 = 52.

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Answer:

s = 12 and p = 17

Step-by-step explanation:

→ Set up 2 simultaneous equations

p + s = 29

3s + 2p = 70

→ Rearrange the first equation for p as the subject

p = 29 - s

→ Substitute into 2nd equation

3s + 58 - 2s = 70

→ Solve

s = 12

→ Substitute into first equation

p + 12 = 29

→ Solve

p = 17

The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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Answer:

Your question does not make much sense but that was only because you were missing one variable which was 4.25 which was what you picked up on Saturday. but anyways you just add 7.75 and 4.25 and you'd end up with 12 so she has 12 pints of the blueberries she needs and to find out the remanding you just subtract from the 20.5 but its better to look at it like 20.50 because that's what it is and then you subtract 12 from 20.50 and you are left with 8.50.

Your answer is 8.5

The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

A mathematical notion called the line of the best fit connects points spread throughout a graph.

It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

From the data given, we can write the slope and y-intercept form:

y = mx + b

here, m = 10 and b = 300

y = 10x + 300

The number of fat grams in an item has that number of fat calories.

As we have the regression line:

y = 10x + 300

Put x = 1 in the regression line:

y = 10(1) + 300

y = 310 calories

For x = 14

y = 10(14) + 300 = 440

But the actual value from the graph is 330.

Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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Answer:

B - fixed rental for the book.

Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.

Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.

Answer:

Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save

Average speed of the whole trip is equals to 37.5 mph.

" Average speed is defined as the ratio of the total distance travelled to the total time taken."

Formula used

Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]

According to the question,

Total distance travelled = 300miles

Speed for first 150 miles = 30 miles per hour

For,  30  miles = 1hour

    ⇒150 miles = 5 hours

Speed for remaining 150 miles = 50 miles per hour

For,  50  miles = 1hour

    ⇒150 miles = 3 hours

Substitute the value in the formula to get average speed,

Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]

                          [tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]

Hence, average speed of the whole trip is equals to 37.5 mph.

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Answer:

B.

Step-by-step explanation:

It is the only one that is not a fraction or a decimal that terminates or repeats.

Answer:

Step-by-step explanation:

       [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is the y-intercept

  Find the slope with the given two points.

   [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]

Slope = -2/3 and choose any one the given points.

Substitute m = -2/3  and (5,6)  in the above equation and find 'b'

      [tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]

Equation of the line:

            [tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]

The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Carla babysits and tutors to make extra money.

She babysits for $5 an hour and tutors for $10 an hour.

She can only work at most 15 hours a week.

Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.

Then the system of inequalities to represent this situation will be

Let x be the number of babysits hours and y be the number of tutor's hours.

     x + y ≤ 15

5x + 10y ≤ 95

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Answer:

0.00893 feet elevation per 1 foot distance.

Step-by-step explanation:

The hill reaches an elevation of 250 ft (above sea level) over the course of 28,000 feet.  The average rate of change would be (250 ft)/(28,000 ft), or 0.00893 feet elevation/1 foot distance.

((0.00893 (feet up/foot distance))*(28,000 feet distance) = 250 feet  up (elevation).

Step-by-step explanation:

(X1,Y1) = (-2,2)

(X2,Y2) = (0,1)

• Find slope.

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 2)/(0 - (-2))

m = -1/2

The answer is C.

Answer:

radius = 8

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 64 ← is in this form

with r = [tex]\sqrt{64}[/tex] = 8

The slant height of the given cone will be 12.06 inches.

The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.

Given that:-

The slant height will be calculated as:-

Surface area = π r l

151.58 = π x 4 x l

l = 151.58 / ( π x 4 )

l = 12.06 inches.

Therefore slant height of the given cone will be 12.06 inches.

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Answer:

y = 5z

Step-by-step explanation:

added in the picture

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[ let the point at which line segments SV and RT intersects be O ]

[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]

[ Exterior angle = sum of opposite interior angles ]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]

( let it be equation 1 )

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]

[ Sum of angles of Triangle ]

[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]

( let it be equation 2 )

____________________________________

By comparing both equations :

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]

[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]

( Add 180° on both sides )

[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]

[tex]\qquad \tt \rightarrow \: y = 5z[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Median: 6

Range: 9

Mode: 7, appeared 3 times

The options that are true of the triangles include:

The complete question is given below:-

ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

The process of changing the location of the image on the coordinate system will be known as the translation.

It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.

This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.

Therefore the options that are true of the triangles include:

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Answer:

It is located to the right of the 0 on the line,

Step-by-step explanation:

the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.

Answer: [tex](x-10)^{2}+(y+3)^{2}=16[/tex]

Step-by-step explanation:

We know the center of the original circle is (-6, -3). After reflecting this over the line x=2, the new center is now (10, -3).

Thus, the equation of the circle is [tex](x-10)^{2}+(y+3)^{2}=16[/tex].

Answer:

x = 0 y = -5

x = 3 y = 4

Step-by-step explanation:

x² + y² = 25

y - 3x = -5

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

y = 3x-5

x² + y² = 25

x² + (3x-5)² = 25

(3x-5)(3x-5) = 9x² -15x -15x + 25

x² + 9x² -15x -15x + 25 = 25

x² + 9x² -15x -15x = 0

x² + 9x² - 30x = 0

10x² - 30x = 0

x(10x-30)=0

x = 0

10x-30=0

x = 3

y - 3x = -5

y - 3(0) = -5

y = -5

y - 3(3) = -5

y - 9 = -5

y = 4

Answer:

(4,3) and (0,-5) are both solutions where we have (x,y).

Step-by-step explanation:

Here are simplified steps:

https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input

Symbolab is an excellent tool for just most math.

Answer:

[tex] \sqrt[2]{3} + \sqrt{5} = \sqrt[2]{8} [/tex]

[tex] \sqrt{3 } - \sqrt[3]{5} = \sqrt[3]{2} [/tex]