A college student is moving into a campus dormitory. The student rents a moving truck for $19.95 plus $.99 per mile. Before returning the truck, the student fills the tank with gasoline, which costs $65.32. The total cost is $144.67. How many miles did the student drive the truck?

Answer: x=6  y=6

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{4x-3y=6} \atop {6x-5y=6}} \right.\\[/tex]

Since the right parts of the equation are equal, therefore the left parts of the equation are also equal:

[tex]4x-3y=6x-5y\\4x-3y+5y=6x-5y+5y\\4x+2y=6x\\4x+2y-4x=6x-4x\\2y=2x\\[/tex]

Divide both parts of the equation by 2:

[tex]y=x\\Hence,\\4x-3x=6\\x=6\\Thus,\\x=y=6[/tex]

The measurement that is closest to the volume of the cylinder in cubic feet is: 15.7 Feet. (Option B)

Recall that volume is

V = πr²h

Given:

h = 5 feet

r = 2/2 = 1

Hence

V = 5 x 1 x 22/7

= 15.7142857143

Hence, the cylinders volume in cubic feet is given as:

[tex]$\approx$[/tex] 15.7 ft

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Answer: 15.7 ft3

Step-by-step explanation:

Measure of angle 1 is 50° and that of angle 2 is 130°

The sum of all the angles on a straight line is equal to 180°.

Here, we are given two angles ∠1 and ∠2

Also, we are given that

m∠1 = (x+24)°

and m∠2 = 5x°

As we can see from the given figure, ∠1 and ∠2 lie on a straight line

⇒ m∠1 + m∠2 = 180

⇒ (x+24) + 5x = 180

x + 24 + 5x = 180

x + 5x + 24 = 180

6x + 24 = 180

6x = 180 - 24

6x = 156

x = 156/ 6

x = 26

Therefore,

m∠1 = 26 + 24

= 50

and m∠2 = 5(26)

= 130

Thus, the measure of the two angles is 50° and 130°

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Your question was incomplete. Check for the missing figure below.

One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

Here,

A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .

We have to find the leg of each piece.

What is Length, Width and height?

The length, width and  height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.

Now,

If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.

And, since the other piece is 12 inches longer than your first piece, its length is x + 12.

And, when you place these two pieces back together, their lengths should add up to be 72 inches.

You can write this last statement about adding the two pieces together to get a 72 inch piece

In equation form as:

x + (x+12) = 72

2x + 12 = 72

To solve this begin by subtracting 12 from both sides;

2x = 60

Now just divide both sides by 2 to find that:

x = 30

So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.

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Answer:

yes it can be bc it is repeating

Answer:

12/15

Step-by-step explanation:

The equation for DE is [tex]8+9x[/tex]

According to the question statement, Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x. We are supposed to find DE.

For solving this we need to know about Linear Equations and Bisector of a line.

Given that, DS = 10 + 3x and ES = -2 + 6x.

S is mid point of line DE as RQ bisects it.

So DS = SE

And DE = DS + SE

Hence, DE = [tex]10 + 3x + (-2 + 6x)[/tex]

DE = [tex]10 + 3x -2 + 6x[/tex]

DE = [tex]10 -2 +3x+6x[/tex]

DE = [tex]8+9x[/tex]

Hence equation of DE is 8+9x.

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Answer: $4.55

Step-by-step explanation:

Just subtract $10.00 from $5.45 and you will get $4.55

Answer:

$4.55

Step-by-step explanation:

To find the change, we have to subtract the money they give you ($10) with the guest total ($5.45).

10 - 5.45

= $4.55

$4.55 is your answer.

Take care and have a lovely rest of your day! :)

The required function is d = 360 - 35h, 0 ≤ h ≤ 10.29.

We know that distance travelled is equalled to speed multiplied by time.

Let d be the distance from the destination.

Let d₁ be the distance travelled in h hour.

And h be the number of hours driven.

Given that the average speed is 35 miles per hour.

Therefore, we have d₁ = 35h

And the initial distance from the destination is 360 miles.

Note at time h= 0 the distance from the destination is the maximum which is 360 miles.

Therefore, we have d₁ = 35h

Distance from the destination is 360 - d₁.

⇒ d = 360 - d₁

⇒ d = 360 - 35h

Time taken to reach destination = d/v = 360/35 = 10.29 hours

Therefore the required function is d = 360 - 35h, 0 ≤ h ≤ 10.29

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Answer:

b

Step-by-step explanation:

The equation for the line that connects the locations is y = 2x + 5.

The slope of a line, commonly known as the gradient, is defined as the value of the steepness or direction of a line in a coordinate plane. Slope can be determined using many ways given the equation of either a line or the coordinates of points on the straight line. . The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

x₁ = 1

y₁ = 7

x₂ = -3

y₂ = -1

To obtain the equation of a line, we must first determine its slope. This is computed as:

m = [y₂ - y₁ ]/[x₂ - x₁]

Substituting the value we get:

m = [(-1) - 7 )/((-3) - 1)]

  = -8/-4

   = 2

The slope of the line = 2.

The line's intercept is:

The slope is the next step toward solving for  a such equation of the line.

A typical linear equation is presented as:

y = mx + c

Let us substitute the slope and intercept values.

y = 2x + 5

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Answer: No solution

Step-by-step explanation:

5r + 5 = 3(5r - 4) - 10r  Do multiplication

5r + 5 = 15r - 12 - 10r  combine like terms

5r + 5 = 5r - 12        This is impossible. 5r cannot equal 5 and 12 meaning there is no value of r that makes this equation true so there's No Solution.

You could continue

5r + 17 = 5r

-5r       =-5r

17=0 which is also not true

Answer:

Step-by-step explanation:

The line passes through the points:

Since all x- coordinates are same, the line is vertical and its equation is:

Answer:

n = 18

Step-by-step explanation:

The sides in a regular polygon are equal in length.

⇒ BC = CD

If BC = CD then ΔDCB is an isosceles triangle.

As the base angles of an isosceles triangles are equal:

⇒ ∠DBC = ∠BDC = 10°

Interior angles in a triangle sum to 180°.

⇒ ∠DBC  +∠BDC + ∠DCB = 180°

⇒ 10° + 10° + ∠DCB = 180°

⇒ 20° + ∠DCB = 180°

⇒ ∠DCB = 180° - 20°

⇒ ∠DCB = 160°

Therefore, the interior angle of the regular polygon is 160°.

The interior angles of a regular polygon are equal in size.

[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Interior angle of a polygon}\\\\$\dfrac{(n-2) \times 180^{\circ}}{n}$\\\\where $n$ is the number of sides.\\ \end{minipage}}[/tex]

To find the number of sides, equate the formula to the found value of the interior angle and solve for n:

[tex]\begin{aligned}\implies\dfrac{(n-2) \times 180^{\circ}}{n} & =160^{\circ}\\(n-2) \times 180^{\circ} & =n \times 160^{\circ}\\ 180(n-2) & = 160n\\180n-360 & = 160n\\180n & = 160n+360\\180n-160n & = 360\\20n & = 360\\n &= \dfrac{360}{20}\\n & =18\\\end{aligned}[/tex]

Therefore, the regular polygon has 18 sides.

As given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

As given in the question,

Let 'h' represents the number of hours

Paul's Bikes rents bikes for $11 plus $4 per hour

Amanda paid $31 to rent a bike

Required equation is:

31 = 11 + 4h

⇒4h = 20

⇒h = 5hours

Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

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Answer:

Both sentences are false.

Step-by-step explanation:

Let's solve for x:

2x + 4y - 31 = 123

2x = 123 - 4y + 31

2x = 154 - 4y

x = 77 - 2y

Let's solve for y:

x = 77 - 2y

2y = 77 - x

y = 38.5 - 0.5x

The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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Answer:

The multiple of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+ 45+48+51+54+57+60+63

=690

A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9

[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)

Divide the given equation (1)  by [tex]$\sqrt{ y} $[/tex]  giving

[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.

Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]

Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].

Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get

[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]

(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex]  or

[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]

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The equation -2x=3/8 is not a literal equation.

A literal equation can be defined as an equation which primarily of letters.

It is an equation  made up of several variables or letters.

Examples of literal equations are;

We can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.

Given the equation;

-2x=3/8

We can see that there is only one variable to be worked out and hence, is not a literal equation.

Thus, the equation -2x=3/8 is not a literal equation.

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When the value of x = 1, the value of y = 729.

An inverse relationship is one where the value of one parameter decreases as the value of the second parameter increases. It is frequently described as a bad relationship.

Now, as per the question.

y varies inversely with the cube of x.

y ∝ 1/x³

Removing inverse, a constant of proportionality will come (say k)

y = k/x³

k = x³y.

When x = 9 then y = 1. Substitute the values and find k.

k = 9³(1)

k = 729

Now, estimate the value of y when x = 1.

y = k/x³ ( put the value of k and x )

y = 729/1³

y = 729

Thus, the value of y when the value of x = 1 is 729.

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The change of Mandy's score is 600 points.

Here,

Mandy is playing a game.

Early in the game she had - 250 points.

Now, Mandy has 350 points.

We have to find the change of Mandy's score.

What is difference of two number?

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.

Now,

Early in the game she had - 250 points.

And, now Mandy has 350 points.

So, The change of Mandy's score = 350 - (-250) = 350 + 250 = 600

Hence, The change of Mandy's score is 600 points.

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diamater:

[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]

circumference:

[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]

Hope that I helped you!

Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

A midpoint is simply a point that divides a segment into two equal halves.

Given the data in the question;

Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.

2( Line segment YE ) = Line segment YT

Plug in the given values and solve for x.

2( Line segment YE ) = Line segment YT

2( 3x + 1 ) = 14

Expand using distributive property

2 × 3x + 2 × 1 = 14

6x + 2 = 14

Collect like terms

6x = 14 - 2

6x = 12

6x/6 = 12/6

x = 12/6

x = 2

Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

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Answer:

Step-by-step explanation:

1/144

hope this helps :)

Answer: 2000π mm^2

Step-by-step explanation:

A=area of entire circle. B=Area of Inside circle. C=Area of shaded region

A-B=C

π(120/2)^2 -π(80/2)^2=

π(60)^2 -π(40)^2=

3600π-1600π=2000π mm^2

The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .

Absolute Error is defined as the difference between The Actual value and the estimated value .

Percent Error is defined as the difference between The Actual value and the estimated value in comparison to actual value expressed in percent .

[tex]Percent Error=\frac{|Estimated Value-Actual value|}{Actual Value} *100[/tex]

Given that the Estimated value =300 pounds

Actual Value=286 pounds

Absolute Error=300-286=14 pounds

Percent Error=[tex]\frac{|300-286|}{286} *100[/tex]

=[tex]\frac{14}{286} *100=4.89[/tex]%

Therefore , The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .

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Answer:

Step-by-step explanation:

[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]

simplest form : [tex]\frac{53}{30}[/tex]