Use slopes and y-intercepts to determine if the lines −3x+2y=−3 and 3x−2y=−3 are parallel.

In the given problem,  the skaters might collide at the point (7, 35) or (3, 51). This is derived by solving a system of created equations.

To find the points where the two skaters might collide, we need to solve the system of equations:

y = -4x + 63

y = -3x^2 + 26x

We can substitute the first equation into the second equation to eliminate y:

-4x + 63 = -3x^2 + 26x

Rearranging and simplifying, we get:

3x^2 - 30x + 63 = 0

Dividing both sides by 3, we get:

x^2 - 10x + 21 = 0

Factoring, we get:

(x - 7)(x - 3) = 0

So the possible values of x where the skaters might collide are x = 7 and x = 3.

To find the corresponding y-values, we can substitute these values of x into either equation. Using y = -4x + 63, we get:

When x = 7, y = -4(7) + 63 = 35

When x = 3, y = -4(3) + 63 = 51

Therefore, the skaters might collide at the point (7, 35) or (3, 51).

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-7 \(\frac{9}{16}\)

-2 3/4 = -2.75

-2.75^2 = -7.5625

-7.5625 = -7  \(\frac{9}{16}\)

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

D) 19

Step-by-step explanation:

biggest number minus smallest number

25-6=19

The length of the curve (and thus the total distance traveled by the particle along the curve) is

\(\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt\)

We have

x(t) = 3 sin²(t )   ==>   x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )

y(t) = 3 cos²(t )   ==>   y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )

Then

√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|

and the arc length is

\(\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt\)

Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.

Now,

• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)

• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)

so we split up the integral as

\(\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)\)

which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.

Answer:

AB is equal to AD because if you move from A to B, you would have to go 3 points toward the B, and then move one point toward B. Same for D. You must move 3 points toward D, then move one down.

Step-by-step explanation:

If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).

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Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.

Therefore option A is correct.

The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.

With reference to the table, the occupations that do not require a college degree are:

We were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.

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Answer:

24+12=36you find the total length

Answer:

3 feet

Step-by-step explanation:

Answer:

18%

Step-by-step explanation:

20.35-17.25=3.1

3.1/17.25=0.1797

0.1797x100=17.97

rounded to the nearest 10th

Answer:

2.1 < x <2.5

Step-by-step explanation:

i’m taking the test rn i’m not sure if it’s correct i’ll lyk!

Answer:

B on Edge

Step-by-step explanation:

Given that the region is enclosed by the x-axis and this curve:

You can graph the function using a Graphic Tool:

Noice that the area region you must calculate is:

Notice that it goes from:

To:

Therefore, you can set up that:

In order to solve the Definite Integral, you need to:

- Apply these Integration Rules:

Then, you get:

- Evaluate:

Hence, the answer is:

Answer:

OkStep-by-step explanation:

Answer:

12 x 2 − 54 x

Step-by-step explanation:

Answer:

(7x^2 -1)(x - 2).

Step-by-step explanation:

7x^3 - 14x^2 - x + 2

We can factor this by grouping - that is factoring the first 2 terms and the last 2:

= 7x^2(x - 2)  - 1(x - 2)      <-- the x - 2 is common to both parts so we have:

(7x^2 -1)(x - 2).

Answer:

You end up at point (7,5).

Step-by-step explanation:

Starting point:

The coordinates of the starting point are: x = 4, y = 6.

So

(4,6).

Move 3 units right:

Moving 3 units right is adding 3 to the x-coordinate. So

x = 4 + 3 = 7

(7,6).

Move 1 unit down:

Moving 1 unit down is subtracting 2 from the y-coordinate. So

y = 6 - 1 = 5.

You end up at point (7,5).

Answer:

Step-by-step explanation:

f(3)=-5(x+5)

     =5(3) +5

     =15+5

f(3)      =20

The given statement is true.

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

A similar problem about the volume of rectangular prisms is presented at brainly.com/question/22070273

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Answer:

-4/3

Step-by-step explanation:

(9-5)/(4-7)

4/-3

-4/3

Answer:

\(P(x\le 4\ or x> 10) = \frac{4}{7}\) or \(P(x\le 4\ or x> 10) = 0.5714\)

Step-by-step explanation:

Given

\(x = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}\)

Required

Determine \(P(x\le 4\ or x> 10)\)

Because the events are independent, the probability can be solved using:

\(P(A\ or\ B) = P(A) + P(B)\)

So, we have:

\(P(x\le 4\ or x> 10) = P(x \le 4) + P(x > 10)\)

When \(x \le 4\), we have: \(x = \{1,2,3,4\}\)

So:

\(P(x \le 4) = \frac{4}{14}\)

Also:

When \(x > 10\), we have: \(x = \{11,12,13,14\}\)

So:

\(P(x>10) =\frac{4}{14}\)

\(P(x\le 4\ or x> 10) = P(x \le 4) + P(x > 10)\) becomes

\(P(x\le 4\ or x> 10) = \frac{4}{14} + \frac{4}{14}\)

\(P(x\le 4\ or x> 10) = \frac{4+4}{14}\)

\(P(x\le 4\ or x> 10) = \frac{8}{14}\)

\(P(x\le 4\ or x> 10) = \frac{4}{7}\)

\(P(x\le 4\ or x> 10) = 0.5714\)

Answer:

15&12

Step-by-step explanation:

24-9=15

15-3=12

Answer

if there is 24 cookies in the jar and 9 cookies are eaten 15 cookies will left and if 3 cookies are also eaten so 12 cookies will left.

Step-by-step explanation:

Answer: I think it’s A sorrykf I’m wrong

Step-by-step explanation:

The sales Sam need to make $733.50 per week before taxes is $3475.

Given, Sam is paid $14 per hour plus 6% of sales.

If he worked 37.5 hours in one week, what would his sales need to make

$733.50 per week before taxes = ?

Let the sales be represented by x

Amount made from no of hours worked :

= $14 × 37.5 hours

=$525

Sales made = 6% of x

=0.06x

Total = 0.06x+$525

=$733.50

0.06x=733.50-$525

=$208.5

x=$3,475

Hence we get the required answer.

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Answer:

$652.89

Step-by-step explanation:

i believe this is the answer hope i helped :D

Answer:

d = 291 + n

Step-by-step explanation:

Given that,

Last week, Kira drove 291 miles. Then this week she drove n miles.

We need to find an expression for the total number of miles she drove in the two weeks. It can be calculate by adding distance force 2 weeks. So,

d = 291 + n

Hence, this is the required solution.