Ms. Remi is planning a dance recital for her students. The maximum duration for the recital is 120 minutes. Group dance performances last 8 minutes and solo dance performances last 3 minutes. x = the number of group dances on the program y = the number of solo dances on the program Which inequality in standard form represents this situation?
A) 3x + 8y ≥ 120
B) 3x + 8y ≤ 120
C) 8x + 3y ≥ 120
D) 8x + 3y ≤ 120

Answer:

Step-by-step explanation:

The  coordinates of E(4a, 0).

A midpoint is a point in the middle of the line connecting two points that lies between them. The midpoint is a point that lies in the middle of the line and is equidistant from the two points if a line is drawn to connect them.

The midpoint between two points whose coordinates are known to us can be found using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can also use the midpoint formula to determine the coordinates of the endpoint.

Given coordinates

A(-3a, -2b),  D(a, -2b), C(5a, -2b) and B(3a, 2b)

to find the coordinates of E,

and E is midpoint of B and C

for coordinates of midpoint is (x, y) = [(x₂ + x₁)/2, (y₂ + y₁)/2]

here B  = (3a, 2b) = (x₁, y₁)

and C = (5a, -2b) = (x₂, y₂)

x = (5a + 3a)/2 = 8a/2 = 4a

y = (-2b + 2b)/2 = 0/2 = 0

E(4a, 0)

Hence coordinates of E are (4a, 0).

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The area of the rectangular roof (both sides of the roof) = 1,360 ft²

Cost to cover both sides = $1,020

The area of a rectangle = (length)(width)

Area of both sides of the roof = 2(area of rectangle) = 2(40×17) = 1,360 ft²

Cost to cover both sides = 1,360 × 0.75 = $1,020

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Answer:

Z = 1.25

Step-by-step explanation:

[tex]\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=\frac{x-\mu}{\sigma}\\ \\Z=\frac{87-82}{4}\\ \\Z=\frac{5}{4}\\ \\Z=1.25[/tex]

Hence, Michael's z-score is 1.25, which means that he scored 1.25 standard deviations above the class average.

B. X is less than or equal to -4

Answer:

Step-by-step explanation:

Use a couple of ordered pairs on the graph and get the equation of the line:

The y-intercept is 2 and the slope is 10 - 2 = 8

The line is

Solve the system of equations by substitution to find the intersection

They will work 4 hours to get same amount of saving

Answer:

4 hours

Step-by-step explanation:

First, create a linear equation for Carlos using the graph.

Two points on the line:  (0, 2) and (1, 10)

[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{10-2}{1-0}=8[/tex]

Use the point-slope equation with the found slope and one of the points:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=8(x-0)[/tex]

[tex]\implies y=8x+2[/tex]

Now equate the equations for Mary Ann and Carlos, and solve for x:

[tex]\implies 6x+10=8x+2[/tex]

[tex]\implies 8=2x[/tex]

[tex]\implies x=4[/tex]

Therefore, Mary Ann and Carlos have saved the same amount after 4 hours work.

Answer:

is the ratio of the circumference of any circle to the diameter of that circle.

Step-by-step explanation:

Answer:

centre : (4;-5)

radius : 2

Answer:

x = 2 ; y = 12

Step-by-step explanation:

2x + 3y = 40

+ -2x +2y = 20

You solve for one of the variables by cancelling out one and making one the subject.

2x + 3y = 40.

+ -2x +2y = 20

5y = 60

5y/5 = 60/5

y = 12

Next, you solve for X by replacing the value of y in any of the equations.

2x + 3y = 40

2x + 3(12) = 40

2x + 36 = 40

2x = 40 - 36

2x = 4

2x/2 = 4/2

x = 2

To prove the equations are set, replace the values of X and Y in one of the equations.

2x + 3y = 40

2(2) + 3(12) = 40

4 + 36 = 40

40 = 40

Answer:

Step-by-step explanation:

Simplifying

2x + 13 = 0

Reorder the terms:

13 + 2x = 0

Solving

13 + 2x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 2x = 0 + -13

2x = 0 + -13

Combine like terms: 0 + -13 = -13

2x = -13

Divide each side by '2'.

x = -6.5

Simplifying

x = -6.5

Answer:

1134

Step-by-step explanation:

Formula for diameter=2 x r

(π is 3.14)

Formula for area= π x r^2

So all you basically have to do is go backwords with the first one then plug the radius into the second one normally

38/2=19

Now just plug it into your second equation

π x 19^2=1134.11494795

And lastly round that to 1134, easy! :)

The perimeter of the polygon will be (2x + 2xy + y + xz). Then the correct option is D.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The figure is given below.

The sides of the polygon are given as x, y, xz, x, xy, and xy.

Then the perimeter of the polygon will be

The perimeter of the polygon is given as the sum of all the sides of the polygon.

Then the perimeter will be

P = x + y + xz + x + xy + xy

P = 2x + y + 2xy + xz

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Answer:

I believe one is the answer your looking for

Step-by-step explanation:

Step-by-step explanation:

the upper (smaller) triangle and the complete triangle are similar.

that means the angles in both triangles are the same. and the lengths of all corresponding pairs of sides correlate with the same scaling factor.

therefore,

(8x - 10) / (8x - 10 + 18) = 25 / (25 + 15)

(8x - 10) / (8x + 8) = 25 / 40 = 5/8

8(8x - 10) = 5(8x + 8)

64x - 80 = 40x + 40

24x = 120

x = 5

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be

Then the intersection point will be given as

[tex]\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214[/tex]

Then by the integration, we have

[tex]\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\[/tex]

[tex]\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\[/tex]

On solving, we have

[tex]\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75[/tex]

Thus, the area of the region is 3.75 square units.

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The reference angle for a 240° angle is 60°

A reference angle is the angel that is found on the first quadrant of a a circle.

The angle that is being measured is in the third quadrant of a circle, we will subtract 180° from the given angle.

Therefore, the reference angle for a 240° is =

240-180= 60°

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Answer:

The original price

Step-by-step explanation:

I got it right

Answer:

I think option C is correct or it can be. B OPTION

As if we join B to C it will form a diagonal BC which will cut the shape into two right angled triangle

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

The maximum number of months the computer could be kept so that it is cheaper to rent than to buy is 10 months.

The first step is to determine the month in which the two options would have the same cost. The equation that can be used to determine this value is:

$1890 = $900 + 90t

90t = 1890 - 900

90t = 990

t = 990 / 90

t  = 11 months

The maximum number of months = 11 months - 1 = 10 months

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The factors of the given quadratic expression are (3x+4) and (2x-15)

From the question, we are to determine the factors of 6x²+37x-60

The given quadratic expression can be factored as shown below

6x² + 37x -60

This becomes

6x² -45x + 8x -60

3x(2x-15) +4(2x-15)

Then,

(3x+4)(2x-15)

Hence, the factors of the given quadratic expression are (3x+4) and (2x-15). The correct option is the second option (3x+4) and (2x-15)

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Answer:

(3x+4) and (2x-15)

Step-by-step explanation:

Explanation:

The x coordinates of points A and B are 2 and -2 respectively. Add them up and divide by 2 and we would get (A+B)/2 = (2+(-2))/2 = 0/2 = 0.

The x coordinate of the midpoint is 0.

The y coordinate of the midpoint follows the same idea, but we focus on the y coordinates of course. You should find the y coordinate of the midpoint is 0.

The midpoint is at (0,0) as the diagram shows.

Answer: Choice A.

(0, b)

==================================================

Explanation:

Pick any random 3 numbers you want for a,b,c.

The points U, W and Z become

Or in short,

Plot each of those points on the same xy grid.

Next, using a different color, plot each of the answer choices.

You should find that point A helps form a parallelogram, while the other answer choices don't lead to a parallelogram.

See the screenshot below. I used GeoGebra to make the diagram. Desmos is another useful tool as well.

Answer:

See below

Step-by-step explanation:

4 sin^2 -1 =0

sin^2 = 1/4          Take sqrt of both sides

sin = ± 1/2       < ===== this is likely where he went wrong (forgot + - )

 answer:  pi/6    5pi/6    7 pi/6     11pi/6

Interpreting (1,15) with (4,60), found that (4,60) is 4 times of the coordinate (1,15).

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.

For interpreting we have to find the relation between (1,15) and (4,60)

We have, (1,15)

For x- coordinate 1, y- coordinate will be 15

Now,

let us take x- coordinate=2 then y- coordinate =30

again, if x-coordinate = 3 then y-coordinate  = 45

lastly, if the x-coordinate =4 then y-coordinate = 60

That means (4,60) is the 4 times of the coordinate (1,15) i.e., the x-coordinate is 4 times as well as the y- coordinate is 4 times.

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The equivalent expression of the provided expression g²h√(5g) is √(5g⁵h²). Then the correct option is B.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

→ g²h√(5g)

Then the function can be written as

→ √(5g⁵h²)

Then the equivalent expression of the provided expression g²h√(5g) is √(5g⁵h²).

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Answer:

7.5 - 3.8 = m

Step-by-step explanation: