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11 months ago

K(2, 7), L(6, 12), M(13, 13), N(9.8) (Slope Formula) is it a parallelogram?

1 answer:

8 0

angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.

What in mathematics is a parallelogram?

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).
A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Slope Formula: y2-y1/x2-x1

KL: 12-7/6-2 = 5/4

LM; 13-12/13-6 = 1/7

MN: 8-13/9-13 = 5/4

KN: 7-8/9-2 = 1/7

Since angles and sides opposite one another on a parallelogram are congruent, we can say this is a parallelogram because there are congruent.

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A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

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6 0

2 years ago

Need help. greatly appreciated

gizmo_the_mogwai [7]

1. It must be divisible by 2 and 3. It IS divisible by 2. it IS divisible by 3. No remainder.
2. Add the digits and see if the sum is divisible by 3. Apply this rule to both numbers. 3 is not a common factor.
3a. 639
3b. 1035
3c. 179

7 0

2 years ago

HELP PLS Last year 15 students earned an A in math class. If I had 128 students, what percent of students did NOT earn an A?

BabaBlast [244]

Answer:

88%

Step-by-step explanation:

128-15=113

113/128=.882

88%

8 0

2 years ago

30 point for this plz help!! And explain how you got you answer

ch4aika [34]

To find the sales price of the DVD, you would multiply the price and sale percent to get the sale price.

You would need to turn 20% into a decimal to multiply it with 9, so you would move the decimal place two times to the left: From 20. to→ .20

In this case: 9 × .20 = 1.8

Then you would subract the sub price by the sales price

9 - 1.8 = 7.2

The sales price of the DVD would be $7.20

4 0

3 years ago

Read 2 more answers

A scout troop planned to take a bus for an overnight trip to a campground in a nearby state. The bus will cost $360 to rent. The

joja [24]

Let x represent the number originally signed up.
.. 360/x -6 = 360/(x +3)
.. 360*(x +3) -6x(x +3) = 360x . . . . . multiply by the product of denominators
.. 360x +1080 -6x^2 -18x = 360x
.. x^2 +3x -180 = 0
.. (x +15)(x -12) = 0
Solutions are x = {-15, 12}

12 members went on the trip.
_____
The problem wording does not make clear whether the original number (12) or the number suggested by the bus company (15) went on the trip. It would be most reasonable for 15 to go, if the troop had people who were willing.

8 0

3 years ago