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2 years ago

Find the point of intersection of the lines:

Mathematics

2 answers:

avanturin [10]2 years ago

8 0

Answer:

the answer is a

Step-by-step explanation:

Marta_Voda [28]2 years ago

3 0

The answer is A my guy hope this helps

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A number n, decreased by 10

Anettt [7]

Answer:

n - 10

Step-by-step explanation:

7 0

1 year ago

Read 2 more answers

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

What is the relationship among direct variation,lines,rates of change, and slope?

JulsSmile [24]

A direct variation is a proportional equation. Such as:

For every 3 cookies, linda gets 1 glass of milk. The equation for this is y=3x where y is the glasses and x is the cookies. this is a direct variation. It also has a linear line. Linear means straight. Rate of change and slope are the exact same thing. They are the value of 'm' in y=mx+b

5 0

3 years ago

NEED HELP PLEASE ITS URGENT <br> thanks- BRAINLIST only for correct answers love :)<br> Thank you!!

Rashid [163]

Answer:

true flase true

Step-by-step explanation:

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2 years ago

A box is to be made from a rectangular piece of corrugated cardboard, where the length is 8 more inches than the width, by cut

Ksenya-84 [330]

The volume of a box like this is found by multiplying the length times the width times the height. We are told that the length is 8 more inches than the width, so the width is w and the length is w + 8. If we cut away 3 square inches from each corner, the height when we fold up those corners is going to be 3. The volume is given as 27, so our formula looks like this: $27=(3)(w)(w+8)$ . When we do that multiplication, we have $27=3w^2+24w$ . We need to solve for w so we can then solve for h. Move the 27 over and set the quadratic equal to 0. $3w^2+24w-27=0$ . We can then factor out a 3 to make the job easier: $3(w^2+8w-9)=0$ . Now we can factor to solve for w. The 2 numbers that add up to 8 and multiply to -9 are 9 and -1. So (w+9) = 0, (w-1) = 0, or 3 = 0. Of course 3 doesn't equal 0, so that's out. w + 9 = 0 so w = -9. w - 1 = 0 so w = 1. There are 2 things in math that can never EVER be negative and those are time and distance/length. So -9 is out. That means that w = 1. But don't forget that there was 6 inches cut off each side, so the width is 1 + 3 + 3 which is 7. The length is w + 8 which means that the length is 7 + 8 or 15. Those are the dimensions of the rectangle before it was cut.

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3 years ago