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3 years ago

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Helen designs a rectangle with an area of 225 square units. her rectangle is the largest rectangle( that is the rectangle with l

argest area) with whole-number side lengths that can be made from the perimeter of the rectangle. what are the lengths and width of the rectangle

1 answer:

givi [52]3 years ago

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A (0, 2) and B (6,6) are points on the straight line ABCD.

elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance is denoted by: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Let's find the distance between A and B:

d = $\sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}$

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = $\sqrt{(6-a)^2+(6-b)^2}$

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0

3 years ago

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a store is selling uniform shirts for 18.95 each. if samuel has a coupon for 1/4 off the price, how much would he pay for the sh

balandron [24]

First take the original price and multiple by 1/4 or .25. You should get 4.73 then you subtract that from 18.95 and your answer is 14.22

5 0

3 years ago

3x+y=115x-y=21 Directions: Solve each system of equations by elimination. Clearly identify your solution.

olchik [2.2K]

To solve, we will follow the steps below:

3x+y=11 --------------------------(1)

5x-y=21 ------------------------------(2)

since y have the same coefficient, we can eliminate it directly by adding equation (1) and (2)

adding equation (1) and (2) will result;

8x =32

divide both-side of the equation by 8

x = 4

We move on to eliminate x and then solve for y

To eliminate x, we have to make sure the coefficient of the two equations are the same.

We can achieve this by multiplying through equation (1) by 5 and equation (2) by 3

The result will be;

15x + 5y = 55 ----------------------------(3)

15x - 3y =63 --------------------------------(4)

subtract equation (4) from equation(3)

8y = -8

divide both-side of the equation by 8

y = -1

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1 year ago

It took Brian 6 hours to drive to the sales conference. He took the same route on the way back home, but

g100num [7]

Answer: 54 mph

Step-by-step explanation:

d-the distance

s+9 - the speed to the conference

d=6*(s+9)

s- is the speed on the way back home

d=7*s

so 6*(s+9)=7*s

6s+54=7s

-6s -6s

54= 7s-6s

s=54 mph

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3 years ago

When a principal amount, P, is invested at an annual interest rate,r, and compounded n times per

romanna [79]

Answer:

2

Step-by-step explanation:

A = P( 1+r/n) ^ (nt)

P is the amount invested

r is the rate

n is the number of times per year the interest is compounded

t is the number of years

every 6 months is twice a year

so n is 2

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3 years ago

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