Angelita and Cynthia like to play a video game against each other that is scored by round. The goal is to

AysviL [449]

9514 1404 393

Answer:

y = 21

Step-by-step explanation:

In straightforward fashion, we can find the midpoints of the two segments, and set the distance between them equal to 10.

M = midpoint of AB

M = (A+B)/2 = ((-1, 0) +(-3, 6))/2 = (-4, 6)/2 = (-2, 3)

N = midpoint of CD

N = (C+D)/2 = ((3, 1) +(5, y))/2 = (8, 1+y)/2 = (4, (1+y)/2)

Then the distance MN is given by the distance formula.

|N-M| = 10 = √((4 -(-2))² +((1+y)/2 -3)²) . . . . . distance formula*

100 = 36 +((1+y)/2 -3)² . . . . . square both sides

64 = ((1 +y)/2 -3)² . . . . . . . . . subtract 36

8 = (1 +y)/2 -3 . . . . . . . . . . . . (positive) square root

11 = 1+y/2 . . . . . . . . add 3

22 = 1+y . . . . . . . . . multiply by 2

21 = y . . . . . . . . . . . subtract 1

_____

* The distance formula is an application of the Pythagorean theorem. Basically, the differences of x- and y-coordinates are taken to be the legs of a right triangle. They length of the hypotenuse is the distance between the two points.

d² = (x2 -x1)² +(y2 -y1)² . . . . . . . from the Pythagorean theorem

d = √((x2 -x1)² +(y2 -y1)²) . . . . . the usual distance formula

8 0

3 years ago

I NEED HELP WILL GIVE BRAINLIEST!! PLEASE HELP ME ASAP!!!!

GenaCL600 [577]

Answer:

A. The length of the second leg is 8.5 inches

B. The length of the three-dimensional diagonal is 9.9 inches

Step-by-step explanation:

Let us revise the relation between the hypotenuse and the two legs of a right triangle

(hypotenuse)² = (vertical leg)² + (horizontal leg)²

∵ The length of the rectangular box = 8 inches

∵ The width of the rectangular box = 3 inches

∵ The height of the rectangular box = 5 inches

∵ Length and width are perpendicular to each other

∴ The Δ whose legs are 3 and 8 is a right triangle

In the right Δ whose legs are 3 and 8

∵ (hypotenuse)² = (3)² + (8)²

∴ (hypotenuse)² = 9 + 64

∴ (hypotenuse)² = 73

- Take √ for both sides

∴ hypotenuse = $\sqrt{73}$ = 8.544003745

- Round it to the nearest tenth of one inch

∴ hypotenuse = 8.5 inches

A.

The 3-dimensional diagonal is the hypotenuse of a right triangle whose legs are the vertical edge and the hypotenuse of the right triangle whose legs are 3 and 8

∵ The hypotenuse of the right triangle whose legs are 3 and

8 is 8.5 inches

∴ The length of the second leg is 8.5 inches

B.

In the right triangle whose hypotenuse is the 3-dimensional diagonal and legs are the vertical edge , the hypotenuse of the right triangle whose legs are 3 and 8

∵ (3-dimensional diagonal)² = (5)² + (73)²

∴ (3-dimensional diagonal)² = 25 + 73

∴ (3-dimensional diagonal)² = 98

- Take √ for both sides

∴ 3-dimensional diagonal = $\sqrt{98}$ = 9.899494937

- Round it to the nearest tenth of an inch

∴ 3-dimensional diagonal = 9.9 inches

∴ The length of the three-dimensional diagonal is 9.9 inches

<em>V.I.N: you can find the length of the three-dimensional diagonal by using this rule → </em> $d=\sqrt{l^{2}+w^{2}+h^{2}}$ <em> </em>

3 0

3 years ago

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that

malfutka [58]

Answer:

$3+2(log_{2}(x+1) )$

Step-by-step explanation:

First simplify the quadratic present $8(x^{2}+2x+1)=8(x+1)^{2}$

$log_{2}8+log_{2}(x+1)^{2}$

⇒ $3+2(log_{2}(x+1) )$

7 0

4 years ago

Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589 usi

Ray Of Light [21]

X = 18, correct me if i'm wrong.

4 0

4 years ago

Hi im stuck on this problem, is anybody able explain to me how to do it? This is Two-Variable Substitution

Free_Kalibri [48]

The answer is a. the first step is to divide the whole bottom equation by -1 because x can’t be negative. you then plug in y + 9 into the first equation to solve. so the equation would be (y + 9) + y = 11. you do this because in substitution you plug in one of the equations into the other equation. you then get 2y + 9= 11. you would next subtract 9 to both sides which leaves you with 2y= 2, divide by both sides, y = 1. you then plug the why value into the first equation to figure out the value for x. so it would be x + 1 = 11, subtract 1, x equals 10.

sorry this was hard to explain! hope this helps!

6 0

4 years ago