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3 years ago

Line segment BC will be reflected over line m to form line segment BC. Which of the following statements must be true?

Mathematics

1 answer:

Len [333]3 years ago

7 0

Answer:

Option A

Step-by-step explanation:

To reflect line segment BC over line m, BB' will be perpendicular to the line m

and line m bisector of BB'.

So, the correct answer is option A

A) Line m is the perpendicular bisector of line segment BB' and the line segment CC'

Option b is wrong , it is impossible for the line B'C' to be perpendicular to line BC. B'C' is the image of BC.

Both option c and d is wrong because the perpendicular distance from b to the line m not equal to the perpendicular distance from c to the line m.

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Find the values of x and y. Pls helpI’m helpless at math

Svetradugi [14.3K]

Answer:

x = 1

$y=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

The adjacent to the angle ∠60° is 1/2.

The opposite to the angle ∠60° is y.

The hypotenuse = x

Determining the value of x:

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

$cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}$

$\cos \left(60^{\circ \:}\right)=\frac{1}{2x}$

$\frac{1}{2}=\frac{1}{2x}$ ∵ cos (60°) = 1/2

$2x=2$

Dividing both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Thus, the value of hypotenuse x is:

x = 1

Determining the value of y:

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

$y=\frac{\sqrt{3}}{2}$ ∵ $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

Therefore, the value of y is:

$y=\frac{\sqrt{3}}{2}$

Summary:

x = 1

$y=\frac{\sqrt{3}}{2}$

5 0

3 years ago

Coefficiants of (2x+y)^4

sattari [20]

By the binomial theorem,

$(2x+y)^4=\displaystyle\sum_{k=0}^4\binom 4k(2x)^{4-k}y^k=\sum_{k=0}^4\binom 4k2^{4-k}x^{4-k}y^k$

where

$\dbinom nk=\dfrac{n!}{k!(n-k)!}$

Then the coefficients of the $x^{4-k}y^k$ terms in the expansion are, in order from $k=0$ to $k=4$ ,

$\dbinom 402^{4-0}=1\cdot2^4=16$

$\dbinom412^{4-1}=4\cdot2^3=32$

$\dbinom422^{4-2}=6\cdot2^2=24$

$\dbinom432^{4-3}=4\cdot2^1=8$

$\dbinom442^{4-4}=1\cdot2^0=1$

3 0

3 years ago

10% as a decimal? Just want to make sure I'm correct

shutvik [7]

10% as a decimal would be .10

7 0

4 years ago

Read 2 more answers

Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = -1.

IgorLugansk [536]

Answer:

The possible y-coordinate of point C is 6

Step-by-step explanation:

The coordinate of a point is given by (x,y) where x is the horizontal distance from the origin on the x axis and y is the vertical distance from the origin.

Given Segment AB is on the line y = 2 and is 3 units long and Segment AB is on the line y = 2 and is 3 units long. The area of triangle ABC is 6 square units.

The area of a triangle = 1/2 × base × height

6 = 1/2 × 3 × height

height = (2 × 6) / 3 = 4 units

Since point C is perpendicular to line y = 2, they coordinates is either 2 + 4 = 6 or 2 - 4 = -2

The coordinate of point C is either (-1, 6) or (-1, -2)

7 0

3 years ago

Help me

aivan3 [116]

Answer:

Step-by-step explanation:

It is the only answer where the negative signs do not even out on both sides of the equation.

7 0

3 years ago