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2 years ago

Lines l and m are parallel

Mathematics

1 answer:

soldi70 [24.7K]2 years ago

4 0

Answer:

m∠ABC = 15°

Step-by-step explanation:

Given

m∠ABC = x°
m∠BCD = 25°
m∠CDE = 55°
m∠DEF = 3x°

Add two more parallel lines passing through points C and D.

Consider alternate interior angles formed by the four parallel lines.

The angles between the two middle lines are equal to:

m∠BCD - m∠ABC = m∠CDE - m∠DEF

Substitute values and solve for x:

25 - x = 55 - 3x
3x - x = 55 - 25
2x = 30
x = 15

m∠ABC = 15°

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ElenaW [278]

Answer:

The point at which center of the image circle located is (-2, -3) so second option is correct.

Step-by-step explanation:

Given equation of circle is:

$(x-3)^{2} + (y+4)^{2} = 9$ (i)

The general equation of circle is mentioned below,

$(x-h)^{2} + (y-k)^{2} = r^{2}$ (ii)

Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.

By comparing equation (i) and equation (ii), we get

r^2 = 9

r = 3

$(x-3)^{2} = (x-h)^{2}$

$(x-3) = (x-h)$

$h = 3$

$(y+4)^{2} = (y-k)^{2}$

$(y+4) = (y-k)$

$k = -4$

So the center of given circle is (h,k) = (3,-4)

Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2

Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3

Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.

6 0

2 years ago

Read 2 more answers

How do I find the slope of a line that passes through?

Natali [406]

Answer:

the slope is m = 0.4

Step-by-step explanation:

use symbolab I use it all the time it gives correct answer and is gives good explanations (this isn't a sponser I've just been using it since the 6th grade lol)

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3 years ago

What is the value of x? Enter your answer in the box.

Tamiku [17]

It's a hexagon.

The formula of the sum of internal angles in the polygon:

$S=(n-2)\cdot180^o$

Therefore

$112^o+133^o+128^o+100^o+120^o+x^o=(6-2)\cdot180^o\\\\593^o+x^o=720^o\ \ \ \ |-593^o\\\\x^o=127^o$

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3 years ago

If the function f(x)=-1/2x-7 were graphed, which of the following would be true? A. The y-values would be negative. B. As the x-

vagabundo [1.1K]

f(x)= -1/2x-7 (better expressed as f(x) = (-1/2)x - 7 ) has a negative slope, so as x increases, y decreases. Answer D is correct.

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3 years ago

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What value(s) of x will make each equation below true

Dahasolnce [82]

We need to solve for x. Let's try problem b:

$2x-6=3x+1-x-7$

Let us first combine line terms. 3x and -x as well as 1 and -7 can be combined. Let's do that:

$2x-6=2x-6$

Since this is true, your answer would be:

All real numbers

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Let's solve for problem c:

$3x+1=43$

Let's isolate x, so subtract 1 from both sides:

$3x=42$

Since x can't have a coefficient, divide both sides by 3:

$\frac{3x}{3}=\frac{42}{3}$

$x=14$

So, only the value of 14 would make this equation true.

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Let's try problem d:

$4x-1=4x+7$

Let's get our whole numbers on the right side. Add 1 to both sides:

$4x=4x+8$

Subtract 4x from the right side on both sides:

$0=8$

Since this is not true, your answer would be:

No solution

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3 years ago