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Goshia [24]
4 years ago
9

If ∠3 = 5x - 1, and ∠5 = 3x + 11, then x =

Mathematics
1 answer:
erma4kov [3.2K]4 years ago
8 0

5 = 3x + 11

Reorder the terms:

5 = 11 + 3x

Solving

5 = 11 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

5 + -3x = 11 + 3x + -3x

Combine like terms: 3x + -3x = 0

5 + -3x = 11 + 0

5 + -3x = 11

Add '-5' to each side of the equation.

5 + -5 + -3x = 11 + -5

Combine like terms: 5 + -5 = 0

0 + -3x = 11 + -5

-3x = 11 + -5

Combine like terms: 11 + -5 = 6

-3x = 6

Divide each side by '-3'.

x = -2

Simplifying

x = -2

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Which statement is logically equivalent to the following statement: “If it is raining, I will stay home from the concert”?
Gnoma [55]

Answer:

It’s If I do not stay home from the concert then it is not raining.

Step-by-step explanation:

it’s the answer that I have because in the question it’s asking what is the same but I guess opposite. Which is why I chose the first answer as my answer since if it’s not raining then they would go to the concert.

8 0
2 years ago
Q5: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.
MAVERICK [17]

Answer:

d.\:ellipse;\:3x^2+y^2+6x-6y+3=0.

Step-by-step explanation:

The given conic has equation;

3x^2+y^2=9

Divide through by 9.

\Rightarrow \frac{3x^2}{9}+\frac{y^2}{9}=\frac{9}{9}

\Rightarrow \frac{x^2}{3}+\frac{y^2}{9}=1.

This is an ellipse centered at the origin;

This ellipse has been translated so that the center is now at;

(-1,3)

The translated ellipse has equation;

\frac{(x+1)^2}{3}+\frac{(y-3)^2}{9}=1.

Clear the fraction;

3(x+1)^2+(y-3)^2=9.

Expand;

3(x^2+2x+1)+(y^2-6y+9)=9.

3x^2+6x+3+y^2-6y+9=9.

Write in general form;

3x^2+y^2+6x-6y+9-9+3=0.

3x^2+y^2+6x-6y+3=0.

The correct choice is D

4 0
3 years ago
Read 2 more answers
.
Dahasolnce [82]

Answer:

Option A is correct.

Step-by-step explanation:

Given

  • The point (4, -8)
  • Slope m = 1/4

To determine

What is the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4.

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where

  • m is the slope of the line
  • (x₁, y₁) is the point

substituting the values m = 1/4 and the point (4, -8)

y-y_1=m\left(x-x_1\right)

y-\left(-8\right)=\frac{1}{4}\left(x-4\right)

y+8=\frac{1}{4}\left(x-4\right)

Subtract 8 from both sides

y+8-8=\frac{1}{4}\left(x-4\right)-8

y=\frac{1}{4}x-1-8

y=\frac{1}{4}x-9

Writing the equation in the standard form

As we know that the equation in the standard form is

Ax+By=C

where x and y are variables and A, B and C are constants

so

y=\frac{1}{4}x-9

x=4y+36

x - 4y = 36

Therefore, the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4 will be:

x - 4y = 36

Hence, option A is correct.

3 0
3 years ago
Plz help this is due tomorrow
lesya [120]
He would change his tires a total of 4 times.
You divide the numbers like so:
160,000/40,000=4
5 0
3 years ago
Read 2 more answers
Angle A is twice the size of Angle B.Their sum is 87 degrees.Find x
Nataliya [291]
A=2b
a+b=87
a=4x-2
a=87-2x+1
4x-2=88-2x
6x=90
x=15
b=29
a=58

6 0
3 years ago
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