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Svetach [21]
2 years ago
13

Two parallel lines are cut by a transversal and two of the same-side interior angles formed have measures of (4x + 3) degrees an

d (x+2) degrees.
1. How are the angles related?

2. What does x =

3. What are the two angle measures?
Mathematics
1 answer:
oksano4ka [1.4K]2 years ago
4 0

Answer:

See answers below

Step-by-step explanation:

1. If two parallel lines cut by a transversal, then the two same-side interior angles  are equal

2.  (4x + 3 )+ (x + 2) = 180

       5x + 5 = 180

      5x = 175

        x = 35

3.    one angle = 4(35) +3 = 143°

      the other angle = 35 + 2 = 37°

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6
Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. 2x-4y=12

-3x+6y=-15

b. 2x-4y=12

-5x+3y=10

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0

1. One solution:

There will be one solution to the system of equations,  If we have:

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

2. Infinitely Many Solutions: (Identical lines in the system)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}

3. No Solution:(Parallel lines)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Now, let us discuss the system of equations one by one:

a. 2x-4y=12 OR 2x-4y-12=0

-3x+6y=-15 OR -3x+6y+15=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15

Here, the ratio:

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Therefore, no solution i.e. parallel lines.

b. 2x-4y=12 OR 2x-4y-12=0

-5x+3y=10 OR -5x+3y-10=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10

\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0
3 years ago
Work out the unknown angles. Give reasons for each answer.
zalisa [80]
A)

Because the sum of angles in a triangle must equal 180° we can say:

62+α+90=180

α+152=180

α=28°

b)

Since all sides have equal length, all angles must have equal measure.  (This is an equilateral triangle).  And again, because the sum of the angle must be 180° we can say:

b+b+b=180

3b=180

b=60°
8 0
3 years ago
PLZZ HELP URGENT
Mashcka [7]

Answer:

5x + 2x.....combine like terms..... = 7x

5x + 2x....subbing in 1                               7x - 1....subbing in 1

5(1) + 2(1) = 5 + 2 = 7                               7(1) - 1 = 7 - 1 = 6

5x + 2x...subbing in 2                                 7x - 1...subbing in 2

5(2) + 2(2) = 10 + 4 = 14                            7(2) - 1 = 14 - 1 = 13

5x + 2x...subbing in 3                                 7x - 1...subbing in 3

5(3) + 2(3) = 15 + 6 = 21                            7(3) - 1 = 21 - 1 = 20

5x + 2x...subbing in 4                                 7x - 1....subbing in 4

5(4) + 2(4) = 20 + 8 = 28                            7(4) - 1 = 28 - 1 = 27

5x + 2x...subbing in 5                                 7x - 1...subbing in 5

5(5) + 2(5) = 25 + 10 = 35                          7(5) - 1 = 35 - 1 = 34

5x + 2x result values are 1 more then 7x - 1 result values

there are no values that will make the 2 expressions equal....

because 5x + 2x = 7x......and the other one is 7x - 1......so the 7x - 1 values will always be 1 number less...because ur subtracting one

Step-by-step explanation:

5 0
3 years ago
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