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2 years ago

A) What is the size of angle ABC?

Mathematics

1 answer:

Debora [2.8K]2 years ago

3 0

The measure of the angle ∠ABC is 110° and the measure of the reflex angle ∠CBD is 70°.

<h3>What is an angle?</h3>

Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The measure of the angle ABC will be

∠ABC = 110°

The angle ∠ABC and ∠CBD are the linear angles. Then we have

∠ABC + ∠CBD = 180°

110° + ∠CBD = 180°

∠CBD = 70°

More about the angled link is given below.

brainly.com/question/15767203

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1. What is the solution of the system?

andreyandreev [35.5K]

Answer:

The given system of equations has solutions below:

1) The solution is (2,3)

2) The solution is ( $\frac{-8}{7}, \frac{5}{7}$ )

3) The solution is infinitely many solutions

4) No solution

Step-by-step explanation:

Given system of equation are

$-x+2y=4\hfill (1)$

$-4x+y=-5\hfill (2)$

To solve equation by using elimination method

Multiply eqn (2) into 2

$-8x+2y=-10\hfill (3)$

Now subtracting (1) and (3)

$-x+2y=4$

$-8x+2y=-10$

_________________

7x=14

x= $\frac{14}{7}$

$x=2$

Substitute x=2 in equation (1)

-2+2y=4

2y=4+2

$y=\frac{6}{2}$

y=3

Therefore the solution is (2,3)

2) Given equation is

$-2x+y=3\hfill (1)$

4y-4=x

Rewritting as below

$x-4y=-4\hfill (2)$

To solve equation by using elimination method

multiply (2) into 2

$2x-8y=-8\hfill (3)$

Adding (1) and (3)

-2x+y=3

2x-8y=-8

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-7y=-5

$y=\frac{5}{7}$

substitute $y=\frac{5}{7}$ in (1)

$-2x+\frac{5}{7}=3$

$-2x=3-\frac{5}{7}$

$-2x=\frac{21-5}{7}$

$x=-\frac{8}{7}$

Therefore the solution is ( $\frac{-8}{7},\frac{5}{7}$ )

3) Given equation is $6x+2y=10\hfill (1)$

$3x+y=5\hfill (2)$

equation (1) can be written as

2(3x+y)=10

$3x+y=\frac{10}{2}$

3x+y=5

Therefore equations (1) and (2) are same therefore it has infinitely many solutions

4) Given equation is $-x-2y=14\hfill (1)$

$-2x-4y=12\hfill (2)$

multiply equation (1) into 2

$-2x-4y=28\hfill (3)$

To solve equation by using elimination method

subtracting (2) and (3)

-2x-4y=28

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3 years ago

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Answer:

$ST = 12$

Step-by-step explanation:

By AA Similarity, triangles ASR and EST are similar.

The ratio of the lengths of the sides of triangle ASR to those of EST is 6/8 or 3/4.

$\dfrac{SR}{ST} = \dfrac{3}{4}$

Also,

$SR + ST = 21$

By a rule of proportions, you get

$\dfrac{SR + ST}{ST} = \dfrac{3 + 4}{4}$

$\dfrac{21}{ST} = \dfrac{7}{4}$

$7ST = 4 \times 21$

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