ILL GIVE BRAINLIEST IF YOU GET IT RIGHT AND EXPLAIN

Mathematics

1 answer:

koban [17]2 years ago

4 0

Answer:

y = 2

x = 50

Step-by-step explanation:

We can first find y by doing 12y+5 = 18y-7 since vertical angles are always congruent.

We want to combine like terms so we subtract 12y from both sides (what you do on one side needs to be done to the other) and we get 5 = 6y-7 and now we add 7 to both sides to get 12 = 6y.

Like I said we did this because we combine like terms!!!

Now we want to isolate the y and we do this by dividing 6 from both sides which lets us get 2 = y

Now that we know what y is we can plug it into any of the equations using y.

I plugged it into the top right equation cause it was easier.

12(2)+5

24+5

29!

That angle is 29!

Now that we know that we can begin solving for x.

The equation that has x + 29 make 180 degrees because it is a straight line so we use this to solve for x!

3x+1+29=180 (We want to start combining like terms now)

3x+30=180(Subtract 30 from both sides)

3x=150 (Isolate the x by dividing 3 from both sides)

x=50!

We can prove this is right by inserting x into it's expression. That tells us the angle is 151. Now we add 151+151+29+29 and we get 360!

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How many solutions are possible for a triangle with A = 113° , a = 15, and b = 8

statuscvo [17]

Answer:

One solution.

Step-by-step explanation:

To determine the number of possible solutions for a triangle with A = 113° , a = 15, and b = 8, we're going to use the law of sines which states that: "<em>When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C</em>".

Using the law of sines we have:

$\frac{sin(A)}{a} = \frac{sin(B)}{b}$

$\frac{sin(113)}{15} = \frac{sin(B)}{8}$

Solving for B, we have:

$sin(B)=0.4909$

∠B = 29.4°

Therefore, the measure of the third angle is: ∠C = 37.6°

There is another angle whose sine is 0.4909 which is 180° - 29.4° = 150.6 degrees. Given that the sum of all three angles of any triangle must be equal to 180 deg, we can't have a triangle with angle B=113° and C=150.6°, because B+C>180.

Therefore, there is one triangle that satisfies the conditions.

7 0

3 years ago

A square with an area of 196 ft2 is reduced by a factor of 1/4. How long the new sides of the square?

soldier1979 [14.2K]

Answer:

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