All categories

3 years ago

In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.

Mathematics

1 answer:

lesya692 [45]3 years ago

6 0

9514 1404 393

Answer:

x = 19

A = 30°

B = C = 75°

Step-by-step explanation:

In an isosceles triangle, the angles opposite the congruent sides have the same measures.

A = B

3x +18 = 7x -58

76 = 4x . . . . . . . . add 58-4x

19 = x . . . . . . . . . divide by 4

Then the equal angles measure ...

A = B = 3(19) +18 = 75

C = 2(19) -8 = 30

Angles A, B, C measure 75°, 75°, 30°, respectively.

_____

Alternate solution

The sum of angles in a triangle is 180°, so you could write ...

(3x +18) +(7x -58) +(2x -8) = 180

12x = 228 . . . . . add 48

x = 19 . . . . . divide by 12

You might be interested in

Complete parts a through c for the given function.

victus00 [196]

Answer:

a. The critcal points are at

$x=0,-5,3$

b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

Step-by-step explanation:

(a)

Remember that you need to find the points where

$f'(x)=0$

Therefore you have to solve this equation.

$20x^4 + 40x^3 - 300x^2 = 0$

From that equation you can factor out $20x^2$ and you would get

$20x^2 ( x^2 +2x - 15) = 0$

And from that you would have $20x^2 = 0$ , so $x = 0$ .

And you would also have $x^2 +2x-15 = 0$ .

You can factor that equation as $x^2 +2x -15 = (x+5)(x-3) = 0$

Therefore $x=-5 , x=3$ .

So the critcal points are at

$x=0,-5,3$

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

$f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\$

Then, $x = -5$ is a maximum and $x=3$ is a minimum

The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

6 0

3 years ago

Read 2 more answers

What’s 7= y-2/3 if you’re solving for y

Rus_ich [418]

Answer:

y = 23/3

Step-by-step explanation:

Simplify both sides of equation

7 = y + -2/3

Flip equation

y + -2/3 = 7

Add 2/3 to both sides

y + -2/3 + 2/3 = 7 + 2/3

y = 23/3

6 0

3 years ago

Simplify 10 + 4(x + 1) + 5

Levart [38]

Distribute
10+4x+4+5

Combine like terms
19+4x

Final answer: 4x+19

4 0

3 years ago

if Sandy can afford car payments of $140/month for 4 years what is the price of a car that she can afford now?

Galina-37 [17]

6720 would be the correct answer

5 0

3 years ago

10. Giselle invests $16,250 in an account that earns 4.25% interest, compounded continuously.

denis-greek [22]

Answer: 24 years

Step-by-step explanation:

% • total = Answer

4.25% • $40,000 = Answer

.0425 • $40,000 = Answer

Answer = $1,700 per year

40,000 ÷ 1,700 = 23.5

23.5 rounded to the nearest year is 24

3 0

3 years ago