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Basile [38]
3 years ago
10

In triangle ABC, Angle A is twice the size of angle B, angle C measures 20 degrees less than angle A, find the measurements of a

,b, and c
Mathematics
1 answer:
Vlada [557]3 years ago
5 0

I assume a, b, and c are the measures of the angles A, B, and C themselves. (If you meant lengths of the sides opposite these angles, this would be impossible.)

The interior angles to any triangle sum to 180° in measure, so

A + B + C = 180°

Now,

• A is twice the size of B, so A = 2B or B = A/2

• C measures 20° less than A, so C = A - 20°

Substitute these into the first equation and solve for A :

A + A/2 + (A - 20°) = 180°

5/2 A - 20° = 180°

5/2 A = 200°

A = 80°

Solve for B and C :

B = 80°/2

B = 40°

C = 80° - 20°

C = 60°

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Factor completely 9x3 36x2 − x − 4. (3x 4)(3x − 4)(x 1) (3x 1)(3x − 1)(x 4) (9x2 − 1)(x 4) (3x 1)(3x − 1)(x − 4).
Arlecino [84]

The factor of the provided polynomial after the factorization process are similar to option B, which is

(x+4)(3x+1)(3x-1)

<h3>How to find the factor of polynomial?</h3>

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

Find these factors by taking out the common factors.

The given polynomial equation in the problem is,

9x^3 +36x^2 - x - 4

The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 9x², which can divide each term of the first two terms of equation (9x³, 36x²). Thus,

9x^2(x +4) - x - 4

Take out the highest common factor -1 from the second two terms as,

9x^2(x +4) -1( x + 4)

Now take out the common group (x+4) as,

(x +4) ( 9x^2 -1)

The second group can be rewritten using the difference of square formula as,

(x +4) ( (3x)^2 -1^2)\\(x+4)(3x+1)(3x-1)

Thus, the factor of the provided polynomial after the factorization process are similar to option B, which is

(x+4)(3x+1)(3x-1)

Learn more about factor of polynomial here;

brainly.com/question/24380382

4 0
3 years ago
Dena has 6.25 inches of blue ribbon, 0.375 foot of orange ribbon, and 0.5 yard of green ribbon. How many inches of ribbon does D
ipn [44]

Answer:

<h2>28.75in</h2>

Step-by-step explanation:

We are expected to convert all units to inches in this problem

Step one:

given data

blue ribbon=6.25 inches

orange ribbon=0.375 foot

green ribbon=0.5 yard

Step one:

convert orange ribbon=0.375 foot to inches

1 ft = 12 in

0.375ft=xin

cross multiply

x=12*0.375

x=4.5in

orange ribbon= 4.5in

convert green ribbon yd to inches

1 yd = 36 in

0.5 yd=xin

cross multiply

x=36*0.5

x=18in

green ribbon= 36in

total lenght in inches =6.25+4.5+18

=28.75in

3 0
3 years ago
Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be
kvv77 [185]
Answer:

Angle A must be acute.

Explanation:

Both angle A and C must be acute. The sum of the angles in a triangle is 180°.

An obtuse angle is more than 90°, so the sum of the remaining 2 angles has to be less than 90°.

Note that it is impossible to have:

<span>2 right angles in a triangle, because <span>90°+90°=180</span>° and the third angle still needs to be added.1 obtuse and 1 right angle in a triangle, their sum is more than 180°2 obtuse angles in a triangle, their sum is more than 180°</span>

It is possible to have an obtuse-angled isosceles triangle, but the vertex angle must be obtuse and the equal base angles will be acute.

8 0
3 years ago
Please help, I’ll give you brainliest!
larisa [96]
For the first question it is (3x-5) degrees second question is (x-5)
8 0
2 years ago
Name 3 properties of A in a quadratic formula.
Svetlanka [38]
The answer is 100 if you want to get it correct
6 0
4 years ago
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