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DIA [1.3K]
2 years ago
14

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

Mathematics
1 answer:
statuscvo [17]2 years ago
7 0

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.

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Simplify 2^-6 times 2^3
IgorC [24]

Answer:

(2^-6)*(2^3)

=2^(-6+3)

=2^-3

=1/(2^3)

=1/8

3 0
3 years ago
Read 2 more answers
Factor x2+4x+3.
Alexxx [7]

Answer:

c. (x +3)(x + 1)

Step-by-step explanation:

Factoring an equation is a way of expressing an equation as the product of other linear expressions. The following expression,

x^2 +4x +3

Can be represented as the product of the following,

(x+3)(x+1)

To check this, one can distribute, one of the expressions over the other, then simplify, the result should be the starting expression,

(x+3)(x+1)\\

Distribute,

(x)(x)+(1)(x)+(3)(x)+(3)(1)

Simplify,

x^2 +x +3x + 3\\

x^2 +4x +3

8 0
3 years ago
1)The original price of concert is $100. They are on sale for 21% off. How much will the tickets cost after the discount? 2)Ms.B
mel-nik [20]
1.  79%  Take 100 x 21%=21, then subtract 21 from 100 = 79
2.  $138  Take 1200 x 11.5%= $138
3 0
3 years ago
To test for the significance of a regression model involving 3 independent variables and 51 observations, the numerator and deno
LenKa [72]

Answer:

numerator degree of freedom = 3

Denominator degree of freedom = 47

Step-by-step explanation:

The numerator degree of freedom is given by :

p - 1 ; where p = number of predictors ;

p = number of independent variables + 1

Number of independent variables = 3

p = 3 + 1 = 4

Numerator degree of freedom = p - 1 = 4 - 1 = 3

The denominator degree of freedom = n - p ; where n = number of observations

Number of observations, n = 51

Denominator degree of freedom = n - p = 51 - 4 = 47

6 0
2 years ago
Help me pls!!!!!!!!!
Dominik [7]

Answer:

x^2+18=-9x : x = -3, x = -6

Step-by-step explanation:

x^2+18=-9x

Add 9x to both sides:

x^2+18+9x=-9x+9x

Simplify:

x^2+9x+18=0

Solve with the quadratic formula:

For a quadratic equation of the form ax^2+bx+c=0 the solutions are:

x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

For a=1,\:b=9,\:c=18:\quad x_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}

x =\frac{-9 + \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1} : -3

x =\frac{-9 - \sqrt{9^2-4\cdot \:1\cdot \:18}}{2\cdot \:1} : -6

The solution to the quadratic equation are:

x=-3,\:x=-6

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day!

6 0
3 years ago
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