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STatiana [176]
3 years ago
6

I need the solution to 5x+2y=7 and 7x+6y=-3

Mathematics
1 answer:
OverLord2011 [107]3 years ago
6 0

Answer:

1. x=7/5-2y/5

2. x = − 8 √ 3 ( − 1 − 2 y )

Step-by-step explanation:

i did it

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When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation
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A pair of jeans priced 20 $ are subjected 5 % sales tax. how much are the jeans
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Cosθ=−2√3 , where π≤θ≤3π2 .
Alex787 [66]

Answer:

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

Step-by-step explanation:

step 1

Find the  sin(\theta)

we know that

Applying the trigonometric identity

sin^2(\theta)+ cos^2(\theta)=1

we have

cos(\theta)=-\frac{\sqrt{2}}{3}

substitute

sin^2(\theta)+ (-\frac{\sqrt{2}}{3})^2=1

sin^2(\theta)+ \frac{2}{9}=1

sin^2(\theta)=1- \frac{2}{9}

sin^2(\theta)= \frac{7}{9}

sin(\theta)=\pm\frac{\sqrt{7}}{3}

Remember that

π≤θ≤3π/2

so

Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

sin(\theta)=-\frac{\sqrt{7}}{3}

step 2

Find the sec(β)

Applying the trigonometric identity

tan^2(\beta)+1= sec^2(\beta)

we have

tan(\beta)=\frac{4}{3}

substitute

(\frac{4}{3})^2+1= sec^2(\beta)

\frac{16}{9}+1= sec^2(\beta)

sec^2(\beta)=\frac{25}{9}

sec(\beta)=\pm\frac{5}{3}

we know

0≤β≤π/2 ----> II Quadrant

so

sec(β), sin(β) and cos(β) are positive

sec(\beta)=\frac{5}{3}

Remember that

sec(\beta)=\frac{1}{cos(\beta)}

therefore

cos(\beta)=\frac{3}{5}

step 3

Find the sin(β)

we know that

tan(\beta)=\frac{sin(\beta)}{cos(\beta)}

we have

tan(\beta)=\frac{4}{3}

cos(\beta)=\frac{3}{5}

substitute

(4/3)=\frac{sin(\beta)}{(3/5)}

therefore

sin(\beta)=\frac{4}{5}

step 4

Find sin(θ+β)

we know that

sin(A + B) = sin A cos B + cos A sin B

so

In this problem

sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)

we have

sin(\theta)=-\frac{\sqrt{7}}{3}

cos(\theta)=-\frac{\sqrt{2}}{3}

sin(\beta)=\frac{4}{5}

cos(\beta)=\frac{3}{5}

substitute the given values in the formula

sin(\theta + \beta) = (-\frac{\sqrt{7}}{3})(\frac{3}{5})+ (-\frac{\sqrt{2}}{3})(\frac{4}{5})

sin(\theta + \beta) = (-3\frac{\sqrt{7}}{15})+ (-4\frac{\sqrt{2}}{15})

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

8 0
3 years ago
Which of the following sentences is true? 30.744 is greater than 30.844. 9.542 is greater than 9.532. 182.348 is less than 182.3
Arturiano [62]

Answer:

the first sentance is wrong, the second one is right, the third one is right and the last one is wrong

Step-by-step explanation:

5 0
3 years ago
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