Solve each word problem by setting up a system of equations.

Suppose that y varies directly with x and y=10 when x=20. What is y when x=15

Likurg_2 [28]

Answer:

y=kx

subst y=10 and x=20 into the above

10=k20

k=10/20

k=1/2

therefore relationship: y=1/2x

subst x=15 into the relationship

y=1/2(15)

y=7,5

Step by step explanation:

Step 1: when they say y varies directly with x they mean y is proportional to x
step 2: so y=kx where k is the constant
step 3: is to substitute y=10 and x=20 into the above equation y=kx
step 4: you will end up with 10=k20 then divide both sides by 20 so that k becomes the subject of the formula 
step 5: your answer from the above will be k=10/20 so the relationship is y is directly proportional to 1/2 x what you did here is that you substituted k for 1/2 in the equation in step 3
step 6: is to finally substitute x=15 into the equation y=1/2x to finally get your answer y=7,5.

4 0

3 years ago

Write <img src="https://tex.z-dn.net/?f=%28-%20x%5E%7B2%7D%29%20-4x%2B2" id="TexFormula1" title="(- x^{2}) -4x+2" alt="(- x^{2})

marin [14]

Because the coefficient of x^2 is -1, we know that a will be -1. Knowing that the coefficient of x is -4, we can calculate that p=2. Thus, we have -1(x+2)^2+q is our equation. This is equal to -x^2-4x-4+q. As the constant term must be 2, we can then see that q is 6.

As such, we have -1(x+2)^2+6=0 as our factorization.

To solve this equation, we can use the quadratic formula. Plugging in values, we have:

$\frac{4+-2 \sqrt{6} }{-2}$
which is equal to: (when the fraction is simplified)
$-2+- \sqrt{6}$

7 0

3 years ago

Enrollment at a school last year was 1220 this year the student population decreased by 10% how many total students are attendin

Umnica [9.8K]

I think 37%......................................................

8 0

3 years ago

Can anyone explain this to me? I don’t get it

Mama L [17]

Answer:

Sin x = 0.56976744186

Step-by-step explanation: