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3 years ago

8

What is the value of p in the linear equation 24p + 12 – 18p = 10 + 2p – 6?

2 answers:

stira [4]3 years ago

6 0

we have

$24p+12-18p=10+2p-6$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$24p-18p-2p=10-6-12$

Combine like terms

$4p=-8$

Divide by $4$ both sides

$4p/4=-8/4$

$p=-2$

therefore

<u>the answer is</u>

the value of p in the linear equation is $-2$

Volgvan3 years ago

4 0

Answer:

The value of p is -2 .

Step-by-step explanation:

As given the equation

24p + 12 – 18p = 10 + 2p – 6

Simplify the above

24p - 18p + 12 = 10 - 6 + 2p

6p + 12 = 4 + 2p

6p - 2p = 4 - 12

4p = -8

$p = \frac{-8}{4}$

p = -2

Therefore the value of p is -2 .

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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

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2 years ago

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