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Kitty [74]
3 years ago
15

Write an equation in point-slope form of the line that passes through the given point and has the given slope. (12, 5); m = -3

Mathematics
1 answer:
givi [52]3 years ago
7 0

Answer:

y - 5 = -3(x - 12)

Step-by-step explanation:

Point slope form is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Plug in the point and the slope:

y - y1 = m(x - x1)

y - 5 = -3(x - 12)

So, y - 5 = -3(x - 12) is the equation in point slope form of the line.

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grandma's cake recipe calls for 2 cups of flour and 3 ounces of oil.how many ounces of oil would be needed for 15 cups of flour?
podryga [215]
42 ounces of oil would be needed
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Please help me with this #5
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2 years ago
Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

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3 years ago
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abruzzese [7]

Answer:

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Step-by-step explanation:

IN a parallelogram consecutive angles are supplementary, thus

5a - 52 + 5a - 98 = 180, that is

10a - 150 = 180 ( add 150 to both sides )

10a = 330 ( divide both sides by 10 )

a = 33

8 0
3 years ago
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