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2 years ago

Which ordered pair is a solution of this equation? -3x + 7y - 6 =

Mathematics

1 answer:

Mumz [18]2 years ago

5 0

Answer:

There are actually an infinite number of ordered pairs that will satisfy the equation y=3x+7 including (-1,4), (0,7) and (1, 10).

Step-by-step explanation:

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

I need help on this question. Does anybody know how to do it??

marta [7]

1/3 x 14
2/3 x 7
4/6 x 7
2/6 x 14
1/3 x 28/2
1/3 x 42/3

4 0

3 years ago

The area of the base of this right rectangular prism is 14 square centimeters, and the height is 3 centimeters. What is the volu

Crank

Answer:

42cm^3

Step-by-step explanation:

Given data

Area of base= 14 square centimeters,

Height= 3 centimeters

Volume = Area* Height

Volume= 14*3

Volume= 42 cm^3

Hence the volume of the prism is 42cm^3

5 0

2 years ago

If y is 12 when x is 5, find x when y is 30

I am Lyosha [343]

We have no idea how 'x' responds to changes in 'y'.
We don't even know their units, to make a guess with.

-- If 'x' and 'y' are the ages of two people, then when y = 30, 'x' will be 23.

-- If they are the frequency and wavelength of a wave on the lake,
then when y = 30, 'x' will be 2 .

-- If 'x' is the weight of a rock in your front yard and 'y' is the number of pages
in today's newspaper, then 'y' has no effect on 'x'. No matter what happens
to 'y' . . . 'x' will always be 5 .

With the information given in the question, we just don't know.

We need either an equation, or else one more example.

3 0

3 years ago

Find the vertex of the parabola whose equation is y = x^2 + 8x + 12.

horsena [70]

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.

The vertex of the parabola whose equation is y = x^2 + 8 x + 12 will be :
(x , y) = (-4,-4)

4 0

3 years ago

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