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2 years ago

Find the slope and the y-intercept of the line. 5x + 8y = 31

Mathematics

2 answers:

Sunny_sXe [5.5K]2 years ago

8 0

Step-by-step explanation:

1.) Move the 5 to the other side of the equation

8y = -5x + 31

2.)

Divide by 8

y= .625x + 3.8

Ghella [55]2 years ago

3 0

Answer:

5x + 8y = 31

8y = -5x + 31

y = -0,625x + 3,875

y = mx + b

m = slope

b = intercept

y = -0,625x + 3,875

slope = -0,625

intercept = 3,875

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3 years ago

Find all points on the curve that have the given slope.x = 2cost, y= 8sint, slope =-1

tatuchka [14]

Answer:

$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

$t_{2} = 1.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

Step-by-step explanation:

In the case of parametric equations, the slope of the curve is equal to:

$\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

Where $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are the first derivatives of $x$ and $y$ regarding $t$ . Let be $x(t) =2\cdot \cos t$ and $y(t) = 8\cdot \sin t$ , their first derivatives are found:

$\frac{dx}{dt} = -2\cdot \sin t$ and $\frac{dy}{dt} = 8\cdot \cos t$

Thus, equation for the slope is:

$\frac{dy}{dx} = -\frac{8\cdot \cos t}{2\cdot \sin t}$

$\frac{dy}{dx} = -\frac{4}{\tan t}$

If $\frac{dy}{dx} = -1$ , then:

$-1 = -\frac{4}{\tan t}$

$\tan t = 4$

Tangent is positive at 1st quadrant and is a function with a periodicity of $\pi$ , the set of solutions are:

$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

$t_{2} = 1.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

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3 years ago

Which graph is defined by the function given below? y=(x+2)(x+7)

densk [106]

Answer: Graph A
We can determine the x-intercepts from the equation. X-intercepts are x=-2 and x=-7 which is what Graph A shows.

3 0

3 years ago

Read 2 more answers

Henry located 2 1/4 and 2.1 on a number line. He wrote the following related story:

Rzqust [24]

Answer:

Jerry ran a farther distance and not Henry.

Step-by-step explanation:

We are given the following information in the question:

Jerry rain $2\frac{1}{2}$ miles and Henry ran 2.1 miles.

Henry claimed that he ran a farther distance.

This is a wrong claim because when we compare:

$2\frac{1}{2}$ and 2.1

$2\displaystyle\frac{1}{2} = \displaystyle\frac{5}{2} = 2 + 0.5 = 2.5\\\\2.5 > 2.1$

Hence, Jerry ran a farther distance and not Henry.

Henry may have made some mistake in plotting $2\frac{1}{2}$ and 2.1 on the number line.

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3 years ago

Complete the equation of the line through (2, -2) and (4, 1)

posledela

Answer:

y=1.5x-5

Step-by-step explanation:

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3 years ago