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3 years ago

What is the slope and y-intercept from the table below?

Mathematics

1 answer:

Nataliya [291]3 years ago

4 0

Answer:

The equation is y = -5x + 55

Slope = -5

y-intercept = 55

Step-by-step explanation:

The given table shows the different coordinates of points on a straight line.

The general equation of a line is y = mx + b

where m is the slope and b is the y intercept.

Actually , here only 2 values are needed but there are 4 values given which is just to check whether our line is correct or not.

Substitute values of x and y in the equation.

Put (1,50),

50 = m + b ----------(1)

Put (2,45),

45 = 2m + b -----------(2)

Solve (1) and (2),

Slope , m = -5

y-intercept , b = 55

Hence , the equation is y = -5x + 55.

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Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

<u>Equation Solving</u>

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

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3 years ago

Choose an appropriate unit of measurement for each quantity

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3 years ago

Use the zero product property to find the solutions to the equation x2 + x - 30 = 12

ycow [4]

Answer is x=-7 x=6 or choice A

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2 years ago

Please answer this thanks

olganol [36]

Answer:

It's C! 75%

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A circle with center at (12,−1) passes through (0,−1). Find the circumference and area of the circle in terms of p.

madreJ [45]

Answer:

C = 75.36

A = 452.16

Step-by-step explanation:

Find the radius r by finding the distance between (12,-1) and (0,-1) using the distance formula.

$d = \sqrt{(12-0)^2 + (-1--1)^2} =\sqrt{(12)^2 + (0^2} =\sqrt{144+0} =\sqrt{144}=12$

The radius is 12.

So the circumference of the circle is $C = 2\pi r = 2\pi 12 = 24\pi = 75.36$

So the area of the circle is $A = \pi r^2\\A = \pi 12^2\\A = 144\pi\\A = 452.16$

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3 years ago