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3 years ago

What is the slope of a line parallel to the line whose equation is x-6y = 42. Fully reduce your answer.

Mathematics

1 answer:

Maksim231197 [3]3 years ago

4 0

The slop would be 1/6.

you put it into slope intercept form (y=mx+b). parallel lines always have the same slope.

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Please help! Thanks in advance.

alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
$2 - 5 - 14 + a + b = 0$
$- 17 + a + b = 0$
$a + b = 17$

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
$2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0$
$512 - 320 - 224 + 4a + b = 0$
$- 32 + 4a + b = 0$
$4a + b = 32$

Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
$3a = 15$

Simplify:
$a = 5$

Now we have a, we can plug in one of those equations to find b:
$5 + b = 17$
$b = 17 - 5$
$b = 12$

So, the answers are $a=5$ and $b=12$ .

6 0

3 years ago

2-7x-3x=-8x-8 Explain Thanks

Agata [3.3K]

$2-7x-3x=-8x-8\\\\-7x-3x+8x=-8-2\\\\-2x=-10 \ \ /:(-2)\\\\\huge\boxed{x=5}$

4 0

2 years ago

Read 2 more answers

Identify the volume of the composite figure, rounded to the nearest tenth. PLEASE HELP!!!

Anni [7]

Answer:

The volume of the composite figure is:

312 ft^3

Step-by-step explanation:

To identify the volume of the composite figure, you can divide it in the known figures there, in this case, you can divide the figure in a cube and a pyramid with a square base. Now, we find the volume of each figure and finally add the two volumes.

VOLUME OF THE CUBE.

Finding the volume of a cube is actually simple, you only must follow the next formula:

Volume of a cube = base * height * width

So:

Volume of a cube = 6 ft * 6 ft * 6 ft
Volume of a cube = 216 ft^3

VOLUME OF THE PYRAMID.

The volume of a pyramid with a square base is:

Volume of a pyramid = 1/3 B * h

Where:

B = area of the base.

h = height.

How you can remember, the area of a square is base * height, so B = 6 ft * 6 ft = 36 ft^2, now we can replace in the formula:

Volume of a pyramid = 1/3 36 ft^2 * 8 ft
Volume of a pyramid = 96 ft^3

Finally, we add the volumes found:

Volume of the composite figure = 216 ft^3 + 96 ft^3
Volume of the composite figure = 312 ft^3

5 0

2 years ago

Can anyone help me with this one please

bulgar [2K]

A. 314 sq cm

Explanation: pi•r^2
3.14 x 10^2
3.14 x 100 =314

7 0

2 years ago

Solve the quadratic inequalities, by either graphing, or pure algebraic method:

BlackZzzverrR [31]

Answer:

less than/equal to -2

Or, greater than/equal to 2.5

Step-by-step explanation:

2x² - x - 10 ≥ 0

2x² - 5x + 4x - 10 ≥ 0

x(2x - 5) + 2(2x - 5) ≥ 0

(x + 2)(2x - 5) ≥ 0

Roots: -2, 5/2

x《 -2 or x》5/2

6 0

2 years ago