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3 years ago

What is the slope and the y-intercept of the line 12x+2y=-60

Mathematics

1 answer:

aivan3 [116]3 years ago

8 0

Answer:

The slope is -6 and the y intercept is (0, -30)

Step-by-step explanation:

Rearrange the equation into y = mx + b form, where m is the slope and b is the y intercept:

12x + 2y = -60

Subtract 12x from both sides:

2y = -12x - 60

Divide each side by 2:

y = -6x - 30

So, the equation in slope intercept form is y = -6x - 30

The slope is -6 and the y intercept is (0, -30)

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Find the surface area of this figure

jok3333 [9.3K]

It's a rectangular parallelepiped, also known as a box. It has three pairs of congrurent rectangular faces, so adding them all up,

Area = 2 × (8×6 + 5×6 + 8×5) = 236 sq ft

Answer: 236 sq ft

5 0

3 years ago

Read 2 more answers

If you are given a3=2 a5=16, find a100.

ra1l [238]

I suppose $a_n$ denotes the n-th term of some sequence, and we're given the 3rd and 5th terms $a_3=2$ and $a_5=16$ . On this information alone, it's impossible to determine the 100th term $a_{100}$ because there are infinitely many sequences where 2 and 16 are the 3rd and 5th terms.

To get around that, I'll offer two plausible solutions based on different assumptions. So bear in mind that this is not a complete answer, and indeed may not even be applicable.

• Assumption 1: the sequence is arithmetic (a.k.a. linear)

In this case, consecutive terms <u>d</u>iffer by a constant d, or

$a_n = a_{n-1} + d$

By this relation,

$a_{n-1} = a_{n-2} + d$

and by substitution,

$a_n = (a_{n-2} + d) + d = a_{n-2} + 2d$

We can continue in this fashion to get

$a_n = a_{n-3} + 3d$

$a_n = a_{n-4} + 4d$

and so on, down to writing the n-th term in terms of the first as

$a_n = a_1 + (n-1)d$

Now, with the given known values, we have

$a_3 = a_1 + 2d = 2$

$a_5 = a_1 + 4d = 16$

Eliminate $a_1$ to solve for d :

$(a_1 + 4d) - (a_1 + 2d) = 16 - 2 \implies 2d = 14 \implies d = 7$

Find the first term $a_1$ :

$a_1 + 2\times7 = 2 \implies a_1 = 2 - 14 = -12$

Then the 100th term in the sequence is

$a_{100} = a_1 + 99d = -12 + 99\times7 = \boxed{681}$

• Assumption 2: the sequence is geometric

In this case, the <u>r</u>atio of consecutive terms is a constant r such that

$a_n = r a_{n-1}$

We can solve for $a_n$ in terms of $a_1$ like we did in the arithmetic case.

$a_{n-1} = ra_{n-2} \implies a_n = r\left(ra_{n-2}\right) = r^2 a_{n-2}$

and so on down to

$a_n = r^{n-1} a_1$

Now,

$a_3 = r^2 a_1 = 2$

$a_5 = r^4 a_1 = 16$

Eliminate $a_1$ and solve for r by dividing

$\dfrac{a_5}{a_3} = \dfrac{r^4a_1}{r^2a_1} = \dfrac{16}2 \implies r^2 = 8 \implies r = 2\sqrt2$

Solve for $a_1$ :

$r^2 a_1 = 8a_1 = 2 \implies a_1 = \dfrac14$

Then the 100th term is

$a_{100} = \dfrac{(2\sqrt2)^{99}}4 = \boxed{\dfrac{\sqrt{8^{99}}}4}$

The arithmetic case seems more likely since the final answer is a simple integer, but that's just my opinion...

3 0

2 years ago

How much larger than 3/4 is 25/32

kvv77 [185]

First change the denominator to the same denominator so you can easily compare them.

3/4= 24/32. The difference between them is 1/24, or 25/32 is larger than 3/4 by 1/24.

Hope this helped.

8 0

3 years ago

Find the simplified product :

Molodets [167]

The last one 6x the power of 4

3 0

3 years ago

Read 2 more answers

Help on 25-29! I do not understand!!!

Aleksandr-060686 [28]

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26. If 15 scoops makes 5 gallons, then divide 15/5. That's 3 scoops per gallon. It's asking how many gallons can be made with 6 scoops. That would be 2 gallons.
27. All it's asking is 38 times 5, which would be 190.
28. Since 5 gallons goes into 15 gallons three times, you would divide $22.20 by 3. That would be $7.40 each 5 gallons.

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3 years ago