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2 years ago

8th term of 1/4,1/8,1/16,1/32

1 answer:

4 0

$a_1=\dfrac{1}{4};\ a_2=\dfrac{1}{8};\ a_3=\dfrac{1}{16};\ a_4=\dfrac{1}{32};...\\\\it's\ a\ geometric\ sequence\ where\ a_1=\dfrac{1}{4}\ and\ r=\dfrac{1}{8}:\dfrac{1}{4}=\dfrac{1}{2}\\\\a_n=a_1r^{n-1}\\\\n=8\\\\a_8=\dfrac{1}{4}\cdot\left(\dfrac{1}{2}\right)^{7-1}=\dfrac{1}{4}\cdot\left(\dfrac{1}{2}\right)^6=\dfrac{1}{4}\cdot\dfrac{1}{64}=\dfrac{1}{256}$

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Which of the following is parallel to the line 2x+4y=16

k0ka [10]

Answer:

Option C: y=-1/2x + 8

Step-by-step explanation:

So we have the options:

A) y=2x+5

B) y=-1/2x+4

C)y=-1/2x+8

D)y=-2x+5

But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.

So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y

Original equation

2x+4y=16

Subtract 2x from both sides

4y=-2x+16

Divide both sides by 4

y = -1/2x + 4

Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.

Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel

Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel

Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer

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A university has 28,980 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of st

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3 years ago

Richard bought a pair of shoes for $37.00, a tie for $22.00, and a new belt for $17.00. If the sales tax is 7.5%, how much sales

nadezda [96]

It seems to me, that if you were to add the price of all three items together, then multiply by 7.5%, you'd have the answer. Remember that 7.5% = .075 ... in other words, that is the number you would multiply the sum of the items by. Does that help?

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2 years ago

There are two cubes, one smaller than the other. The two cubes combined has a volume of 118.125in. Find the side length of each

Sunny_sXe [5.5K]

Step-by-step explanation:

let the big cube side be b

small cube side be s

s = 2/3 * b

bv + sv = 118.125

b^3 + 8/9 b^3= 118.125

17 b^3/8 = 118.125

b^3 = 55.58

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2 years ago

Pls help need it ASAP can’t figure it out

Pie

Answer:

-25

Step-by-step explanation:

10^2 ÷ -2^2 = -25

That's why the answer is -25.

4 0

2 years ago