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3 years ago

Write an equation of the

1 answer:

6 0

Answer:

y = -2x - 2

Explanation:

1. Find the slope (m) using the equation (y2-y1) / (x2-x1)

(y2-y1) / (x2-x1)
(-12 - 12) / (5 - -7)
(-24) / (12)
-2

2. To find “b”, plug in one of the points into the equation (e.g. if you choose the point (-7, 12), plug in -7 for x and 12 for y)

y = -2x + b
12 = -2(-7) + b
12 = 14 + b
-2 = b

3. Rewrite the equation using the information you have

y = -2x -2

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Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. E

Elenna [48]

Answer:

Step-by-step explanation:

a₃ = -2

a₇ = -10

The nth term of an arithmetic sequence is:

a = a₁ + d (n − 1)

Therefore:

-2 = a₁ + d (3 − 1) = a₁ + 2d

-10 = a₁ + d (7 − 1) = a₁ + 6d

Subtract the equations:

8 = -4d

d = -2

Plug into either equation to find the first term.

-2 = a₁ + 2(-2)

a₁ = 2

5 0

3 years ago

The volume of a cylinder is 252π cm3 and its height is 7 cm. What is the cylinder’s radius? A. 36 B. 80 C.16 D.6

REY [17]

Put the given information into the formula and solve for the variable of interest.
.. V = π*r^2*h
.. 252π = π*r^2*7
.. (252π)/(7π) = r^2
.. 36 = r^2
.. 6 = r

The radius is 6 cm. Selection D is appropriate.

_____
We would prefer that the offered selections had the appropriate cm units attached.

5 0

4 years ago

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

4 years ago

What is the next number in this geometric sequence?

Anna11 [10]

Answer:

C. -262.44

Step-by-step explanation:

-3.24, 9.72,-29.16, 87.48

-3.24*-3= 9.72, 9.72*-3= -29.16, -29.16*-3= 87.48

the rule for this sequence is multiplying by -3

87.48*-3= -262.44

8 0

3 years ago

F a gambler rolls two dice and gets the sum of 7, he wins $20. if he gets a sum of 4, he wins $40. the cost of playing is $14. w

DaniilM [7]

The expectation of this game is that the house (casino) takes in roughly $3.83 every time someone plays, and after enough plays, they will typically always win.

We can determine this case by looking at all of the possibilities and how much you can win or lose off of each. There are 36 total cases for what can happen when we roll the dice. Of those 36 cases, 9 of them produce positive winnings and 27 of them produce losses.

To calculate the winnings, we need to look at what type they are. 6 of them will be 7's which earn the gambler $20. 3 of them would be 4's, which earns the gambler $40.

6($20) + 3($40)
$120 + $120
$240

Then we look at the losses. This is easier to calculate since every time the gambler loses, he losses exactly $14. There are 27 of these instances.

27($14)
$378

Now we can look at the average loss per game by subtracting the losses from the gains and finding the average.

(Winnings - losses)/options
($240 - 378)/36
$3.83

3 0

3 years ago