HEY GUYS CAN SOMEONE PLEASE HELP I NEED TO PASS THIS!!<br> THANKS SO MUCH FOR THE HELP!

What is the value of x when 3x < -2x + 15

Solnce55 [7]

Answer:

−

3 x = 15 Divide each term in − 3 x = 15 by - 3 . − 3 x − 3 +15 =− 3 Cancel the common factor of − 3 . Cancel the common factor. − 3 x − 3 = 15 − 3 Divide x by 1 . x = 15 − 3 by − 3 . x = − 5

8 0

3 years ago

Read 2 more answers

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

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Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

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The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

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As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Complete the equation describing how x and y are related.<br> Please need help!!!

yKpoI14uk [10]

Answer:

3

Step-by-step explanation:

The equation being used to express the answer is called slope-intercept form.

y = m x + b

m is the slope, b is the y-intercept (where x = 0)

The formula to find slope (m) using two points is called point slope form.

m = (y1 - y2)/(x1 - x2)

Pick two coordinates and plug them in.

m = (1 - 4)/(0 - 1)

m = (-3/-1)

m = 3

5 0

3 years ago

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Please help 100 points!!! :)<br> Who ever answers right first get's brainliest!!! :)

igomit [66]

Answer:

1/7

Step-by-step explanation:

3 0

3 years ago

Ben and Josh went to the roof of their 40-foot tall high school to throw their math books off the edge.

krok68 [10]

Answer:

Josh's book lands first
Ben's lands about 0.648 seconds later

Step-by-step explanation:

Using the given equation for v=60 and s=40, the height of Ben's book is ...

h(t) = -16t² +60t +40

We want to find t when h(t) = 0, so we're looking for the solution to ....

0 = -16t² +60t +40

Using the quadratic formula, we find the positive value of t to be ...

t = (-60 -√(60² -4(-16)(40)))/(2(-16)) = (15 +√385)/8 ≈ 4.3277

__

Similarly, the height of Josh's book is ...

0 = -16t² +48t +40

t = (-48 -√(48² -4(-16)(40)))/(2(-16)) = (12 +√304)/8 ≈ 3.6794

__

The time before Josh's book lands is shorter by ...

4.3277 -3.6794 ≈ 0.6482 . . . . . seconds

Josh's book reaches the ground first, by about 0.648 seconds.

3 0

3 years ago

HEY GUYS CAN SOMEONE PLEASE HELP I NEED TO PASS THIS!! THANKS SO MUCH FOR THE HELP!