What is the volume of the prism? ft³

Anyone I need help whit this question

zepelin [54]

Answer: 94.3 meters

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

if the slopes of the lines in the system are equal and their y-intercepts are also equal, then the system is blank and blank

Tems11 [23]

Answer:

Step-by-step explanation:

same slope and same y-intercept = dependent system and represent the same line.

I'm not sure if those are words they want you use, as you didn't provide the answer choices.

6 0

3 years ago

Find all complex solutions of 7x^2-7x+3=0

Sedaia [141]

Answer:

The complex solutions are

$x = (\frac{7-\sqrt{35} i }{42} , ) x = \frac{7 + \sqrt{35} i }{42})$

Step-by-step explanation:

Step(i):-

Given equation 7 x² - 7 x +3=0

$x = (\frac{-b -\sqrt{b^{2}-4ac } }{2ac} , \frac{-b +\sqrt{b^{2}-4ac } }{2ac})$

Given standard equation

a x² +b x +c =0

a = 7 , b= -7 and c=3

Step(ii):-

$x = (\frac{-(-7) -\sqrt{(-7)^{2}-4(7)(3) } }{2(7)(3)} , \frac{-(-7) +\sqrt{(-7)^{2}-4(7)(3) } }{2(7)(3)})$

$x = (\frac{7-\sqrt{(49-84 } }{42} , \frac{7 +\sqrt{(49-84 } }{42})$

$x = (\frac{7-\sqrt{35i^{2} } }{42} , \frac{7 + \sqrt{35i^{2} } }{42})$

$x = (\frac{7-\sqrt{35} i }{42} , \frac{7 + \sqrt{35} i }{42})$

8 0

3 years ago

Dont really understand how to do this

bija089 [108]

Answers:

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

========================================================

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

-----------------------

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

Anyone Know the Answer?

White raven [17]

The relationship between the number of rose plants and the number of roses is proportional

3 0

3 years ago

What is the volume of the prism? ft³​

What is the volume of the prism? ft³