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3 years ago

What is the next term in the geometric sequence 4, -12, 36

1 answer:

7 0

The sequence is to multiply by -3. Therefore, you want to multiply by -3 which gives you 108. Since it is a negative by a positive the answer would be negative. The next term would be -108.

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If gas cost $1.35 per gallon and Jose has $81 budgeted for gasoline, what os the maximum distance in miles he can travel if his

MA_775_DIABLO [31]

So you times 1.35 by 60 and It gives you 81 so its 60 times 34 = 2040

3 0

3 years ago

There are 257 people at a dance performance. Orchestra seats cost $12 and balcony seats cost $8. The total receipts were $2,716.

solniwko [45]

x = # of balcony seats

y = # of orchestra seats

We have to create a system of equations to solve this problem

x + y = 256

$8x + $12y = $2,716

We will solve this system of equations by elimination.

Multiply the first equation by -8

-8x - 8y = -2048

8x + 12y = 2716

Let's add the equations together

0 + 4y = 668

Simplify the left side

4y = 668

Divide both sides by 4

y = 167

We can subtract 167 from 257 to get the number of balcony seats.

257 - 167 = 90 balcony seats

There are 167 orchestra seats and 90 balcony seats

5 0

2 years ago

Can someone help me with this question? Thank you!

Natali [406]

Answer:

Step-by-step explanation:

22 is the largest number you are given in this diagram. 0 is the smallest. that would be your first step.

Next think about it as if you already know your midpoint, as in, midpoint being half of your ending value.

Lastly, you want to divide 22 in half, since midpoint is half of your line segment, and then answer you get is 11

3 0

3 years ago

Solve <img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D

Nostrana [21]

Answer:

$\displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}$

Step-by-step explanation:

we would like to solve the following equation for x:

$\displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x}$

to do so isolate $\frac{1}{x}$ to right hand side and change its sign which yields:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x}$

simplify Substraction:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)}$

get rid of only x:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)}$

simplify addition of the left hand side:

$\displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)}$

divide both sides by q+p Which yields:

$\displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)}$

cross multiplication:

$\displaystyle x(p + q + x) = - pq$

distribute:

$\displaystyle xp + xq + {x}^{2} = - pq$

isolate -pq to the left hand side and change its sign:

$\displaystyle xp + xq + {x}^{2} + pq = 0$

rearrange it to standard form:

$\displaystyle {x}^{2} + xp + xq + pq = 0$

now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so

factor out x:

$\displaystyle x( {x}^{} + p ) + xq + pq = 0$

factor out q:

$\displaystyle x( {x}^{} + p ) +q (x + p)= 0$

group:

$\displaystyle ( {x}^{} + p ) (x + q)= 0$

by Zero product property we obtain:

$\displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}$

cancel out p from the first equation and q from the second equation which yields:

$\displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}$

and we are done!

3 0

2 years ago

What 2D shape can be created by slicing a cone vertically?

Triss [41]

Answer:

C) triangle

Step-by-step explanation:

Honestly I have no clue how to explain slicing shapes. but basically if a cone was a 2-D figure what shape would it be? a triangle

3 0

2 years ago

Read 2 more answers