Use the reverse tabular method to solve division problem: (x^3+2x^2+2x+1)/(x+1)

A corner store sells two kinds of baked goods: cakes and pies. A cake costs $10 and a pie costs $7. In one

Ede4ka [16]

I think the answer would be 4 cakes because they would have bought 6 pies for it to cost $42 and then the extra $40 which will be converted to 4 cakes. So the answer is 4. Hope I helped.

7 0

3 years ago

Pls help me ill give brailiest do very soon

Nikitich [7]

A.6x+34
B.8t+38
C.2y-14
D.11n+16

5 0

3 years ago

I need help with this word problem it’s urgent please help.

harkovskaia [24]

Starting with some solution of volume v and an alcohol concentration of 100c % , if you add 180 mL of 45% isopropyl to it, you get a mixture with a total volume of 180 mL + v.

Each mL of the starting solution contains c mL of alcohol. For example, if the concentration of the starting solution is 80% (so c = 0.8), then each mL contains 80% = 0.8 of one mL of alcohol.

Similarly, each mL of the added solution with 45% concentration contains 0.45 mL of alcohol.

You want the new solution to have a concentration of 70%, so that the ratio of the amount of alcohol in it to the total volume is 70%, meaning

cv + 0.45 (180 mL) = 0.7 (180 mL + v)

and you want to solve for v :

cv + 81 mL = 126 mL + 0.7v

cv - 0.7v = 126 mL - 81 mL

(c - 0.7) v = 45 mL

v = (45 mL) / (c - 0.7)

Judging by context clues, c lies somewhere between 0.7 and 1. (It can't be less than 0.7 because mixing this solution with any other solution of smaller concentration will never yield a solution of higher concentration.)

If, for example, c = 0.8, so that your starting solution is at 80% concentration, then you would need

v = (45 mL) / (0.8 - 0.7) = 450 mL

to be mixed with 180 mL of 45% solution to end up with 180 mL + 450 mL = 630 mL of 70% solution.

As another example, if you're mixing pure alcohol, so that c = 1, you would need

v = (45 mL) / (1 - 0.7) = 150 mL

to make a 180 mL + 150 mL = 330 mL batch of 70% solution. The fact that you would need less of a higher concentration solution is not surprising.

3 0

3 years ago

The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

8 0

2 years ago

If f(x)=0 what is x

kotykmax [81]

Answer: If f(x)=0 then x is 0. Good luck!

Step-by-step explanation: GIVE ME BRAINLY A VOTE AND A THANKS BYE

3 0

3 years ago