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MA_775_DIABLO [31]
2 years ago
7

1. You and your friend mix water and citric acid. You add 3 cups of citric acid for every

Mathematics
1 answer:
Novosadov [1.4K]2 years ago
4 0

Answer:

Mine will be more acidic

Step-by-step explanation:

16 cups × 12 cups

192 cups

For me: 3 citric acid every 3 cups

192÷16= 12

12×3= 36

Friend:

192÷12=16

16×2=24

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Express the product of 2x^2+7x-10 and x+5 in standard form
zimovet [89]

Answer:

2x³+17x²+25x-50

Step-by-step explanation:

Standard Form: All your numbers and variables in order of the highest exponent.

(2x²+7x-10)(x+5)

We want to distribute x and 5 to every single value.

2x³+7x²-10x+10x²+35x-50

Simplify.

2x³+17x²+25x-50

This is standard form because the highest values are on the left (x³ is larger than x²).

4 0
2 years ago
Rewrite in mathematical language. Every negative integer J is less than or equal to its inverse.
Luda [366]

Answer:

-J \leq J

Step-by-step explanation:

Given

Negative integer J

Required

Represent as an inequality of its inverse

The question didn't state if it's additive inverse or multiplicative inverse;

<em>Since the question has to do with negation, I'll assume it's an additive inverse</em>

<em></em>

The inverse of -J is +J

To represent as an inequality (less than or equal), we have:

-J \leq +J

Solving further, it gives

-J \leq J

3 0
3 years ago
Can you tell me which statements go in "agree" and "disagree"?
stepan [7]

Answer:

Step-by-step explanation:

wefasv

4 0
3 years ago
Each game costs $1.25 and each ride costs $2.75. A boy spent $20.25 all together at the carnival and the number of rides he went
a_sh-v [17]

Answer:

3 games and 6 rides

Step-by-step explanation:

3 0
3 years ago
Find the sum or difference. a. -121 2 + 41 2 b. -0.35 - (-0.25)
s344n2d4d5 [400]

Answer:

2

Step-by-step explanation:

The reason an infinite sum like 1 + 1/2 + 1/4 + · · · can have a definite value is that one is really looking at the sequence of numbers

1

1 + 1/2 = 3/2

1 + 1/2 + 1/4 = 7/4

1 + 1/2 + 1/4 + 1/8 = 15/8

etc.,

and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

How do we find this value?

If we assume it exists and just want to find what it is, let's call it S. Now

S = 1 + 1/2 + 1/4 + 1/8 + · · ·

so, if we multiply it by 1/2, we get

(1/2) S = 1/2 + 1/4 + 1/8 + 1/16 + · · ·

Now, if we subtract the second equation from the first, the 1/2, 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1 which means S/2 = 1 and so S = 2.

This same technique can be used to find the sum of any "geometric series", that it, a series where each term is some number r times the previous term. If the first term is a, then the series is

S = a + a r + a r^2 + a r^3 + · · ·

so, multiplying both sides by r,

r S = a r + a r^2 + a r^3 + a r^4 + · · ·

and, subtracting the second equation from the first, you get S - r S = a which you can solve to get S = a/(1-r). Your example was the case a = 1, r = 1/2.

In using this technique, we have assumed that the infinite sum exists, then found the value. But we can also use it to tell whether the sum exists or not: if you look at the finite sum

S = a + a r + a r^2 + a r^3 + · · · + a r^n

then multiply by r to get

rS = a r + a r^2 + a r^3 + a r^4 + · · · + a r^(n+1)

and subtract the second from the first, the terms a r, a r^2, . . . , a r^n all cancel and you are left with S - r S = a - a r^(n+1), so

(IMAGE)

As long as |r| < 1, the term r^(n+1) will go to zero as n goes to infinity, so the finite sum S will approach a / (1-r) as n goes to infinity. Thus the value of the infinite sum is a / (1-r), and this also proves that the infinite sum exists, as long as |r| < 1.

In your example, the finite sums were

1 = 2 - 1/1

3/2 = 2 - 1/2

7/4 = 2 - 1/4

15/8 = 2 - 1/8

and so on; the nth finite sum is 2 - 1/2^n. This converges to 2 as n goes to infinity, so 2 is the value of the infinite sum.

8 0
3 years ago
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