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olasank [31]
3 years ago
13

A rectangle has an area of 82 ft2. What is the length if the width is 10 ft?

Mathematics
1 answer:
Luda [366]3 years ago
7 0

Answer:

187

Step-by-step explanation:

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"10 less 2 times a number"<br> O 10r - 2<br> 0 2r - 10<br> O 2 - 10<br> O 10 - 2r<br> 10 - 2
4vir4ik [10]

the answer to the question is 2r-10

4 0
3 years ago
Read 2 more answers
Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

3 0
3 years ago
How many solutions exist for the system of equations graphed below?
Anestetic [448]

Answer:

One

General Formulas and Concepts:

<u>Algebra I</u>

  • Reading a coordinate plane
  • Solving systems of equations by graphing

Step-by-step explanation:

If 2 lines are parallel, they will have no solution.

If 2 lines are the same, they will have infinite amount of solutions.

We see from the graph that the 2 lines intersect at one point, near x = 1.5.

∴ our systems has 1 solution.

4 0
2 years ago
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In a herd of cattle, the ratio of the number
Neko [114]

Answer:

In a herd no. of Cattle are: x

The ratio of bulls to cows is 1:6

\frac{bulls}{cows}  =  \frac{1}{6}  

6 bulls = 1 cows

bulls \:  + cows = x

bulls + 6 \: bulls \:  = x

7bulls = x

7 0
3 years ago
How many triangles can be made if one angle is 95° and another angle is acute?
Oksana_A [137]
Theoretically, the answer will be infinite.

Since one angle of 95 degrees means the other two angles must be acute. You can pick any two real numbers with the sum of 85.
8 0
3 years ago
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