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stealth61 [152]
2 years ago
11

Please help top and bottom.

Mathematics
1 answer:
Helga [31]2 years ago
3 0
1. Perimeter
22a + 2(6a + 8) -4 = p

[I got 22a from 12a + 10a]

2. If p = 250, what is a?

22a + 2(6a + 8) - 4 = 250
Distributive property
22a + 12a + 16 - 4 = 250
Add like terms
34a + 12 = 250
Subtract 12 by both sides
34a = 238
Divide 34 by both sides
a = 7
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What is the value of 4*(-1+2-3+4-3+6-7+....+100) Show your work. [Pls help I am really drowning in work. 50 points + brainliest
KengaRu [80]

Answer:

200

Step-by-step explanation:

We have:

4(-1+2-3+4-5+6-7...+100)

We can rearrange the numbers to obtain:

4((-1-3-5-7-...-99)+(2+4+6...+100))

From the left, we can factor out a negative. So:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

In other words, we want to find the sum of all the odd numbers from 1 to 99.

And the sum of all the even numbers from 2 to 100.

Let's do each one individually:

Odd Terms:

We have:

(1+3+5+7+...+99)

We can use the arithmetic series formula, where:

S=\frac{k}{2}(a+x_k)

Where k is the number of terms, a is the first term, and x_k is the last term.

Since it's all the odd numbers between 1 and 99, there are 50 terms.

Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:

S=\frac{50}{2}(1+99})

Divide the fraction. Add within the parentheses:

S=25(100)

Multiply:

S=2500

So, the sum of all the odd terms is 2500.

Even Terms:

We have:

(2+4+6+...+100)

Again, we can use the above formula.

Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:

S=\frac{50}{2}(2+100)

Divide and add:

S=25(102)

Multiply:

S=2550

We originally had:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

Substitute them for their respective sums:

4(-(2500)+2550)

Multiply:

4(-2500+2550)

Add:

=4(50)

Multiply:

=200

So, the sum of our sequence is 200.

And we're done!

Note: I just found a <em>way</em> easier way to do this. We have:

4\cdot(-1+2-3+4-5+6-7+...+100)

Let's group every two terms together. So:

=4((-1+2)+(-3+4)+(-5+6)...+(-99+100))

We can see that they each sum to 1:

=4((1)+(1)+(1)+...+(1))

Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:

=4(50)

Multiply:

=200

Pick which one you want to use! I will suggest this one though...

Edit: Typo

8 0
3 years ago
How do you find the property of 34 + 0 + 18 + 26 using Common Core math?
Flauer [41]
I assume you're looking for the sum.

I would use the null property to eliminate 0
34+0+18+26
=34+18+26
then use commutativity to rearrange
=34+26 + 18
Add 34+26=60
=60+18
=78
8 0
3 years ago
I need to figure out how many solutions does the system of equations below have.
Aleonysh [2.5K]

Answer:

The system has one solution.

Step-by-step explanation:

To find the number of solutions of the system, we equal both equations for y.

If we have ax = b, in which both a and b are different of 0, we have one solution.

If both a and b are 0, we have infinite solutions.

If a is 0 and b is not, there are no solutions.

y=6/7x-8 and y=7/9x+10/9

So

\frac{6x}{7} - 8 = \frac{7x}{9} + \frac{10}{9}

\frac{6x}{7} - \frac{7x}{9} = \frac{10}{9} + 8

\frac{54x - 49x}{63} = \frac{10}{9} + \frac{72}{9}

\frac{5x}{63} = \frac{82}{9}

45x = 63*82

Both a and b are different of 0, so the system has one solution.

6 0
2 years ago
How to didvide6 divided by 8,654
Lelechka [254]

Answer: 0.0007

Step-by-step explanation:

6/8654

3 0
3 years ago
When you add 6 to the product of a number and 10, the result is 36. What is the number?
n200080 [17]

Answer: the number is 3.

Step-by-step explanation:

(x × 10) + 6 = 36

[(3) × 10] + 6 = 36

5 0
2 years ago
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