Find the sum of these polynomials. (x^2

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

There are 205 coins in a jar all of which are either nickles or quarters . The vaule of the coin in the jar is $31.85. if both o

Gnesinka [82]

Answer: There are 97 nickels and 108 quarters.

Step-by-step explanation:

Let x = Number of nickels, y = Number of quarters.

As per given,

x+y = 205 ...(i)

0.05x+0.25y = 31.85 ... (ii) [1 nickel = $0.05, 1 quarter = $ 0.25]

Multiply (ii) by 20, we get

x+5y=637 ...(iii)

Eliminate (i) from (iii)

4y = 432

⇒ y = 108 [Divide both sides by 4]

Put value of y in (i), we get

$108+x=205\Rightarrow\ x= 97$

Hence, there are 97 nickels and 108 quarters.

6 0

3 years ago

How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixe

Fantom [35]

The amount of cashew mixed is 5 pounds

<h3>Word problem on total cost</h3>

Cost of 1 pound of cashew = $14

Cost of 1 pound of peanut = $6.50

Total cost of 1 pound of the mixed nuts = $10.25

Cost of 5 pounds of peanuts = 5 x $6.50

Cost of 5 pounds of peanuts = $32.50

Let the amount of cashew be x

Total cost of x cashew = 14x

Total amount of the mixed nuts = x + 5

Total cost of the mixed nuts = 10.25(x+5)

Total cost of the mixed nuts = 10.25x + 51.25

14x + 32.50 = 10.25x + 51.25

14x - 10.25x = 51.25 - 32.50

3.75x = 18.75

x = 18.75/3.75

x = 5

Therefore, the amount of cashew mixed is 5 pounds

Learn more on word problem on cost here: brainly.com/question/21405634

#SPJ1

8 0

1 year ago

Read 2 more answers

Which of the following could be used to calculate the area of a sector in the circle shown below

lara [203]

Answer:

Therefore the Last option is correct

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

Step-by-step explanation:

Given:

Radius = r = 8 in

θ = 42°

To Find:

Area of Sector = ?

Solution:

We know that

$\textrm{Area of Sector}=\pi (Radius)^{2}\times \frac{\theta}{360}$

Substituting the given values in the formula we get

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

Which is the required Answer.

Therefore the Last option is correct

$\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})$

8 0

2 years ago

Kevin traveled at a constant speed on the highway from Hickory Hills to Chicago in 20 minutes. The distance from Hickory Hills t

beks73 [17]

Answer: $V=51\ \frac{mi}{h}$

Step-by-step explanation:

You need to used the following formula:

$V=\frac{d}{t}$

Where "V" is the speed, "d" is the distance and "t" is the time.

In this case you know that Kevin traveled at a constant speed on the highway from Hickory Hills to Chicago in 20 minutes (which is $\frac{1}{3}\ h$ ) and the distance is 17 miles. Then, you can identify that:

$t=\frac{1}{3}\ h\\\\d=17\ mi$

Therefore, knowing these values, you can substitute them into the formula. Then, you get:

$V=\frac{17\ mi}{\frac{1}{3}\ h}\\\\V=51\ \frac{mi}{h}$

8 0

2 years ago

Find the sum of these polynomials. (x^2 - x + 7) + (9x^2 + 6)