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garik1379 [7]
3 years ago
12

find the sum of even numbers between 1001 and 10,000 (Arithmetic progressions) DO STEP BY STEP PLEASE ​

Mathematics
1 answer:
love history [14]3 years ago
7 0

Step-by-step explanation:

arithmetic progression

even numbers between 1001 and 10000

1002,1004,.......9998

Tn=a+(n-1)d

Tn = 9998 last term in the progression of even numbers

a = 1002 first term

d = 2 distance

9998=1002+(n-1)(2)

8996=2n-2

8998=2n

n = 4499 the number of terms

sum = n/2 (a+Tn) = 4499/2(1002+9998)

= (4499/2)(11000) = 24744500

Logic:

notice what happens when you add the first and last terms

1002+9998=11000

1004+9996=11000

.......

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16x^2-vox=0 when x=2 so

16x^2-vox=0

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3 years ago
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Raylan opened a savings account with $100. After 5 years there is $122. 50 in the account. What is his simple interest rate?
serious [3.7K]
<h3>Answer:</h3>

4.5% annually

<h3>Step-by-step explanation:</h3>

Simple interest is the amount of interest added to a singular sum of money at a fixed rate.

Formula

The formula for simple interest is A = P(1+rt). In this formula, A is the total amount of money in the account, P is the original amount deposited, r is the rate of interest as a decimal, and t is the time in years.

Calculations

To find the rate, plug the information we know into the formula above

  • 122.50 = 100(1+r*5)

Divide both sides by 100

  • 1.225 = 1 + r*5

Subtract 1 from both sides

  • 0.225 = r*5

Divide both sides by 5

  • 0.045 = r

This gives us the rate as a decimal. So, to find the rate as a percent. Do this by moving the decimal 2 places to the right (or just multiply by 100, they do the same thing). This means that the rate of simple interest is 4.5%.

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2 years ago
Which statement about 2(×+4) is true ?<br>​
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What is the factored form of the expression?<br><br> d^2 = 36d + 324
Veseljchak [2.6K]

Answer:

(x-43.45)(x+7.45)=0

Step-by-step explanation:

We have the quadratic equation d^{2}=36d+324  i.e. d^{2}-36d-324=0

As, the roots of the quadratic equation ax^{2}+bx+c=0 are given by x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}.

So, from the given equation, we have,

a = 1, b = -36 , c = -324.

Substituting the values in x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}, we get,

x=\frac{36\pm \sqrt{(-36)^{2}-4\times 1\times (-324)}}{2\times 1}

i.e. x=\frac{36\pm \sqrt{1296+1296}}{2}

i.e. x=\frac{36\pm \sqrt{2592}}{2}

i.e. x=\frac{36\pm 50.9}{2}

i.e. x=\frac{36+50.9}{2}  and x=\frac{36-50.9}{2}

i.e. x=\frac{86.9}{2}  and x=\frac{-14.9}{2}

i.e. x = 43.45 and x = -7.45

Thus, the roots of the equation are 43.45 and -7.45.

Hence, the factored form of the given expression will be (x-43.45)(x+7.45)=0

3 0
3 years ago
Please help with this
Svetllana [295]
To solve this equation, all you need to do is substitute the value of x that would be like this y = -2 (-3) -7 and solve, the answer would be -1.
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