MATHEMATICS MIDDLE SCHOOL

What is the difference between.....

Answers

Answer 1

Answer:

Taking first summation ∑(1+3n) first

First see few terms of this series. To get first term plug n =0 in 1+3n

So for n =0, $a_(1) = 1 + 3(0) = 1+0 =1$

similarly for next term plug n =1

For n = 1, $a_(2) = 1 + 3(1) = 1+3 = 4$

For n =2, $a_(3) = 1 + 3(2) = 1+6 = 7$

So on ,........and last term will be for n =4

For n =4, $a_(5) = 1 + 3(4) = 1 + 12 = 13$

So we get terms as 1,4,7,.. with constant difference of 3 between succesive terms. So its arithemetic series. Sum formula for arithmetic series is

$S_(n) = (n(a_(1) + a_(n)))/(2)$

where n is total number of terms, $a_(1)$ and $a_(n)$ are first and last term in series

So here n = 5 ( as n is from 0 till 4). so plug value of n as 5, $a_(1)$ as 1 and $a_(5)$ as 13 in sum formula

$S = (5(1 + 13))/(2)$

$S = (5(14))/(2) = (70)/(2) =35$

So sum of first series is 35

Similarly find sum of second series. Plug i values in 3i-5 as shown and find few terms in series

for i =2, $a_(1) = 3(2) - 5 = 6 - 5 = 1$

for i =3, $a_(2) = 3(3) - 5 = 9 - 5 = 4$

so on .... and for last term plug i as 6

for i =6, $a_(5) = 3(6) - 5 = 18 - 5 = 13$

So for sum we will plug n as 5 ( i =2,3,4,5,6 so total 5 terms), then plug $a_(1)$ as -2 and $a_(5)$ as 13 in sum formula

$S = (5(1 + 13))/(2) = (5(14))/(2) = (70)/(2) =35$

So sum of second series is also 35

So difference between sums of both series will be 35-35 =0

Final answer here is 0

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Which measurement facts are true?Select each correct answer.

a.1 gallon = 4 quarts

b. 1 pint = 2 cups

c. 1 quart = 2 pints

d . 1 gallon = 2 quarts

e . 1 pint = 4 cups

f . 1 quart = 2 cups go by

Answers

Answer:

The correct answers are

A. 1 gallon = 4 quarts

B. 1 pint = 2 cups

C. 1 quart = 2 pints

E. 1 pint = 4 cups

What is the width of a rectangle with sn area of 300 square feet if it's length is 1 foot? if it's length is 2 feet?

if it's length is 3 feet?

Answers

well since we know the formula for area is length×width, we can divide area by length to find width. 300÷1=300. your first answer is 300.

if its 2 feet, 300÷2=150, 150 feet is your answer

if its 3 feet, 300÷3=100, 100 feet is your answer

Mrs. Kennedy wants to save $632 to buy a new washing machine. She saves $70 each month. About how many total months will it take Mrs. Kennedy to save enough money to buy the washing machine?

Answers

if you divide 632 by 70 it would be 9.02 so it would be 9 months and 2 day i think

What is 1/4 of 24 solve using a tape diagram

Answers

1/4 of 24 is equals to 6

Two angles in a triangle measure 33 and 112 What is the measure of the third angle?

Answers

All the angles of a triangle always add up to 180 degrees.

For now, x represents the missing angle.
180 = 33 + 112 + x

Add 33 + 112.
180 = 145 + x

Subtract 145 from both sides.
35 = x

So, the measure of the third angle is 35 degrees.

Answer:

35 I got it right on the test.

Step-by-step explanation:

Uma wants to buy a video game system for $400. She has $50 and is saving $25 each week. Solve the equation 25w + 50 = 400 to find how many weeks w it will take Uma to save enough to buy the system.

Answers

Move all terms that don't contain ww to the right side and solve.
w=14

Hope this helps,

kwrob

First take away fifty from both sides
25w = 350
Divide 25 from both sides
Answer is: w = 14

So, it will take Uma 14 weeks to save enough money to but the video game system.

Hope that helps!!!

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