MATHEMATICS MIDDLE SCHOOL

A rectangle is eight inch long and its diagonal is ten inches. What's the width of the rectangle?

Answers

Answer 1

Answer:

Diagonal = $\sqrt{length^(2) + width^(2) }$

10 = $\sqrt{8^(2) + width^(2) }$

10 = $\sqrt{64 + width^(2) }$

100 = 64 + $width^(2)$

$width^(2)\n$ = 100 - 64

$width^(2)$ = 36

width = $√(36)$

width = 6 inches

Answer 2

Answer:

Answer:

the answer is 6 inches

Step-by-step explanation:

To find the diagonal we use the Pythagorean Theorem:

l² + w² = d² where the is d hypotenuse

8² + w² = 10²

64 + w² = 100

w² = 100 - 64

w² = 36

w = √36

w = 6

therefore the width of the rectangle is 6 inches

I hope this was helpful !!!!!!!!!

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Please need help on this

Solve the inequality

Answers

Answer:

$\large\boxed{x>-25}$

Step-by-step explanation:

$-(3)/(10)x-7<(1)/(2)\qquad\text{multiply both sides by 10}\n\n10\!\!\!\!\!\diagup^1\cdot\left(-(3)/(10\!\!\!\!\!\diagup_1)x\right)-(10)(7)<10\!\!\!\!\!\diagup^5\cdot(1)/(2\!\!\!\!\diagup_1)\n\n-3x-70<5\qquad\text{add 70 to both sides}\n\n-3x<75\qquad\text{change the signs}\n\n3x>-75\qquad\text{divide both sides by 3}\n\nx>-25$

Beulah used 3/5 pounds of dough, 3/4 pound of sugar, & 2/3 pounds of sprinkles to make donuts. How many pounds of donuts did Beulah make?

Answers

Number of pounds of dough used = 3/5 pounds.

Number of pounds of sugar used = 3/4 pounds

Number of pounds of sprinkles used = 2/3 pounds.

Total number of pounds of donuts = Number of pounds of dough used + Number of pounds of sugar used + Number of pounds of sprinkles used.

Plugging values.

Total number of pounds of donuts = 3/5 + 3/4 + 2/3.

We need to add all those fractions.

In order to add fracions, we need to find common denominator (lcd).

We have 5,4 and 3 in denominators.

Least common denominator(lcd) of 5, 4 and 3 is 60.

We need to make each denominator equals 60.

Multiplying first fracion by 12 in top and bottom, we get

3*12/5*12 = 36/60

Multiplying first fracion by 5 in top and bottom, we get

3*15/4*15 = 45/60

Multiplying first fracion by 20 in top and bottom, we get

2*20/3*20 = 40/60.

Therefore,

3/5 + 3/4 + 2/3 = 36/60 + 45/60 + 40/60

= 121/60

Let us convert 121/60 into mixed fraction.

Dividing 121 by 60 we get quotient =2 and remainder =1.

So, the mixed fraction is 2 1/60.

Therefore, Beulah made total 2 1/60 pounds of donuts.

Final answer:

The total weight of the donuts can be found by adding together the weights of the dough, sugar, and sprinkles, which comes to approximately 2.02 pounds.

Explanation:

The total weight of the donuts Beulah made can be found by adding the weights of the ingredients - dough, sugar, and sprinkles - together. First, she used 3/5 pounds of dough, to which she added 3/4 pound of sugar. Lastly, she used 2/3 pounds of sprinkles.

Now, let's add these quantities:

3/5 + 3/4 + 2/3 = 1.2 + 0.75 + 0.67 approximately.
Alternatively use a common denominator (60 for instance) to simplify the addition:
36/60 + 45/60 + 40/60 = 121/60 =2.02 pounds approximately.

Therefore, "Beulah made about 2.02 pounds of donuts".

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8(t + 2)—3(t—4)=6(t—7)+8

Answers

The solution to the given equation is t = 62.

We have,

Let's simplify the given equation step by step:

8(t + 2) - 3(t - 4) = 6(t - 7) + 8

Step 1: Apply the distributiveproperty by multiplying each term inside the parentheses by the coefficient outside the parentheses:

8t + 16 - 3t + 12 = 6t - 42 + 8

Simplifying the equation further:

8t - 3t + 16 + 12 = 6t - 42 + 8

Step 2: Combine liketerms on both sides of the equation:

(8t - 3t) + 28 = 6t - 34

Simplifying the equation further:

5t + 28 = 6t - 34

Step 3: To isolate the variable t, we will move all terms containing t to one side and the constants to the other side:

5t - 6t = -34 - 28

Simplifying the equation further:

-1t = -62

Step 4: Since -1t is equivalent to -t, we can rewrite the equation as:

-t = -62

Step 5: To solve for t, we need to multiply both sides of the equation by -1 to eliminate the negative sign:

(-1)(-t) = (-1)(-62)

Simplifying the equation further:

t = 62

Therefore,

The solution to the given equation is t = 62.

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8t + 2 -3t +12 = 6t - 42 +8
5t +2 +12 = 6t - 34
5t +14 = 6t - 34
-14 = - 14
5t = 6t - 20
-6t = -6t
-t = -20
t = 20

1. You have no debt and $2,000 in your savings account. On your current budget, you figure that you can save an additional $2,000 each year. You want to put your money to work. Calculate the return on each of the investment options described below. a. Continue putting your money into your savings account, which earns an annual interest rate of 3 percent. What will be the balance of your savings account at the end of 10 years, and how much interest will you have earned?

Savings Balance:

Interest Earned:

b. Put your savings and the extra $2,000 into a mutual fund that earns 8 percent annually. If you reinvest your profits each year (earning compound interest), how much will you have in the mutual fund at the end of 10 years, and how much interest will you have earned?

Total in Mutual Fund:

Interest Earned:

c. Leave half of your $2,000 in savings, and invest the other half in the stock market. Do the same each year, putting $1,000 in stocks and the other $1,000 in savings. You earn 3 percent on your savings account and 10 percent on your stock investments. How much will you have earned from your savings account after 10 years? How much will you have earned from your stock investments after 10 years? How much money will you have between your savings account and your stocks combined after 10 years?

Money Earned from Savings Account:

Money Earned from Stock Market:

Total Money:

2. Your family gives you $5,000 as a college graduation present. You are about to start paying off $50,000 in student loans at a 4 percent interest rate for a 15-year loan. You could use this money to pay some of your loans, but you could also invest it.

a. Calculate the monthly payments and total payment you will be making on your loan if you do not use the $5,000 to make an initial payment.

Monthly Payment:

Total Amount Paid:

b. Calculate the monthly payments and total payment you will be making on your loan if you do use the $5,000 to make an initial payment.

Monthly Payment:

Total Amount Paid:

c. List two ways you could invest the money, and describe the expected returns from each method over a 15-year period.

d. What would you do with the $5,000? Explain why your choice makes financial sense to you.

Answers

Answer: $\n$ (a) Saving balance = $20,600

$\n$ Interest = $600

$\n$ (b) Total in Mutual fund = $26,503.34

$\n$ Interest earned = $3,903.34

$\n$ (c) Money Earned from Savings Account= $11,330

$\n$ Money Earned from Stock Market:$12,100

$\n$ (2a) Monthly Payment = $7,503.93

$\n$ Total Amount Paid = $90,047.18

$\n$ (b) Monthly Payment =$6,753.53

$\n$ Total Amount Paid = $81,042.46

$\n$ (c) Peer - peer lending and index fund

Step-by-step explanation:

$\n$ The Original money, which is the principal , in the savings account is $2,000

$\n$ Savings each year = $2,000

$\n$ Savings for 10 years = $2,000 x 10 = $20,000

$\n$ Annual Interest rate = 3%

$\n$ Interest for 10 years = PTR/100

$\n$ = 2000 x 10 x 3 / 100

$\n$ = 600

$\n$ Total savings after 10 years = saving + interest

$\n$ = $20,000 + $600

$\n$ = $20,600

$\n$ Therefore:

$\n$ Savings balance = $20,600

$\n$ Interest earned = $ 600

$\n$ (b) The savings + the extra $2000 = $20,600 + $ 2,000

$\n$ = $22,600

$\n$ Interest rate = 8%

$\n$ Interest = 22,600 x 1 x 8 / 100

$\n$ = $1,808

$\n$ That means profit = $ 1,808

$\n$ Re – investing the profit, we will take the profit as the principal and then calculate the compounded interest for 10 years using the formula

$\n$ A = P $(1+r)^(t)$

$\n$ = 1,808 (1.08)10

$\n$ = $3,903.34

$\n$ Amount in the mutual fund at the end of ten years implies

$\n$ $22,600 + $3,903.34 = $26,503.34

$\n$ Total in Mutual fund = $26,503.34

$\n$ Interest earned = $3,903.34

$\n$ (c) Since half of the $2,000 is left in savings, it means we have $\n$ $1,000 in savings

$\n$ Savings after 10 years = $1,000 + 10 x $1,000 = $ 11,000

$\n$ 3% of savings = 0.03 x 11.000 = $330

$\n$ Total money in Savings = $11,000 + $330

$\n$ = $11,330

$\n$ Also for Stock

$\n$ Money in stock after 10 years = $1,000 + 10 x $1,000 = $11,000

$\n$ 10% of stock = 0.1 x $11,000 = $1,100

$\n$ Total money in Stock = $11,000 + $1,100

$\n$ = $12,100

$\n$ Total money = money in savings + money in stock

$\n$ = $11,330 + $12,100

$\n$ = $23,430.00

$\n$ (2) Amount given = $5,000

$\n$ Loan = $50,000

$\n$ Interest rate on loan = 4%

$\n$ Calculating the amount the loan will yield after 15 years using the formula

$\n$ A = P $(1+r)^(t)$

$\n$ A = 50,000 ( 1 + 0.04)15

$\n$ A = $90,047.18

$\n$ Therefore the compounded interest ( C.I) = $90,047.18 - $50,000

$\n$ = $40,047.18

$\n$ (a) If you do not use the $5,000 , the monthly payment = $90,047.18 / 12

$\n$ = $7,503.93

$\n$ And the total payment = $90,047.18

$\n$ (b) If , $5,00 is used as the initial payment then the remaining loan will be

$\n$ $50,000 - $5,000 = $45,000

$\n$ So , we will have to calculate the amount $45,000 will yield after 15 years using the same formula

$\n$ That is : A = 45,000 (1.04)15

$\n$ A =$ 81,042.46

$\n$ Therefore the C.I = $81,042.46 - $45,000

$\n$ = $36,042.46‬

$\n$ Monthly payment = $ 81,042.46/ 12

$\n$ = $6,753.53

$\n$ Total payment = $81,042.46

$\n$ (c) Method of investing the money

$\n$ (i) Peer to peer Lending. Giving helping hand one could earn $\n$ money as they pay back the loan with interest. If the interest is set to be 20%, for 15 years , 5000 will yield

$\n$ 5000(1.2)15 = $77,035.10

$\n$ (ii) Index fund : Index funds are a collection of stocks, so your investment is automatically diversified. Index fund like E-trade could be invested into. Using the stock calculator , it would yield $141,144

$\n$ (d) I would rather invest the money in E- trade since I am sure it would bring a profit more than the amount of the loan will yield after 15 years , I will even have more money to hold at habd

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