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3 years ago

Explain how solving an equation with several variables is similar to and different from the

Mathematics

1 answer:

matrenka [14]3 years ago

4 0

Answer:

Step-by-step explanation:

To solve an equation for a particular variable, we can perform the same actions we did when solving equations that only had one variable. We can add the same number to both sides, multiply both sides by the same number, etc.

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Find the sum of the sequence.<br> 39 +40 +41 +42 + ... + 138

Elis [28]

Answer:

Sol1 you can use "first(first+last)/2" is 138(138+1)/2 - 38(38+1)/2 = 8850

Sol2 or you can look this 39+40+41+....+100+(100+1)+(100+2)+....+(100+38) = 1+2+3+.....+99+100+100(38) = 5050+3800 =8850

6 0

3 years ago

Victor earns a gross annual income of $64,570 and is buying a home for $125,340. He is making a 15% down payment and financing t

Oliga [24]

Part A:

Given that <span>Victor is buying a home for $125,340 and that he is making a 15% down payment.

The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.

Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539

Part B

</span>Given that he earns a gross annual income of $64,570 <span>and that the loan of $106,539 will be spread for 20 years at 3.75% interest.

$106,539 / 20 = $5,326.95

Roughly he will be paying about $5,000 every year which is way below his annual gross income.

Therefore, he can afford the mortgage.

Part C

The monthly mortgage payment can be calculated using the present value of annuity formula given by

</span> $PV=P\left( \frac{1-\left(1+\left( \frac{r}{t} \right)\right)^{-nt}}{ \frac{r}{t} } \right)$
<span>
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.

Here, PV = </span>$106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.

Thus, we have:

$106,539=P\left( \frac{1-\left(1+\left( \frac{0.0375}{12} \right)\right)^{-20\times12}}{ \frac{0.0375}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+0.003125\right)^{-240}}{0.003125} \right)=P\left( \frac{1-\left(1.003125\right)^{-240}}{0.003125} \right) \\ \\ =P\left( \frac{1-0.472919}{0.003125} \right)=P\left( \frac{0.527081}{0.003125} \right)=168.666P \\ \\ \Rightarrow P= \frac{106,539}{168.666} =631.66$

Therefore, the monthly mortgage payment is $631.66

Part D

Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40

Therefore, his total payment for the house will be $151,598.40

Part E

Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.

Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40

7 0

3 years ago

-3(-5)-3y=-6 find the value of y

julia-pushkina [17]

-3 (-5) - 3y = -6

15 - 3y = -6

-3y = -6 + (-15)

-3y = -21

y = -21 / -3

y = 7

The value of y is 7.

6 0

3 years ago

The perimeter of a rectangle is 24 m. The length is 30 m less than five times the width. Find the dimensions of the rectangle. L

Len [333]

Answer:

<h2>width = 7 m</h2><h2>length = 5 m</h2>

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 24m

The statement

The length is 30 m less than five times the width is written as

l = 5w - 30

Substitute the expression into the above formula and solve for the width

That's

24 = 2( 5w - 30) + 2w

24 = 10w - 60 + 2w

84 = 12w

Divide both sides by 12

w = 7

Substitute this value into l = 5w - 30

That's

l = 5(7) - 30

l = 35 - 30

l = 5

Therefore the dimensions are

width = 7 m

length = 5 m

Hope this helps you

6 0

3 years ago

Is a/b +b/c rational number<br>

Anarel [89]

Answer:

Yes.

Step-by-step explanation:

Yes.

Assuming a, b and c are integers (not = 0)

a/b + b/c

= (ac + b^2) / bc which is a rational number.

3 0

2 years ago