MATHEMATICS HIGH SCHOOL

The area of a rectangular painting is 4275cm². if the length of the painting is 75cm, what is its width?

Answers

Answer 1

Answer:

Answer:

Width = 57cm

Step-by-step explanation:

The area of a rectangle can be found by using the formula:

Area = Length * Width

Since we know that the area is 4275cm² and the length of the painting is 75cm, we can plug these into the above equation to solve for the width.

Area = Length * Width

4275cm² = 75cm * Width

To find the width, we can simply divide both sides by 75 so that the width measurement is isolated:

Width = 57cm

To verify this, we can multiply the length and width to see if the area equals 4275cm²:

75cm * 57cm = 4275cm²

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Is hand lotion homogeneous or heterogeneous

Answers

Homogeneous; its all the same mixture
Remember: homo- meaning same
hetero- meaning different

heterogeneous!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Simplify expression:
3^{−(4a+1)} −3^{−(4a−1)} + 3^{−4a}

Answers

$3^(-(4a+1))-3^(-(4a-1)) + 3^(-4a) =3^(-4a-1 )-3^(- 4a+1 ) + 3^(-4a)=\n \n=3^( -4a )*3^(-1)-3^( - 4a )*3^1 + 3^(-4a) =3^(-4a)(3^(-1)-3+1)=3^( -4a )*((1)/(3)-2)=\n \n=3^( -4a )*(-1(2)/(3))=3^( -4a )*(-(5)/(3))=3^( -4a )*(-5)*(1)/(3) =-5 *3^( -4a )*3^(-1)=\n \n =-5 *3^( -4a +(-1))=-5 *3^( -4a -1)$

Emily has a coupon for 20 percent off her purchase. She finds a backpack she likes on the discount rack. It's original price is $60, but everything on the rack comes with a 30 percent discount. Emily says, "thirty percent and twenty percent make fifty percent so ur will cost $30. Is emy correct?

Answers

Answer: she is incorrect

Step-by-step explanation:

If Emily had a coupon for 20 percent off her purchase, this means that whatever she bought, the total amount would be reduced by 20%. She will be paying 80%

She finds a backpack she likes on the discount rack. It's original price is $60, but everything on the rack comes with a 30 percent discount.

This means that ordinarily,the amount she is meant to pay on the total goods she is buying is 30% lesser than $60. She will be paying

60 - (30/100 ×60)

60 - 0.3×60 = 60-18 = $42

Since she has a 20% coupon on total cost of goods bought, she would be paying

42 - (20/100 ×42)

42 - 0.2×42

= 42 - 8.4 = $33.6

Therefore,

If Emily says, "thirty percent and twenty percent make fifty percent so that her cost will be $30. She is incorrect. Her cost is $33.6

Answer:

she is incorrect.

Step-by-step explanation:

In which of the following stores would you pay the least amount for an item that is priced $360? Store A: Sale of 10% off and a successive discount of 10% off. Store B: Sale of 15% with no additional discount. Store C: Sale of $35 off and a successive discount of 10% off

Answers

The right answer for the question that is being asked and shown above is that: "A: Sale of 10% off and a successive discount of 10% off." The store that would let you pay the least amount for an item that is priced $360 is the Store A.

The correct answer is Store A: Sale of 10% off and a successive discount of 10% off.

Further explanation:

Discount is the reduction of amount in the cost price of any item.

The following formula for discount can be used when the rate of discount and the cost price is given.

$\boxed{{\text{Discount}}=\left( {\frac{{{\text{rate of discount}}}}{{100}}}\right)*{\text{cost price}}}$

The following formula for selling price can be used when the discount and the cost priceis given.

$\boxed{{\text{Selling price}}={\text{Cost price}}-{\text{Discount}}}$

Given:

The price of an item is $\boxed{\$360}$ .

Calculation:

Store A is allowing 10% off and then allowing a successive discount of 10%.

The first discount of an item by the use of the formula can be calculated as,

$\begin{aligned}{\text{discount}}&=\left( {\frac{{10}}{{100}}}\right)* 360\n&= 36\n\end{aligned}$

Now, the selling price after allowing the first discount is,

$\begin{aligned}{\text{Selling price}}&={\text{360}}-36\n&=324\n\end{aligned}$

The successive discount on the item can be calculated as,

$\begin{aligned}{\text{discount}}&=\left( {\frac{{10}}{{100}}}\right)*324\n&=32.4\n\end{aligned}$

Now, the selling price after allowing second discount is,

$\begin{aligned}{\text{Selling price}}&={\text{324}}-32.4\n&=291.6\n\end{aligned}$

Therefore, the amount we have to pay to Store A is $\boxed{\$291.6}$ .

Store B is giving 15% off with no additional discount.

The discount of an item by the use of the formula can be calculated as,

$\begin{aligned}{\text{discount}}&=\left( {\frac{{15}}{{100}}}\right)*360\n&=54\n\end{aligned}$

Now, the selling price after allowing discount can be calculated as,

$\begin{aligned}{\text{Selling price}}&={\text{360}}-54\n&=306\n\end{aligned}$

Therefore, the amount we have to pay to Store B is $\boxed{\$306}$ .

Store C is giving $35 off and then allowing a successive discount of 10%.

Now, the selling price after allowing first discount can be calculated as,

$\begin{aligned}{\text{Selling price}}&={\text{360}}-35\n&=325\n\end{aligned}$

The successive discount on the item can be calculated as,

$\begin{gathered}{\text{discount}}=\left( {\frac{{10}}{{100}}}\right)*325\n=32.5\n\end{gathered}$

Now, the selling price after deducting second discount can be calculated as,

$\begin{aligned}{\text{Selling price}}&={\text{325}}-32.5\n&=292.5\n\end{aligned}$

Therefore, the amount we have to pay to Store C is $\boxed{\$292.5}$ .

It can be clearly seen that if we buy an item which is priced at $360 from Store A then we have to pay least amount of $291.6.

Learn more:

1. Learn more about profit and loss brainly.com/question/2479097

2. Learn more about domain and range of thefunctionbrainly.com/question/3412497

3. Learn more about the word problem for magnitude of the acceleration brainly.com/question/1597065

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Profit and Loss

Keywords: Percentage , profit , loss, discount, cost price, selling price, marked price, rate of discount, amount, succesive discount, reduction, maximum, price .

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answers

For this case we have the following recursive formula:
$f (n + 1) = f (n) - 2$
What we must do in this case is to evaluate different values of n until we find f (5)
We have then:
For n = 1:
$f (1 + 1) = f (1) - 2 f (2) = f (1) - 2 f (2) = 18 - 2 f (2) = 16$
For n = 2:
$f (2 + 1) = f (2) - 2 f (3) = f (2) - 2 f (3) = 16 - 2 f (3) = 14$
For n = 3:
$f (3 + 1) = f (3) - 2 f (4) = f (3) - 2 f (4) = 14 - 2 f (4) = 12$
For n = 4:
$f (4 + 1) = f (4) - 2 f (5) = f (4) - 2 f (5) = 12 - 2 f (5) = 10$
Answer:
The value of the recursive formula for f (5) is given by:
$f (5) = 10$

$f(2)=18-2=16\n f(3)=16-2=14\n f(4)=14-2=12\n \boxed{f(5)=12-2=10}$

The supplement of an angle is six and a half times as large as the complement of the angle. What is the measure of the supplement angle to the nearest hundredth of a degree?A) 101.25°

B) 104.22°

C) 106.36°

D) 108.63°