MATHEMATICS HIGH SCHOOL

Which is the value of this expression when a = 5 and k=-2?*
32a-2
75
9
* 25
25
9
75

Answers

Answer 1
Answer:

The value of the expression  ((3^(2)a^(-2) )/(3a^(-1) ) )^(k) when a = 5 and k = -2 is (25)/(9)

How to substitute and get the value of an expression?

The expression is as follows:

((3^(2)a^(-2) )/(3a^(-1) ) )^(k)

using law of indices

Hence,

when a = 5, k = -2

((3^(2)a^(-2) )/(3a^(-1) ) )^(k) = ((9(5^(-2) ))/(3(5^(-1) )))^(-2)

Then,

((9(5^(-2) ))/(3(5^(-1) )))^(-2)=(((9)/(25) )/((3)/(5) ) )^(-2)

(((9)/(25) )/((3)/(5) ) )^(-2)=((9)/(25) ((5)/(3)))^(-2)

((9)/(25) ((5)/(3)))^(-2)=((3)/(5))^(-2)

((3)/(5))^(-2)=(25)/(9)

Therefore, the value of the expression is 25 / 9

learn more on expression here:brainly.com/question/12879207

#SPJ5
Answer 2
Answer:

Answer: it’s A

Step-by-step explanation: I got it right, hope it helps ✨

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Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?A. Removing the outlier will not change the spread of the graph of the data set.
B. Removing the outlier will not change the variance of the data set.
C. Removing the outlier will increase the variance of the data set.
D. Removing the outlier will decrease the spread of the graph of the data set.

Answers

Answer:

D.

Step-by-step explanation:

if you remove the low value outlier, the variation from the mean will decrease therefore decreasing the varianc.

Answer:

D. Removing the outlier will decrease the spread of the graph of the data set.

Step-by-step explanation:

Outliers increase the spread of the data set.

So removing an outlier will generally decrease the spread or variance or standard deviation of a data set.

The answer is

D. Removing the outlier will decrease the spread of the graph of the data set.

9/10( -2/3) ( symplify )

Answers

-3/5 because you multiply 9/10 by -2/3

A triangle has sides with lengths of 72 miles, 85 miles, and 36 miles. Is it a right triangle?

Answers

Answer:

Your answer is: No, it is not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem to determine if a triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle:

Side A = 72 miles

Side B = 85 miles

Side C = 36 miles

To check if it's a right triangle, we can compare the lengths of the sides using the Pythagorean theorem:

1. Calculate the squares of the lengths of Side A and Side B:

- A^2 = 72^2 = 5184

- B^2 = 85^2 = 7225

2. Calculate the square of the length of Side C:

- C^2 = 36^2 = 1296

3. Check if the sum of the squares of the two shorter sides (A^2 + B^2) is equal to the square of the longest side (C^2):

- A^2 + B^2 = 5184 + 7225 = 12409

- C^2 = 1296

Since A^2 + B^2 is not equal to C^2 (12409 ≠ 1296), we can conclude that the given triangle is not a right triangle.

A businessman buys 1,440 dozen pens at $2.50 a dozen and then sells them at a price of 25¢ apiece. What is his total profit on the lot of pens?

Answers

he spend: 1440*2.5=3600 
he earn: 0.25*1440*12=4320
[because he sells 0.25/each and buy 1440 dozen so 1440*12]

4320-3600=720

Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair on the graph of the line relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?

Answers

The amount of gas Berto can buy with $12 = 12/3.75 = 3.2 gallons.

Therefore the required ordered pair is (3.2, 12)
If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12). I hope that this is the answer that you were looking for and it has helped you.

The sum of three consecutive even numbers is one hundred sixty - two.What is the smallest of the three numbers ?

Answers

Answer:

 52

Step-by-step explanation:

Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...

  x + (x+2) +(x+4) = 162

  3x = 156 . . . . . . . . . . . .subtract 6

  x = 156/3 = 52

The smallest of the three numbers is 52.

___

I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.
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