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Ierofanga [76]
2 years ago
11

Which is the simplified form of the expression ((p^2)(q^5))^-4 * ((p^-4)(q^5))^-2 ?

Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
6 0
\bold{ANSWER:}
OPTION A

\bold{EXPLANATIONS:}

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Kenya applied for a bank loan. Kenya calculated he would pay $78.00 interest if the rate was 12%. Use the percent equation to fi
Morgarella [4.7K]

78 is 12% of what number

78 is 12% of c 650

8 0
2 years ago
Read 2 more answers
Simplify 4x + 8y - 3x + 2y
mezya [45]

Answer: 4x-3x, and 8y+2y. x+10y is the equation in simplest form.

Step-by-step explanation:

Step 1. You need to combine like terms:

 4x-3x, and 8y+2y. x+10y would make the equation( 4x + 8y - 3x + 2y) in simplified form.

Hope I could help! :)

7 0
3 years ago
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The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Darina [25.2K]

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

7 0
2 years ago
Which of the following pairs represent a function ​
denis23 [38]

Option D: \{(-9,8),(-5,-8),(-7,8),(-6,-8)\} are the ordered pairs represents a function.

Explanation:

Given that the options of the set of ordered pairs.

We need to determine the ordered pairs that represents a function.

Option A: \{(-12,8),(-15,8),(-5,-8),(-12,-8)\}

A relation is said to be a function if each element of x is related to exactly one element in y.

From this set of ordered pairs, it is obvious that the element -12 of x is related to two different element in y.

Thus, the ordered pairs \{(-12,8),(-15,8),(-5,-8),(-12,-8)\} is not a function.

Hence, Option A is not the correct answer.

Option B: \{(8,-9),(-8,-5),(8,-7),(-8,-6)\}

From this set of ordered pairs, it is obvious that the elements -8 and 8 of x are related to two different element in y.

Thus, the ordered pairs \{(8,-9),(-8,-5),(8,-7),(-8,-6)\} is not a function.

Hence, Option B is not the correct answer.

Option C: \{(13,-3),(13,0),(13,-1),(13,-1)\}

From this set of ordered pairs, it is obvious that the element 13 of x is related to three different element in y.

Thus, the ordered pairs \{(13,-3),(13,0),(13,-1),(13,-1)\} is not a function.

Hence, Option C is not the correct answer.

Option D: \{(-9,8),(-5,-8),(-7,8),(-6,-8)\}

A relation is said to be a function if each element of x is related to exactly one element in y.

From this set of ordered pairs, it is obvious that the each element of x is related exactly one element in y.

Thus, the ordered pairs \{(-9,8),(-5,-8),(-7,8),(-6,-8)\} is a function.

Hence, Option D is the correct answer.

7 0
3 years ago
Raychel drove to the mountains last week there was heavy traffic on the way there and on the trip took 12 hours when Raychel dro
nevsk [136]
Suppose that this person drives at r mph going to the mountains, and gets there in 12 hours.  Returning, this person drives at (r+20) mph and gets home in 8 hours.  We don't know the distance yet, but can solve for the initial speed, r, by setting

d = 12r = (r+20)(8).  Solving for r, r=40 mph (going) and (40+20)mph = 60 mph (returning.  Since d=12 r, d = (12 hrs)(40 mph) = 480 miles (answer).
4 0
3 years ago
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