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kompoz [17]
1 year ago
7

Simplify each expression using Product to a Power Property a. (9a)^2 b. ( 3x)^2

Mathematics
1 answer:
antiseptic1488 [7]1 year ago
8 0
\begin{gathered} a)81a^2 \\ b)9x^2 \end{gathered}

1) Let's simplify those expressions making use of exponents rules:

(9a)^2=81a^2

Note that the exponent outside the parenthesis is 'distributed' over each term inside.

2) Similarly for the second expression we can state that:

(3x)^2=9x^2

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Solve the system. I need help solving these problems. but I have to show my work
Yuki888 [10]
3x - 5y = 7
2x + 3y = 11

multiply the first equation by 2 and the second by -3:-

6x - 10y = 14
-6x - 9y = -33   Adding these 2 equations we eliminate the term in x:-
-19y =  -19
y = 1
Substtute  y = 1 in the first equation:_
3x - 5(1) = 7
3x = 12
x = 4

Answer is x=4,y=1  Answer

Second system of equation:-s

Here one equation is linear and the other is quadratic  so we substitute fro y in the quadratic:-
From second equation y = 10x - 38, so substituting:- 
10x - 38  = x^2 - 4x - 17

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4 0
4 years ago
Which expression is equivalent to x^4 - 12x^2 + 36
lord [1]
X⁴ - 12x² + 36

This is the equivalent expression.
(x²-6)²

1) (x²-6)*(x²-6)
2) x²(x²) + x²(-6) -6(x²) -6(-6)  (distributive multiplication)
3) x⁴ - 6x² - 6x² + 36 = x⁴ - 12x² + 36  (group together figures that are the same value)



7 0
3 years ago
Read 2 more answers
Hello can u please help
Andrei [34K]

y = mx + b

-3 = -2(-5) + b

-3 = 10 + b

-13 = b

y = -2m - 13

The line would pass through -13 on the y-axis and it would go down 2 and move to the right 1 for every new point.

Hope this helps! ;)

6 0
3 years ago
Read 2 more answers
A single card is drawn from a deck of 52 cards, find the following
aleksandr82 [10.1K]

Answer:

a. 1/13

b. 1/78

c. 1/4

d. 1/12

e. 1/6

f. 1/4

Step-by-step explanation:

First, lets write some basic data

  • There are total 52 cards.
  • 26 cards are red and 26 cards are black
  • Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart
  • Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs
  • In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack

<u>a. result is a queen</u>

<em>Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart</em>

There are total 4 queens

Total number of cards is 52

<em>Probability = Number of favourable outcomes/total number of outcomes</em>

Probability = 4/52

Probability = 1/13

<u>b. result is a queen result is a face card </u>

<em>From my understanding, this question is result is a queen given that result is a face card.</em>

<em>Queen: 4 cards</em>

<em>Face card means King, Queen and Jack</em>

<em>Each set has one King, one Queen and one Jack</em>

<em>There are total 4 sets</em>

<em>Therefore, there are 4 Kings, 4 Queens and 4 Jacks</em>

<em>Face cards: 12-4 (because 4 queens have already been taken out) = 8</em>

<em>Total number of cards: 52-4 (because 4 queens have already been taken out) = 48</em>

Probability (A|B) = P(A) * P(A|B)

P(A) = result is a queen = 4/52 = 1/13

P(A|B) = result is a face card = 8/48 = 1/6

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/13 * 1/6

Probability (A|B) = 1/78 or 0.01282

<u>c. result is a heart</u>

<em>Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart</em>

Heart = 13 cards

Total number of cards = 52 cards

<em>Probability = Number of favourable outcomes/total number of outcomes</em>

Probability = 13/52

Probability = 1/4

<u>d. result is a heart | result is a red card </u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator</em>

= 13/39 = 1/3

Result is a heart given that result is a red card P(A|B) = 1/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1/3

Probability (A|B) = 1/12

<u>e. result is a heart result is a black card </u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator</em>

<em>= 26/39 = 2/3</em>

Result is a heart given that result is a black card P(A|B) = 2/3

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 2/3 = 1/6

<u>f. result is a heart result is not a diamond</u>

Result is a heart = P(A) = 13/52 = 1/4

<em>Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39</em>

Total cards = 52 - 13 (because hearts are already taken out) = 39

= 39/39 = 1

Probability (A|B) = P(A) * P(A|B)

Probability (A|B) = 1/4 * 1 = 1/4

!!

4 0
4 years ago
Derrick has 72 inches of ribbon to make bows. He uses all of his ribbon to make 9 bows of equal length l . How many inches of ri
Anastasy [175]

Answer:

the bows are 8 inches in length

Step-by-step explanation:

he has <em>divided</em><em> </em>the ribbon into 9 equal parts so 72÷9 is the equation which equals 8 inches for every bow

5 0
3 years ago
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