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kari74 [83]
3 years ago
6

Apply the distributive property to create an equivalent expression.

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
4 0

Answer:

3 + 2k

Step-by-step explanation:

Given:

1/5(15 + 10k)

= (1/5 * 15) + (1/5 * 10k)

= (1 * 15)/5 + (1 * 10k)/5

= 15/5 + 10k/5

= 3 + 2k

Therefore,

1/5(15 + 10k) = 3 + 2k

The equivalent expression is 3 + 2k

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1-SCPS
Anton [14]

Answer:

6

Step-by-step explanation:

5 0
3 years ago
Factor by grouping 2u^3+3u^2-14u-21
mariarad [96]
\bf 2u^3+3u^2-14u-21\implies (2u^3+3u^2)-(14u+21)
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u^2(2u+3)-7(2u+3)\implies \stackrel{\stackrel{common}{factor}}{(2u+3)}(u^2-7)
6 0
3 years ago
Read 2 more answers
Let f be the function defined as follows:1. If a = 2 and b = 3, is f continuous at x = 1? Justify your answer.2. Find a relation
Arada [10]

Answer:

1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.

2.

2 = a + b

3.

0 = 2a + b

4.

a = -2

b = 4

Step-by-step explanation:

the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.

1. that means that for x=1

3 - x = ax² + bx

so,

3 - 1 = a×1² + b×1 = a + b

2 = a + b

we have to use a=2 and b=3

2 = 2 + 3 = 5

2 is not equal 5, so the assumed equality is false, so the function is not continuous there.

2. point 1 gave us already the working relationship between a and b.

2 = a + b

only if that is true, is the function continuous at x=1.

3. now for x=2

5x - 10 = ax² + bx

5×2 - 10 = a×2² + b×2 = 4a + 2b

10 - 10 = 4a + 2b

0 = 4a + 2b

0 = 2a + b

4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.

so, they establish a system of 2 equations with 2 variables.

2 = a + b

0 = 2a + b

a = 2 - b

0 = 2×(2-b) + b = 4 - 2b + b = 4 - b

b = 4

therefore

a = 2 - 4 = -2

5. I cannot draw a graph here.

just use now the function

3 - x, x < 1

‐2x² +4x, 1 <= x < 2

5x - 10, x >= 2

8 0
3 years ago
Consider the number set: 11, 12, 13, 14
KATRIN_1 [288]

Answer:

Answer c)   (13)

Step-by-step explanation:

Begin with 3x+2x-45=20.  Go through the steps of solving this for x.

Combining like terms, we get 5x = 65.

Dividing both sides by 5, we get x = 13.

Answer c)   (13)   is the correct answer/solution/root.

6 0
3 years ago
To purchase $12,300 worth of restaurant equipment for his business, Ahmed made a down payment of $1800 and took out a loan for t
choli [55]

Answer:

Step-by-step explanation:

A) After 2 years of paying monthly of $465.38, he can finally pay off the loan. There are 24 months in 2 years. This means that the total amount that Ahmed paid in 2 years would be

465.38 × 24 = $11169.12

Ahmed made a down payment of $1800 and took out a loan for the rest. Therefore, the total amount that Ahmed ended up paying for the equipment( including the down payment and monthly payment) is

1800 + 11169.12 = $12969.12

B) the initial amount that he took as loan is

12300 - 1800 = $10500

Therefore, the amount of interest that he paid on the loan would be

12969.12 - 10500 = $2469.12

8 0
3 years ago
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