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Komok [63]
3 years ago
13

An item that cost $5.50 is marked up %60. What is the new price of the item after the markup? Show work please​

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

Answer:

$8.80

Step-by-step explanation:

In order to find the new price, you need to add 60% of the original price (5.50) to the original price. You have two options:

1) multiply $5.50*0.6 to get 60% of the original price. You would get $3.30. Then add $3.30+$5.50, which equals $8.80. This way takes longer but shows you all the steps.

2) The shorter way is to simply multiply $5.50*1.6, which also equals $8.80. This works because the "1" automatically adds the 5.50 to 60% of the original price, this way you don't have to multiply then add.

If you don't understand how the second way works or your teacher taught you #1, just do it the first way.

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Solve the equation by factoring. 8x^2+10x-7=0<br><br> What is the solution set?
nydimaria [60]

Answer:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

<u>When factoring trinomials of the form ax² + bx + c</u>:

  • multiply the leading coefficient and the last term.
  • find the product factors that add to give you the coefficient of the middle term.
  • rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

  1. 4x + 7 = 0
  2. 2x - 1 = 0

 

<u><em>Case 1:</em></u>

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = \bold{-\dfrac{7}{4}}

<u><em>Case 2:</em></u>

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = \bold{\dfrac{1}{2}}

Solutions:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

brainly.com/question/27638369

7 0
2 years ago
Read 2 more answers
How to write the equation in standard form using 5x-y+6=0
irga5000 [103]
5x-y=6
Use the formula!
8 0
3 years ago
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WILL MARK BRAINLIEST! PLEASE HELP!<br> Write 206 in base 7
Anna71 [15]

Answer:

413_7

Step-by-step explanation:

Convert the following to base 7:

206_10

Hint: | Starting with zero, raise 7 to increasingly larger integer powers until the result exceeds 206.

Determine the powers of 7 that will be used as the places of the digits in the base-7 representation of 206:

Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value

3 | 7^3 | 343

2 | 7^2 | 49

1 | 7^1 | 7

0 | 7^0 | 1

Hint: | The powers of 7 (in ascending order) are associated with the places from right to left.

Label each place of the base-7 representation of 206 with the appropriate power of 7:

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | __ | __ | )_(_7)

Hint: | Divide 206 by 7 and find the remainder. The remainder is the first digit from the right.

Determine the value of the first digit from the right of 206 in base 7:

206/7=29 with remainder 3

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | __ | 3 | )_(_7)

Hint: | Divide the whole number part of the previous quotient, 29, by 7 and find the remainder. The remainder is the next digit.

Determine the value of the next digit from the right of 206 in base 7:

29/7=4 with remainder 1

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | 1 | 3 | )_(_7)

Hint: | Divide the whole number part of the previous quotient, 4, by 7 and find the remainder. The remainder is the last digit.

Determine the value of the last remaining digit of 206 in base 7:

4/7=0 with remainder 4

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | 4 | 1 | 3 | )_(_7)

Hint: | Express 206_10 in base 7.

The number 206_10 is equivalent to 413_7 in base 7.

Answer: 206_10 =413_7

5 0
2 years ago
A singer makes 2% royalties on the sales of her album. Which proportion could be used to determine her sales if she made $44,000
Nikitich [7]
I believe it is the second one :)
8 0
3 years ago
Is the fraction 1/15 a terminating or repeating decimal?
german
-A terminating decimal is a decimal that NEVER ends

1/15 = 0.666666666.....

Therefore, 1/15 is a terminating decimal.
3 0
3 years ago
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