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Kisachek [45]
3 years ago
13

Which equation represents a line that passes through (2,-1/2) and has a slope of 3?

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
3 0

Answer:

option 3

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (2, - \frac{1}{2} ) , thus

y - (- \frac{1}{2} ) = 3(x - 2) , that is

y + \frac{1}{2} = 3(x - 2)

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Step-by-step explanation:

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3 years ago
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The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?
alexgriva [62]

Answer:

<u>The chemistry class mixed 120 gallons of 12% isopropyl alcohol and 180 gallons of 42% isopropyl alcohol.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of isopropyl alcohol made by the chemistry class = 300 of 30%

Amount of 12% isopropyl alcohol mixed by the chemistry class = x

Amount of 42% isopropyl alcohol mixed by the chemistry class = 300 - x

2. How much of each did they use?

Let's write our equation to solve for x, this way:

30% = 0.3, 12% = 0.12, 42% = 0.42

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12x + 126 - 0.42x = 90

-0.3x = 90 - 126

-0.3x = -36

x = -36/-0.3

<u>x = 120 ⇒ 300 - x = 180</u>

<u>Let's prove x = 120 is correct</u>

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12 * 120 + 0.42 (300 - 120) = 0.3 * 300

14.4 + 75.6 = 90

90 = 90

<u>We proved x = 120 is correct</u>

5 0
3 years ago
A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meter
Margaret [11]

Answer:

1. $0.80 or 80 cents

2. 1.25 meters

Step-by-step explanation:

The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.

1. To find how much the nylon costs per meter, take L = 1 (this means you are calculating the price of a piece of nylon rope that is 1 meter long):

L=1,\\ \\p=\$0.8\cdot 1=\$0.80

2. To find how long a piece of nylon rope that costs $1.00 is, substitute into the equation p = 1:

p=1,\\ \\1=0.8L\\ \\L=\dfrac{1}{0.8}=\dfrac{10}{8}=\dfrac{5}{4}=1.25\ meters

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3 years ago
How do I write a recursive formula for this sequence? 2, 6, 18, 54, 162, ... I already know the common difference is x3.
dmitriy555 [2]
For the sequence 2, 6, 18, 54, ..., the explicit formula is: an = a1 ! rn"1 = 2 ! 3n"1 , and the recursive formula is: a1 = 2, an+1 = an ! 3 . In each case, successively replacing n by 1, 2, 3, ... will yield the terms of the sequence. See the examples below.
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5. Find the area of an equilateral triangle with a<br> perimeter of 24 in.<br> what’s the area?
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Answer:

18

Step-by-step explanation:

24÷3=6 6×6=36 36÷2=18

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3 years ago
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