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Valentin [98]
3 years ago
15

Write the equation of a line that passes the point (-6,9)and is perpendicular to a line that passes through the points (-2,1) an

d (6,7).
Mathematics
1 answer:
stepladder [879]3 years ago
6 0

Answer:

y = 4/3x + 1.

Step-by-step explanation:

The equation of the lines passing through (2,1) and (6,7) is:

y - 7 = (7-1)/(6- -2)(x - 6)

y - 7 = 6/8(x - 6)

y = 3/4(x - 6) + 7

y = 3/4x + 5/2.

So the line perpendicular to it has slope -1/3/4 = -4/3:

y - 9 = -4/3(x  + 6)

y = -4/3 x  - 8 + 9

y = 4/3x + 1.

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There are two mixtures. One mixture contains 5% alchol and the other mixture contains 12% alchol. How much of each should be mix
hichkok12 [17]

Answer:

to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.

Step-by-step explanation:

According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.

We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:

A + B = 1000 gallons. [1]

0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]

(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).

Solving the system of equations:

A + B = 1000 ⇒ A = 1000 - B [3]

[3] → [2]

0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100

⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]

[4] → [1]

A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7

Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'

4 0
3 years ago
Jermain made 6 candles. lukas made 4 times as many candles as jermain did. they plan to pack the candles in boxes with 3 candles
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LenKa [72]

Answer:

A lot of things to be honest!

Step-by-step explanation:

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You could graph  it. I have the graph linked below.

You could Convert it to Interval Notation

[ 0, \frac{1}{e} ]

You could Evaluate  it.

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There are 32 people who voted for Petra for class president.This represents 1/2 of the people who voted. How many people voted i
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The product of two rational numbers is irrational.
PtichkaEL [24]

Answer:

The statement is false.

Step-by-step explanation:

Here we need to remember some things:

Integer numbers are closed under multiplication.

This means that for two integers a and b, the product a*b is also an integer.

A rational number is a number that can be written as the quotient of two integer numbers.

An irrational number is a number that can't be written as the quotient of two rational numbers.

Now let's see the statement:

"The product of two rational numbers is irrational."

The product of two rational numbers is written as:

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We can rewrite that product as:

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Then the product of two rational numbers is a rational number.

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