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Reptile [31]
3 years ago
14

find the equation of the line that is parallel to y=3x-2 and contains the point (2,11), answer all boxes please

Mathematics
1 answer:
stiks02 [169]3 years ago
4 0

Answer:

y = 3x+6

Step-by-step explanation:

y=3x-2

This is in the form

y = mx+b where m is the slope and b is the y intercept

The slope is 3 so a line parallel also has a slope of 3 since parallel lines have the same slope.

Using slope intercept form

y = 3x+b

We have a point (2,11)

11 = 3*2+b

11 =6+b

11-6 = b

5 =b

The equation is

y = 3x+6

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3 years ago
Of the cars sold during the month of July, 89 had air conditioning, 99 had an automatic transmission, and 74 had power steering.
DedPeter [7]

Answer:

There are a total of 23 cars with air conditioning and automatic transmission but not power steering

Step-by-step explanation:

Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.

Remember that for 2 sets E and F, we have that

|E \cup F| = |E| + |F| - |E \cap F|

Also,

|E| = |E ∩F| + |E∩F^c|

We now alredy the following:

|A| = 89

|B| = 99

|C| = 74

|A \cap B \cap C| = 5

|(A \cup B \cup C)^c| = 24

|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).

|B \ (AUC)| = 65

|C \ (AUB)| = 26

|B \cap C| = 11

We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things

For example:

99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|

Therefore, |B∩C^c| = 99-11 = 88

And |A ∩ B ∩ C^c| = |B∩C^c| - |B∩C^c∩A^c| = |B∩C^c| - |B \ (AUC)| = 88-65 = 23.

This means that the amount of cars that have both transmission and air conditioning but now power steering is 23.

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3 years ago
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2 years ago
The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?
GREYUIT [131]

Answer:

Step-by-step explanation:

If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of y^2-10y+24=0 is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.

If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:

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____________

The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:

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Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:

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<u>                4    -24</u>

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And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.

Therefore, the 2 factors that multiply together to give us y^2-10y+24=0 are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!

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3 years ago
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