Mathematics, 15.07.2021 03:50 thao6570

Line l has a slope of 12/11. The line through which of the following pair of points is perpendicular to l A. (21,−4),(−5,7)
B. (−7,−5),(4,7)
C. (7,−7),(−5,4)
D. (−2,−5),(4,7)

Answers: 2

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Answers

Answer from: naomijamieson88

Given:

The slope of a line l is $\dfrac{12}{11}$ .

To find:

The pair of points of a line which is perpendicular to the line l.

Solution:

If the slope of a line is , then the slope of the line which is perpendicular to the line is $-\dfrac{1}{m}$ .

The slope of a line l is $\dfrac{12}{11}$ . So, the slope of the perpendicular line is $-\dfrac{11}{12}$ .

Slope formula:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

In option A, the pair of points is (21,−4) and (−5,7).

$m_1=\dfrac{7-(-4)}{-5-21}$

$m_1=\dfrac{11}{-26}$

In option B, the pair of points is (−7,−5) and (4,7).

$m_2=\dfrac{7-(-5)}{4-(-7)}$

$m_2=\dfrac{12}{11}$

In option C, the pair of points is (7,−7) and (−5,4).

$m_3=\dfrac{4-(-7)}{-5-7}$

$m_3=\dfrac{11}{-12}$

$m_3=-\dfrac{11}{12}$

In option D, the pair of points is (−2,−5) and (4,7).

$m_4=\dfrac{7-(-5)}{4-(-2)}$

$m_4=\dfrac{12}{6}$

m_4=2

The slope of the line is $-\dfrac{11}{12}$ if the line passes through the points (7,−7) and (−5,4).

Therefore, the correct option is C.

Answer from: Quest

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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