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3 years ago

Write the equation of the line perpendicular to y = x+ 5 that passes through the point ( -7,3).

Mathematics

1 answer:

Burka [1]3 years ago

3 0

Answer:

y = - x - 4

Step-by-step explanation:

A line perpendicular to the line: y = x + 5

must have a slope that is the "opposite of the reciprocal" of the slope of the given line. Then the slope of the perpendicular line must be "-1".

Now that we know the slope of the perpendicular line, we use the point (-7, 3) to complete the equation of the line:

y = -1 x + b

3 = -1 (-7) + b

then we solve for "b":

3 = 7 + b

3 - 7 = b

b = -4

Now we can write the total equation of the perpendicular line in slope-intercept form as:

y = - x - 4

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Given that f(x) = x2 + 2x + 3 and g(x) = quantity of x plus four, over three , solve for f(g(x)) when x = 2.

Sidana [21]

$f(x)=x^2+2x+3$
$g(x)=\frac{x+4}{3}$
$f(g(x))=(\frac{x+4}{3})^2+2(\frac{x+4}{3})+3$
$f(g(x))=\frac{x^2+8x+16}{9}+\frac{2x+8}{3}+3$
$f(g(2))=\frac{2^2+8(2)+16}{9}+\frac{2(2)+8}{3}+3$
$f(g(2))+\frac{4+16+16}{9}+\frac{4+8}{3}+3$
$f(g(2))=\frac{36}{9}+\frac{12}{3}+3$
$f(g(2))=4+4+3$
$f(g(2)=11$

Check:
g(2)=(2+4)/3=2
f(2)=2^2+2(2)+3=4+4+3=11 Checks.

4 0

3 years ago

Read 2 more answers

HELP PLZ.....I NEED THIS....One wheel of a bicycle has 24-inch diameter. About how many feet will the bicycle travel when the wh

Ne4ueva [31]

First, find the circumference of the wheel using $C=2 \pi r$

You know that your diameter is 24. To find the radius, divide the diameter by 2, which is 12.

Input 12 as r and simplify. -> $C=2 \pi (12)$
$C=24 \pi$

estimate your Pi as 3.14
$C=24(3.14)$

and multiply. C=75.36

Now you know the distance of one full revolution in inches. To find 200 revolutions, multiply that answer by 200.

75.36 * 200 = 15,072 inches

But because this is in inches, you have to find the answer in feet, so just divide that answer by 12.

15,072 / 12 = 1,256 ft

7 0

3 years ago

15 POINTS

mafiozo [28]

B i would say I'm sure

7 0

3 years ago

Read 2 more answers

Can someone help me with this?

deff fn [24]

Answer:

the answer is 200

Step-by-step explanation:

4 0

3 years ago

WHAT IS THE ANSWER FOR 12 1/3 + 8 3/4 +17 2/8 +23 2/3=

gulaghasi [49]

$12 \dfrac{1}{3} + 8 \dfrac{3}{4} +17 \dfrac{2}{8} +23 \dfrac{2}{3}$

Simplify
$= 12 \dfrac{1}{3} + 8 \dfrac{3}{4} +17 \dfrac{1}{4} +23 \dfrac{2}{3}$

Change the denominators to be the same
$= 12 \dfrac{1 \times 4}{3 \times 4} + 8 \dfrac{3 \times 3}{4 \times 3} +17 \dfrac{1 \times 3 }{4 \times 3} +23 \dfrac{2 \times 4}{3 \times 4}$

$= 12 \dfrac{4}{12} + 8 \dfrac{9}{12} +17 \dfrac{3 }{12} +23 \dfrac{8}{12}$

Combine into single fraction
$= 60 \dfrac{24}{12}$

$= 62$

6 0

3 years ago