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saw5 [17]
3 years ago
13

. Given ????(5, −4) and T(−8,12):

Mathematics
1 answer:
damaskus [11]3 years ago
7 0

Answer:

a)y=\dfrac{13x}{16}-\dfrac{129}{16}

b)y = \dfrac{13x}{16}+ \dfrac{37}{2}

Step-by-step explanation:

Given two points: S(5,-4) and T(-8,12)

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: y = mx + c where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

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

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

m = \dfrac{12 - (-4)}{(-8) - 5}

m = \dfrac{-16}{13}

to find the perpendicular of this gradient: we'll use:

m_1m_2=-1

both m_1and m_2 denote slopes that are perpendicular to each other. So if m_1 = \dfrac{12 - (-4)}{(-8) - 5}, then we can solve for m_2 for the slop of ther perpendicular!

\left(\dfrac{-16}{13}\right)m_2=-1

m_2=\dfrac{13}{16}:: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope m and the points (x,y). And plug into the equation: (y - y_1) = m(x-x_1)

side note: you can also use the y = mx + c to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

(y - y_1) = m(x-x_1)

we have the slope of the perpendicular to ST i.e m=\dfrac{13}{16}

and the line should pass throught S as well, i.e (5,-4). Plugging all these values in the equation we'll get.

(y - (-4)) = \dfrac{13}{16}(x-5)

y +4 = \dfrac{13x}{16}-\dfrac{65}{16}

y = \dfrac{13x}{16}-\dfrac{65}{16}-4

y=\dfrac{13x}{16}-\dfrac{129}{16}

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for T(-8,12)

(y - y_1) = m(x-x_1)

(y -12) = \dfrac{13}{16}(x+8)

y = \dfrac{13x}{16}+ \dfrac{104}{16}+12

y = \dfrac{13x}{16}+ \dfrac{37}{2}

this is the equation of the line that is perpendicular to ST and passes through T

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Answer:

The next step is to combine constants

Step-by-step explanation:

4 0
1 year ago
Mrs. Jacobs is making several batches of cookies and is using 84 total ounces of chips. The cookies have chocolate chips and pea
WARRIOR [948]

The ounces of chocolate chips used by Mrs Jacob is 70 ounce

<em><u>Solution:</u></em>

Given that Jacob is making several batches of cookies and is using 84 total ounces of chips

Let "c" be the ounces of chocolate chips

Let "p" be the ounces of peanut butter chips

To find: ounces of chocolate chips used by Mrs Jacob

Given that There are 5 times as many ounces of chocolate chips as peanut butter chips

<em><u>Thus we can frame a equation as:</u></em>

ounces of chocolate chips = 5 x ounces of peanut butter chips

c = 5p -------- eqn 1

Jacob used 84 total ounces of chip. Therefore,

ounces of chocolate chips + ounces of peanut butter chips = 84

c + p = 84 ---- eqn 2

Substitute eqn 1 in eqn 2

5p + p = 84

6p = 84

<h3>p = 14</h3>

Substitute p = 14 in eqn 1

c = 5(14) = 70

<h3>c = 70</h3>

Thus the ounces of chocolate chips used by Mrs Jacob is 70 ounce

8 0
3 years ago
Find the value of y for the given value of x. Round to the nearest hundredth.
BlackZzzverrR [31]

Answer:

20.922

Step-by-step explanation:

Evaluate ln 7.2 on a calculator; the correct result is 1.974.

Multiply that by 3, obtaining 5.922.

Finally, add 15 to that result:  y = 15 + 3 In 7.2 = 20.922

5 0
3 years ago
What is the result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3?
Greeley [361]

The answer is -9x

If you want explanation let me know!

I didn't provide one since you said ''What is the result''

5 0
3 years ago
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Anna71 [15]
Let x  =  the numbers of girls
thus
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2x = 2 . 9 =18
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3 0
3 years ago
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