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sesenic [268]
2 years ago
10

Urgent help needed!

Mathematics
1 answer:
zalisa [80]2 years ago
6 0

To write this in standard form, you need to eliminate the fraction in the coefficient of variable x. You can do this by multiplying 8 to the two sides of the equation:

8(y) = 8[(-5/8)x + 3]

8y = -5x + 24

Transpose the variable x to the other side:

5x + 8y = 24        

 

 

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. Given ????(5, −4) and T(−8,12):
damaskus [11]

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

7 0
3 years ago
What is the area of this figure?<br> (click photo) IXL AA.19 7th grade
oee [108]

Answer:

multiply all those numbers together

Step-by-step explanation:

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Clyde bought a steak that weighs 1.4 pounds. The price is $4.50 per pound. how
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six dollars and 30 cents

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(x³ + ³) / (x - y)<br> Do not include parentheses in your answer.
Lubov Fominskaja [6]

The simplified expression of \frac{x^3 + (-y)^3}{(x - y} is x^2+xy+y^2

<h3>Complete question</h3>

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

<h3>How to simplify the expression?</h3>

The expression is given as:

\frac{x^3 + (-y)^3}{(x - y}

Open the inner bracket

\frac{x^3 -y^3}{(x - y}

Apply the difference of two cubes to the numerator

\frac{(x-y)(x^2+xy+y^2)}{(x - y}


Cancel out the common factors

x^2+xy+y^2

Hence, the simplified expression of \frac{x^3 + (-y)^3}{(x - y} is x^2+xy+y^2

Read more about expressions at:

brainly.com/question/723406

#SPJ1

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Use the properties of exponents to write an equivalent expression that is a product of unique
jolli1 [7]

Ummm I just need to answer questions sorry!!!

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