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2 years ago

What is the slope y+2=1/4(x-3)

Mathematics

1 answer:

ioda2 years ago

6 0

Answer:

$m=\frac{1}{4}$

Step-by-step explanation:

Given

$y+2=\frac{1}{4}(x-3)$

Required

Find the slope

$y+2=\frac{1}{4}(x-3)$

Subtract 2 from both sides

$y+2-2=\frac{1}{4}(x-3) - 2$

$y=\frac{1}{4}(x-3) - 2$

Open bracket

$y=\frac{1}{4}x-\frac{1}{4}*3 - 2$

$y=\frac{1}{4}x-\frac{3}{4} - 2$

Take LCM

$y=\frac{1}{4}x+\frac{-3 - 8}{4}$

$y=\frac{1}{4}x+\frac{-11}{4}$

$y=\frac{1}{4}x-\frac{11}{4}$

An equation has the form:

$y = mx + b$

Where

$m = slope$

By comparing: $y = mx + b$ and $y=\frac{1}{4}x-\frac{11}{4}$

$m=\frac{1}{4}$

So, the slope is 1/4

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2 years ago

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

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2 years ago

((PLEASE HELP ASAP!! D:)) Natasha bought a tennis racket that was marked down in price, p, by 20%. Write an expression with TWO

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Answer: p - 0.2p

Step-by-step explanation:

Given the following :

Original Price of tennis racket = p

Mark down or discount on original price = 20% of original price = (20/100) × p = 0.2p

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Amount after discount = Original price - Discount

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3 years ago

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3 years ago

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Paraphin [41]

Answer: The steps and answers to the first two are below but you need to understand slope = change in y / change in x = y2 - y1/ x2 - x1

And you need to understand y = mx + c

m= slope c is y intercept

Substitute either point given - only use one as the x and y and find c

Step-by-step explanation:

1. You need to follow the steps -

the point is given as (2,5) = (x,y)

So what this means is x =2 and y =5

Simple substitutions is the step 5 = 3 x 2 + c

5 = 6 + c or easier to see is c + 6 =5

subtract 6 from both sides c + 6 = 5

-6 -6

__________________

c = -1

x1,y1 x2,y2

( 3,2) and (5,6) are two points on the line

you already calculate the slope which is m = noy2-y1/x2-x1 = 6-2/5-3 = 4/2 = 2

Remember y= mx + c

y = 2 x + c

now substitute in (3,2) which is (x1, y1) into the x and y in your equation

2 = 2 (3) + c

2 = 6 + c

subtract 6 from both sides

-4 = c

Now you should use this and do your last question yourself

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2 years ago