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2 years ago

What is the factored form of 5xy − 40x − 15y + 120?

Mathematics

1 answer:

aleksandr82 [10.1K]2 years ago

5 0

5xy-40x-15y+120=0
5(xy-8x-3y+24)=0
xy-8x-3y+24=0
(x-3)(y-8)=0

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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER

BartSMP [9]

$\bold{FULL ANSWERS:}$

3 0

1 year ago

Read 2 more answers

Y=5x-1<br>2x+y=13 how to solve

ira [324]

Answer:

x = 2, y = 9 or (2,9)

Step-by-step explanation:

Hello!

The first equation "y = 5x - 1" is telling us that y is equal to 5x - 1

We can plug in the first equation into the second like this:

2x + y = 13 (we know y so we can plug it in)

2x + (5x - 1) = 13

2x + 5x - 1 = 13

7x - 1 = 13

Now we add 1 to both sides

7x - 1 + 1 = 13 + 1

7x = 14

x = 2

Now we plug in x to find y:

y = 5x - 1

y = 5(2) - 1

y = 10 - 1

y = 9

4 0

2 years ago

100 points! simplify write as a product compute

Rom4ik [11]

Answer:

a) $\sqrt{61 - 24 \sqrt{5} } = - 4 + 3 \sqrt{5}$

b) $( \sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } + {2 \sqrt{bc} } )$

c) $\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} } = - 1$

Step-by-step explanation:

We want to simplify

$\sqrt{61 - 24 \sqrt{5} }$

Let :

$\sqrt{61 - 24 \sqrt{5} } = a - b \sqrt{5}$

Square both sides of the equation:

$(\sqrt{61 - 24 \sqrt{5} } )^{2} = ({a - b \sqrt{5} })^{2}$

Expand the RHS;

$61 - 24 \sqrt{5} = {a}^{2} - 2ab \sqrt{5} + 5 {b}^{2}$

Compare coefficients on both sides:

${a}^{2} + 5 {b}^{2} = 61 - - - (1)$

$- 24 = - 2ab \\ ab = 12 \\ b = \frac{12}{b} - - -( 2)$

Solve the equations simultaneously,

$\frac{144}{ {b}^{2} } + 5 {b}^{2} = 61$

$5 {b}^{4} - 61 {b}^{2} + 144 = 0$

Solve the quadratic equation in b²

${b}^{2} = 9 \: or \: {b}^{2} = \frac{16}{5}$

This implies that:

$b = \pm3 \: or \: b = \pm \frac{4 \sqrt{5} }{5}$

When b=-3,

$a = - 4$

Therefore

$\sqrt{61 - 24 \sqrt{5} } = - 4 + 3 \sqrt{5}$

We want to rewrite as a product:

${b}^{2} {c}^{2} - 4bc - {b}^{2} - {c}^{2} + 1$

as a product:

We rearrange to get:

${b}^{2} {c}^{2} - {b}^{2} - {c}^{2} + 1- 4bc$

We factor to get:

${b}^{2} ( {c}^{2} - 1) - ({c}^{2} - 1)- 4bc$

Factor again to get;

$( {c}^{2} - 1) ({b}^{2} - 1)- 4bc$

We rewrite as difference of two squares:

$(\sqrt{( {c}^{2} - 1) ({b}^{2} - 1) })^{2} - ( {2 \sqrt{bc} })^{2}$

We factor the difference of square further to get;

$( \sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } + {2 \sqrt{bc} } )$

c) We want to compute:

$\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} }$

Let the numerator,

$\sqrt{9 - 4 \sqrt{5} } = a - b \sqrt{5}$

Square both sides of the equation;

$9 - 4 \sqrt{5} = {a}^{2} - 2ab \sqrt{5} + 5 {b}^{2}$

Compare coefficients in both equations;

${a}^{2} + 5 {b}^{2} = 9 - - - (1)$

and

$- 2ab = - 4 \\ ab = 2 \\ a = \frac{2}{b} - - - - (2)$

Put equation (2) in (1) and solve;

$\frac{4}{ {b}^{2} } + 5 {b}^{2} = 9$

$5 {b}^{4} - 9 {b}^{2} + 4 = 0$

$b = \pm1$

When b=-1, a=-2

This means that:

$\sqrt{9 - 4 \sqrt{5} } = - 2 + \sqrt{5}$

This implies that:

$\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} } = \frac{ - 2 + \sqrt{5} }{2 - \sqrt{5} } = \frac{ - (2 - \sqrt{5)} }{2 - \sqrt{5} } = - 1$

3 0

2 years ago

Read 2 more answers

Find the mininum value of y<br><img src="https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B2x%20%2B%201%7D%7Bx%20%5E%7B2%7D%20%7D%20

DIA [1.3K]

Min = c - b^2/4a

Hope it helps

4 0

2 years ago

Read 2 more answers

Jackie paid $6.20 for 7 peaches. How much will 20 peaches cost.

NARA [144]

Answer:

About $17.8

Step-by-step explanation:

-Each peach costs less than a dollar.

-The answer cannot be more than $20

-6.20/7=17.8

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2 years ago