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3 years ago

Using Factors to Write Equivalent Expressions

Mathematics

1 answer:

bixtya [17]3 years ago

3 0

Answer:

(x + 1)(x + 8)

Step-by-step explanation:

You can try expanding each of these expressions to check if they equal

x^2 + 9x + 8

or you can use the Diamond Method to factor this trinomial.

1*8 = 8 and 1 + 8 = 9

x^2 + x + 8x + 8 = x^2 + 9x + 8

x(x + 1) + 8(x + 1) = x^2 + 9x + 8

(x + 8)(x + 1) = x^2 + 9x + 8

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3 years ago

How much simple interest will be due on a loan of $6000 at a 3.5 annual interest rate for one year

Brilliant_brown [7]

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3 years ago

Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th

NeX [460]

As long as Loren drove, the law of motion was

$200 = st_1 \implies t_1 = \dfrac{200}{s}$

As long as Loid drove, the law of motion was

$100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}$

So, the total time they took is

$t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}$

Had Loren driven the whole time, the law of motion would have been

$300=st_3 \implies t_3 = \dfrac{300}{s}$

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

$t_3 = t_1+t_2-0.5$

This translates into

$\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}$

If we subtract 200/s from both sides, we have

$\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}$

We can simplify the right hand side by summing the two fractions:

$\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}$

So, we have to solve

$\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}$

If we cross multiply the denominators, we have

$200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0$

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$s=-40,\quad s=50$

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

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3 years ago

Read 2 more answers

Slope-intercept form.Give the slope and y-intercept. Thanks for helping :D

zlopas [31]

1) 8y=-5x+12
y= (-5/8)x+3/2
2) 2y=3x+7
y= (3/2)x+7/2
3) -3y= -2x+7
y=(2/3)x-7/3
4) -4y= -12x+16
y=3x-4
5) -2y= -x+10
y=(1/2)x-5
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4 years ago

A rectangle is formed by the intersection of the lines x = −1, y = −1, x = 5

Gekata [30.6K]

Answer:

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Step-by-step explanation:

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3 years ago