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4 years ago

The sum of a positive number and its square is 20. find the number.

2 answers:

8 0

So x+x^2=20
subtract 20 from both sdies
x^2+x-20=0
factor
find what 2 nmbers multiply to get -20 and add to get 1

factors of 20=2 times 2 times 5
the combos are
2 times 10
4 times 5
1 times 20

4 and 5 are 1 in diference
5-4=1
5 times 4=20

(x-4)(x+5)=0
if xy=0 then x and/or y=0
set each to zero
x-4=0
add 4
x=4

x+5=0
subtract 5
x=-5
but you want positive so this is an extranius answer so discard this

the number is 4

blagie [28]4 years ago

8 0

The answer is 4

4 + 16 = 20

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What is the sum of all values of m that satisfy 2m (squared) -16m+8=0?

vodomira [7]

<h2>Steps:</h2>

So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:

$2m^2-16m=-8$

Next, divide both sides by 2:

$m^2-8m=-4$

Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:

-8 ÷ 2 = -4, (-4)² = 16

Add 16 to both sides of the equation:

$m^2-8m+16=12$

Next, factor the left side:

$(m-4)^2=12$

Next, square root both sides of the equation:

$m-4=\pm \sqrt{12}$

Next, add 4 to both sides of the equation:

$m=4\pm \sqrt{12}$

Now, while this is your answer, you can further simplify the radical using the product rule of radicals:

Product rule of radicals: √ab = √a × √b

√12 = √4 × √3 = 2√3.

$m=4\pm 2\sqrt{3}$

<h2>Answer:</h2>

In exact form, your answer is $m=4\pm \sqrt{12}\ \textsf{OR}\ m=4\pm 2\sqrt{3}$

In approximate form, your answers are (rounded to the hundreths) $m=7.46, 0.54$

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3 years ago

Which line has a slope of 1, and which has a slope of 2?

aleksley [76]

Answer:

Line "L" has the slope of 1 and line "K" has the slope of 2.

In order to graph a line with the slope of $\frac{1}{3}$ think of the numerator as the "rise" (how much you move up/down on the y-intercept) and the denominator as the "run" (how much you move to the side on the x-intercept)

Step-by-step explanation:

A slope of "1" is simply $\frac{1}{1}$ so you rise up one and move to the right once. This clearly demonstrated on line "L".

A slope of "2" is $\frac{2}{1}$ so you rise up two and move to the right once, as is demonstrated on line "K".

For the 2nd question, line "A" will have a slope of $\frac{1}{3}$ therefore it will move up once and then to the side three times. It will look like the image attached to this answer.

I hope this helped! Feel free to ask questions if needed!

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Answer:

A is your answer

Step-by-step explanation:

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Step-by-step explanation:

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