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3 years ago

Solve the system of equations. 13x−y=90 y=x^2−x−42

1 answer:

7 0

Solve the first for y

y=13x-90 and the second is y=x^2-x-42

When there is/are solutions y=y so we can say:

x^2-x-42=13x-90 subtract 13x from both sides

x^2-14x-42=-90 add 90 to both sides

x^2-14x+48=0 expand so that it is easy to factor...

x^2-6x-8x+48=0 now factor 1st and 2nd pair of terms

x(x-6)-8(x-6)=0

(x-8)(x-6)=0

So there are two solutions, when x=6 and 8.

Using either original equation we can find the corresponding values for y. I'll use y=13x-90 because it is easier...

y(6)=-12, y(8)=14 so the two solutions are the points:

(6,-12) and (8,14)

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Which choice is equivalent to the fraction below when x is an appropriate

garri49 [273]

The rationalized form of the expression will be $-1+\sqrt{2}}$

<h3>Rationalization of rational functions</h3>

Given the rational function

$\frac{\sqrt{12}}{\sqrt{3}-3}\\$

Multiplying by the conjugate of the denominator

$=\frac{\sqrt{12}}{\sqrt{3}-3}\times \frac{\sqrt{3}+3}{\sqrt{3}+3}\\=\frac{\sqrt{12}(\sqrt{3}+3)}{3-9}\\ =\frac{(\sqrt{36}+3\sqrt{12})}{3-9}\\=\frac{6+6\sqrt{2}}{-6}\\ =$

Simplifying further will give:

$-1+\sqrt{2}}$

Hence the rationalized form of the expression will be $-1+\sqrt{2}}$

Learn more on rationalization here: brainly.com/question/14261303

6 0

2 years ago

X + 8 = -3 solution for x

Finger [1]

The answer is -5 because

7 0

2 years ago

At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawals,

denis-greek [22]

At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawls, each in the same amount.

Let x be the amount of one of Derek's withdrawals

Each of John's withdrawals was $5 more than each withdrawal that Derek made.

x + 5 is t the amount of one of John's withdrawals

Derek made 7 withdrawals

So amount withdraw 7 times = 7x

John made 5 withdrawals

So amount withdraw 5 times = 5(x+5)

Both Derek and John withdrew the same amount of money in the end

(A)7x = 5(x+5)

(B) Solve for x

7x = 5x + 25

Subtract 5x from both sides

2x = 25

Divide by 2

x = 12.5

we plug in 12.5 for x in 7x= 5x + 25

7(12.5) = 5(12.5) + 25

87.5 = 62.5+ 25

87.5 = 87.5

(D) Each brother withdrawal 87.5 dollars

5 0

3 years ago

The rectangle below has an area of x^2-4x-12x 2 −4x−12x, squared, minus, 4, x, minus, 12 square meters and a length of x+2x+2x,

solniwko [45]

Answer:

Width = x-6 metres

Step-by-step explanation:

The formula for the area of a rectangle is represented by Length (l) × Width (w).

If the area is x^2-4x -12, which is an algebraic expression, The best way to find its length and breadth which would be a product of themselves is by FACTORIZATION.

To factorize x^2-4x -12, we say:

×^2 = a, -4x = b, -12 = c

Product: a×c; -12 × x^2= -12x^2

Sum: b; -4x derived by saying (-6x+2x)

Note that the expression of the sum (-6x+2x) must be able to be multiplied to give product (-12x^2).

Hence, we rewrite our algebraic expression using the sum expression.

x2 - 6x + 2x - 12

We then factorize by using a common factor (x and 2)

x( x - 6) + 2 (x - 6)

(x+2) (x-6)

Thus, the factors are x+2 and x-6

This means that (x+2) and (x-6) will be multiplied to give x^2-4x-12. Therefore, if x+2 metres is the Length, x-6 metres is the width.

6 0

4 years ago

Read 2 more answers

How many liters of water must Sharon add to 2 liters of a sugar and water solution that is 36% sugar to create a solution that i

Dahasolnce [82]

The amount of sugar $x$ in the starting solution contributes to a 36% concentration, so we have

$\dfrac x2=0.36\implies x=0.64$

units of sugar in the solution.

Into this solution, Sharon wants to pour $y$ liters of water to obtain a smaller concentration of sugar in the overall solution:

$\dfrac{0.64}{2+y}=0.12\implies\dfrac{16}3=2+y\implies y=\dfrac{10}3\approx3.33$

So Sharon needs to add $\dfrac{10}3$ liters of water to the solution to get the desired concentration.

3 0

4 years ago