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3 years ago

Find the solutions to the system; y=x^2-3x-1 and y=8x-1

1 answer:

8 0

${x}^{2} - 3x - 1 = 8x - 1 \\ {x}^{2} - 11x = 0 \\ x(x - 11) \\ x = 0 \: or \: x = 11$

When x = 0,
$y = 8x - 1 \\ y = 0 - 1 \\ y = - 1$

When x = 11
$y = 8(11) - 1 \\ y = 87$
x = 0, y = - 1
x = 11, y = 87

Answer is B.

Hope this helps. - M

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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$

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3 years ago

Algebra: Find x<br> ....

luda_lava [24]

Answer:

Step-by-step explanation:

The triangles are similar, thus the ratios of corresponding sides are equal, that is

$\frac{2x+1}{x+4}$ = $\frac{40}{25}$ = $\frac{8}{5}$ ( cross- multiply )

5(2x + 1) = 8(x + 4) ← distribute parenthesis on both sides )

10x + 5 = 8x + 32 ( subtract 8x from both sides )

2x + 5 = 32 ( subtract 5 from both sides )

2x = 27 ( divide both sides by 2 )

x = 13.5 → d

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4 years ago

Sahra is three times as old as her daughter. If the sum of their age is 32. what is the age of the daughter?

Andrews [41]

So Sahra is 3 times as old as her daugter. That means that the sum of their age is the daughters age times 4.
We can prove that by saying the daughters age is x. Sahra's age must be 3x. Their sum must be x+3x = 4x.
So to get the daughters age we divide the sum by 4, which is 8.

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4 years ago

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Find the 35th term in the arithmetic sequence: -10,-14,-18,-22,..

ivanzaharov [21]

The 35th term is -146 :)

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