The first three steps of completing the square to solve the quadratic equation x^2+4x-6=0 are shown below.

1 answer:

5 0

Take the sqrt of both sides of (x+2)^2=10:

x+2 = plus or minus sqrt(10)

Solve for x: x = -2 plus or minus sqrt(10)

Evaluate x: x = -2 + sqrt(10) AND x = -2 - sqrt(10) (answers)

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I need help with this math problem

boyakko [2]

Consider the right triangle HBF. The Pythagorean theorem tells you ...
HF² = HB² + BF²

The lengths HB and BF can be determined by counting grid squares, or by subtracting coordinates. Here, it is fairly convenient to count grid squares. When we do that, we find ...
HB = 2
BF = 5
Using these values in the equation above, we get
HF² = 2² + 5²
HF² = 4 + 25 = 29
Taking the square root gives the length HF.
HF = √29

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4 years ago

Mr. Whittaker’s science class uses tide gauges to measure annual variations in water levels at different parts of a river, and t

strojnjashka [21]

Answer:

-1.05 mm/year

2.48 years

Step-by-step explanation:

5 0

3 years ago

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What is 5 and 2/3 as an improper fraction?

OLga [1]

Answer:

17/3

Step-by-step explanation:

You would need to convert 5 into a fraction with the denominator 3, so 5 = 15/3. 15/3 + 2/3 = 17/3

4 0

3 years ago

What is the perimeter of this quadrilateral? (5,5) (2, 4) (4, 1) (6, 1)

lbvjy [14]

$~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{[ 2- 5]^2 + [ 4- 5]^2} \\\\\\ AB=\sqrt{(-3)^2+(-1)^2}\implies \boxed{AB=\sqrt{10}} \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hfill BC=\sqrt{[ 4- 2]^2 + [ 1- 4]^2}$

$BC=\sqrt{2^2+(-3)^2}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ C(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) ~\hfill CD=\sqrt{[ 6- 4]^2 + [ 1- 1]^2} \\\\\\ CD=\sqrt{2^2+0^2}\implies \boxed{CD=2} \\\\[-0.35em] ~\dotfill\\\\ D(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) ~\hfill DA=\sqrt{[ 5- 6]^2 + [ 5- 1]^2}$

$DA=\sqrt{(-1)^2+4^2}\implies \boxed{DA=\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{\sqrt{10}~~ + ~~\sqrt{13}~~ + ~~2~~ + ~~\sqrt{17}}~~ \approx ~~ 12.89$

8 0

3 years ago

I really need help on this question

Zielflug [23.3K]

Answer:

$r = 107 \\ q + s = 180 - 107 \\ = 73 \\ q = 73 \div 2 \\ = 36.5$

3 0

3 years ago