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jasenka [17]
3 years ago
15

Three consecutive even integers have a sum 78

Mathematics
1 answer:
andreev551 [17]3 years ago
6 0
The answer is 24, 26, and 28
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X2 - 6x + 12 and y = 2x - 4, algebraically are
olga_2 [115]

<em><u>The solution is (4, 4)</u></em>

<em><u>Solution:</u></em>

<em><u>Given system of equations are:</u></em>

y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2

<em><u>Substitute eqn 2 in eqn 1</u></em>

x^2 - 6x + 12 = 2x - 4

Make the right side of equation 0

x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0

<em><u>Solve by quadratic equation</u></em>

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4

<em><u>Substitute x = 4 in eqn 2</u></em>

y = 2(4) - 4

y = 8 - 4

y = 4

Thus solution is (4, 4)

5 0
3 years ago
Need help + explanation!! ^_^
Paha777 [63]
780, or C, is correct.  Since 9.75 is 1/80th of the actual measurement, we can set up an equation like this:

9.75 = 1/80x

Then multiply each side by 80:

780 = x

The actual building's height is 780 ft.

We can check this answer by plugging in 780 for x in the original equation:

9.75 = 1/80(780)

9.75 = 9.75

Check! <span>✓</span>
3 0
3 years ago
What are the coordinates of the x-intercepts of the parabola y = x² - 8x + 15?
tamaranim1 [39]

Answer:

(3, 0) and (5, 0)

Step-by-step explanation:

we have

y=x^{2}-8x+15

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

x^{2}-8x+15=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^{2}-8x+15=0  

so

a=1\\b=-8\\c=15

substitute in the formula

x=\frac{-(-8)\pm\sqrt{-8^{2}-4(1)(15)}} {2(1)}

x=\frac{8\pm\sqrt{4}} {2}

x=\frac{8\pm2} {2}

x=\frac{8+2} {2}=5

x=\frac{8-2} {2}=3

so

x=3, x=5

therefore

The x-intercepts are (3,0) and (5,0)

4 0
3 years ago
If the policy premium on a 30 year $1,000,000 term life policy for a 35-year-old female is increased to $714, what is the percen
Andru [333]
I believe the answer might be B
3 0
3 years ago
Read 2 more answers
The coordinates A(2, 1), B(7, 1), C(2, 4) form what type of polygon?
Elena L [17]
It makes and obtuse right triangle.
5 0
3 years ago
Read 2 more answers
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