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Mariulka [41]
3 years ago
15

What is the area of the triangle below?

Mathematics
1 answer:
Nady [450]3 years ago
7 0

Answer:

36

Step-by-step explanation:

1/2 × b× h

= 1/2 × 9×8

= 9×4

= 36 sq. in

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What is the result of substituting for y in the bottom equation<br> y=x+3<br> y=x^2+2x-4
8_murik_8 [283]

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

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

Given that,

y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4  ----- eqn 2

<em><u>We have to substitute eqn 1 in eqn 2</u></em>

x + 3 = x^2 + 2x - 4

\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0

\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\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=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}

x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}

x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925

Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925

Substitute x = 2.1925 in eqn 1

y = 2.1925 + 3

y = 5.1925

Substitute x = -3.1925 in eqn 1

y = -3.1925 + 3

y = -0.1925

Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

6 0
3 years ago
A plumber charges a base fee of $55 for service call plus &amp;35 per hour for each hour worked during the service call. Write a
Tasya [4]

Answer:

  p = 55 + 35h

Step-by-step explanation:

Let p and h represent the price of the service call and the hours worked, respectively. The price charged is 35 dollars for each hour, so the time-based part of the price is 35h. The base fee of 55 dollars is added to that for a total price of ...

  p = 55 + 35h

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3 years ago
A submarine was located 800 feet below sea level. There is a drone
fgiga [73]

Answer:

1,050

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
If 3 of the Roberts 4 dogs are black, what percent are NOT black
Annette [7]

since 3/4 or 75% ARE black, 1/4 will not be black. 1/4=.25 which is 25%.

3 0
3 years ago
Glen invited 25 people to his birthday party.
Trava [24]

Answer:

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Step-by-step explanation:

5 out of 25 people invited didn't attend Glen's party. That means the following:

\frac{5}{25}  people didn't come which simplifies to  \frac{1}{5}

Multiply \frac{1}{5} by the giant one \frac{20}{20} so the denominator is 100 which is the denominator used to find percentages.

You end up with \frac{20}{100}

\frac{20}{100} = 20%

8 0
3 years ago
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