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nekit [7.7K]
3 years ago
12

Solve using perfect square factoring patterns. x2 – 12x + 36 = 4 A. {–8, –4} B. {–2, 10} C. {4, 8} D. {10, –2}

Mathematics
1 answer:
Nataliya [291]3 years ago
3 0
<span> x2 – 12x + 36 = 4
(x - 6)^2 = 2^2

x - 6 = 2
x = 8

-(x - 6) = 2
-x + 6 = 2
-x = -4
x = 4

answer
</span><span>C. {4, 8}</span>
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It will take them 4.24 hours together to paint the area together

Step-by-step explanation:

If Emily takes eight hours to paint the area then she will paint 1/8 of the house in one hour

Similarly, if Mike can paint the same area in 9 hours, then he will paint 1/9 of the same area

Let x be the number of hours in which they will together paint the area.

If x hours are taken by them to paint the area then 1/x of the area will be painted in one hour

So,

\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\\Multiplying\ both\ sides\ with\ the\ LCM\\72x\\(72x)*\frac{1}{8}+(72x)*\frac{1}{9}=72x * \frac{1}{x}\\9x+8x=72\\17x=72\\Dividing\ both\ sides\ by\ 17\\\frac{17x}{17}=\frac{72}{17}\\x=4.24\ hours

It will take them 4.24 hours together to paint the area together

Keywords: Linear equation, Variables

Learn more about linear equations at:

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4 0
3 years ago
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Erica bought 3 1/2 yards of fabric if she uses 2/3 of the fabric how much will she have left?
RoseWind [281]
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Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people ans
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Answer:

Step-by-step explanation:

From the information given:

We can compute the required calculations into a table as shown below.

\mathbf{Data \ value  }       \mathbf{ Frequency   } \mathbf{Relative  \ frequency}   \mathbf{Cumulative \  relative }

                                                                                              \mathbf{Frequency}

5                                     14                14/65 = 0.22                           14  

6                                     19                19/65 = 0.29               19+14 = 33

7                                      12                12/65 = 0.19               33+12 = 45

8                                       9                 9/65 = 0.14               45 + 9 = 54

9                                 <u>     11     </u>            11/65  = 0.17              54 + 11 = 65

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Note: that the relative frequency is determined by  dividing each value in the frequency by the total of the frequency.                        

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For this case we have that by definition, the slope of a line is given by:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}

Where:

(x_ {1}, y_ {1})and(x_ {2}, y_ {2})are two points through which the line passes

According to the statement we have:

(x_ {1}, y_ {1}): (- 8,4)\\(x_ {2}, y_ {2}) :( 3, -4)

Substituting we have:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-4-4} {3 - (- 8)} = \frac {-8} {3 + 8} = \frac {-8} {11} = - \frac {8} {11}

Thus, the slope of the line is:

m = - \frac {8} {11}

Answer:

m = - \frac {8} {11}

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Step-by-step explanation:

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