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Elden [556K]
3 years ago
12

Write x2 − 8x + 13 = 0 in the form (x − a)2 = b, where a and b are integers

Mathematics
1 answer:
Marrrta [24]3 years ago
3 0
X^2 - 8x + 13 = 0
subtract 13 from both sides
x^2 - 8x = -13
-8/2 = -4,   (-4)^2 = 16,  add 16 to both sides
x^2 - 8x + 16 = -13 + 16
factor the left side
(x - 4)^2 = 3
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2 years ago
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Answer:

41

Step-by-step explanation:

Use the correct order of operations and do one step at a time to avoid making mistakes.

16 \div 4 + 2^3 \times 5 - 3 =

= 4 + 8 \times 5 - 3

= 4 + 40 - 3

= 44 - 3

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6 0
3 years ago
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An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m
SVETLANKA909090 [29]

Answer:

a) y=-6.254 x +75.064  

b) r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y)     Interest Rate (X)

       22                               9.2

       20                               7.6

       10                                10.4

       45                                5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

m=\frac{S_{xy}}{S_{xx}}  

Where:  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}  

With these we can find the sums:  

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225  

And the slope would be:  

m=\frac{-91.225}{14.5875}=-6.254  

Nowe we can find the means for x and y like this:  

\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125  

\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25  

And we can find the intercept using this:  

b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064  

So the line would be given by:  

y=-6.254 x +75.064  

Part b

For this case we need to calculate the correlation coefficient given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937  

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by r^2 and on this case -0.932^2 =0.8687, so then the % of variation explained by the linear model is 86.87%.

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Blizzard [7]

Answer:

x=280

Step-by-step explanation:

We have, 15% × x = 42

or,

15

100

× x = 42

Multiplying both sides by 100 and dividing both sides by 15,

we have x = 42 ×

100

15

x = 280

If you are using a calculator, simply enter 42×100÷15, which will give you the answer.

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3 years ago
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natka813 [3]

Answer:

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Step-by-step explanation:

this is the solution

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2 years ago
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