1. The rectangle shown is dilated by a scale factor of 3.

10x + 60 = 9x - 30<br><img src="https://tex.z-dn.net/?f=10x%20%2B%2060%20%3D%209%20%5Ctimes%20%20-%2030%20%5C%5C%20" id="TexForm

EastWind [94]

Answer:

x = - 90

Step-by-step explanation:

Given

10x + 60 = 9x - 30 ( subtract 9x from both sides )

x + 60 = - 30 ( subtract 60 from both sides )

x = - 90

4 0

3 years ago

The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.

raketka [301]

Use the polynomial remainder theorem. It says that a polynomial $f(x)$ has remainder $f(c)$ upon division by $x-c$ .

Here we have

$f(x)=x^4+3x^3-8x^2+5x-9$

and $c=-5$ , so the remainder is

$f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}$

6 0

3 years ago

In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, th

earnstyle [38]

Answer:

Step-by-step explanation:

new length=15+x

width=19+x

then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²

original area=15×19=285 ft²

then 285+98=x²+34x+285

or

x²+34x-98=0

x²+34x+17²=98+17²

(x+17)²=98+289=387

x+17=√387=3√43

x=3√43-17 ft

8 0

3 years ago

Kid got 50 things of ravioli. He puts 30 rats in his ravioli. What is the percentage of ravioli that doesn't have rats in it com

GREYUIT [131]

Answer:

60% to 40%

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes

ale4655 [162]

Answer:

The sample mean is $\bar{x}=14.371$ min.

The sample standard deviation is $\sigma = 18.889$ min.

Step-by-step explanation:

We have the following data set:

$\begin{array}{cccccccc}0.15&0.82&0.81&1.44&2.70&3.28&4.00&4.70\\4.96&6.49&7.25&8.03&8.40&12.15&31.89&32.47\\33.79&36.80&72.92&&&&&\end{array}$

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.

The formula for the mean of a sample is

$\bar{x} = \frac{{\sum}x}{n}$

where, $n$ is the number of values in the data set.

$\bar{x}=\frac{0.15+0.82+0.81+1.44+2.7+3.28+4+4.7+4.96+6.49+7.25+8.03+8.4+12.15+31.89+32.47+33.79+36.80+72.92}{19}\\\\\bar{x}=14.371$

The standard deviation measures how close the set of data is to the mean value of the data set. If data set have high standard deviation than the values are spread out very much. If data set have small standard deviation the data points are very close to the mean.

To find standard deviation we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }$

The mean of a sample is $\bar{x}=14.371$ .

Create the below table.

Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 6422.0982$

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 6422.0982 }{ 19 - 1} } \approx 18.889$

7 0

3 years ago