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3 years ago

What is the solution to 9x−6<21?

Mathematics

1 answer:

Alisiya [41]3 years ago

7 0

Answer:

$x > 3$

Step-by-step explanation:

1) Add 6 to both sides.

$9x > 21 + 6$

2) Simplify 21 + 6 to 27.

$9x > 27$

3) Divide both sides by 9.

$x > \frac{27}{9}$

4) Simplify 27/9 to 3.

$x > 3$

Therefor, the answer is option B. x > 3.

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Line L1 passes through points P(n,4) and Q(1,-2). Line L2 passes through R(4,3) and S(1,5). What is the value of n if the lines

Elena L [17]

Answer:

Step-by-step explanation:

For two lines to be parallel, they must have the same slope

Get the slope of each line

For L1;

m1 = -2-4/1-n

m1 = -6/1-n

For L2;

m2 = 5-3/1-4

m2 = 2/-3

m2 = -2/3

Since they have the same slope, m1 = m2

-6/1-n = -2/3

6/1-n = 2/3

Cross multiply

2(1-n) = 6(3)

2-2n = 18

-2n = 18 - 2

-2n = 16

n = -16/2

n = -8

Hence the value of n is -8

4 0

3 years ago

8r.) Find the amount A in an account after t years given the following conditions.

Elden [556K]

You can rewrite the differential equation as

$50\cdot\dfrac{dA}{A}=dt\\\\50\ln{(A)}+C=t\qquad\mbox{integrating}\\\\t=50\ln{\left(\dfrac{A}{4000}\right)}\qquad\mbox{applying the boundary condition}$

This last expression looks like the one you describe. If you solve for A instead of t, you get

$A=4000\cdot e^{0.02t}$

This is the same as your other answer.

8 0

3 years ago

Read 2 more answers

I don't get this question

vichka [17]

About $1.80 because 8.7590 divide by 4.80 is about$1.80

4 0

4 years ago

A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

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

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

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:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

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

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

3 years ago

A ____ is a pair of equal ratios.

12345 [234]

A proportion is a pair of equal ratios.

6 0

3 years ago