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3 years ago

Given a+b=7 and a–b=3, find: 2^a·2^b

Mathematics

1 answer:

Semmy [17]3 years ago

8 0

a +b = 7

a-b = 3

Rewrite the second equation as a = 3+b

Replace a in the first equation with that:

3+b + b = 7

Simplify:

3 +2b = 7

Subtract 3 from both sides:

2b = 4

Divide both sides by 2:

b = 4/2 = 2

Now replace b in the first equation with 2 to solve for a:

a + 2 =7

a = 7-2 = 5

so you now have a and b.

Now solve the given equation:

2^a * 2^b

2^5 * 2^2

32*4

128

The answer is 128.

You might be interested in

If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2

IgorLugansk [536]

Answer: 10

Step-by-step explanation:

Since integral from 1 to 4 of f(x) =10

To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method

Let U = 2x, dU = 2dx, dx = dU/2

Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.

Since this limit are the same as the limit for the question,

Therefore, F(4) - F(1) = F(8) - F(2) = 10

Substituting dx=dU/2

Gives,

Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10

6 0

3 years ago

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%.

6 0

3 years ago

12.54 + (-24.673)<br><br><br> What’s the answer if you compute?

Zinaida [17]

Answer:

-12.133 would be your answer

8 0

3 years ago

Based on the graph, what are the solutions of the equation

olga_2 [115]

It's C. move all terms to the left side and set equal to zero. then set each factor equal to zero.

4 0