All categories

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

The first term of a sequence is -12. The recursive formula for the sequence is an = an-1 + 9. What are the next 3 terms in the s

Bess [88]

The next three terms are: -3, 6, and 15

To get each new term, we simply add 9 to the last term. So we add 9 to -12 to get -3. Then we add 9 to -3 to get 6. Finally we add 9 to 6 to get 15

In other words,
first term = -12
second term = first term+9 = -12+9 = -3
third term = second term + 9 = -3+9 = 6
fourth term = third term + 9 = 6+9 = 15

This process repeats forever though we only need three terms in this case.

So that's why the answer is the three values -3, 6 and 15

8 0

3 years ago

Find the measure of the are or angle indicated. Assume that lines which appear tanget are tangents.

Brilliant_brown [7]

9514 1404 393

Answer:

85°
60°

Step-by-step explanation:

1. Angle JKL is half the measure of the intercepted arc JK.

(1/2)JK = 1/2(360° -190°) = (1/2)(170°) = 85°

angle JKL is 85°

2. The angle between tangents is the supplement of the intercepted arc.

angle JKL = 180° -(360° -240°)

angle JKL = 60°

8 0

3 years ago

What is m angle ABC

victus00 [196]

Answer:

3rd option: 60 degrees

Step-by-step explanation:

We can see in the diagram that the angle on C is a supplementary angle, which means that the sum of 135 and internal angle will be equal to 180 degrees.

Let x be the internal angle,

Then

x+135 = 180

x = 180-135

x = 45 degrees

So now we know that two interior angles of the triangle.

Also we know that sum of all internal angles of triangle is 180 degrees.

Using the same postulate:

A+B+C = 180

75 + B + 45 = 180

120+B = 180

B = 180 - 120