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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.

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Segment AB has endpoints A(-1,3) and B(0,7). What is the length of AB?

ololo11 [35]

Answer:

$\sqrt{17}$

Step-by-step explanation:

Calculate the length (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (0, 7)

d = $\sqrt{(0+1)^2+(7-3)^2}$

= $\sqrt{1^2+4^2}$

= $\sqrt{1+16}$

= $\sqrt{17}$ ≈ 4.1 ( to 1 dec. place )

5 0

3 years ago

Holli's house is located at (−1, 4). She can walk in a straight line to get to Jedd's house. A fast food restaurant is located a

GrogVix [38]

Answer:

The coordinates of Jedd's house is (-5, 0)

Step-by-step explanation:

Given;

Location of Holli's House = (−1, 4)

Location of fast food restaurant = (−3, 2)

To Find:

The coordinate of Jedd's house.

Solution:

If the distance between the two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is divided by the point (x,y) in the ratio of m : n then

$x=\frac{x_{1}n+x_{2}m}{m + n}$

$y=\frac{y_{1}n+y_{2}m}{m + n}$

Hollis house is located at (-1 , 4)

So, $(x_{1},y_{1}) = (-1 , 4)$

She walks in a straight line to get to Jedds house

The restaurant is located at (-3 , 2) and partitions the way from

(x , y) = (-3 , 2)

The ratio of Hollis house to Jedds house is 1 : 1

(m : n) = 1 : 2

Lets consider that Jedds house is located at $(x_{2},y_{2})$

Then $x_2$ will be

$-3=\frac{-1(1)+x_{2}(1)}{1+1}$

$-3=\frac{-1 +x_{2}}{2}$

$-3 \times 2=-1 +x_{2}$

$-6 = -1 +x_{2}$

$-5 = x_{2}$

Now $y_{2}$ will be

$2=\frac{4(1)+y_{2}(1)}{1+1}$

$2=\frac{4+y_{2}}{2}$

$2 \times 2=4+y_{2}$

$4 = 4+y_{2}$

$4 - 4 = y_{2}$

$y_{2} = 0$

∴ The coordinates of Jedd's house is (-5, 0)

5 0

3 years ago

What is the product of 1 1/2 and -1 1/4

ch4aika [34]

I'm pretty sure its −1 7/8

7 0

4 years ago

Read 2 more answers

PLZ HELP ASAP

topjm [15]

It would be D: 181

3 17
---- = ------
32 X

Then you would cross multiply and divide.

6 0

3 years ago

The teacher assigns an essay that must be around 1,000 words long. Specifically, it has to be within 50 words of 1,000. What is

Georgia [21]

That would be 1000-49 to 1000+49

Answer is w = 951 to 1049 words long.

6 0

4 years ago