Select the correct answer consider the function f(x)=2^x and the function g(x).

puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let $x$ represent the width.

Since the length is 7 feet longer, we can represent the length by $x+7$ .

Now that we have our values for the length and the width we can multiply them together to find our area.

$(x)(x+7)=x^{2} +7x$

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

$(x+7)(x+14)$

And multiply our area by 3.

$3(x^{2} +7x)$

set these equal to each other to find your new equation.

$(x+7)(x+14)=3(x^{2} +7x)$

Now you need to solve for $x$ . To do this first muliply $(x+7)$ and $(x+14)$ .

$(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98$

Then multiply $3(x^{2} +7x)$

$3(x^{2} +7x)=\\3x^{2} +21x$

Now you can begin solving for $x$ .

$x^{2} +21x+98=3x^{2} +21x$

Subtract $x^{2}$ from both sides.

$21x+98=2x^{2} +21x$

Subtract $21x$ from both sides.

$98=2x^{2}$

Divide by 2.

$49=x^{2}$

And finally take the sqaure root of both sides.

$\sqrt{x^{2} }=\sqrt{49}\\x=7$

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 and -7, in this case we only get +7.

Now that we have the value of $x$ , we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

7 0

3 years ago

Help me quickkkk!! A = 1/2(a+b)h solve for b

nasty-shy [4]

Answer:

2A/h - a = b

Step-by-step explanation:

Using A= 1/2(a+b)h

Divide both side by h

⇒A/h = 1/2(a + b)

Mutiply both sides by 2

⇒2A/h = a + b

Take the 2 over to the other side

2A/h - a = b

Keep in mind, that the (a) is not on the bottom, rather on its own

3 0

3 years ago

A 3-pack of beaded necklaces costs $4.47. What is the unit price?

inysia [295]

Answer:

1.49 per necklace

Step-by-step explanation:

there are 3 necklaces sold for 4.47. if we divide the three necklaces by the overall price we get the price per necklace. 4.47 divided by 3 = 1.49

7 0

3 years ago

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Which of the following is equivalent to 140 centiliters?

Norma-Jean [14]

The answer is C) because one litre=100 centiliters, and one kilolitre=one litre which means that one kilolitre =100000 centiliters
So 140 centiliters are 140 divided by 100000 kiloliters=0.00140 kiloliters

6 0

3 years ago

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A dartboard consists of a circle inscribed in a square. The area of the circle is 16π square centimeters. The area of the square

lapo4ka [179]

The solution would be like this for this specific problem:

Area of Circle = 16(π)

= 16 * 3.14

= 50.24

Area of Square = 64

= 64 – 50.24

= 13.76

Area of Square but not on the circular board = 13.76 / 64

= 0.215

Percentage value = 0.215 * 100%

= 21.5%

So, to the nearest percent, the probability that the dart lands inside the square but not on the circular dartboard is 21.5%.

4 0

3 years ago

Read 2 more answers