Evaluate the following expression if x=3: (1/2)^x

Answer:

A

Step-by-step explanation:

We are given two functions:

[tex]\displaystyle f(x)=\frac{x-16}{x^2+6x-40}\text{ and } g(x)=\frac{1}{x+10}[/tex]

And we want to find:

[tex]f(x)+g(x)[/tex]

Thus:

[tex]\displaystyle =\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}[/tex]

We can factor the denominator of the first term:

[tex]\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}[/tex]

In order to add the two terms, we must have a common denominator. To achieve this, we can multiply to second term by (x - 4). Therefore:

[tex]\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}\Big(\frac{x-4}{x-4}\Big)[/tex]

Multiply:

[tex]\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{x-4}{(x+10)(x-4)}[/tex]

Combine:

[tex]\displaystyle =\frac{(x-16)+(x-4)}{(x+10)(x-4)}[/tex]

Simplify:

[tex]\displaystyle =\frac{2x-20}{(x+10)(x-4)}[/tex]

We can expand the denominator:

[tex]\displaystyle =\frac{2x-20}{x^2+6x-40}[/tex]

Therefore, our answer is A.

Answer:

A

Step-by-step explanation:

Answer:

A,C,D

Step-by-step explanation:

The only one you might use it the triangle

Answer:

Answer: Sin0 = 8/8.5

Step-by-step explanation:

Step-by-step explanation: What we have is a right angled triangle, with two sides given and one angle which is the reference angle (unknown angle).

The Sine of the angle is calculated as

Sin0 = opposite/hypotenuse

We have the opposite side (facing the reference angle) as 8 units and the hypotenuse (facing the right angle unknown), which we shall label as X.

To calculate the hypotenuse, we shall apply the Pythagoras theorem which is,

X² = 3² + 8²

X² = 9 + 64

X² = 73

Adding the square root sign to both sides of the equation, we now have

X = √73

X = 8.5 (approximately)

Now that we have the hypotenuse as 8.5, the Sine of the angle can now be calculated as

Sin0 = opposite/hypotenuse

Sin0 = 8/8.5

Answer:

table 2.

Step-by-step explanation:

in table 2 you can see that if you multiply any number on the distance side of the chart by 10 you will see that the answer is by the money side

Answer:

where

Step-by-step explanation:

where's the number line???

Answer:

where the number line

Step-by-step explanation:

you can screen shot the number line

Answer:

10

Step-by-step explanation:

Answer:

sorry I can't know the answer

The scale factor used is {k} = 164.4.

Scale factor is the ratio of original dimensions to the scaled dimensions.

Given is that Eiffel Tower is 986 feet tall. Caroline built a scale model that is 6 inches tall.

We can write the scale factor as -

{k} = 986/6

{k} = 164.4

Therefore, the scale factor used is {k} = 164.4.

To solve more questions on scale factor, visit the link-

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Answer:

Distance between the two planes after 1 hour = 410 miles

Step-by-step explanation:

Given - A plane leaves and flies due north at 280 miles per hour. At

            the same time another plane takes off from the same airport

            and flies due east at a speed of 300 miles per hour.

To find - What is the distance between the two planes after 1 hour ?

Proof -

Given that , Plane 1 flies due north at a speed of 280 miles per hour.

So,

Total distance traveled in 1 hour = 280 miles

Also,

Plane 2 flies due east at a speed of 300 miles per hour.

So,

Total distance traveled in 1 hour = 300 miles.

The diagram is as follows :

Now,

We have to find the distance after 1 hour i.e. AC

In Triangle ABC ,

By using Pythagoras theorem, we get

AC² = BC² + AB²

⇒AC² = (300)² + (280)²

⇒AC² = 90,000 + 78,400

⇒AC² = 168,400

⇒AC = √168,400

⇒AC = 410.366 ≈ 410

∴ we get

Distance between the two planes after 1 hour = 410 miles

Answer:

m = 2

Step-by-step explanation:

Using the slope formula, we can find the slope of two points:

        y2 - y1

m = --------------

        x2 - x1

The slope is the same thing as change in y over change in x. Now, plugging in the points (0, -2) and (3, 4):

       4 - (-2)       4 + 2     6

m = -----------  =  ------- = ------  =  2

        3 - 0            3         3

So the slope is 2.

Answer:

Step-by-step explanation:

length = 120/8 = 15 feet

perimeter = (15 + 8) x 2 = 46 feet

The area is the product of the length and width then the length of the rectangle is 15 feet.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle has an area of 120 square feet and a width of 8 feet.

Then the length of the rectangle will be

Area = Length × Width

 120 = 8L

     L = 15

Then the length of the rectangle is 15 feet.

More about the rectangle link is given below.

https://brainly.com/question/10046743

Answer:

C

Step-by-step explanation:

Hey There!

So if you didn't know in an isosceles trapezoid the non parallel sides are congruent

So given the base lengths and the perimeter we subtract the given length from the perimeter and divide that by 2

40-10=40

30-14=16

16/2=8

so the lengths of the non parallel sides would be 8 cm and 8 cm

Answer:

c=7p

e.g. 21=7*3

hope this helps. if not, send me a message :)

The equation representing the cost c in dollars and different amounts of meat in pounds p, is c = 7p

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, A butcher displays the cost, in dollars, of different amounts of meat in the table shown.

Finding the unit price,

3 pounds = $21

1 pound = 21/3 = $7

Therefore, if c is cost and p is total pounds,

c = 7p

Hence, the equation representing the cost c in dollars and different amounts of meat in pounds p, is c = 7p

Learn more about equations, click;

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Answer:

x=6

look at the picture i sent please

Answer:

5 units  or B

Step-by-step explanation:

Answer:

It is 5 units

Step-by-step explanation:

Answer:

m<8 is 30°

Step-by-step explanation:

Here are some images that can help you have a better understanding :

Answer:

130.50 X 13% = $16.97

130.50 - 16.97 = 113.53

Answer 113.53

Step-by-step explanation:

Answer:

Step-by-step explanation:

area=(6+3)/2×4+7×3+1/2×2×3

=18+21+3

=42 ft²

Answer:

I think its decreasing and then at a slower rate than

Step-by-step explanation:

Because if you look at the graph it's decreasing between the 3rd and 6th months, and the revenue is just at a slower rate because the line isn't at an aburpt angle.

Answer:

Edmentum correct answer based on comments from the other answer !! :)

Answer:

Step-by-step explanation:

Equations:

Multiply the first equation by 5 and subtract from the second one:

Find n:

Answer:

I would say D I'm not to sure though

Step-by-step explanation:

Good Luck

Answer:

18 minutes earlier

Step-by-step explanation:

Given

[tex]Distance =119km[/tex]

[tex]Speed\ 1 = 70km/h[/tex]

[tex]Speed\ 2 = 85km/h[/tex]

Required

Determine how much sooner if traveled at speed 2 instead of speed 1

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

Make Time the subject

[tex]Time= \frac{Distance}{Speed }[/tex]

For Speed 1

[tex]Time= \frac{119km}{70km/h}[/tex]

[tex]Time= 1.7hr[/tex]

For Speed 2

[tex]Time= \frac{119km}{85km/h}[/tex]

[tex]Time= 1.4hr[/tex]

Calculate the difference

[tex]Difference = 1.7hr - 1.4hr[/tex]

[tex]Difference = 0.3hr[/tex]

Convert to minutes

[tex]Difference = 0.3*60\ min[/tex]

[tex]Difference = 18\ min[/tex]

If traveled at 85km/h, the van will arrive 18 minutes earlier

Answer:

The answer is p = 2.

Step-by-step explanation:

1) Divide both sides by 9.

[tex]p - 4 = - \frac{18}{9} [/tex]

2) Simplify 18/9 to 2.

[tex]p - 4 = - 2[/tex]

3) Add 4 to both sides.

[tex]p = - 2 + 4[/tex]

4) Simplify -2 + 4 to 2.

[tex]p = 2[/tex]

Therefor, the answer is p = 2.

Answer:

p =2

Step-by-step explanation:

9(p-4) =-18

9p-36=-18

9p = -18 +36

9p = 18

divide both side by 9

p =2

Answer:

13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

First, we do 3x3 which is 9.

Then, we do 9+4=13

Hope this helps =]

Answer:

92.86%

Step-by-step explanation:

Total questions, T = 50.

Colin thought 8 questions were right.

Colin got 5 questions right that he thought he got wrong.

Total score, s = 45.

So, actual number of questions which are wrong are 5.

Score according to him = 50 - 8 = 42.

Now, we know percentage accuracy is given by :

Therefore, percentage accuracy he had with predicting his scores is 92.86%.

Answer:

a. 35 degrees

b. 145 degrees

Step-by-step explanation:

a. Since the two base angles of this triangle are congruent, we can conclude that the triangle is isosceles, which means that the two base angles and sides are congruent.

Now, knowing that information, we can subtract 110 from 180 (the sum of all interior angles in a triangle) and we get 70. But this isn't our answer. This is the sum of both base angles. Since the base angles are congruent, we can divide the 70 by 2 to get the measure of ONE base angle, which is 35 degrees.

b. There are two approaches to solve this problem. I have worked both out.

1) We can use the Exterior Angle Theorem, which states that the sum of the interior angles is equal to the exterior angle. We can add 110 to 35, so we get 145 degrees as the measure of <1.

2) The second approach is supplementary angles. Since we see that one of the base angles and <1 is on the same line, we can subtract 35 from 180 to find the measure of <1 to get 145 degrees.

Either way you use, you get the correct answer. Hope this helped!