1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Korvikt [17]
2 years ago
14

How do you simplify 6 to the power of 2 plus 15

Mathematics
1 answer:
Sonja [21]2 years ago
5 0

Answer:

D

Step-by-step explanation:

6 to the power of 2 just means 6 squared. To solve this, just multiply 6 by itself. 6x6 is 36. Now, we have to add that to 15. 36+15 is 51.

Therefore, the correct answer is D!

Hope I helped!!!!!!!!!

You might be interested in
What fraction of 2 1/3 is 5/6?
taurus [48]
I think it’s D or a I think so
5 0
3 years ago
What do you do to the equation y = x to make its graph move up on the y-axis?
densk [106]

Recall that in Linear Functions, we wrote the equation for a linear function from a graph. Now we can extend what we know about graphing linear functions to analyze graphs a little more closely. Begin by taking a look at Figure 8. We can see right away that the graph crosses the y-axis at the point (0, 4) so this is the y-intercept.

Then we can calculate the slope by finding the rise and run. We can choose any two points, but let’s look at the point (–2, 0). To get from this point to the y-intercept, we must move up 4 units (rise) and to the right 2 units (run). So the slope must be

\displaystyle m=\frac{\text{rise}}{\text{run}}=\frac{4}{2}=2m=

​run

​

​rise

​​ =

​2

​

​4

​​ =2

Substituting the slope and y-intercept into the slope-intercept form of a line gives

\displaystyle y=2x+4y=2x+4

HOW TO: GIVEN A GRAPH OF LINEAR FUNCTION, FIND THE EQUATION TO DESCRIBE THE FUNCTION.

Identify the y-intercept of an equation.

Choose two points to determine the slope.

Substitute the y-intercept and slope into the slope-intercept form of a line.

EXAMPLE 4: MATCHING LINEAR FUNCTIONS TO THEIR GRAPHS

Match each equation of the linear functions with one of the lines in Figure 9.

\displaystyle f\left(x\right)=2x+3f(x)=2x+3

\displaystyle g\left(x\right)=2x - 3g(x)=2x−3

\displaystyle h\left(x\right)=-2x+3h(x)=−2x+3

\displaystyle j\left(x\right)=\frac{1}{2}x+3j(x)=

​2

​

​1

​​ x+3

Graph of three lines, line 1) passes through (0,3) and (-2, -1), line 2) passes through (0,3) and (-6,0), line 3) passes through (0,-3) and (2,1)

Figure 9

SOLUTION

Analyze the information for each function.

This function has a slope of 2 and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. We can use two points to find the slope, or we can compare it with the other functions listed. Function g has the same slope, but a different y-intercept. Lines I and III have the same slant because they have the same slope. Line III does not pass through (0, 3) so f must be represented by line I.

This function also has a slope of 2, but a y-intercept of –3. It must pass through the point (0, –3) and slant upward from left to right. It must be represented by line III.

This function has a slope of –2 and a y-intercept of 3. This is the only function listed with a negative slope, so it must be represented by line IV because it slants downward from left to right.

This function has a slope of \displaystyle \frac{1}{2}

​2

​

​1

​​  and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. Lines I and II pass through (0, 3), but the slope of j is less than the slope of f so the line for j must be flatter. This function is represented by Line II.

Now we can re-label the lines as in Figure 10.

Figure 10

Finding the x-intercept of a Line

So far, we have been finding the y-intercepts of a function: the point at which the graph of the function crosses the y-axis. A function may also have an x-intercept, which is the x-coordinate of the point where the graph of the function crosses the x-axis. In other words, it is the input value when the output value is zero.

To find the x-intercept, set a function f(x) equal to zero and solve for the value of x. For example, consider the function shown.

\displaystyle f\left(x\right)=3x - 6f(x)=3x−6

Set the function equal to 0 and solve for x.

⎧

⎪

⎪

⎨

⎪

⎪

⎩

0

=

3

x

−

6

6

=

3

x

2

=

x

x

=

2

The graph of the function crosses the x-axis at the point (2, 0).

Q & A

Do all linear functions have x-intercepts?

No. However, linear functions of the form y = c, where c is a nonzero real number are the only examples of linear functions with no x-intercept. For example, y = 5 is a horizontal line 5 units above the x-axis. This function has no x-intercepts.

Graph of y = 5.

Figure 11

A GENERAL NOTE: X-INTERCEPT

The x-intercept of the function is value of x when f(x) = 0. It can be solved by the equation 0 = mx + b.

EXAMPLE 5: FINDING AN X-INTERCEPT

Find the x-intercept of \displaystyle f\left(x\right)=\frac{1}{2}x - 3f(x)=

​2

​

​1

​​ x−3.

SOLUTION

Set the function equal to zero to solve for x.

\displaystyle \begin{cases}0=\frac{1}{2}x - 3\\ 3=\frac{1}{2}x\\ 6=x\\ x=6\end{cases}

​⎩

​⎪

​⎪

​⎪

​⎪

​⎪

​⎨

​⎪

​⎪

​⎪

​⎪

​⎪

​⎧

​​  

​0=

​2

​

​1

​​ x−3

​3=

​2

​

​1

​​ x

​6=x

​x=6

​​  

The graph crosses the x-axis at the point (6, 0).

Analysis of the Solution

A graph of the function is shown in Figure 12. We can see that the x-intercept is (6, 0) as we expected.

Figure 12. The graph of the linear function \displaystyle f\left(x\right)=\frac{1}{2}x - 3f(x)=

​2

​

​1

5 0
2 years ago
The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their master Trigonomos
VikaD [51]

Answer:

60.2 m

Step-by-step explanation:

Let x represent the width of the river.  The distance from the point across from the tree to the second point is 15 m.  The angle from this point to the tree across the river is 76°.

This makes the side opposite the angle x, the width of the river.  It also means the 15 m side is adjacent to this angle.

The ratio opposite/adjacent is the ratio for tangent; this gives us the equation

x/15 = tan(76)

Multiply both sides by 15:

15(x/15) = 15(tan(76))

x = 15(tan(76)) ≈ 60.2

5 0
3 years ago
Nine out of ten students prefer math class over lunch. How many students do not prefer math if 200 students were asked?
fredd [130]
So, 9 out of 10 students prefer class, so, obviously, it would not be 100. It would be 150. So in conclusion, 50 students prefer lunch over math class, whilst 150 other students prefer math class over lunch.
3 0
3 years ago
I drove 380 miles using 14 gallons of gas. At this rate, how many gallons of gas would I need to drive 418 miles?
ser-zykov [4K]

Answer:

15.4 gallons .

Step-by-step explanation:

The rate of gas used  = 380/14 = 27.14 gallons per gallon.

So for each gallon used  you drive 27.14 miles.

So number of gallons used when travelling 418 miles = 418/27.14

= 15.4 gallons .


8 0
3 years ago
Read 2 more answers
Other questions:
  • A one year member ship to a gym cost $725. The registration fee is $125, and the remaining amount is paid monthly. Define a vari
    13·1 answer
  • 125 students have volunteered to be on the prom committee. 2 of those students will be randomly chosen to win free tickets to th
    6·1 answer
  • an assistant recieved a 3% raise bringing the salary to 43,989 what was the salary defore the raise? (round to the nearest dolla
    8·2 answers
  • Apply the distributive property to create an equivalent expression. 1/5(15+10k)
    6·2 answers
  • Greatest comnon factor for 12 20 24
    11·2 answers
  • find the area of each Arc. Use the 3.14 as the value of pi. Round your answer to the nearest tenth. Label unit​
    10·1 answer
  • Grant attended 75% of his Student Council meetings. If there were 40 meetings, how many did Grant NOT attend?
    5·1 answer
  • A model of a statue is
    5·1 answer
  • Need help on this<br><br> Please help
    11·1 answer
  • Find the area of each circle. Round to the nearest tenth.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!