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
Natali5045456 [20]
1 year ago
6

For the piecewise function, find the values h( - 6), h(0), h(5), and h(9).- 5x – 13, for x < -3h(x) = { 5, for - 35x<5for

x>5x+1,h(-6)=
Mathematics
1 answer:
sleet_krkn [62]1 year ago
5 0

Given the piecewise function h(x):

h(x)=\begin{cases}-5x-13,x

-When x is less than "-3", h(x)=-5x-13

-When x is between -3 and 5, h(x)=5

-When x is greater than or equal to 5, h(x)=x+1

1) For h(-6), this notation indicates that you have to determine the value of h(x) when x=-6

-6 is less than -3, which means that for this value of x, the function has the following shape

h(x)=-5x-13

Replace the expression with x=-6 and calculate the corresponding value of x:

\begin{gathered} h(-6)=-5(-6)-13 \\ h(-6)=30-13 \\ h(-6)=17 \end{gathered}

2) For h(0), you have to determine the value of h(x) when x=0. Zero is between -3 and 5, for this value of x, the function h(x) has the following shape:

h(x)=5

This equation represents a horizontal line, which means that for every value within the interval of definition -3≤x<5, the function always has the same value h(x)=5

We can conclude that:

h(0)=5

3) For h(5), you have to determine the value of h(x) for x=5, for values of x greater than or equal to 5, h(x) has the following shape:

h(x)=x+1

Replace the expression with x=5 and calculate the corresponding value of h(x):

\begin{gathered} h(5)=5+1 \\ h(5)=6 \end{gathered}

4) For h(9), you have to determine the value of h(x) when x=9, 9 is greater than 5, for this value of x, the function has the following shape:

h(x)=x+1

Replace the expression with x=9, and calculate the corresponding value of h(x):

\begin{gathered} h(9)=9+1 \\ h(9)=10 \end{gathered}

So, to sum up:

undefined

You might be interested in
The sum of three consecutive odd number is 51
krok68 [10]
If u add up 15,17, and 19 they add up to 51
6 0
3 years ago
Which inequality correctly orders the numbers -5,-3, and 2 from greatest to least?
lozanna [386]

Answer:

1) 2 > -3 > -5

Step-by-step explanation:

that is mathematically correct

8 0
3 years ago
Read 2 more answers
What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

A_s=\frac{\theta}{360}*\pi r^2 where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

A_s=\frac{60}{360}*\pi (\sqrt{3})^2 which simplifies a bit to

A_s=\frac{1}{6}*\pi(3) which simplifies a bit further to

A_s=\frac{1}{2}\pi which of course is the same as

A_s=\frac{\pi}{2}

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \frac{\sqrt{3} }{2}. Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

A=\frac{1}{2}bh. There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2 which simplifies to

3=h^2+\frac{3}{4} and

3-\frac{3}{4}=h^2 and

\frac{12}{4} -\frac{3}{4} =h^2 and

\frac{9}{4} =h^2

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

A=\frac{1}{2}(\sqrt{3})(\frac{3}{2}) which simplifies to

A=\frac{3\sqrt{3} }{4}

Therefore, the area in terms of pi for that little segment is

A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}, choice A.

8 0
3 years ago
Select the correct answer from the drop-down menu.
LenKa [72]

Answer:

D

Step-by-step explanation:

Got 100%

7 0
3 years ago
3b + 4 ≥ 7<br> what is b ?
Tasya [4]
This is just the answer digitally i cant explain the process

3 0
3 years ago
Read 2 more answers
Other questions:
  • on a tour of an old gold mine, you find a gold nugget containing .82 ounces of gold. gold is worth $1566.80 per ounce. how much
    14·2 answers
  • Last night, the two dinner specials at Henry's favorite restaurant were salmon filet and steak. The restaurant served 55 special
    14·2 answers
  • Write the equivalent logarithmic equation to 10^a = x+b
    10·1 answer
  • Lexi measured the dolls in her collection so she could build a new display case the 7 dolls heights were 7in 5in 6in 9in 8in 9in
    6·1 answer
  • A store has a sale for 10% off. You decide to buy a $15 t-shirt.
    8·2 answers
  • Simplify: (3x2 - 4x + 6) + (7x - 2)
    7·1 answer
  • 5^3=? Can someone help me with this I am stuck lol
    12·2 answers
  • A file that is 272 megabyte la is being downloaded. If the download is 12.9% complete, how many megabytes have been downloaded?
    9·1 answer
  • The rule Rx-axis o is applied to the point (-3,-2). Where is the image in the coordinate
    7·1 answer
  • Help 20 point question
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!