Answers
The graph is attached.
Why?To solve the given piecewise function, we need to graph each of the functions that compound the main function with their respective domain restrictions.
So, solving we have:
- First function: Positive slope line (red line).
[tex]f(x)=x+1=y\\\\y=x+1, if x<0[/tex]
Let's find the axis intercepts in order to be able to graph the function.
Finding the x-axis intercept, we need to make "y" equal to 0, so:
[tex]y=x+1\\\\0=x+1\\x=-1[/tex]
So, we have that the x-axis intercept is located at the point (-1,0)
Finding the y-axis intercept, we to mate "x" equal to 0, so:
[tex]y=x+1\\\\y=0+1\\y=1[/tex]
So, we have that the y-axis intercept is located at the point (0,1)
Hence, we have that the function exists from the values of "x" less than 0 to the negative infinite or (-∞,0)
- Second function: Horizontal line (blue line).
[tex]y=2,if0\leq x\leq 1[/tex]
Since there is not variable, we know that it's a horizontal line that passes through y equal to 2.
Hence, we have that the function exists between the values of "x" from 0 to 1 or [0,1]
- Third function: Positive slope line (green line).
[tex]y=x,ifx>0[/tex]
Let's find the axis intercepts in order to be able to graph the function.
Finding the x-axis intercept, we need to make "y" equal to 0, so:
[tex]0=x+\\\\0=x+\\x=0[/tex]
So, we have that the x-axis intercept is located at the point (0,0)
Finding the y-axis intercept, we to make "x" equal to 0, so:
[tex]y=x\\\\y=0\\y=0[/tex]
We have that the function only pass through the point (0,0) or origin.
Hence, we have that the function exists from the values of "x" greater than 2.
So, the graph of the given function is attached.
Have a nice day!
Related Questions
Rounded to the nearest tenth, what is the value of x
Answers
Answer:
0.6 ft
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{2.3}{x}[/tex] = [tex]\frac{16.8}{4.5}[/tex] ( cross- multiply )
16.8x = 10.35 ( divide both sides by 16.8 )
x ≈ 0.6 ft ( to the nearest tenth )
solution set of 2x + y < 4
Answers
Step-by-step explanation:
Subtract
2
x
from both sides of the equation.
y
=
4
−
2
x
x
−
y
=
2
Subtract
x
from both sides of the equation.
y
=
4
−
2
x
−
y
=
2
−
x
Multiply each term in
−
y
=
2
−
x
by
−
1
Tap for more steps...
y
=
4
−
2
x
y
=
−
2
+
x
Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.
(
2
,
0
)
ANSWER
See attachment
EXPLANATION
The given inequality is
[tex]2x + y \: < \: 4[/tex]
To solve we need to graph this inequality.
To do that we graph the corresponding linear equation
[tex]y = - 2x + 4[/tex]
This is a straight line with slope
[tex]m = - 4[/tex]
and y-intercept (0,4)
The graph of this function is to the right of the origin.
The solution set of the corresponding inequality is the half plane that is shaded.
We plot the point (0,0) into the given inequality to determine which half plane must be shaded
[tex]2(0) + 0 \: < \: 4[/tex]
[tex]0 < 2[/tex]
This is true so we shade the lower half plane. The solution set is the lower half plane shaded in the attachment.
Note that the boundary line must be a dashed line because the inequality does not involve equal sign.
factor 200t+8t^3-80t^2
Answers
Answer:
8t(t - 5)^2
Step-by-step explanation:
I would immediately rearrange these terms in descending order by powers of t:
8t^3 - 80t^2 + 200t
Then I'd factor out 8t:
8t(t^2 - 10 t + 25).
Finally, I'd factor the quadratic t^2 - 10 t + 25:
(t - 5)^2
and so 200t+8t^3-80t^2 in factored form is 8t(t - 5)^2.
Answer:
Step-by-step explanation:
It would be better to list the terms in descending order.
8t^3 - 80t^2 + 200t Take out a common factor of t
t(8t^2 - 80t + 200) Now take out 8
8t (t^2 - 10t + 25) Now factor the polynomial
8t(t - 5)(t - 5)
In a u.s. Poll 8 out of 12 citizens said they were happy with the job Obama is doing.if 126 people were surveyed how many people were happy with Obama?
Answers
Answer:
84 people
Step-by-step explanation:
create a proportion
8 x
----- = ---------
12 126
solve.. cross multiply
128x8 =1008
1008/12 =84
The number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
What is number?
" Number is defined as the count of any given quantity."
According to the question,
Total number of people surveyed [tex]= 126[/tex]
As per U.S. poll,
Out of [tex]12[/tex] citizen number of people happy [tex]= 8[/tex] people
Out of [tex]1[/tex] citizen number of people happy [tex]= \frac{8}{12}[/tex] people
Out of [tex]126[/tex] number of people happy [tex]= \frac{8\times 126}{12}[/tex]
[tex]= 84[/tex] people
Hence, the number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
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i live in a house that 3 metets below sea level go to school 5 meters above sea level how many meters do i go
Answers
From -3 to 0 is 3
3 + 5 above sea level = 8 meters
There are 8 meters between the house and the school
I need help please?!!!!):
Answers
Answer:
4
Step-by-step explanation:
The mean of a set of data: (n₁ + n₂ + n₃...)/n, where n₁,₂,₃... are numbers in the set, and n is the number of numbers.
Plug in: (1 + 5 + 5 + 7 + 3 + 3 + 4)/7
Add: 28/7
Divide: 4
Answer:
4
Step-by-step explanation:
When finding the mean of a data set you add up all the numbers and divide it my how many numbers there is
1+5+5+7+3+3+4= 28
28 divided by 7 = 4
Mean of the set of data is 4
Hope this helps :)
if it does please mark brainliest :D
- A. Hazle <3
A stereo system is being installed in a room with a rectangular floor measuring 14 feet by 9 feet and a 7- foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. What is the shortest connection
Answers
Answer:
Approximately 24 feet.
Step-by-step explanation:
Refer to the two diagrams attached (created with Geogebra.)
The wire between the speaker and the amplifier shall be routed along the wall. The length of the connection depends on the height of the point P at which the wire turns. Point P is shown in green in both diagrams.
To find the optimal position of that turning point, imagine that the two adjacent walls of the room are unfolded into two rectangles in the same plane (diagram 2.) Consider the claim: the shortest connection shall be a straight line that links the two devices when the two walls are unfolded. This explanation will show why this claim is true using the triangle inequality theorem.
Assume this claim is false: the connection will be even shorter if the wire turns at P', which is a point other than P. The length of the connection is now the sum of the two segments:
the distance between the amplifier and P', and the distance between P' and the speaker.In contrast, if the wire is routed through point P, the length of the connection will simply be
the length of the segment between the amplifier and the speaker.Point P is on the line that connects the amplifier and the speaker in diagram 2. However, P' is a point other than P, meaning that P' is off the line between the speaker and the amplifier. It is thus possible for the following three points to form a triangle:
The amplifier,The speaker, andPoint P'.By the triangle inequality theorem, the sum of any two sides of a triangle is greater than the length of the third side. To make full use of this theorem, consider the length of the three sides in this triangle:
[tex]\left\{\begin{array}{ll}\left.\begin{aligned}&\text{distance between amplifier and P}'\text{.}\\&\text{distance between P}' \text{ and speaker.}\end{aligned}\right\}&\text{Length of the second connection}\\\text{distance between amplifier and speaker}\end{array}\right.[/tex].
The sum of the first two distances shall be greater than the third. In other words, the length of the connection through P' will be greater than the length of the connection through P. This fact contradicts the assumption that the original claim is false. In other words, the claim that P gives the shortest connection is true.
Find the length of the shortest connection using the Pythagorean Theorem. Refer to the second diagram, the connection is the hypotenuse of a right triangle with
a leg of length [tex]14 + 9 = 23[/tex] feet, andanother leg of length [tex]7[/tex] feet.The length of the connection (the hypotenuse) will be:
[tex]\sqrt{23^{2} + 7^{2}}\approx 24[/tex] feet.
I to the exponent of 65
Answers
Answer:
Step-by-step explanation:
A= 1 * 1 = 2
A2 = 1 * (1 * 1)
A2 = 1 * 1
A2 = 1
a3 = 1 * 1 * (1 * 1)
a3 = 1 *1 * 1
a3 = 1 * (1*1)
a3 = 1* 1
a3 = 1
You keep on going in this manner until you hit 1^65 = 1
The only thing you have to accept is that (1 * 1) = 1
Divide 6K2 - 15k-5 by 3k
Answers
Answer:
Step-by-step explanation:
6k^2
------- = 2k; and:
3k
-15k
------- = -5
3k
-5 cannot be evenly divided by 3k, so there's a remainder instead.
6k^2 - 15k - 5
-------------------- = 2k -5 with remainder -5.
3k
Answer:
2k
-5
Step-by-step explanation:
Complete the square for 2x2 - 4x = 14.
Answers
Answer:
2x^2-4x=14
x^2-2x=7
x^2-2x+1=8
(x-1)^2=8
How many solutions exist for given equation 12x + 1 = 3(4x + 1
Answers
Answer:
no solutions
Step-by-step explanation:
12x + 1 = 3(4x + 1)
Distribute the 3
12x + 1 = 12x + 3
Subtract 12x from each side
12x-12x +1 = 12x-12x+3
1 =3
This is never true, so there are no solutions
Answer:
There are no solution
Step-by-step explanation:
A(B+C)=ab+ac
3(4x+1)=12x+1
12x+1=12x+3
Subtract by 1 both sides of equation.
12x+1-1=12x+3-1
Simplify.
3-1=2
12x=12x+2
Then subtract by 12x both sides of equation.
12x-12=12x+2-12x
Simplify, to find the answer.
0=2
The sides are not equal.
It's should be no solution.
No solution is the correct answer.
what is the domain of (g°f)(x)
A.all real numbers except x=-4
B.all real numbers except x=0
C.all real numbers except x=4
D.all real numbers
Answers
Factor the polynomial 3x4 – 2x2 + 15x2 - 10 by grouping.
Which product is the factored form of the polynomial?
(x2 - 5)(3x2 + 2)
O (22 – 2)(3x2 + 5)
(22 + 5)(3x2 – 2)
0 (372 - 5)(2+2)
Answers
Answer:
see explanation
Step-by-step explanation:
Given
3[tex]x^{4}[/tex] - 2x² + 15x² - 10
Factor the first/second and third/fourth terms )
= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term
= (3x² - 2)(x² + 5)
Answer: (3x² - 2)(x² + 5)
Step-by-step explanation:
Twice a certain number is tripled. The resulting number is
Answers
Answer:
6x the number.
Step-by-step explanation:
"Twice a certain number" means that you are multiplying that number (x) by 2.
"Tripled" means that the number (x) would be further multiplied by 3.
Simplify: 3 x 2 = 6
The resulting number would be 6x greater than the original number.
~
Given: AB= 4
AD= 6
What point is in the interior of both circles?
H
A
B
Answers
That would be point A. Point A is inside the outer bigger circle AND the smaller inner circle
Hope this helped!
~Just a girl in love with Shawn Mendes
For this case we have that, if we look at the figure, we have two circles. The large circle is of radius AD = 6, while the small circle is of radius AB = 4.
We can see that point A is inside the small circle, since the small circle is inside the large one, so A is inside the two circles.
Answer:
Point A
The graph for the equation y=x-4 is shown below.
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
A. y - x = -4
B. y - x = -2
C. y - 4 = x
D. y + 4x = 1
Answers
Answer:
A. y - x = -4
Step-by-step explanation:
y=x-4
To get infinite equations, the equation must be equal to y=x-4
We will solve each of these for y to see if they are identical
A. y - x = -4
Add x to each side
y-x+x = x-4
y = x-4
This is the same
It will give infinite solutions
B. y - x = -2
y-x+x = x-2
y =x-2
This is not the same.
It is parallel and will give no solutions
C. y - 4 = x
y-4+4 = x+4
y = x+4
This is parallel and will give no solutions
D. y + 4x = 1
y +4x-4x = -4x+1
This will intersect at a point
Answer: The correct answer is c.
Step-by-step explanation:
I just answered the question for school
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate. This table gives the number of shakes of each flavor sold during three shifts on one day. Mango Strawberry Chocolate Shift 1 16 13 29 Shift 2 26 19 45 Shift 3 6 11 0 Total sales were $419 in the first shift, $649 in the second shift, and $96 in the third shift. If you form a linear system representing the data in the table and create a matrix from it, the determinant is 578. What is the price of one chocolate shake?
Answers
Step-by-step explanation:
you need to add together all the milkshakes sold and then add together the amount of money made and then divide the two numbers. i think this is right. hope i helped. i think your answer should be around 7 dollars for a milkshake.
The price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate.
Let x be the price of one mango shake
Let y be the price of one strawberry shake
Let z be the price of one chocolate shake
From the question we can frame three linear equations in three variables:
16x + 13y + 29z = 419
26x + 19y + 45z = 649
6x + 11y + 0z = 96
After solving the above system of equations:
x = $5
y = $6
z = $9
Thus, the price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
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which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answers
Answer:
B
Step-by-step explanation:
You are given two right triangles PQR and XYZ with PQ=12, PR=6, XY=4, XZ=2. Note that
[tex]\dfrac{PQ}{XY}=\dfrac{12}{4}=3\Rightarrow PQ=3XY\\ \\\dfrac{PR}{XZ}=\dfrac{6}{2}=3\Rightarrow PR=3XZ[/tex]
So, in these triangles:
∠P=∠X=90°;PQ=3XY;PR=3XZ.Hence, by SAS theorem these triangles are similar.
SAS Similarity Theorem states that given two triangles are similar if their two sides are in proportion and their angles adjacent to these sides have the same measure.
g(x)=x2-16x
b=-16, so =16 = 64
9(x) = (x2 - 16x + 64) - 64
9(x) = (x - 1)2-
Answers
What is 510° expressed in radian measure?
Answers
Answer: π/180
Step-by-step explanation:
510 Degree (°) =. 8.90118 Radian (rad) Degree : A degree, a degree of arc or arc degree is a measurement of plane angle, on behalf of 1/360 of a full rotation. The symbol for degree is °. It is not an SI unit, however, it is accepted for use with SI. One degree is equal to π/180 radians.
Answer:
17pi/6 rad
Step-by-step explanation:
2 pi radians = 360 degrees
Divide both sides by 2.
pi radians = 180 degrees
From the statement above, you get the conversion factors:
(pi rad)/(180 deg) = (180 deg)/(pi rad) = 1
Both fractions above equal 1. Since multiplying by 1 does not change the number, multiply 510 deg by the fraction above that will cancel out degrees and will leave you with radians.
510 deg * (pi rad)/(180 deg) = 510pi/180 rad = 17pi/6 rad
calculate the scale factor for thr dilation. What is AB?
6 units
7.6 units
9.5 units
12 units
Answers
Answer:
AB is 6 units
Hope this helps
Step-by-step explanation:
The scale factor of the dilation is: 2.5.
The length of AB is: 6 units.
What is the Scale Factor of a Dilation?The scale factor of a dilation (reduction or enlargement) = dimension of new figure / corresponding dimension of original figure.
The scale factor of the image given = B'C'/BC
Scale factor = 9.5/3.8 = 2.5
To find the length of AB, divide the length of A'B' by the scale factor of the dilation.
AB = 15/2.5
AB = 6 units. (option A)
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What is the midpoint of the line segment with the endpoints J(-9,-4) and K(7,8)?
Answers
Answer:
Step-by-step explanation:
22
The radius is 14 and CD = 22. Find EB.
Answers
Answer:
14 - [tex]\sqrt{23}[/tex]
Step-by-step explanation:
CD=22 => ED=11
AD=14 (radius). With Pythagorean theorem, [tex]AE^{2}[/tex]=[tex]AD^{2}[/tex]-[tex]ED^{2}[/tex] => AE = [tex]\sqrt{23}[/tex]
EB= AB-AE = 14 - [tex]\sqrt{23}[/tex]
The measure of EB from the expression is 5.34
The given diagram is A circle with the following sides
radius AB = 14
CD = 22
From the diagram, AB = AE + EB
Determine the measure of AE using Pythagoras theorem
AD² =AE² + ED²
14² = AE² + 11²
AE² = 14² - 11²
AE² = 196 - 121
AE² = 75
AE = √75
AE = 8.66
EB = AB - AB
EB = 14 - 8.66
EB = 5.34
Hence the measure of EB from the expression is 5.34
Find the difference 7/8 - 3/10
Answers
Hello
Good Luck
Goodbye ♥
(1/(x-1))-(3/(x^2+2x-3))
[tex] \frac{1}{x - 1} - \frac{3}{x {}^{2} + 2x - 3 } [/tex]
Answers
[tex]
\dfrac{1}{x-1}-\dfrac{3}{x^2+2x-3} \\
\dfrac{1}{x-1}-\dfrac{3}{(x+3)(x-1)} \\
\dfrac{1\cdot(x+3)-3}{(x+3)(x-1)} \\
\dfrac{x+3-3}{(x+3)(x-1)} \\
\dfrac{x}{(x+3)(x-1)}
[/tex]
Hope this helps.
r3t40
Classify the following triangle
Answers
Answer:
B acute
D equilateral
Step-by-step explanation:
All the sides are equal (line in the middle of each side) = equilateral
All the angles are equal (single line in each angle) = equilangular
That means 180/3 = 60
Each angle is 60 degrees 60 degree angles are acute
5/6 + 1/8 what is it?
Answers
Answer:
Step-by-step explanation:
[tex]\frac{5}{6} +\frac{1}{8} = \frac{20}{24} +\frac{3}{24} = \frac{23}{24}[/tex]
Answer:
23/24
Step-by-step explanation:
5/6 = (5×4)/(6×4)=20/24
1/8 = (1×3)/(8×3)=3/24
5/6 + 1/8 = 20/24 + 3/24 =23/24
Choose the function whose graph is given by:
A. y=3sin(x-2)+1
B. y=3cos(x-3)+1
C. y=6sin(x-2)-2
D. y=3sin(x-2)+2
Answers
Answer:
A
Step-by-step explanation:
a site called desmos, its a graphing calculator and you should use it :)
The function whose graph is given below is:
A) [tex]y=3\sin (x-2)+1[/tex]
Step-by-step explanation:From the graph that is provided to us we observe that,
when x=2
then f(x)=1
Hence, we will check which function satisfies this point.
B)
[tex]y=3\cos(x-3)+1[/tex]
At x=2 we have:
[tex]y=3\cos (3-2)+1\\\\i.e.\\\\y=3\cos(1)+1\\\\y>1[/tex]
Hence, option: B is incorrect.
C)
[tex]y=6\sin (x-2)-2[/tex]
when x=2 we have:
[tex]y=6\sin (2-2)-2\\\\i.e.\\\\y=6\sin 0-2\\\\i.e.\\\\y=-2\neq 1[/tex]
Hence, option: C is incorrect.
D)
[tex]y=3\sin (x-2)+2[/tex]
when x=2 we have:
[tex]y=3\sin (2-2)+2\\\\i.e.\\\\y=3\sin 0+2\\\\i.e.\\\\y=2\neq 1[/tex]
Hence, option: D is incorrect.
So, we are left with option: A
A)
[tex]y=3\sin (x-2)+1[/tex]
when x=2
we get: y=1
Similarly all the other points are satisfied.
Also, the graph of this function matches the given graph.
A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h,of the prism. Which expression gives the volume of the pyramid
Answers
Answer:
[tex]\large\boxed{V_{pyramid}=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism}}[/tex]
Step-by-step explanation:
[tex]B-\text{base area}\\h-\text{height of the prism}\\\dfrac{1}{2}h-\text{height of the pyramid}\\\\\text{The formula of a volume of a prism:}\\\\V_{prism}=Bh\\\\\text{The formula of a volume of a pyramid:}\\\\V_{pyramid}=\dfrac{1}{3}Bh\to V_{pyramid}=\dfrac{1}{3}B\left(\dfrac{1}{2}h\right)=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism{[/tex]
Answer:
V = 1/6 BH
Step-by-step explanation:
the volume of a pyramid is 1/3 BH , since the pyramid is only half the height of the prism you'll have to multiply 1/3 x 2 = 1/6
TIMED! Which expression is equivalent to is m∠4?
Answers
Answer:
The correct answer is first option m<2 + m<3
Step-by-step explanation:
From the figure we can see a triangle with angles, <1, <2 and <3
By angle sum property we can write,
m<1 + m< 2 + m<3 = 180°
m<1 = 180 - (m<2 + m<3) ----(1)
Also we know that, <1 and <4 are linear pairs
m<1 + m<4 = 180°
m<1 = 180 - m<4 ---(2)
Compare (1) and (2) we get
m<4 = m<2 + m<3
Answer:
You answer would be A.
Step-by-step explanation:
m<2+m<3