How do you solve and graph a piece wise function and state the domain and range?
Answers
now for 4) check the picture on the left-hand-side
if you notice the intervals, it goes from -∞ and stops at -2, then goes from 2 over to 3, then from 3 onwards, so the domain will also be (-∞ , +∞).
Now, the range...
the 1st subfunction 3-x is just a line coming down form -∞....
the 2nd subfunction is just 2x, also a line going up, now once you get to
the 3rd subfunction is just 5, meaning y = 5, or f(x) = 5, which is just a horizontal line at y = 5.
since the 3rd subfunction goes from x > 3 onwards to +∞, and is just a horizontal line, it doesn't go below 5, so one would think the range is -∞, 5.
however, from the 2nd subfunction if we use say x = -1.9999, 2x ---> 2(-1.9999) = -3.9998 , that's lower than 5, and that's the lowest the piece-wise goes, thus, the range comes from -∞ and goes as low as -3.9998, (-∞ ,-3.9998]
notice, we didn't use -2, because the 2nd subfunction 2x, doesn't include it in its range -2 < x ⩽ 3.
now, for 4) I used -1.9999 but your teacher might be expecting something like -1 or thereabouts, just an integer amount. But the idea being, the 2nd subfunction, does not include the -2.
Related Questions
All I know is it's not B.
Answers
How can you prove that a constructed line is parallel to a given line? assume that the transversal line is not perpendicular to the other lines?
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To prove that a line is parallel to another, one usually shows that two lines cut by a transversal have either congruent corresponding angles or alternate interior angles. In the lack of perpendicular transversal or angle knowledge, projecting lines onto a new coordinate system can show matching slopes to confirm parallelism.
Explanation:In mathematics, proving that a constructed line is parallel to a given line typically involves showing that the lines do not intersect and have the same slope or use a parallel postulate. The most common method is taking two lines l and m and a transversal t. If the corresponding angles or alternate interior angles created by t are congruent, then l and m are parallel.
For example: If line l and line m are cut by a transversal t and the corresponding angles (∠1 and ∠2) are congruent, then lines l and m are parallel. The same can be said if the alternate interior angles are congruent.
In some cases, if the transversal line is not perpendicular and we do not know about corresponding or alternate interior angles, we can establish a different coordinate system, project the lines onto the x-axis and y-axis, and show that they have the same slope which proves them to be parallel.
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Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used.
10 30 40 50 60 70
10 30 40 60 60 80
20 30 50 60 70 90
20 30 50 60 70 90
Number Frequency Relative Frequency
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
Answers
10 2 2/24 = 8.3%
20 2 2/24 = 8.3%
30 4 4/24 = 16.7%
40 2 2/24 = 8.3%
50 3 3/24 = 12.5%
60 5 5/24 = 20.8%
70 3 3/24 = 12.5%
80 1 1/24 = 4.2%
90 2 2/24 = 8.3%
total : 24
Help a brother out here! Thank you!!!
Answers
7 blue cards
26 total cards
probability = 7/26
Say you want to buy x shirts which cost 2$ each and add tax which is $0.75. You have 13$ to make your purchase.
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2x + 0.75 = 13
Add like terms
2x= 13-0.75
2x= 12.25
x= 12.25/2
x=6.125
You can buy 6 whole shirts with $0.25 left over
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Julie is a math tutor. She charges each student $210 for the first 7 hours of tutoring and $20 for each additional hour. When the number of hours (h) that Julie spends tutoring a student is greater than 7 (h > 7), the equation that gives the amount (A) that Julie earns in dollars is . If Julie earns $410 tutoring one student, the total number of hours she spent tutoring the student is .
Answers
if she earns 410 tutoring...
410 = 210 + 20(h - 7)
410 = 210 + 20h - 140
410 = 20h + 70
410 - 70 = 20h
340 = 20h
340/20 = h
17 = h <=== she spent 17 hrs tutoring
Answer:
box 1- A=210+20(h-7) box 2- 17
Step-by-step explanation:
I got it right on plato, watch out for positive and negative answers i almost got it wrong
Joel is laying pipe for a sprinkler system before he plants his lawn. The lawn is a rectangle, 15 feet long and 8 feet wide. He needs to lay a piece of pipe that will be run along the diagonal of the lawn. It will divide the area of the lawn into two right triangles. What will be the length of that diagonal piece of pipe?
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So, we will have to use the Pythagorean Theorem in order to find the length of the pipe that will be run along the diagonal of the lawn. So, this theorem states that,
[tex]a^2+b^2=c^2[/tex]
Let's plug in the values.
[tex]15^2+8^2=c^2[/tex]
Simplify.
[tex]289=c^2[/tex]
Let's take the square root.
[tex] \sqrt{289} = \sqrt{c^2} [/tex]
Simplify.
[tex]17 ft=c[/tex]
This tells us that the length of the diagonal piece of pipe will be 17 feet.
Thanks!
-TetraFish
Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3
Answers
We first find the value of k
When y = 7 and x = 2/3, then
[tex]y= \frac{k}{x} [/tex]
[tex]7= \frac{k}{ \frac{2}{3} } [/tex]
[tex]7( \frac{2}{3})=k [/tex]
[tex]k= \frac{14}{3} [/tex]
Now we have k = 14/3, we can work out y when x = 7/3
[tex]y= \frac{k}{x} [/tex]
[tex]y= \frac{14/3}{7/3} [/tex]
[tex]y= \frac{14}{7} [/tex]
[tex]y=2[/tex]
The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth
Answers
5(2x-8) i dont get how to do distributive prop on this
Answers
Quadrilateral ABCD is similiar to quadrilateral EFGH The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 2nd longest side on quadrilateral EFGH
?
Answers
They are similar, so the sides of one of them and the other one are in proportion.
We have to find the proportion. Notice that the 12 feet side and the 18 feet side must be the one in common. 3 longest ones ... one is missing, then, two shortest ones ... two are missing, but they must share that one:
The ratio is the 18:12 or 3:2.
Now we can complete both quadrilaterals:
ABCD: 24, 16, 12, ?
EFGH: ?, ?, 18, 9
ABCD: 24, 16, 12, 6
EFGH: 36, 24, 18, 9
24 is the answer!!
Answer:
A.) 24 feet
Step-by-step explanation:
I got it correct on founders edtell!
What is the volume of the sphere? Round the answer to the nearest cubic unit. Diameter: 22 cm
1) 507 cm^3
2) 1,394 cm^3
3) 5,575 cm^3
4) 16,725 cm^3
Answers
4/3pi11^3 and approximately simplify you will get 5,575 cm^3.
The volume of the Sphere is 5,575 cm^3.
What is the volume of the Sphere ?
The volume of the Sphere is the capacity it has. It is the space occupied by the sphere.
Formula used to find volume of the Sphere is :
V = 4/3 × π × r^3
Given : diameter = 22 cm
r = diameter/2
r = 11 cm
So ,
V = 4/3 × π × 11 ^3
⇒ 4/3 × π × 1331
⇒ 1.34 × 4179.34
V = 5575.28 cm^3
The nearest cubic unit is 5,575 cm^3.
Hence , the volume of the Sphere is 5,575 cm^3 .
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The pie store is having a 15% percent off sale on all of its pies. If the pie you want regularly costs $11 how much would you save with the discount?
Answers
We would have saved $1.65 on the pie
The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 20 + 38.7t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points) (10 points)
Answers
We are given the functions:
h(t) = -16t^2 + 60t + 95
g(t) = 20 + 38.7t
Part A. All we have to do is to plug in the value of t = 1 to 4 on the two functions
t h(t) g(t)
1 139 58.7
2 151 97.4
3 131 136.1
4 79 174.8
Looking at
the table, we can say that the time when h(t)=g(t) must be between t=2 and t= 3
seconds
At t=2 seconds h(t) is above g(t), and at t = 3 seconds h(t) is below g(t).
Therefore the two functions must be at the same height in between.
Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that h(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.
two adjacent sides of a rhombus are represented by 5x + 7 and 6x -1. find the value of x
Answers
The value of x in equation 5x + 7 = 6x -1 is 8.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
5x + 7 and 6x -1
Now,
The equation is:
5x + 7 = 6x - 1
To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5x from both sides and adding 1 to both sides. This gives us:
5x + 7 - 5x = 6x - 1 - 5x
7 + 1 = x - 1 + 1
8 = x
Therefore, by the given equations the answer will be x = 8.
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Which of the following is a parent function
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What is 2(x+6)=20 pls I need help
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2x = 32
32/2x
X= 16
Distributive Property
2×x=2x
2×6=12
2x+12=20
Subtract 12 both sides.
2x=8
Divided them by 2
X=4
Solve by factoring: 8p2 - 64p = 0
Answers
If the correlation between two variables is .496, how much of the variance has not been accounted for
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If the correlation between two variables is .496, it has 24.6 percent (24.6%) of the variance that has not been accounted for. Hence, correlation is a statistical technique that is used to measure and describe the strength and direction of the relationship between two variables and 24.6% has not been accounted for the two variables which is .496.
Final answer:
About 75.40% of the variance between two variables with a correlation coefficient of .496 is unaccounted for, as it is the complement of the coefficient of determination (24.60%) obtained by squaring the correlation coefficient.
Explanation:
To determine the amount of variance not accounted for by the correlation between two variables with a correlation coefficient of .496, we must use the coefficient of determination. The coefficient of determination is the square of the correlation coefficient (r₂), which represents the proportion of the variance for the dependent variable that's explained by an independent variable in a regression model.
First, we calculate r₂:
.4962 = .246016, or approximately 24.60%. This means that about 24.60% of the variance in the dependent variable is explained by the independent variable.
Next, we find the unexplained variance by subtracting r₂ from 1:
1 - .246016 = .753984, or approximately 75.40%. Therefore, 75.40% of the variance has not been accounted for by the correlation.
Thompson Alberts purchased a pack of 12 pencils for $4.99. What is the unit price per pencil rounded to the nearest tenth of a cent?
Answers
divide total coast by number of pieces
4.99/12 = 0.415833
rounded to 0.42
42 cents each
$0.416
This is the correct answer for primavera
$4.99/12=0.4158 Rounded to the nearest tenth of a cent is $0.416
Help!!!!! how do i slove this equation
Answers
There are values of t so that the equation cos t= 5/3
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impossible, the maximum value of either cos(t) or sin(t) is 1; look to the unit circle for proof
A 100-foot ramp is tilted at a 45° angle. How high is the top of the ramp from the ground?
Answers
now, let's rationalize the denominator.
[tex]\bf \cfrac{100}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{100\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{100\sqrt{2}}{2}\implies 50\sqrt{2}[/tex]
10 POINTS PLEAAAAAASE HELP
Answers
Suzie drew the line of best fit on the scatter plot shown. A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1. The ordered pairs 0, 3 and 1, 3 and 2, 4 and 3, 7 and 4, 6 and 5, 8 and 6, 10 and 7, 10 and 8, 12 and 9, 14 and 10, 15 are shown on the graph. A straight line joins the ordered pairs 0, 3 and 10, 15. What is the approximate equation of this line of best fit in slope-intercept form?
Answers
Answer:
y = 1.2 x + 3
Step-by-step explanation:
Hope this helps
3x-4y=-5 y=4x-2 Is (1,2) a solution of the system?
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3(1) - 4(2) = -5
3 - 8 = -5
-5 = -5
2 = 4(1) - 2
2 = 4 - 2
2 = 2
Since both of these checks are true, then (1,2) is a solution to the system.
Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 point
Answers
b(x) = 2x − 8
(a+b)(x)=(3x+10)+(2x-8)=5x+2
(a*b)(x)=(3x+10)(2x-8)=
6x^2-24x+20x-80=
6x^2-4x-80
a[b(x)]=3*b(x)+10=
=3*(2x-8)+10
=6x-24+10
=6x-14
75% of a number is 4.5 cm
Answers
Answer: 6 cm
Step-by-step explanation: 4.5 cm is 75/100
75/100=4.5/x
100*4.5=75*x
450=75x
divide both sides by 75
6=x
The number 4.5 is 75 percent of the number 6.
The given number is 4.5 cm.
Let 75% of x is 4.5 cm.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 75% of x=4.5
[tex]\frac{75}{100} \times x=4.5[/tex]
[tex]\frac{75x}{100}=4.5[/tex]
[tex]75x=4.5\times100[/tex]
[tex]75x=450[/tex]
[tex]x=\frac{450}{75}[/tex]
[tex]x=6[/tex]
Therefore, the number 4.5 is 75 percent of the number 6.
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"Your question is incomplete, probably the complete question/missing part is:"
75% of what number is 4.5 cm.
What is the rule for the sequence with the first four terms below? 0.5, 0.25, 0, –0.25
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The rule for the given sequence (0.5, 0.25, 0, -0.25) is to subtract 0.25 from the previous term. Each consecutive term decreases by 0.25 to form the sequence.
The sequence given is 0.5, 0.25, 0, -0.25. To find the rule of this sequence, look at the differences between terms. Each term is subtracted by 0.25 to get to the next term.
Step-by-Step Explanation:
Start with the first term which is 0.5.Subtracting 0.25 from the first term gives the second term, 0.25.Continuing this pattern, subtracting 0.25 from the second term gives the third term, which is 0.Finally, subtracting 0.25 from the third term gives the fourth term, which is -0.25.Therefore, the rule for this sequence is subtracting 0.25 from the previous term to obtain the next term in the sequence.
The area of a rectangle is 65 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.
Answers
2x-3 = length
[tex]x(2x-3) = 65\\ 2x^2 - 3x - 65 = 0 \\ D=b^2-4ac=(-3)^2-4*2*(-65)=529\\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{3б 23}{4} \\ x_1=-5 \ \ \O \\ x_2=6.5 \ \ [/tex]
width = 6.5 m
length = 2x-3 = 2*6.5 - 3 = 10 m
The dimensions of the rectangle are 10 meters and 6.5 meters
Let the width of the rectangle be represented by w.
The length of the rectangle will then be:
= 2w - 3
Area of the rectangle = 65m²
Note that length × width = Area
Therefore, w × (2w - 3) = 65
2w² - 3w = 65
2w² - 3w - 65 = 0
2w² - 13w + 10w - 65 = 0
2w(w - 6.5) + 10(w - 6.5) = 0
Therefore, w - 6.5 = 0
w = 0 + 6.5
w = 6.5
Width = 6.5 meters
Length = 2w - 3
Length = 2(6.5) - 3
Length = 13 - 3
Length = 10 meters.
The dimensions of the rectangle is 10 meters and 6.5 meters
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