Answers
Answer:
[-6, -2](-2, 1](1, 5]Step-by-step explanation:
The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.
ObservationThe first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.
The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.
Bottom pieceThe first part of the function definition is ...
f(x) = -4
This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...
-6 ≤ x ≤ -2
In interval notation, a square bracket is used when the end point is included in the interval.
f(x) = -4 if x ∈ [-6, -2]
Middle pieceThe second part of the function definition is ...
f(x) = -3
This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...
-2 < x ≤ 1
We use a round bracket (parenthesis) when an end point is not included in the interval.
f(x) = -3 if x ∈ (-2, 1]
Top pieceThe third part of the function definition is ...
f(x) = 4
This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...
1 < x ≤ 5
In interval notation, this is ...
f(x) = 4 if x ∈ (1, 5]
Related Questions
A sequence starts with: 234375, 46875, 9375, 1875...
Find the next 4 terms.
Answers
The next 4 terms are 375, 75, 15 and 3
How to determine the next 4 terms?The sequence is given as:
234375, 46875, 9375, 1875...
Notice that the current term of the sequence is 1/5 of the previous term.
So, the next four terms are:
Next 1 = 1/5 * 1875 = 375
Next 2 = 1/5 * 375 = 75
Next 3 = 1/5 * 75 = 15
Next 4 = 1/5 * 15 = 3
Hence, the next 4 terms are 375, 75, 15 and 3
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2x-5
-------- = 2
8
(2x-5/8 = 2)
Answers
Step-by-step explanation:
2×-5=-8 and 2×-5/8=-1.25
Answer:
x = 10.5
Step-by-step explanation:
I'll assume this is the equation: (2x-5)/8 = 2
(2x-5)/8 = 2
(2x-5) = 16 [Multiply both sides by 8]
2x = 21 [Add 5 to both sides]
x = (21/2) [Divide both sides by 2]
or x = 10.5
find the value of x if 7,x and 11 are in A.p.
Answers
Answer:
x = 9
Step-by-step explanation:
since the terms are in AP then there is a common difference between consecutive terms, that is
a₂ - a₁ = a₃ - a₂ ( substitute values )
x - 7 = 11 - x ( add x to both sides )
2x - 7 = 11 ( add 7 to both sides )
2x = 18 ( divide both sides by 2 )
x = 9
Answer:
9
Step-by-step explanation:
The nth term of an AP has the formular
a+ ( n - 1 ) d
a = first term
n = number of terms
d = common difference
common difference d = T2 - T1 0r T3 - T2
d = x - 7 or 11 - x
Therefore,
3rd term
a + (3 - 1)d
a + 2d
Hence,
7 +2d = 11
substitute the value of d above
7 + 2 (x -7) = 11
7 + 2x - 14 = 11
2x = 11 +14 -7
2x = 18
dividing bothsides by 2
x = 18/2
x = 9
Use the drawing tools to form the correct answer on the graph.
Plot the vertex of f(x) = (x - 2)² +2.
Answers
Answer:
Step-by-step explanation:
Comment
You are only asked to draw the figure. You are not asked about anything to do with the standard form. So the drawing you need is below what is written here.
You should notice that the graph is in the shape of a cup that contain a liquid. It has a low point at (2,2) and a y intercept at 6. The y intercept occurs when x = 0.
The low point is reached when (x - 2) = 0. That makes x = 2. If x is anything but 2 something will be added on to the graph and f(x) will larger than 2.
Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
Answers
Answer:
parallel lines a and b
parallel lines l and m
Step-by-step explanation:
25 A.
Angles 3 and 7 are alternate interior angles of lines a and b cut by transversal l.
Since angles 3 and 7 are congruent, lines a and b are parallel by the theorem:
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
25 B.
Angles 5 and 12 are same side interior angles of lines l and m and transversal b.
Since the sum of the measures of the angles 5 and 12 is 180, then angles 5 and 12 are supplementary angles making lines l and m parallel by the theorem:
If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.
Select the correct answer.
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted left 3 units and up 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted right 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and down 4 units.
Answers
=============================================================
Explanation:
When going from f(x) to f(x-3), we replaced x with x-3.
Doing this shifts the xy axis 3 units to the left since each x input is three units smaller than before. If we had the f(x) curve fixed in place while the axis moves like this, then it gives the illusion of the curve moving 3 units to the right.
The +4 at the end adds 4 to each y coordinate to shift things 4 units up.
13 = t/9 + 5 whats the value of t?
Answers
A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour ? There are 5,289 feet in one mile
Answers
We will see that the bison is faster, by 9.9 miles per hour.
Which animal is faster?
We know that the deer's speed is:
D = 30 mi/h
The bison's speed is:
B = 3,520 ft/min.
We want to convert the second speed to miles per hour, then we can use:
1 hour = 60 min
1 mile = 5289 ft
So, to get the speed in miles per hour, we need to multiply by 60 and divide by 5289, we will get:
B = 3,520 ft/min = 3,520*(60/5289) mi/h = 39.9 mi/h
So we can see that the bison is faster, by 9.9 miles per hour.
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Enter the correct answer in the box. Divide f(x) = | x + 20| by g(x) = x + 1.
Answers
the quotient will be:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
with x ≠ -1
How to get the quotient of functions?
For two functions f(x) and g(x), the quotient:
(f/g)(x) is equal to f(x)/g(x).
Here we have:
[tex]f(x) = |x + 20|\\\\g(x) = x + 1[/tex]
Taking the quotient, we get:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
Where we also need to add the restriction that x must be different than -1, as we can divide by zero.
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Distributive property Multiply.
1. 8(3a+5)
2. 4(6-2d)
3. 9(2x-7y)
Answers
Answer:
1. 24a + 40
2. 24 - 8d or -8d + 24
3. 18x - 63y
Step-by-step explanation:
1.
multiply the 8 by 3a then by 5
8(3a + 5)
24a + 40
2. multiply the 4 by the 6 and -2d
4(6 - 2d)
24 - 8d or -8d + 24
3. multiply the 9 by the 2x and -7y
9(2x-7y)
18x - 63y
The time t required to empty a tank varies inversely as
the rate r of pumping. If a pump can empty a tank in
45 minutes at a rate of 300 gallons per minute, how
long will it take to empty a tank at 500 gallons per
minute?
k
Answers
If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have
[tex]V = tr[/tex]
It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains
[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]
of liquid.
If it's emptied at 500 gal/min, it would take
[tex]13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}[/tex]
I need help :(:(:(:(
Answers
The resulting matrix of the row operation is given as follows:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
How to find the resulting matrix?We apply the row operation on the original matrix, given as follows:
[tex]A = \left[\begin{array}{ccc}4&3&0\\-6&-3&12\end{array}\right][/tex]
The operation is given by:
[tex]R_1 = R_1 - 0.5R_2[/tex]
That is, applying to each element, we have that:
4 - 0.5(-6) = 7.3 - 0.5(-3) = 4.5.0 - 0.5(12) = -6.Hence the resulting matrix is:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
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The playing time X of classical CDs has the normal distribution with mean 54 and standard
deviation 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with playing
time X between 49 and 69 minutes?
Answers
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 54, \sigma = 5[/tex]
The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:
X = 69:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 54}{5}[/tex]
Z = 3
Z = 3 has a p-value of 0.9987.
X = 49:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 54}{5}[/tex]
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8403.
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What is the perimeter of ABC when AB=6
Answers
Which equation matches the graph shown?please help!
Answers
Answer:
y = - x² + 1
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (0, 1 ) , then
y = a(x - 0)² + 1 = ax² + 1
to find a substitute any other point that lies on the graph into the equation
using (1, 0 ) , then
0 = a(1)² + 1 ( subtract 1 from both sides )
- 1 = a
y = - x² + 1 ← equation of graph
Answer:
- x² + 1
Step-by-step explanation:
the vertex of the graph is (0 , 1)
Then the equation of the graph has this form :
(x - 0)² + 1 or - (x - 0)² + 1
Since the parabola is opening down
Then
the equation of the graph is :
- (x - 0)² + 1 = - x² + 1
Which graph represents the solution set of the inequality x+2 less than or equal to 6
Answers
The solution to the given inequality expression is x ≤ 4
Graphing inequalitiesInequality are expressions not separated by an equal sign. Given the inequality expression
x + 2 ≤ 6
Find the solution
Subtract 2 fro both sides
x + 2. - 2 ≤ 6 - 2
x ≤ 4
Hence the graph of the solution is given as shown in the attachment
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What is the answer to the question down below
Answers
Answer:
I'm pretty sure the answer is 4
Step-by-step explanation:
Because SQ is 4 and it looks like QT is the same length
Find the distance CD rounded
to the nearest tenth.
C = (4,7) D= (7,11)
CD= [?]
HINT: Use the distance formula:
d = √(x₂-x₁)² + (Y2 − 1)²
Enter
Answers
√(x₂-x₁)² + (Y2 − 1)²
√(7-4)² + (11− 7)²
√(3)² + (4)²
√(9)+ (16)
√(25) = 5
Thus, CD = 5
Hope this helps!
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
333. (4 − 6y)(4 + 6y)
Answers
Answer:
The product is the difference of squares is[tex]$$\left(4-6y\right)\left(4+6y\right)=16-36{{y}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4-6 y)(4+6y).We have to multiply the given expression.Square the first term 4. Square the last term 6y.[tex]$$\begin{aligned}&(4-6 y)(4+6 y)=(4)^{2}-(6 y)^{2} \\&(4-6 y)(4+6 y)=16-36 y^{2}\end{aligned}$$[/tex]
Can someone help me out on this
Answers
Answer:
Step-by-step explanation:
sharon is participating in basketball practice with her basketball team. She knows that running 40 laps around the rectangular basketball court is equal to running a kilometer (3,280 feet). In addition, the court has an area of 408 square feet. If Sharon's coach tells her to run the length of the longer edge of the basketball court, how many feet must Sharon run
Answers
Answer:
Sharon would have to run 24 ft.
Step-by-step explanation:
Begin by finding the perimeter by dividing 3,280 by 40.
Then eliminate D and E because they are larger than the total perimeter, and then plug in the remaining values into the perimeter and then see which also gives you the area.
This is how you get the answer 24 ft.
Hope this helped :D
The graph of a linear function is shown,
Which word describes the slope of the line?
O positive
O negative
O zero
undefined
Answers
Answer:
postive
Step-by-step explanation:
im asian
For the graph of a linear function the slope of the line is positive, option A is correct.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let the line is passing through points (-4, -1) and (0, 0)
m=1/4
The slope value is positive
Hence, for the graph of a linear function the slope of the line is positive, option A is correct.
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Help pleaseeeeeeeeeeeee
Answers
Answer:
B.$120
Step-by-step explanation:
find 8 on the bottom, and go up until you find the dot. then look to the left to see what number matches it on the left side.
The diagram shows the cross-section of a wall of a cinema. It is to be painted. Paint cost £6 for a tin which covers 25m^2. How much will it cost to paint?
Answers
Answer:
53.04 pounds
Step-by-step explanation:
We find the area of the shape:
10*13=130 is the rectangle
(10+6)*8/2=16*8/2=16*4=64 (area of the right trapezoid)
(10+8)*3/2=18*3/2=9*3=27 (area of the left)
130+27+64=221 is the total area
221/25*6=53.04 pounds
If −6x+y=−4 and −8x−10y=3 are true equations, what would be the value of 2x+11y?
Answers
=========================================================
Reason:
The equation −8x−10y=3 is the same as 8x+10y = -3 after multiplying both sides by -1
We have this system of equations
[tex]\begin{cases}-6x+y = -4\\8x+10y = -3\end{cases}[/tex]
Add the equations straight down.
-6x+8x becomes 2xy+10y becomes 11ythe right hand sides combine to -4+(-3) = -7Therefore, we end up with the equation 2x+11y = -7
An alternative is to solve the system using substitution to get the (x,y) intersection point. Then use those coordinates to compute 2x+11y and you should get -7 as a result.
planing t Tiger Biscuits factory produce f 10,000 units in Month Standard time per 200 units is 8 hours, the Company pays. Rs 40 per her
Answers
If the Company pays. Rs 40 per her. The total cost is Rs 16,000.
Total costFirst step is to calculate the time taken to produce
Time= (10000/200) × 8
Time= 400 hours
Second step is to calculate the total cost
Total cost= 400 × Rs 40
Total cost= Rs 16,000
Therefore the total cost is Rs 16,000.
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A quilt is designed using a square pattern. each square contains two rectangles. each rectangle contains a shaded rhombus. each rectangle contains a shaded rhombus. the left angle is 50 degrees and the top angle is (2 x 20) degrees. what is the value of x?
Answers
The value of x=55
The total angle of each diamond is 360 degrees. The opposite angles of the diamond are congruent.
Congruency: In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
The two adjacent angles are 2x + 20 degrees and 50 degrees.
Opposite angles measure 2x + 20 and 50 degrees.
The sum of the angles of each rectangle is 360
2x + 20 + 50 + 2x + 20 + 50 = 360
Add the line terms and subtract
4x + 140 = 360
Subtracting140 on both sides:
4x = 2
Divide both sides by 4
x = 55
55 is the correct answer.
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Which is equivalent to 16^3/4 x?
Answers
Answer:
The answer is A
If you give me the correct answer I will give you Brainliest
Answers
Answer:
A. [tex]( 8 \times \frac{1}{2} )\frac{1}{3}[/tex]
Explanation:
Associate property of multiplication: a × (b × c) = (a × b) × c
Option A
Shows associate property of multiplication. Does not change final answer.
Option B
The grouping does not change inside the parenthesis.
Option C
This does show associate property but multiplying first 8 × 1/3 is complex.
Option D
Product of this changes the final answer. Not correct.
3/8-2/7=2/7-3/8 is the statement true
Answers
Answer:
The statement is not true.
Step-by-step explanation:
[tex]\frac{3}{8} -\frac{2}{7} =\frac{2}{7} -\frac{3}{8}[/tex]
First, let us solve the left side.
[tex]\frac{3}{8} -\frac{2}{7} \\\\\frac{3*7}{8*7} -\frac{2*8}{7*8}\\\\\frac{21}{56} -\frac{16}{56}\\\\\frac{21-16}{56} \\\\\frac{5}{56}[/tex]
And now let us solve the right side.
[tex]\frac{2}{7}-\frac{3}{8} \\\\ \frac{2*8}{7*8}-\frac{3*7}{8*7} \\\\\frac{16}{56}-\frac{21}{56}\\\\\frac{16-21}{56}\\\\\frac{-5}{56}[/tex]
Therefore, it is clear that the left side is not equal to the right side.
∴ Left side ≠ Right side
∴ [tex]\frac{5}{56}[/tex] ≠ [tex]\frac{-5}{56}[/tex]