J(1)²,
x ≤ 0
x > 0
2²,
Complete the table of values for function f, and then plot the ordered pairs on the graph.
-2
-1
0
1
2
f(x)
=
X
f(x)
Drawing Tools
Select
Point
Open Point
>
O
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10
8
6
4-
2-
-2
पं
CC
f(x)
Delete
2
4
Undo
6
3
+00
8
Answers
Answer:
1/2 - 4, 1/2 2, 2 1/4,
Step-by-step explanation:
1/2, - 4 1/2 2,2,1/4
The table when completed looks like this:
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).
What is a function?A function exists as a relation between a dependent variable (f(x)) and an expression of an independent variable (x), utilized to define the value of a dependent variable from a provided value of an independent variable.
We have been given a function,
[tex]$f(x)=\left \{ {{(1/2)^{x},x\leq 0 } \atop {2^x > 0}} \right.[/tex]
We have to estimate the value of f(x) when x = {-2, -1, 0, 1, 2}
If the values of x ≤ 0, take f(x) = (1/2)ˣ then
f(-2) = (1/2)⁻² = 2² = 4
f(-1) = (1/2)⁻¹ = 2¹ = 2
f(0) = (1/2)⁰ = 1
If the values of x > 0, take f(x) = 2ˣ then
f(1) = 2¹ = 2
f(2) = 2² = 4
The table exists as follows
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).
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Related Questions
3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4
Answers
The value of 'x' from the expression is 9/ 11
How to simplify the expressionGiven the expression;
3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4
First, we expand the bracket
3x + 42x - 56 + 18x + 3x + 6 = 4
collect like terms
3x + 42x + 18x + 3x - 56 + 6 = 4
Add up like terms
66x - 50 = 4
66x = 4 + 50
66x = 54
Make 'x' the subject of formula
x = 54/ 66
x = 9/ 11
Thus, the value of 'x' from the expression is 9/ 11
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A company makes Japanese-style lunch boxes called bento boxes. Each bento box is a cube with-foot-long edges. The company ships the bento boxes in a container in the shape of a rectangular prism that measures feet by feet by feet. A manager correctly finds the volume of the container using a formula. An employee double-checks the calculation by packing the container full of bento boxes. Use the drop-down menus to explain how both volume calculations compare. Click the arrows to choose an answer from each menu. The manager can find the volume of the container using the formula Choose... The employee correctly determines that the container can be filled with Choose... bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the Choose... of one bento box. The volume found by using the formula is of bento boxes in the container. Y Choose... ▼ the volume of the total number
Answers
The volume of a container shows the amount of space that it has inside of it.
The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.
How to calculate volume?Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:
V = L × W × H
Where:
L= Length
W= Width
H= Height
It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.
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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total numberof bento boxes in the container.
Select the correct answer. In the given diagram, . Prove: The transversal line intersects two parallel lines m and n with values of corresponding angles are congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6) Statements Reasons 1. given 2. alternate exterior angle theorem 3. ? vertical angles theorem 4. transitive property of congruence Which statement is missing in the proof? A. B. C. D.
Answers
Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.
Based on these reasons, we can prove the following statements:
m || n (given)m∠1 ≅ m∠7 (alternate exterior angle theorem).m∠7 ≅ m∠5 (vertical angles theorem).m∠1 ≅ m∠7 (transitive property of congruence).In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.
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Answer:
here you go
Step-by-step explanation:
a train started from Howrah to Allahabad and another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9 hours
Answers
The speed ratio of the two trains is 4:3, that is, for every 4 hours that one train is delayed, the other is delayed 3.
How to find the speed ratio of the trains?To find the speed ratio of the trains we must do the following operation:
V1 = [tex]\frac{x}{t} = \frac{l - x }{9}[/tex]V1 = [tex]\frac{x}{l - x} = \frac{t}{9}[/tex]T = [tex]\frac{t}{9} = \frac{16}{t}[/tex]V2 = [tex]\frac{x}{t} = \frac{x}{12}[/tex]V1 : V2 = [tex]\frac{x}{12}[/tex]:[tex]\frac{x}{16}[/tex]Note: This question is incomplete because there is some information missing. Here is the complete information in:
A train started from Howrah for Allahabad another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9hours and 16 hours respectively after they meet each other. Find the ratio of speed of the two trains.
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As a cold front approaches the weather forecast over the next 5 days calls for the following temperatures In degrees Fahrenheit 12,5,18,8,2 which graph below represents the temperature over this 5 day period
Answers
The graph showing the temperature over the 5-day period will look exactly like the attached. On the y-axis, we have the Temperature and the x-axis the number of days.
What is the value of a Graph forecast?Graphs and charts are useful visual aids because they make information accessible and easy to understand.
Therefore, it is not unexpected that print and electronic media frequently employ graphs.
When data is displayed as a graph rather than a table, it can often be easier to understand since the graph might show a pattern or comparison.
What is the interpretation of the graph?The graph shows the forecasted data against the actual data. It is to be noted that the data for the actual 5-day temperatures are made-up to help the analyst understand the differences between the forecasted and the actual data.
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The line 2x + 3y - k = 0 bisects the line segment joining the points A(4, -3) and B(-2, 5). Find the value of k.
Answers
Answer:
5
Step-by-step explanation:
The midpoint of segment AB is (1, 1).
Substituting these coordinates into the equation of the line,
[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]
|x-4| if x>4 please answer
Answers
Step-by-step explanation:
if , X>4
---> y= x-4
if , X<4
---> y= -(x-4)
y= 4- X
because , the value of |x-4| is Always positive ....
Solve the proportion: 3/2 = 4/p + 9
Answers
The answer is p = -8/15
Proportion can simply be defined as equating two ratios
The proportion of 3/2 = 4/p +9 can be calculated as follows
3/2 - 9/1 = 4/p
-15/2 = 4/p
cross multiply both sides together to find the value of p
-15×p= 4×2
-15p= 8
p= -8/15
Hence the answer is p= -8/15
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2.
David swam 800 m in 20 minutes. Find his average speed in m/min.
Answers
Answer:
40 meters a minute
Step-by-step explanation:
800m - 20 min
800/20
40m-1 min
Let A, B, C be three points on a circle
with AB = BC. Let the tangents at A and
B meet at D. Let DC meet again
at E. Prove that the line AE bisects the segment
BD. (Hint: Why do we care about a chord bisecting a tangent line?)
Answers
The proof that the line AE bisects the segment can be seen below.
How to get the proof
Let us have
Γ1 and 2 are the two intersecting circles. to be the circumcircle of the shape ADE. Then we can see that Γ1 is tangent to the line DB.
A common tangent would have to touch T1 at A and also touch T2 at B
Such that what we would have would be
<ADB = 180◦ − 2<ABD = <ABC = <AEC
This would then tell us that the line is tangent to the segment.
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The radius of a circle is 9.5 cm find the circumference to the nearest tenth
Answers
For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.
C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm
Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²
The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.
Solve:|x-3|=7 pls answer
Answers
Answer:
x=10 and x=-4
Step-by-step explanation:
When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.
| x - 3 | = 7
x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.
Here is the second equation:
x - 3 = -7
It is the left side copied, without the bars, but the right side has the opposite sign.
Solve these both separately to find the answers.
x-3=7 and x-3=-7
x=10 and x=-4
(2) Veena made 5 frocks of the same size out of 14 metres of cloth. How many metres of cloth did she use for each frock? Ans.
Answers
Answer:
2.8 metres each
Step-by-step explanation:
14/5
2.8
rearrange the equation a = 1/2 b to make b the formula
Answers
Answer:
b = 2a
Step-by-step explanation:
a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )
2a = b
Answer: b = 2a
Step-by-step explanation:
Original equation
a = (1/2) b
Multiply 2 on both sides
a * 2 = (1/2) b * 2
[tex]\Large\boxed{b=2a}[/tex]
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A cone is 10cm high and has a base radius of 8cm.
Find the radius and height of a cylinder that is inscribed in the cone such that the volume of the cylinder is a maximum. Find the maximum volume of the cylinder and leave the answer in exact form.
Answers
The maximum volume of the cylinder in exact form is; V_max = 2560π/27
How to maximize the volume of a cylinder?Let us define the variables as:
Radius of cone = r
Radius of cylinder = x
Height of Cone = h
Height of Cylinder = y
The general equation for volume of the cylinder is;
V = πx²y
Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:
Height of triangle above cylinder/Base of Triangle above cylinder = Height of full triangle/Base of full triangle
This gives;
(h - y)/2x = h/2r
Making y the subject gives us;
h – y = hx/r
y = h – hx/r
y = h(1 – x/r)
Plug in y into our Volume equation:
V(x) = πx²h(1 – x/r)
V(x) = πh(x² - x³/r)
To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:
V'(x) = πh(2x - 3x²/r)
V'(x) = 0
Thus;
(2x - 3x²/r) = 0
x( 2r – 3x) = 0
Thus;
x = 0 or x = 2r/3
Put x = 2r/3 in our volume equation to find V_max
V_max = πh((2r/3)² – (2r/3)³/r)
V_max = πh(4r²/9 - 8r²/27)
V_max = πh(12r²/27 - 8r²/27)
V_max = 4πhr²/27
Thus, at r = 8 and h = 10, we have;
V_max = 4π(10)8²/27
V_max = 2560π/27
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PLEASE HELP ASAP!
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1 4
Sample 2 1
Sample 3 9
How do the sample statistics compare to the population mean and standard deviation?
Answers
The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
According to the statement
We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.
And we have to find the how many sheep are grazing on each acre.
So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,
we have to find the average of number of sheep in per acre.
We know that
The total area of the rancher’s herd = 40 acre
The number of sheep grazes in the land = 250 sheep
Now, we have to find the Average number
Average number of sheep grazed in per acre = 250/40
Average number of sheep grazed in per acre = 6 approx.
So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
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6 A survey was given to 12th-grade students of West High School to
determine the location for the senior class trip. The results are shown
in the table below.
To the nearest percent, what percent of the boys chose Niagara Falls?
Answers
Total of 24.03% of boys choose Niagara falls.
What is a frequency table?
A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
A frequency table, then, is a table that contains some facts and their frequency.
Given,
Total number of boys
56 + 74 + 103 = 233
Number of boys who chose Niagara falls = 56
Percentage of 56 out of 233
(56/233) × 100⇒ 24.03%
Hence the percent of the boys chose Niagara Falls will be 24.03%.
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Sue has sourced four wholesalers from where she will buy most of her stock, including arrangements with two suppliers for 30 days credit, while the others are Cash on Delivery (COD).
She has purchased her store fittings and has $15000 of stock (Stock at Valuation - or SAV), with a further $10000 on 30-day credit). The business has an operating cash reserve of $20000.
How many wholesalers require terms of cash on delivery?
Answers
The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2
How can the question be analyzed to find the required number of wholesalers?The number of wholesalers Sue has sourced = 4
Terms of two suppliers = 30 days credit
Amount of stock Sue has = $15000
Amount of stock on credit = $10000
Operating cash reserve of the business = $20000
Required:
The number of wholesalers that require terms of cash on delivery
Solution:
Given that the number of wholesalers = 4
The number number of suppliers (wholesalers) that supply on 30-day credit = 2
Therefore;
The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2
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The equation 2x = 3y − 5 when written in slope-intercept form
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
[tex]\hookrightarrow \text {Slope-intercept form}[/tex]
What is the slope-intercept form:
[tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]
Let's apply our knowledge:
[tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]
Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]
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Find the area of the trapezoid 3cm 3cm 4cm 1cm
Answers
Answer:
8√2 cm²
Refer to the attached page,I've shown the complete calculation over there
kerri said that the quotient of 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths /5 do you agree with Kerris reasoning?
Answers
Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
How to interpret Kerris reasoning?The quotient is given as:
4.2/5
Kerris reasoning is that
4.2/5 is approximately 0.8
We start by calculating the actual value of the quotient 4.2/5
Using a calculator, we have:
4.2/5 = 0.84
Approximate to the nearest tenth
4.2/5 = 0.8
This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
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A pair of ladders whose lengths are 4.2m and 5.6m are leaned onto a wall such that they reach the same height. The base of the longer ladder is 1.96 further away from the base of the wall then the base of the shorter ladder. The distance of the shorter ladder form the wall is:
Answers
Answer:
2.52 m
Step-by-step explanation:
let the height be h m.
let the shorter ladder be x m away from the base of wall.
(x+1.96)²+h²=5.6²
x²+h²=4.2²
subtract
(x+1.96)²-x²=5.6²-4.2²
(x+1.96+x)(x+1.96-x)=31.36-17.64
(2x+1.96)(1.96)=13.72
2x+1.96=13.72/1.96=7
2x=7-1.96=5.04
x=5.04/2=2.52
Calculate the perimeter and area of this shape.
Perimeter =
Answers
Perimeter → 25cm
Area → 25.5cm²
Explanation:[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]
[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]
PLEASE HELP FAST (6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
Answers
Answer:
0.524
Step-by-step explanation:
That is the answer not really sure tho
The perimeter of a football field is 1040 feet. The length of the field is 120 feet less than 3 times the width. What are the dimensions of the field?
Answers
Answer:
length: 360 ftwidth: 160 ftStep-by-step explanation:
The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.
SetupLet w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...
P = 2(L +W)
1040 = 2((3w-120) +w)
SolutionDividing by 2 and simplifying, we have ...
520 = 4w -120
130 = w -30 . . . . . . divide by 4
160 = w . . . . . . . . . add 30
3w-120 = 3(160) -120 = 360 . . . the field's length
The dimensions of the field are 160 feet long by 360 feet wide.
Will mark brainliest!
Answers
Answer:
Area under the graph = 6 sq.units
I've shown the complete calculation over the attached page
how do i write 4x+5y=20 in slope intercept form
Answers
Answer:
Y=mx+b
Step-by-step explanation:
The answer is y = -4/5x + 4.
We know the general form for slope intercept form is :
y = mx + c
The given equation is in standard form.
4x + 5y = 20
Bring 4x to the other side by subtracting 4x on both sides.
4x + 5y - 4x = 20 - 4x
5y = -4x + 20
Divide 5 on both sides to isolate the variable y.
5y x 1/5 = 1/5 x (-4x + 20)
y = -4/5x + 4
What is the radius and diameter of the following circle?
Radius = cm
diameter= cm
Answers
The value of diameter and radius of circle is 7 cm and 3.5cm.
According to the statement
we have given that the a figure of circle and we have to find the radius and the diameter of the circle.
So, We know that the
The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.
Here from the figure it is clear that the
Diameter of circle = 7cm
and the radius of circle we have to find
So,
Radius of circle = Diameter /2
Substitute the values in it then
Radius of circle = 7cm /2
Radius of circle = 3.5 cm.
So, The value of diameter and radius of circle is 7 cm and 3.5cm.
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Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)
Answers
Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:
[tex]v = \frac{12}{t}[/tex]
Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:
[tex]v + 6 = \frac{12}{3 - t}[/tex]
[tex]v = \frac{12}{3 - t} - 6[/tex]
Then:
[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]
[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]
[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]
18t - 6t² = 24t - 36
6t² + 6t - 36 = 0
t² + t - 6 = 0
(t + 3)(t - 2) = 0. -> t = 2 hours.
Hence her jogging rate in mph is given as follows:
[tex]v = \frac{12}{2} = 6[/tex]
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Write an equation for the function graphed below
Answers
f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.
Write an equation for the function:Let where P(X) and Q(X) are polynomial function.
The function has the following:
From the given graph, we can say that the vertical asymptotes x = - 2 and x = 3, this means that at values of x = -3 or x = 2, the denominator becomes zero and the function becomes undefined.This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is:
⇒ Q(X) = (x + 2)(x - 3)
From the given graph, we can say that the zero is 3, P(X) has the factor (x - 3)
Let a be the leading coefficient of P(X)
⇒ P(X) = a(x - 1)
Now for finding the value of a we can rewrite the equation as,
⇒ f(x) = P(X)/Q(X)
⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]
⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]
Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2
⇒ - 2 = -a/[(2)(- 3)]
⇒ a = - 2 × 2 × 3
⇒ a = - 12
By putting a = -12 in f(x) we get,
⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]
Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.
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