Answers
A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.
A network can be represented mathematically as a graph, which explains the connection between lines and points. A graph consists of some points with connecting lines.
Consider the function,
[tex]f(x)=\frac{||x||+2}{2}[/tex] and 0 ≤ x ≤ 6
To graph the function we will find the points on the graph for different values of x.
When x = 0,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(x)=\frac{||0||+2}{2}=1[/tex]
When x = 1,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(1)=\frac{||1||+2}{2}\\ f(1)=\frac{3}{2}[/tex]
When x = 2,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(2)=\frac{||2||+2}{2}[/tex]
[tex]f(2)=2[/tex]
When x = 3,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(3)=\frac{||3||+2}{2}[/tex]
[tex]f(3)=\frac{5}{2}[/tex]
When x = 4,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(4)=\frac{||4||+2}{2}\\ f(4)=3[/tex]
When x = 5,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(5)=\frac{||5||+2}{2}[/tex]
[tex]f(5)=\frac{7}{2}[/tex]
When x = 6,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(6)=\frac{||6||+2}{2} \\f(6)=4[/tex]
Therefore, the points on the graph of the function [tex]f(x)=\frac{||x||+2}{2}[/tex] are ( 0, 1 ), ( 1, ( 3/2 ) ), ( 2, 2 ), ( 2, ( 5/2 ) ), ( 4, 3 ), ( 5, ( 7/2 ) ), and ( 6, 4).
Hence, the graph of the function is:
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Related Questions
A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?
A.150 feet
B.178 feet
C. 191 feet
D.212 feet
Answers
A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).
As given in the question,
Area of the square field = 22,500square feet
Let 'a' be the side and 'd' be the diagonal length of the square
a² =22,500
⇒a =150 foot
Using Pythagoras theorem
d² =a² +a²
⇒d² = 2(150)²
⇒d² =45000
⇒d =212.13
≈ 212 nearest foot (approximately)
Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with area of 22,500 square feet as given.
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In the following triangle, what is the value of n?
Answers
Given that the triangle is a right triangle, the value of sin (n) is √5/5.
Hence, option D)√5/5 is the correct answer.
What is the value of sin(n) in the triangle?Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.
Given the data in the question;
Hypotenuse = 2√5Opposite of angle n = 2Adjacent of angle n = 4To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.
Sine of angle n = Opposite of angle n / Hypotenuse
sin(n) = Opposite / Hypotenuse
Plug in the given values and simplify
sin(n) = Opposite / Hypotenuse
sin (n) = 2 / 2√5
Next, rationalize the denominator.
Cancel out the common factor 2.
sin (n) = 2 / 2√5
sin (n) = 1 /√5
Multiply both the numerator and the denominator by √5.
sin (n) = (1×√5) / (√5 × √5)
sin (n) = √5/5
Given that the triangle is a right triangle, the value of sin (n) is √5/5.
Hence, option D)√5/5 is the correct answer.
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How would this graph look please help
Answers
The inequality graph of the system of inequalities is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine how the inequality graph would look like?The system of inequalities is given as
-2x + 3y < 9
x^2 - y <= 10
4x + y > 3
In the above system of inequalities, there are two linear inequalities and a parabola inequality
The inequality symbols in the linear inequalities are opposite
This means that the region between both lines would be shaded
Also, for the parabola; the upper part would be shaded.
This is so because when y is made the subject of the formula, the symbol becomes >=
Using the above as a guide, the inequality graph of the system of inequalities is graph (a)
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You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner. How much should you charge per ticket if you expect 50 people to attend? (Round your answer to the nearest cent.)
Answers
Answer:
$13
Step-by-step explanation:
For 50 people it will cost you 150 + 50(10) or 500
150 +500 = 650 Divide that among 50 people and you get a cost of $13 a person.
Subtract. Write your answer as a decimal.
5.5−8.1=
Answers
The solution of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex] which is a negative integer in decimal form.
The numbers of the number line are called integers. They include positive numbers, zero, and negative numbers.
Zero is neither considered a negative nor a positive number.
[tex]5.5\\[/tex] is a positive number and a smaller number when compared from [tex]8.1[/tex].
When a smaller number is subtracted from a larger number it results in subtraction with a negative sign.
[tex]5.5 - 8.1 \\= -2.6[/tex]
The subtraction of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex].
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How can u do the 5th problem
Answers
Answer:
3/4 of 5. It equals 3 3/4.
Step-by-step explanation:
The question asks for 3/4 of 5 cups of milk.
Steve and Jenna go door-to-door selling chocolate bars. Steve sells 23 chocolate
bars and Jenna sells 12 chocolate bars. Together they collect $210. How should
they divide the money so that each person gets a fair share?
Answers
Answer:
Steve: $138.00
Jenna: $72.00
Step-by-step explanation:
Steve:
[tex]\frac{23}{35}[/tex] x 210 = 138
Jenna:
[tex]\frac{12}{35}[/tex] x 210 = 72
I'm not really sure what this means, but i'll do what i think is right!
Answer:
Steve: $138
Jenna: $72
Step-by-step explanation:
If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.
To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.
hope this helps!
If 6 -x = 12, what is x - 6?
Answers
Answer: x - 6 = -12
Step-by-step explanation: first, we'll solve for x in 6 - x = 12. We'll isolate the variable by subtracting 6 from both sides, which gives us -x = 6. Now we'll divide both sides by -1 to get x and we will get -6 = x. So for the expression, we'll sub in the value we got for x from the equation, -6. -6 - 6 = -12.
Answer:
-12
Step-by-step explanation:
help with 5,6,&7 please!! will mark as brailylist
Answers
mous this mobail phonffyuuyy
What is your average speed in miles per hour and in feet per second if you travel a mile in 21 minutes?
Answers
Answers:
2.857142 mph
4.190476 ft per second
Both values are approximate
=======================================================
Work Shown:
21 min = 21/60 = 0.35 hrs which is exact
distance = rate*time
rate = distance/time
rate = (1 mile)/(0.35 hrs)
rate = (1/0.35) mph
rate = 2.857142 mph which is approximate
------------------
21 min = 21*60 = 1260 seconds
1 mile = 5280 ft
rate = distance/time
rate = (5280 ft)/(1260 seconds)
rate = (5280/1260) ft per second
rate = 4.190476 ft per second approximately
Answer: 2.857 miles/hr
4.19 ft/sec
Step-by-step explanation:
60 min=1 hr.
1 mi/21 min*60 min=
60 min*1 mi/21 min=2.857 miles/hr
60 sec=1 min
60*60 sec=1 hr
1 hr=3600 sec
2.857 miles/hr=
2.857/3600 miles/sec=0.00079 miles/sec
1 mile=5280 ft
0.00079 miles/sec=
0.00079*5280 ft/sec=4.19 ft/sec
I need help with this please
Answers
Answer: m<ABC = 45 degrees, m<DBC = 36 degrees
Step-by-step explanation:
set both equations equal to 81 because they add up to form one angle:
5x + 6 + 9x - 9 = 81
Combine like terms
14x - 3 = 81
Add three to both sides
14x = 84
Divide by 14 to find x
x = 6
To find the angles:
Measurement of angle ABC:
9(6) - 9 = 45 degrees
Take the original angle of 81 and subtract the angle you just found to find the remaining angle:
81 - 45 = 36
Therefore, the angle of DBC is 36 degrees
Michael drove from point A to point B at 15 miles
per hour and immediately returned by the same
route at 30 miles per hour. What was his average
speed, in miles per hour, for the entire trip?
E. 20
F. 22.5
G. 24
H.25
Answers
Answer:
E
Step-by-step explanation:
Say the distance is 'd'
time for going = d/15
time for returning = d/30
average speed = total distance / ( total time)
= 2d / ( d/15 + d/30 )
solve for average speed = 20 mi/hr
What is the result of
36 over 9 + 6?
Answers
Answer: 10
Step-by-step explanation:
First you can re-order = 36/9 + 6
36/9=4
Then add 4+6
It equals 10
18
You buy 8 gallons of gasoline and pay $23.20.
a.) Write an equation to represent this situation.
28
So
b.) Find the price of one gallon of gasoline.
Answers
2.9 per gallon.
Express 55 mph in kilometers per hour. Round to the nearest hundredth.
Answers
55mph -> 88.51 kilometers per hour.
Explanation:
Multiply the speed value by 1.609. 88.514 rounded up to the nearest hundredth is 88.51 kilometers per hour.
For what value of x does 3^2x = g^3x-4?
1
2
3
4
Answers
The value of x will be 2. So, Option B is correct for the equation [tex]3^{2x} = 9^{3x - 4}[/tex]
In the given question, the equation is [tex]3^{2x} = 9^{3x + 4}[/tex], we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,
=> [tex]3^{2x} = 9^{3x -4}[/tex] => [tex]3^{2x} = 3^{2(3x - 4)}[/tex]
We know according to the property of exponents if [tex]x^{m} = x^{n}[/tex], then m = n.
Similarly, in this equation the base of both RHS and LHS are the same, We get
=> 2x = 2(3x - 4)
=> 2x = 6x - 8 => 4x = 8
=> x = 2
We get value of x = 2.
Hence the value of x for this equation will be 2 and option B is correct.
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Answers
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.
What is the numerical value of K?A bisector divides an angle or segment into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 6k + 8Segment XY = 11k - 12Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
6k + 8 = 11k - 12
Collect like terms
6k - 11k = -12 - 8
-5k = -20
Divide both sides by the coefficient of k
-5k/-5 = -20/-5
k = 4
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.
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The weight of an organ, an adult males has a bell shaped distribution with a mean of 320 g and a standard deviation of 45 g use the empirical rule to determine the following
A. About 95% of organs will be between what weights?
B. What percentage of organs weighs between 185 grams in 455 grams?
C. What percentage of organs weighs less than 185 grams or more than 455 grams?
D. What percentage of organs weighs between 275 grams in 410 grams?
Answers
(Scientific Notation LC)
WILL MARK BRAINLEIST ONLY IF CORECCT!
!Rewrite 2,290,000 in scientific notation.
2.29 x 10−6
2.29 x 10−4
2.29 x 104
2.29 x 106
Answers
2,290,000 in scientific notation is 2.29 x 10⁶.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.
Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.
Now the given number is,
2,290,000
To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.
So, factorizing 2,290,000 we get,
2,290,000 = 229 x 10,000
Now converting 10,000 into multiples of 10
Since, 10,000 = 10 x 10 x 10 x 10
So, 2,290,000 can be written as,
2,290,000 = 229 x 10 x 10 x 10 x 10
Multiplying and divide 229 by 100 we get,
2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100
Rearranging we get,
2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)
Since, (229 x 100) / 100 = 2.29 x 100
2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)
And 100 = 10 x 10
Therefore we get,
2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10
Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶
Therefore we get,
⇒ 2,290,000 = 2.29 x 10⁶
this is the required scientific notation of 2,290,000 .
Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.
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Line AL is a perpendicular bisector of segment CM. Which of the following are true
Answers
Triangle ABC is an isosceles right triangle.
Because of A(-8,7) B(-4,2) C(1,6)
So AB=√[-8-(-4)]²+(7-2)²
=√41
BC=√(-4-1)²+(2-6)²
=√42
AC=√(-8-1)²+(7-6)²
=√82
AB=BC
AB²+BC²=AC²
So triangle ABC is an isosceles right triangle.
What is isosceles right triangle?
An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
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Simplify the radical √54
Answers
Answer: 3√6
Step-by-step explanation:
√54=
√(9*6)=3√6
The normal cruising speed of a certain airplane is about 250 m/sec. What is this speed in miles per hour? Round to a whole number.
Answers
Answer:
900,000 mph
Step-by-step explanation:
I am assuming the m in he problems is standing for miles.
250m/sec x 60 sec/min x 60min/hour The sec cross out and the minutes cross out and you are left with miles be hour.
A group of people were asked if they had run a red light in the last year. The number of people that
responded yes is 397 and no is 159. Find the probability that if a person is chosen at random, he/she has
run a red light in the last year. Round to two decimal places.
Question Help:
Answers
If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.So, to find the probability:
P = number of favorable terms/number of total termsFavorable terms = 397Total number of terms = 397 + 159 = 556Apply values in the formula:
P = 397/556P = 0.714028On rounding off, P = 71%.Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
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Which is a solution of 2x+6>12? x>0 x>3 x>−1 x>5
Answers
Answer:
x>3
Step-by-step explanation:
2x+6-6 > 12-6 ditch the 6
2x/2 > 6/2 divide by 2
x>3
Solve
31320= x + (.08x)
Answers
Answer:
Step-by-step explanation:
31320=x+0.08x
31320=1.08x
swap the sides
1.08x=31320
Divide by 1.08
x=29000
If one of the points that this relationship passes through is (,)=(300,10), find the
proportionality constant for this relationship. Round your answer to 3 decimal places.
Answers
Answer:
.033
Step-by-step explanation:
When there is a proportional relationship the constant of proportionality is y/x and in this case that would be 10/300 and that would be .033 rounded to three decimal places.
The graph below defines a function f (x). Find f (2).
3
N
7
s
4
m
14
-2 +
771 ?
1
2345
Answers
For the given functions f and g, find the requested function.
Answers
Answer:
its 1
Step-by-step explanation:
i just know
(x-j) (5x + k) = 0
How do i find x from this equation
Answers
Answer:
x = 5j-k
Step-by-step explanation:
(x-j) (5x+k) = 0
(x-j) * (5x+k) = 0
x - 5j + k = 0
x + k = 5j
x = 5j - k
1-7: MathXL for School: Practice & Problem Solving
Challenge You buy 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears. What is your total bill?
Grocery Store Prices
Item
Apples
Peaches
Pears
Cost
$0.99 per pound
$1.09 per pound
$1.19 per pound
Your total bill is:
(Round to the nearest cent as needed.)
Answers
The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
In the given question
The price of 1 pound apple = $0.99
The price of 1 pound Peaches = $1.09
The price of 1 pound Pears = $1.19
Total pounds of apples bought = 3.18 pounds
price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)
=3.18*0.99
=$3.15 ...(i)
Total pounds of Peaches bought = 1.45 pounds
price of 1.45 pounds of peaches = 1.45*1.09
= $1.59 ...(ii)
Total pounds of Pears bought = 1.71 pounds
price of 1.71 pounds of pears = 1.71*1.19
= $2.04 ...(iii)
Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.
Substituting the values from equation (i),(ii)and (iii) we get ,
Total bill = $3.15 + $1.59 + $2.04
= $6.78
Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
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