Answers
{-3 if x ∈ [-2,-5]}, {-2 if x ∈ (-2,3]} and {3 if x ∈ (3,4]} are the required answer for the function f(x).
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers.
Intervals can be classified based on the numbers the set comprises. Some sets include the endpoints specified in the notation, while some might partially or not include the endpoints. In general, there are three types of intervals given as,
open interval shown by round brackets.close interval shown by square brackets.half-open interval shown by mixture of round and square brackets.For the given graph we can conclude the interval one by one.
For the first blank {-3 if x ∈ [-2,-5]}
For the second blank {-2 if x ∈ (-2,3]}
For the third blank {3 if x ∈ (3,4]}
Therefore, {-3 if x ∈ [-2,-5]}, {-2 if x ∈ (-2,3]} and {3 if x ∈ (3,4]} are the required answer for the function f(x).
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Related Questions
6. Imran's father is x² years old while Imran is x years old. In 4x years' time, Imran's father will be twice as old as him.
(i) Form an equation in x and show that it reduces to x² - 6x=0.
(ii) Solve the equation x² - 6x = 0.
(iii) Find the age of Imran's father when Imran was born.
Answers
The solution of the quadratic equation is (ii) 0 and 6. (iii) Imran's father was 30 years old when Imran was born.
Quadratic equation in one variable is generally of the form of ax²+bx+c=0 where x is the variable and a, b and c are constants.
The degree of a quadratic polynomial is 2 and there are 2 solutions for a quadratic equations.
The graph of a quadratic equation is parabolic in shape.
Imran's father is x² years when Imran is x years. So after 4x years:
Imran's father's age=x²+4x
Imran's age=x+4x=5x
Now Imran's father is twice as old as Imran
∴2×(5x)=x²+4x
or, 10x=x²+4x
or, x²-6x=0
Hence the equation reduces to a quadratic equation of the form x²-6x=0.
ii) Solving the quadratic equation:x²-6x=0
Breaking into factors we get:
or, x(x-6)=0
either x=0 or x-6=0 or, x=6
Therefore the solution of the equation is 0,6 .
iii) When x=6 i.e, Imran is 6 years old,
age of his father = x²=6²=36 years.
So when Imran was born 6 years ago age of his father=36-6=30 years old.
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Ann is 4 years older than Julie. 4 years ago, ann was twice as old as julie. find their present ages
Answers
Answer: Julie is 8 years old, Ann is 12 years old
Step-by-step explanation:
A=Ann's age. J=Julie's age
A=J+4
A-4=(J-4)*2
A-4=2(J-4)
A=2(J-4)+4
2(J-4)+4=J+4
2J-8+4=J+4
2J-4=J+4
2J=J+8
J=8
A=J+4
A=8+4
A=12
Julie is 8 years old. Ann is 12 years old. :) hope this wasnt too late
simplify: 3/x+1 - 1/x-1 - 2x/x^2+1
Answers
The simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
How to simplify the expression?The expression is given as
3/x+1 - 1/x-1 - 2x/x^2+1
Take the LCM of the first two terms
So, we have
(3x - 3 - x - 1)/(x^2 - 1) - 2x/x^2+1
This gives
2x - 4/(x^2 - 1) - 2x/x^2+1
Take the LCM
[(2x - 4)(x^2 + 1) -2x(2x^2 - 1)]/(x^4 - 1)
Expand
[2x^3 - 4x^2 + 2x - 4 - 4x^3 + 2]/[x^4 - 1]
Evaluate the like terms
[-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
Hence, the simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
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I WILL GIVE BRAINLIEST
An NFL playing field is a rectangle. The length of the field (excluding end zones) is 40 yards more than twice the width. The perimeter of there playing field is 260 yards. What are the dimensions of the field in yards?
Answers
The length of the NFL playing field is 100 yards and the width is 30 yards.
What is perimeter?
The perimeter of an object is the distance round the shape or object.
The perimeter of a shape is obtained by summing length and width of the shape in two places.
P = 2(L + W)
where;
L is the length of the shapeW is the width of the shapeFrom the given question,
L = 2W + 40
260 = 2(L + W)
260 = 2(2W + 40 + W)
260 = 2(3W + 40)
260 = 6W + 80
260 -80 = 6W
180 = 6W
180/6 = W
30 = W
L = 2W + 40
L = 2(30) + 40
L = 100 yards
Thus, the length of the NFL playing field is 100 yards and the width is 30 yards.
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community gym charges a 60$ membership fee and a 70$ monthly fee. workout gym charges a 190$ membership fee and a 60$ monthly fee
Answers
For 13 months the membership is done using the equivalent of two given monthly fees for community and workout gym.
Why do you use the word equivalent?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value. By dividing both numbers by the same number, one can convert a division problem into an analogous problem while keeping the ratio between the two numbers constant. The equivalent is defined as something that is almost identical to or equal to another object. Two numbers that are equivalent are (2+2) and 4. These two things are equivalent since 2+2=4. equal to make equivalent.
Let x be the months
then community month= workout month
60+70x=190+60x
⇒70x-60x=190-60
⇒10x=130
⇒x=13 be the months be the working.
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Any genius willing to help :) , I'll give you a brainliest if you do.
Answers
Answer:
its in the shape of a tringle
Step-by-step explanation:
Answer:
See attached
Step-by-step explanation:
Definitely not a genius but I took a swing at it. I just plotted the points; I didn't connect anything.
name the intersection of line n and AC
A. point B
B. Point C
C. Point A
D. Point D
Answers
The correct answer is option B which from the diagram is depicted to be is point C
What is a line?
This is a term science and mathematics that represents the interval between two points. This interval shows the distance the points are from each each other. Line is the basic form of representation of graphics, as it takes to represent what the creative designer assigns it to be.
A line is one dimensional, this means that it represents only a dimension which is usually the length.
what is point of intersection?Points of intersection is a point where two lines meet. This point is of importance when describing the position of another. The angle on a straight line is 180 degrees but when another line intersects the angle between the two lines will vary depending on the point of intersection.
As regards the question. the two line intersected at point C
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Please answer this question for me. I’ll mark you as the brainliest.
Find composite numbers that have the following characteristics (options in the photo).
Answers
Answer:
I am not so sure but the answer I think is 1st option
Mr. Rell runs 14 miles every 2 hours. How far
can he run in 7 hours?
Answers
Answer:
28
Step-by-step explanation:
you have to multiply 14 ×2 =28
Answer =49miles
Which expression shows a way to factor 20+12?
2( 11 + 13 )
4( 4 + 3 )
2(10 + 5)
4( 5 + 3 )
Answers
Answer:
4(5+3)
Step-by-step explanation:
4x5 is 20
4x3 is 12
each bit in the brackets gets multiplied by 4
A KLM has coordinates K(4, -2), L(6, -1), and M(5, 5). What
would be the coordinates of the vertices of the image after a reflection
in the x-axis?
OA) K'(-4,-2), L'(-6, -1) and M'(-5, 5)
OB) K'(-4, 2), L'(-6, -1) and M'(-5,-5)
● c) K'(4, 2), L'(6, 1) and M'(5,-5)
OD) K'(-2, 4), L'(-1, 6) and M'(5, 5)
Answers
The coordinates of the vertices of the image after a reflection
in the x-axis is K(4, 2) , L(6, 1) and M(5, 5).
What are transformations?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Given:
A KLM has coordinates K(4, -2), L(6, -1), and M(5, 5).
According to given question we have
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
So,
K(4, -2) can changed to K(4, 2) .
L(6, -1) can changed to L(6, 1).
M(5, 5) can changed to M(5, 5).
Therefore, the coordinates of the vertices of the image after a reflection
in the x-axis is K(4, 2) , L(6, 1) and M(5, 5).
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Really lost on this one :(
Answers
Applying the definition of supplementary angles, x = 18; m<PNO = 70°.
What are Supplementary Angles?If two angles lie on a straight line adjacent to each other, both angles are supplementary, thus, their sum is equal to 180 degrees.
Angle MNO and angle PNO are supplementary angles, therefore:
m<MNO + m<PNO = 180 degrees.
m<MNO = 110°
m<PNO = (3x + 16)°
Substitute
110 + 3x + 16 = 180
126 + 3x = 180
126 + 3x - 126 = 180 - 126
3x = 54
x = 18
m<PNO = 3x + 16 = 3(18) + 16
m<PNO = 70°
Therefore, applying the definition of supplementary angles, x = 18; m<PNO = 70°.
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As of 2016, Chicago, Illinois, has a population of approximately 2.7 million people and covers 227 square miles of land. Miami, Florida, has a
population of approximately 440,000 people and covers 36 square miles of land.
Which city has a greater population density? Move the correct city into the first blank, and move numbers into the remaining blanks to justify
the answer.
The city with the greater population density is
because
Answers
Step-by-step explanation:
Answer: 12,633.7. Step-by-step explanation: population of Chicago, in 2003 = 2,869,121. The area of Chicago = is 227.1 square miles.
Stephanie attempted to solve the equation 5−3k=2(k−5). Her work is shown below. Step 1: 5−3k=2k−10 Step 2: 5=5k−10 Step 3: −5=5k Step 4: −1=k Based on the information provided, which statement justifies why her solution is incorrect? She did not distribute correctly in Step 1. She did not add to/subtract from both sides of the equation equally in Step 2. She did not add to/subtract from both sides of the equation equally in Step 3. She did not multiply/divide both sides of the equation equally in Step 4.
Answers
Stephanie did Step 3 wrong as instead of adding 10, she subtracted it.
We are given that Stephanie attempted to solve the equation 5 − 3 k = 2 ( k − 5 ).
5 - 3 k = 2 ( k - 5)
5 - 3 k = 2 k - 10
5 = 2 k + 3 k - 10
5 = 5 k - 10
5 + 10 = 5 k
15 = 5 k
15 / 5 = k
3 = k
We can see that she did Step 3 wrong as instead of adding 10, she subtracted it.
Therefore, she did Step 3 wrong as instead of adding 10, she subtracted it.
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20. BUSINESS Ramón usually gets one of the routine maintenance options at Annie's Garage. Today, however, he needs a different combination of work than what is listed. + a. Assume that the price of an option is the same price as purchasing each item. separately. Find the prices for an oil change, a radiator flush, and a brake pad replacement. b. If Ramón wants his brake pads replaced and his radiator flushed, how much should he plan to spend? Pls include work
Answers
a) The cost of an oil change, brake pads and radiator flush are $59.99, $40 and $10 respectively
b) He can expect to pay $50
The different combinations available are:
Oil change and radiator flush = $69.99
Brake pads and oil change = $99.99
Oil change, radiator flush and brake pads = $139.99
So, equating the above equations we get the individual prices of the items:
Oil change = $59.99
Brake pads = $40
Radiator flush = $10
Part a:
The price of an oil change is $59.99
The cost of brake pads replacement is $40
The price of a radiator flush is $10
Part b:
Brake pads replacement costs $40
Radiator flush costs $10
So, he can expect to pay $50 for the work
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Can you please help
4x^2-11x+7
Answers
Paul wants to hand out flyers for his new tutoring business. So far he has
handed out 30 flyers. He has 10 more days before his first customers arrive
and would like to hand out a total of 250 flyers. Write and solve an equation
to find how many flyers he would have to hand out each day to meet his
goal.
Answers
The equation to find the number of flyers is 10 x + 30 = 250 and the flyers he will hand over each day is 22.
Number of flyers handed out = 30
Total number of flyers = 250
The equation will be:
30 + 10 x = 250
Solving the equation, we get that:
Subtract 30 from both the sides:
10 x = 250 - 30
10 x = 220
Divide both sides by 10:
x = 220 / 10
x = 22
Therefore, the equation to find the number of flyers is 10 x + 30 = 250 and the flyers he will hand over each day is 22.
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The points (10,w) and ( – 6, – 9) fall on a line with a slope of 1. What is the value of w?
i need an answer ASAP
Answers
Greetings from Brasil...
We have 2 ways to solve:
1 - through the expression of the slope m (attached figure 1)
2 - determinat (attached figure 2)
1:
m = ΔY/ΔX
as m = 1, as stated in the statement, then
1 = (- 9 - w)/(-6 - 10)
w = 7check attachments
________________________________
see something similar in
https://brainly.com/question/28654988
I need help... The question are on the image
Answers
Step-by-step explanation:
One at a time. X F G is an interior angle X F G. That is not true. So that is false. Let's cross that out. That's an exterior angle. E F G is an interior angle E F G. That is true. So put a check by that. F E Z is exterior. So F E Z. That is true. Put a check by that why she E. Is exterior. So why G A. No, that is not true. E G F. So let's mark these E G Aph. So this angle means another color and F G Y our supplementary. That is true. So let's write that angle E G F N F G Y R supplementary. That's true. They sit on a line, right? So they need to some too 1 80. Put a check by that And let's do the last one. F E G an angle F G E. So F E G. Let's mark that. F E G and F G E. No, that is not true. So you want to pick the let's say second, third, 2nd, 3rd and fifth statements as true.
Jane buys candy that costs $6 per pound. She will buy less than 5 pounds of candy. What are the possible amounts she will spend on candy?
Answers
Answer:
Less than $30=========================
GivenCost of candy is $6 per pound,Amount of candy is less than 5 pounds.To findThe possible amounts will be spentSolutionLet the amount of money be x, then, considering she buys more than zero pounds of candy, the total she spends is:
0*6 < x < 5*60 < x < 30Jane will spend between zero and $30.
Answer:
$0 < x < $30
Step-by-step explanation:
To find:-
The possible amounts that Jane will pay for candies .Answer:-
We are here given that , Jane buys candies which are $6 per pound . She buys less than 5 pounds on candies .
Now since she purchased some candies therefore, the amount she spent will be greater than " 0 " .
Now she buys less than 5 pounds of candies . Cost of that would be $6*5 = $30 .
Hence she purchased somewhere between them that is between $0 and $30 .
If we denote the amount spent by Jane on candies by "x" , then ; we can represent this situation as ;
[tex]:\implies \sf \pink{ \$ 0 < x < \$30} \\[/tex]
Hence the required answer is " $0 < x < $30 .
I need your help!
In this diagram,
Answers
Answer:
15
Step-by-step explanation:
I can't explain lol its 15 tho
If QK Bisects ∠MQR, QN ⊥ LM and m∠MQK = 34º, find each missing measure
Answers
Angle of <RQK=34
Angle of<MQN=90
Angle of<MQK=34
Angle of<PQL=68
Angle of<RQL=112
Angle of<PQN=22
An angle may be a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are within the plane where the rays are located. The meeting of two planes also creates angles. We ask for these as dihedral angles. The angle formed by the rays lying perpendicular to the 2 crossing curves at the point of junction is another property of intersecting curves.
Angle also can refer to the length of a rotation or an angle. This metric represents the connection between a circular arc's length and radius. When a geometrical angle is involved
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Rosemary cut 3 wooden sticks to use as the sides of a triangle. Which list below could be the lengths, in inches, of the sticks Rosemary cut?
Answers
The length in inches of the triangle will be (A) 6, 8, 10.
What exactly is Pythagorean Theorem?According to the Pythagorean Theorem, the length of the legs and of a right triangle is related to the length of the hypotenuse h by the following equation:[tex]h^2=l_1^2+l_2^2[/tex]As a result, in item a:
h² = 6² + 8²h² = 100h = 10As a result, it is a right triangle.
Item b:
h² = 2² + 5²h² = 29h = √29 ≠ 100It's not a perfect triangle.
Item c:
h² = 5² + 6²h² = 61h = √61 ≠ 7It's not a perfect triangle.
Item d:
h² = 2² + 3²h² = 13h = √13 ≠ 5Therefore, the length in inches of the triangle will be (A) 6, 8, 10.
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The correct question is given below:
Rosemary is cutting 3 wooden sticks to build part of a kite frame. The part she is building must be a right triangle. Which choice below could be the lengths, in inches, of the sticks rosemary cut?
A. 6, 8, 10.
B. 2, 5, 10.
C. 5, 6, 7.
D. 2, 3, 5.
1. Provide all the details necessary to map △XYZ to △JLK in the picture below. Show your work AND type your explanation.
Answers
The transformation to map triangle XYZ to triangle JLK is a reflection over the y axis, that is (x, y) ⇒ (-x, y)
What is a transformation?Transformation is the change of the location of a point or figure on the coordinate plane. Types of transformations are reflection, translation, rotation and dilation.
Reflection, translation, rotation are rigid transformation since they maintain the shape and size of the figure, where as dilation is not a rigid transformation as it changes the size.
The transformation to map triangle XYZ to triangle JLK is a reflection over the y axis, that is (x, y) ⇒ (-x, y)
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2 1/2 divided by 2 5/8
Answers
Answer:
20/21
Step-by-step explanation:
2 1/2 divided by 2 5/8
2 1/2 is 5/2
2 5/8 is 21/8
5/2 ÷ 21/8 =
5/2 × 8/21 = 20/21
Kai has 4 bags of marbles .there are 3 red,5 green,2 yellow,and 6 black marbles in each bag. How many marbles does kai have? Show how you found the answer
Answers
Answer:
The correct answer is 64 marbles.
Step-by-step explanation:
Let's analyze the information we have:
Jill has 4 bags of marbles.
In each bag she has 16 marbles (in each one she has 3red, 5green, 2 yellow, and 6black)
If each bag has 16 marbles, and she has 4 bags, then we must multiply the contents of each bag by 4.
And we do it as follows:
16 x 4 = 64
Therefore, we can say that Jill has 64 marbles.
Answer:
There is 16 in each bag so there is 64 marbles in total.
Step-by-step explanation:
3 + 2 = 5
5 + 5 = 10
10 + 6 = 16
16 x 4 (16 + 16+ 16+ 16) = 64
Simplify: 35-(15-(19+5)÷3)
Answers
Answer:
38
Step-by-step explanation:
35 - {15 - (19 + 5)} ÷ 3
35 - {15 - (24)} ÷ 3
35 - {15 - 24} ÷ 3
35 - {-9} ÷ 3
35 + 9 ÷ 3
35 + 3
38
Answer:
28
Step-by-step explanation:
35 - (15 - (19 + 5) ÷ 3 ) ← evaluate inner parenthesis
= 35 - (15 - 24 ÷ 3) ← evaluate division before subtraction
= 35 - (15 - 8)
= 35 - 7
= 28
r² + √s
how do i solve this im stuck?
Answers
Answer:
What variable do I solve for?
Step-by-step explanation:
I converted 600 kcal into units of btu, joules, and kwh. the answers were 0.70, 2380, and 2.51x106; except i forgot which number goes with which units. what is the correct pairing of values and units?
Answers
600 kcal, when converted, is equivalent to 2380 BTU, 2.51 x 10^6 joules, and 0.70 kwh.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume, etc. to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
kcal, BTU, joules, and kwh are all units of energy. To convert kcal to these units, we can use the following conversions:
1 kcal = 3.96567 BTU
1 kcal = 4184 joules
1 kcal = 0.00116222 kwh
Converting 600 kcal to BTU, joules and kwh:
1 kcal = 3.96567 BTU
600 kcal = 600(3.96567 BTU)
600 kcal = 2379.4 BTU ≅ 2380 BTU
1 kcal = 4184 joules
600 kcal = 600(4184 joules)
600 kcal = 2.51 x 10^6 joules
1 kcal = 0.00116222 kwh
600 kcal = 600(0.00116222 kwh)
600 kcal = 0.697333 kwh ≅ 0.70 kwh
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How can Aaron find the number of days until he posts a new article and a new podcast
on the same day?
Find the GCF of 3 and 5.
Find the LCM of 3 and 5.
PLEASE HELPPPP
Answers
The required time can be found by using the least common multiple. The waiting time is 15 days.
What is the minimum time to publish a new article and a new podcast on the same day?
In accordance with this question, Aaron publishes a new article every 3 days and a new podcast every 5 days and we need to determine the minimum period until a new article and a new podcast are published on the same time.
Greatest common factor is the maximum integer that can divided two or more integers such that an integer is found and the least common multiple is the minimum integer greater than two or more numbers are part of it. The required time can be found by using the least common multiple.
The integers 3 and 5 are prime numbers and there is no greatest common factor greater than 1 and their least common multiple is the product of the two numbers, that is, 15.
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