The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
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Which sequence is modeled by the graph below?
We can observe
9/3=33/3=1Its a geometric progression having first term 9(3)=27 and common ratio as 1/3
So
The firmula is
a_n=27(1/3)^{n-1}Option C
Answer:
[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]
Step-by-step explanation:
From inspection of the graph, the given points are:
(2, 9)(3, 3)(4, 1)If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
a is the first termr is the common ratio[tex]a_n[/tex] is the nth termRewrite the given points as terms of the sequence:
(2, 9) ⇒ a₂ = 9(3, 3) ⇒ a₃ = 3(4, 1) ⇒ a₄ = 1To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]
Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:
[tex]\implies a_2=9[/tex]
[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]
[tex]\implies \dfrac{1}{3}a=9[/tex]
[tex]\implies a=27[/tex]
Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:
[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]
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An experiment consists of drawing 1 card from a standard 52 card deck. let e be the event that the card drawn is a red card. find p(e)
The probability of drawing a red card from a standard deck of cards is 1/2.
Given that there is a standard deck of cards.
We are required to find the probability of drawing a rd card from a standard deck of cards.
Probability is the calculation of chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Probability=Number of items/Total items.
Total number of cards=52
Number of red cards =26
Number of black cards=26
Probability of drawing a red card =Number of red cards/ Total cards.
=26/52
=1/2
Hence the probability of drawing a red card from a standard deck of cards is 1/2.
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What is the simplest form of this expression? (x − 4)(x^2 + 3x − 5)
Answer:[tex]x^3-x^2-17x+20[/tex]
Step-by-step explanation:
HELP ME ASAP
20 points !!!
q=mc(T₂-T₁)
Solve for T₂
Choose the expression that represents a cubic expression. 2x 11 −3x2 − 2x 11 4x3 − 3x2 − 2x 11 5x4 4x3 − 3x2 − 2x 11
(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
What is a cubic expression?A cubic polynomial has the generic form [tex]p(x): ax^{3} +bx^{2} +cx+d[/tex], a 0, where a, b, and c are coefficients and d is the constant, all of which are real integers. A cubic equation is one that involves a cubic polynomial.To determine which expression represents a cubic expression:
[tex]8x^{3} -7x^{2} -6x+5[/tex] is a cubic expression.The variable is x. [tex]8x^{3} -7x^{2} -6x+5[/tex] : The variable x has the highest power as 3. [tex]8x^{3} -7x^{2} -6x+5[/tex] is a polynomial.[tex]-7x+4[/tex] is a linear expression because the highest power of the variable x is 1.[tex]7x^{2} -5x+6[/tex] is a quadratic expression because the highest power of the variable x is 2.[tex]9x^{4} +8x^{3} -6x^{2} -2x+11[/tex] is a polynomial with the highest power of the variable being 4.Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
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The complete question is given below:
Choose the expression that represents a cubic expression.
(A) −7x + 14
(B) 7x2 − 5x + 6
(C) 8x3 − 7x2 − 6x + 5
(D) 9x4 + 8x3 − 6x2 − 2x + 11
How many of the first 1000 positive integers contain only 0s and 1s when
written in base 3?
There are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
How to determine the count of the numbers?The number base is given as:
Base 3
To determine the count of numbers, we make use of the following Python program
count = 0
for n in range(1,1001):
digits = []
while n:
digits.append(int(n % 3))
n //= 3
myStr = ''.join(map(str,digits[::-1]))
if(myStr.count('0')+myStr.count('1') == len(myStr)):
count+=1
print(count)
The above program counts the numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
The output of the program is 105
Hence, there are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
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solve the equation
14x+7y=28
Find the area of this parallelogram. D(-3,4) c(3,4) a(-6,-4) b(0,-4)
If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)
,C(3,4),D(-3,4).
We are required to find the area of parallelogram ABCD.
Let the point of intersection of height of parallelogram from point A is point E.
When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).
Area of parallelogram=Base*Height
=AB*DE
DE=[tex]\sqrt{(-4-4)^{2} +(-3+3)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36}[/tex]
=6 units
Area=6*8
=48 square units.
Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
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list all the 3-digit numbers that can be created by rearranging these number tiles. 6 7 2
Answer:
627
267
276
762
726
and the no. itself, 672
Each of ten tickets is marked with a different number from 1 to 10 and put in a box. if you draw a ticket from the box, what is the probability that you will draw a number greater than 3?
Answer:
7/10
Step-by-step explanation:
take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3
(06.02) which of these is the algebraic expression for "seven more than the product of three and some number?" 7 3 x 3 10 ÷ x 3x 7 3 7x
Answer:
Step-by-step Explanation:
The correct option is C.
The algebraic expression for "seven more than the product of three and some number = 3x + 7 = 0
What is Algebraic Expression?An algebraic expression is one that is composed of variables, integer constants, and algebraic operations. An algebraic expression is, for instance, 3x² 2xy + c.
According to the given Information:we can search for the product of 3 and "some number",
Let the number be x.
So, the product of x is 3 times = 3x
And now
7 more then the Product .
we add the 7 to the product .
3x + 7 = 0
So the equation will be 3x + 7 = 0
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I understand that question you are looking for is:
Which of these is the algebraic expression for "seven more than the product of three and some number?"
A. 7 + 3 + x
B. 3 + 10 ÷ x
C. 3x + 7
D. 3 + 7x
If B = { p : p is a factor of 12 } list the elements of this set and find n ( B )
Answer:
B={1,2,3,4,6and12}
n (B) =6
Step-by-step explanation:
Greetings !Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Hope it helps!
Prove the cofunction identity using the addition and subtraction formulas. sec 2 − u = csc(u) use a reciprocal identity, then apply a subtraction formula to simplify
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
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A serving of fish contains 50 g of protein and 4. 0 g of fat. How many kcal are in the serving report your answer to 2 significant figures
2 x 10² kcal are in the serving report your answer to 2 significant figures.
According to the question
A serving of fish contains 50 g of protein and 4. 0 g of fat.
i.e. content of protein = 50 g
Content of fat = 4 g
kcal are in the serving report your answer to 2 significant figures:
As the serving of fish contains 50g of protein that is 4.0kcal/g
Calories in 50 g protein = (Content of protein) × (caloric value in protein)
50g × (4.0kcal/g) = 200kcal
That means the kcal of the serving is 200kcal
In 2 significant figures: 2 x 10² kcal
Hence,
2 x 10² kcal are in the serving report your answer to 2 significant figures.
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he cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time: Exceeds 3 minutes
The probability that the service time will be more than three minutes is 0.3012.
Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,
The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.
At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,
[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]
E(x)=1/θ
θ=1/2.5
θ=0.4
The probability that the service time will be longer than three minutes:
[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]
Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.
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The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the
cone. What is the expression for the volume of the pyramid in terms of the radius of the cone?
OA V=²²
OB. V-2²
V=
OC V=2²2²
OD. V-²³
OE V-3²³
base area = B
base area B
The expression for the volume of the pyramid in terms of the radius of the cone is [tex]V=\pi r^{3}[/tex].
What is the pyramid?A pyramid is a structure that substantially resembles a pyramid in the geometric sense when its exterior surfaces are triangular and converge to a single step at the summit. A pyramid foundation might be triangular, quadrilateral, or any other type of polygon. A pyramid therefore has a minimum of three exterior triangular surfaces.The numerous forms of pyramids are categorized based on the base's shape. Let's now go over each sort of pyramid shape individually.It is thought that one of many ramp possibilities was made to drag the stones to the top as they were built higher after being transported across the desert.The expression for the volume of the pyramid in terms of the radius of the cone:
B= base area of the cone.
[tex]V=\pi r^{2}[/tex]
The volume of the Pyramid,
[tex]V=\frac{1}{3} *B*height[/tex]
[tex]$\Rightarrow V=\frac{1}{3} \times \pi r^{2} \times 3 \gamma$[/tex]
[tex]V=\pi r^{3}[/tex]
The expression for the volume of the pyramid in terms of the radius of the cone is [tex]V=\pi r^{3}[/tex]
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6. For what value of p, the binary number 110P/2 represents 25?
Step-by-step explanation:
25 as binary number is
11001
1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 1 = 25
25×2 = 50 = 11001 × 2 = 110010
multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.
and so, we see
110P = 110010
P = 010
FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.
so, the problem should have looked like
110P/10 = 11001
110P = 11001×10 = 110010
P = 010
Answer:
01
Step-by-step explanation:
From decimal to binary;
25/2==> 1 (remainder)
12/2===>0
6/2==>0
3/2===>1
1
=11001
Checking the answer;
11001
=1*2^4+1*2^3+0*2*2+0*1+1*2^0
=1*16+1*8+0+0+1*1
=16+8+0+0+2
=25
Instructions: Find the missing side. Round your answer to the
nearest tenth.
x=
30
38⁰
X
The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.
Find the value of the missing side:Trigonometric identities,
If in a right triangle ΔABC where A is the right angle
sin A = [tex]\frac{opposite\ side}{hypotenuse}[/tex]cos A =[tex]\frac{adjacent\ side}{hypotenuse}[/tex]tan A = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
In the question,
x is the adjacent side of the angle 38° and 30 units is the opposite side.
The ratio with opposite side and adjacent side is tan A
Therefore,
⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
⇒ tan 38° = 30/x
⇒ x = 30/tan 38°
∵ tan 38° = 0.781285627
⇒ x = 30/0.781285627
⇒ x = 38.398249
⇒ x = 38.40
Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.
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How do i solve for the maximum and minimum of z?
Answer:
Step-by-step explanation:
[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]
[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]
i need help please? thank you :)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 14z + 48 }{ {z}^{2} + 6x - 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 8z - 6z+ 48 }{ {z}^{2} + 9z- 3z- 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z(}^{} z- 8) - 6(z - 8) }{ {z}^{} (z+ 9)- 3(z + 9)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(}^{} z- 8) (z - 6) }{ {}^{} (z+ 9)(z - 3)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ (z - 6) }{ {}^{} (z+ 9)}[/tex]
Break into two parts and simplify
[tex]\\ \rm\dashrightarrow \dfrac{z^2-14z+48}{z^2+6z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z^2-8z-6z+48}{z^2+9z-3z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)}{(z+9)(z-3)}[/tex]
Now divide by the denominator
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)(z-3)}{(z+9)(z-3)(z-8)}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z-6}{z+9}[/tex]
i dont know how to do this could someone help
Answer:
17, 5
Step-by-step explanation:
Let the width be x
width = x
length = x + 12
length x width = x(x + 12)
length x width = x² + 12x
x² + 12x = 85
x² + 12x - 85 = 0
Now it is just a quadratic:
The 2 numbers we need are 17 and -5
(x + 17)(x - 5) = 0
x = -17 or x = 5.
Since width and length cannot be negative, x must equal 5.
Width = 5
length = 17
The answer is 17, 5.
We are given two things :
Length exceeds width by 12 inchesArea = 85 square inchesWe can represent the length and width as x + 12 and x respectively.
Now, the formula for the area of a rectangle is :
Area = Length x width
Now, let's substitute the values for length and width in the formula along with the area.
(x + 12)(x) = 85x² + 12x = 85x² + 12x - 85 = 0We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.
x² + 17x - 5x - 85 = 0x (x + 17) - 5 (x + 17) = 0(x + 17)(x - 5) = 0x = 17, 5the senior class was going on a field trip to disneyland. A total of 350 student went on the trip. they filled seven busses . how many student were on each bus
Answer:
50 ^^
Step-by-step explanation:
So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7
7x2=14
7x3=21
7x4=28
7x5=35
So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50
need more explaining tell me ^^
What is the volume of the box pictured below?
fractions 3 and 1 over 10 cubic feet
fraction 3 and 2 over 5 cubic feet
fraction 6 and 5 over 8 cubic feet
fraction 8 and 3 over 4 cubic feet
Pls help quickly!!!!! hector built a tent shaped like a rectangular pyramid. the volume of the tent is 56 cubic ft. the area of the base of the tent is 24 square ft. what is the hieght of hectors tent in feet?
The rectangular pyramid rises 7 feet in height.
What is a rectangle-shaped pyramid?Pyramids are three-dimensional objects with triangle-shaped faces and an all-encompassing polygonal base. It is referred to as a rectangular pyramid if the base of the structure is rectangular. Although all pyramids have a rectangular foundation, they all have triangular edges.
How is the height of the rectangular pyramid determined?
First, we understand that a rectangular pyramid's volume is determined by:
[tex]V=B * H / 3[/tex]
The height H is determined by the base B.
When we know the volume is 56 [tex]ft^{3}[/tex] and the base is 24 [tex]ft^{2}[/tex], we can then swap out those two numbers in the volume calculation to get:
[tex]56 f t^{3}=24 f t^{2} * H / 3[/tex]
When we solve it for H, we get:
[tex]H=3 *\left(56 f t^{\circ} / 24 f t^{2}\right)=7 f t[/tex]
The rectangular pyramid rises 7 feet in height.
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(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent the number of hours the student worked. Which of the following equations could be used to determine how many hours the student worked at his summer job? (answer choices and question is below)
Answer:
[tex]12.50 \space\ h = 2500.75[/tex]
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
∴ Therefore, we can set up the following equation:
[tex]\boxed {12.50 \times h = 2500.75}[/tex]
From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:
h = [tex]\frac{2500.75}{12.50}[/tex]
= 200.6 hours
Answer: 12.50h = 2500.75
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
How long can it take for the body to process the alcohol in one standard drink (0. 6 ounces)? 2 hours 1. 5 hours 1 hour 30 minutes
Answer:
1 hour
Step-by-step explanation:
My street hockey team plays three games each week. My team lost all 12 games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to 2 wins and 13 losses. Each week after that, my team won two games and lost one game. My team first wins at least 50% of all its games by the end of the first n weeks. What is n?
Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:
After n weeks, the team will have won 2 + 2n games.After n weeks, the team will have played 15 + 3n games.The proportion of wins is given as follows:
[tex]\frac{2 + 2n}{15 + 3n}[/tex]
The proportion is of at least 50%, hence:
[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]
We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:
[tex]2 + 2n \geq 7.5 + 1.5n[/tex]
[tex]0.5n \geq 5.5[/tex]
[tex]n \geq \frac{5.5}{0.5}[/tex]
[tex]n \geq 11[/tex]
The value of n is of [tex]n \geq 11[/tex].
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The population of a town in 2007 is 113, 505
and is increasing at a rate of 1.2% per year.
What will the population be in 2012?
What number will you fill in for a to solve the
equation?
(Hint: For this one, how many years
after 2007 is 2012?
from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]
When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A. A linear inequalities graph of dotted boundary line intersects X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) B. A linear graph of solid line intercepts X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) C. A linear inequalities graph of dotted boundary line intercepts at the X-axis (0.5, 0) and Y-axis (0, 2) D. A linear graph of a solid boundary line intersects X-axis at the unit (0.5, 0) and Y-axis at the unit (0, 2)
The correct graph is in the attached image.
Answer:
B. A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)
Step-by-step explanation:
The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.
Form of the lineWhen the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.
When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.
The given inequality
y ≤ 2x -4
includes the "or equal to" case, so the boundary line is solid.
Y-interceptThe equation of the boundary line is written in slope-intercept form:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.
This tells you that the boundary line intercepts the y-axis at the point (0, -4).