The function that is represented by the graph is defined as follows:
A. f(x) = (x - 1)(x + 2)(x + 4).
How to obtain the function represented by the graph?The function represented by the graph is obtained using the Factor Theorem, as we can identify the roots of the function from the graph.
The Factor Theorem states that the function can be declared according to it's linear factors, as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which:
a is the leading coefficient of the polynomial.[tex]x_1, x_2, \cdots, x_n[/tex] are the roots of the polynomial.From the graph given in this problem, the roots of the polynomial are listed as follows:
-4, -2 and 1.
Hence the function can be defined as follows:
f(x) = (x - 1)(x + 2)(x + 4).
Considering a leading coefficient of 1, option A is correct.
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HELP ASAP!!
A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number
Ow=13
Ow=23
Ow=59
Ow=90
Answer:
(a) w = 13
Step-by-step explanation:
You have a regular quadrilateral with interior angle measure (6w+13)°, and you want the value of w to the nearest integer.
Regular quadrilateralA regular quadrilateral is a square. Its interior angles are 90°, so we have ...
6w +13 = 90
6w = 77
w = 12.833...
w ≈ 13
The value of w to the nearest whole number is 13.
Use Pythagoras' theorem to work out the length of
the side AD in the rectangle below.
Give your answer in centimetres to 2 d.p.
B
A
6.3 cm
с
4 cm
D
The value of AD in one decimal place for the given triangle is 9.8 cm.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given by triangle ΔADE
By Pythagoras' theorem,
(AD)² = (AE)² + (ED)²
(AD)² = 4² + 9²
(AD)² = 97
AD = 9.8
Hence "The value of AD in one decimal place for the given triangle is 9.8 cm".
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The missing image is attached below,
determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. check all that apply
Answer: the first one(triangle ABC) is scalene, the second one(triangle TRI) is Isosceles, and the last one(triangle PQR) is
Isosceles
Step-by-step explanation: graph each joint is Desmos online calculator
A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
a. What is the total cost (sandwiches and delivery charge) if an office orders 6 sandwiches?
Type the answer in the box below.
$
b. What is the total cost for x sandwiches?
Type the answer in the box below.
Whitch one is correct a b c or d
Answer:
Step-by-step explanation:
u got it right the first time it is D
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average peed of 52 km/h. A) Find the time at which the lorry the time taken arrive at it detination. B) on the return journey, the lorry leave at 14 55 and arrive at the factory at 18 15. Calculatge the time taken and the average peed of the lorry on the return journey
The time at which the lorry the time taken arrive at it destination is 12.20.
Given :
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.
here,
Distance = 195 km
Speed = 52 km/h
we know that ,
speed = distance / time
on cross muliplicating
speed * time = distance
time = distance / speed
substitute the values
time = 195 / 52
= 3.75 hours
destination time = 8.45 + 3.75
= 12.20
Therefore the time at which the lorry the time taken arrive at it destination is 12.20
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Alan travel 8 2/3 kilometer to get to chool. He ran 1 10/11 kilometer and walked the ret. How many kilometer were left to walk?
If Alan had ran 1 10/11 kilometer and walked the ret so his remaining distance from school is 6 5/11 kilometer.
What is called distance?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
What is the formula for distance?Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two locations.
As the total travel of alan from his school is
=8 2/3 kilometer
according to given condition;
he has traveled;
=1 10/11 kilometer
so his remaining travel from his school is;
=8 2/3 kilometer-1 10/11 kilometer
= 6 5/11 kilometer
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The figure is made up of 10 identical squares. The perimeter is y cm. What is the side
of each square in terms of y?
(answer in cm)
The side of each square in terms of y is y/16.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here, we have
The figure is made up of 10 identical squares. The perimeter is y cm.
The number of outer sides is 16
Let the side be x
then
16x = y
x = y/16
Hence, the side of each square in terms of y is y/16.
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Triangle JKL is similar to triangle STU. What is the length of side LK?
Using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
What are mathematical operations?
A mathematical "operation" is indeed the method by which a value utilizes operands and a math operator.
The supplied operands or numbers must conform to a set of predefined rules that are connected to the symbol of the math operator.
Parentheses, Exponents, Arithmetic, Division, and Addition Simple arithmetic is also known as PEMDAS (from left to right).
So, we know that the given triangles are similar:
Then, the length of line LK will be:
JK/ST = LK/UT
Solve this as follows:
JK/ST = LK/UT
2.5/10 = LK/5
10LK = 2.5(5)
10LK = 12.5
LK = 12.5/10
LK = 1.25
Therefore, using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
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In a math class with 19 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 14 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class completed the homework?
The chance that a student is selected at random from the class who passed the exam and finished the assignment is 0.2105
Describe probability.Probability refers to potential. The occurrence of a random event is the subject. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.
A exam and an assignment were due on the same day in a math class with 19 pupils.
There were 14 students that finished the assignment, and 11 of them completed the test.
3 pupils both failed the exam and didn't finish the assignment.
Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be
The number of the student who has done at least one assignment or passed the test is 19 - 3 = 16
n(A) = passes student
n(B) = given assignment
Then we have
n(A ∩B) = n(A) + n(B) - n (A ∪B )
n(A ∩B) = 11 + 14 - 16
n(A ∩B) = 9
Then the probability will be
P = 9C2 /19C2
P = 36/171
P = 0.2105
The probability that a student chosen randomly from the class completed the homework is 0.2105
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A truth erum ha the property that 90% of the guilty upect are properly judged while, of coure, 10% of the guilty upect are improperly found inno cent. On the other hand, innocent upect are mi judged 1% of the time. If the upect wa elected from a group of upect of which only 5% have ever committed a crime, and the erum indicate that he i guilty, what i the probability that he i innocent
Therefore in this question the probability that he is innocent is 0.1743
What is probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Here,
In this case, let G represent the state of guilt and H represent the state of innocence.
and Let K stand for the situation where the truth serum shows that someone is guilty.
We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.
Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.
When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.
We must therefore determine the probability P(H|K).
A group of people was chosen for the suspect, of which 5% were criminals.
so the probability that selected person is guilty is
P(G) = 0.05
Therefore, the probability that selected person is not guilty is
P(H) = 1 – P(G) = 1 – 0.05 = 0.95
Then,
Using Bayes' Theorem, we get
P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]
= [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex] =0.1743
Therefore in this question the probability that he is innocent is 0.1743
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Line c has an equation of y= 1 /5 x–3. Line d, which is parallel to line c, includes the point (– 1,1). What is the equation of line d?
Answer:
[tex]y=\frac{1}{5}x+\frac{6}{5}[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of line [tex]d[/tex] is [tex]1/5[/tex].
So, the equation of line [tex]d[/tex] is:
[tex]y-1=\frac{1}{5}(x+1) \\ \\ y-1=\frac{1}{5}x+\frac{1}{5} \\ \\ y=\frac{1}{5}x+\frac{6}{5}[/tex]
1 1/2 times 3/5 and write it as a division sentence too.
Answer:
9/10 =0.9
Step-by-step explanation:
We have been given to calculate 1 1/2 times 3/5 . First of all ,we shall convert 1 1/2 ( a mixed fraction form) to a proper fraction form .
1 1/2 is actually 1 + 1/2 =3/2
1 1/2 X 3/5 =3/2 X 3/5 =9/10
9/10 is actually 0.9
Therefore we have finally converted this into division sentence too
Which one is nonlinear
y = x + x + 3
y=x2+6
y = 4x - 5
y=1/x+3
Step-by-step explanation:
I think it's y=x² +6 because this is a quadratic equation
*NOT A QUIZ QUESTION JUST REGULAR HOMEWORK*
Two figures are similar when they have some common properties. The value of PQ as required is 28 units.
Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.
In the given triangle PQR,
ΔPQS ll ΔSTR
Given that PS = RS, and QT = RT.
Then we can say that;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]
But, PR = 2RS;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]
[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]
2ST = PQ
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
18x - 9x = -8 + 44
9x = 36
x = 4
So that,
PQ = 9x - 8
= 9(4) - 8
PQ = 36 - 8
= 28
Thus, the length of PQ is 28 units.
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Convince me that -3to the second power is not equal to (-3) to the second power
Answer:
Yeah, they are not equal.
Step-by-step explanation:
Given statement,
→ -3 to the second power is not equal to (-3) to the second power.
Forming the equation,
→ -3² ≠ (-3)²
Let's check the equation,
→ -3² = (-3)²
→ -(3)² = (-3)²
→ -9 ≠ 9
→ LHS ≠ RHS
Hence, they are not equal.
Leslie creates designer bracelets with gemstones. Her most recent order included a total of 7 bracelets. It takes 14 stones to make one bracelet. Write and solve an equation that represents how many stones were used for the order.
7s = 14; s = 2 stones
s/14 = 7 ; s = 98 stones
s + 7 = 14; s = 7 stones
s − 7 = 14; s = 21 stones
An expression that represents the number of bracelet Leslie designs is
s/14 = 7 ; s = 98 stonesHow to find the number of stones used for the orderInformation from the question include
Her most recent order included a total of 7 bracelets
It takes 14 stones to make one bracelet
let s represent stone
It takes 14 stones to make one bracelet means that one bracelet = 14 s
hence if 1 bracelet is 14 stones then 7 bracelet will be
1 bracelet = 14 s
7 bracelet = ?
cross multiplying
1 * ? = 7 * 14
? = 98 stones
the equation is written as
s/14 = 7 ; s = 98 stones
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Hello, can someone help me out with this question please!?!?!
Answer: C
Step-by-step explanation:
Distributive property 2. combine like terms 3. subtraction proerty of equality 4 division of equality.
Find the circumcenter of the triangle (-2,4) (-2,-1) (1,-1)
Answer:
( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
~~~~~~~~~~~~~~~~~~~~
The figure is right triangle.
The circumcenter is the middle of the hypotenuse.
( - 2, 4 )
( 1 , - 1 )
( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
A clothing company has 4,630 shirts to ship. It can fit 130 shirts in a shipping box .How many boxes are to ship all the shirts?
Answer: 36 boxes
Step-by-step explanation:
4630 divided by 130 = 35.6 boxes
Then we ground up to 36 boxes
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If Y varies directly with X and X=5 and Y=15 what would be the value of Y if X=12
Answer:
i think 3
Step-by-step explanation:
points a and b lie on a circle with radius 4 and arc ab has length meters. the length of arc 4pi/5 is what fraction of the circumference of the circle?
1/10 fraction of the circumference of the circle .
What is arc?
An arc is any straight line that connects two locations. The term "arc length" refers to an arc's length. An ordered pair of adjacent vertices is referred to as a graph arc in a graph.
Any section of the circle's circumference (other than the entire curve) is referred to as an arc.
C = 2πr
C - circumference of a circle
r - radius of a circle
r = 4
Then
C = 2π • 4 = 8π
Writing the fraction:
(4π/5)/8π = 1/10
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a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge. how many ways does a customer have to choose 5 different white wines to taste
a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge 2002 many ways does a customer have to choose 5 different white wines to taste, using the concept of combination formula.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),
Plugging our numbers into the formula we get:
= 14! / (14-5)! 5!
= 2002
After simplifying, we get 2002.
So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.
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a regional director responsible for business development in the state of pennsylvania is concerned about the number of small business failures. if the mean number of small business failures per month is 14, what is the probability that exactly 5 small businesses will fail during a given month? assume that the probability of a failure is the same for any two months and that the occurrence or non occurrence of a failure in any month is independent of failures in any other month. (round your answer to four decimal places.) g
The probability that exactly 5 small businesses will fail during a given month 0.0037268.
The Poisson distribution would be used to calculate the likelihood that different counts of the same event will occur within a constrained time period. It is viewed as a discrete distribution since it evaluates counts. The distribution displays identical mean and dispersion values.
The pmf of the Poisson distribution is
[tex]p(x)=\frac{e^{\lambda} \lambda^{x}}{x!}[/tex]
The mean total number of small business failures λ=14
Let x represent the number of failed small businesses in a given month.
X~P(14)
X follows the Poisson distribution since the likelihood of failure stays constant for two months and the mean number of failures per month is 14.
The likelihood that precisely four small firms would fail in a given month must be calculated.
P(X=5)
[tex]P(X=5)= \frac{e^{14} \ 14^{5}}{5!}[/tex]
P(X=5)= 0.44721/5!
P(X=5)=0.0037268.
In a month there is 0.0037 that is 3.7% probability that a small business fail.
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What is the 9th term of the sequence 2,8,32,128
Answer: 131072
Step-by-step explanation:
Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.
Help me with ixl please
A straight line = 180°. You have: 58° , 40°, and q so:
q = 180° - (58° + 40°)
q = 82°
Answer:
82
Step-by-step explanation:
180 i s the line length so
180-40=140
140-58=82
a trucker driver can expect to make $us55,065 per year in the us. assuming that this driver works 70 hours per week and 52 weeks per year, what is the equivalent salary in canadian dollars per hour?
The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.
Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.
Here's the calculation:
Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90
Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour
Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.
So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
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line L has y- intercept at (0,4) and an x- intercept at (10,0)
Answer:
y = -2/5 x + 4
Step-by-step explanation:
slope = (0-4)/(10-0)
-4/10
-2/5
y intercept = 4
y = -2/5 x + 4
If you flip a coin 300 times, how many times would you expect it to land on
tails?
If you flip a coin 300 times, 150times would you expect it to land on
tails
How many times would you expect it to land on tails?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
There are three primary categories of algebraic expressions, including:
Numeral Expression.
Binary Expression
Expression of a polynomial.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Given
flip a coin = 300
So the coin have 2 sides , one side is head and other side is tail
300/2
=150
So the 150 times the tail will come while Flip a coin.
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To make orange fizz, Noah mixe 4 coop of powder with 6 cup of water. Andre mixe 5 coop of powder with 8 cup of water. Create a double number line or a table that how different amount of powder and water that tate the ame a noah' mixture
5 scoops of powder are combined with 8 glasses of water by Noah.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
Hence, 5 scoops of powder are combined with 8 glasses of water by Noah.
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