Answers
The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).
How determine the zeros of the polynomial?The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.
For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.
Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.
f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
Step 2: Factor the polynomial to solve for x.
[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
x([tex]x^{2}[/tex] - 3x + 4) = 0
Step 3: Factor the quadratic equation.
x(x - 1)(x - 2) = 0
Step 4: Set each factor equal to 0 and solve for x.
x = 0, x = 1, x = 2
Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.
When x = 0, y = 4
When x = 1, y = 0
When x = 2, y = 0
Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).
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Related Questions
Given that 4x³+12x+3x-5=(2x-1)(px²+px+r) find the values of p,q,r
Answers
The cubic equation 4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · (p · x² + q · x + r) use the following coefficients: (p, q, r) = (2, 7, 5).
How to find the values of missing coefficients in a cubic equation
In this problem we find the definition of cubic equation as a product of a linear equation and a quadratic equation, the latter one has four unknown real coefficients, whose values can be found by expanding the product and comparing coefficients. First, write the entire equation:
4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · (p · x² + q · x + r)
Second, expand the expression:
4 · x³ + 12 · x² + 3 · x - 5 = (2 · x - 1) · p · x² + (2 · x - 1) · q · x + (2 · x - 1) · r
4 · x³ + 12 · x² + 3 · x - 5 = 2 · p · x³ - p · x² + 2 · q · x² - q · x + 2 · r · x - r
4 · x³ + 12 · x² + 3 · x - 5 = 2 · p · x³ + (- p + 2 · q) · x² + (- q + 2 · r) · x - r
Third, find the values of p, q, r by comparison:
2 · p = 4
- p + 2 · q = 12
- q + 2 · r = 3
- r = - 5
Then:
p = 2, r = 5
q = - (3 - 2 · r)
q = - (3 - 2 · 5)
q = - (- 7)
q = 7
- 2 + 2 · 7 = 12
- 2 + 14 = 12
12 = 12
The values of real coefficients are (p, q, r) = (2, 7, 5).
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multiply (x+6)(x^2-3x-4)
Answers
The required Product of the given two expression is x³ - 9x² - 22x - 24.
What is multiplication of two expression?The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.
According to question:We have given,
(x+6)(x²-3x-4)
= x(x²) - x(3x) - 4x + 6x² - 6(3x) - 24
= x ³ - 3x² - 4x - 6x² - 18x - 24
= x³ - 9x² - 22x - 24
Thus, required product of the given two expression is x³ - 9x² - 22x - 24.
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The two expression given has a necessary Product of x3 - 9x2 - 22x - 24.
What does a two-fold phrase mean?Algebraic expression multiplication is the operation of multiplying two supplied expressions made consisting of variables and constants.Algebraic expressions combine variables and integer constants to form sentences.The information that we have provided,(x+6)(x²-3x-4)= x(x²) - x(3x) (3x) - 4x + 6x² - 6(3x) - 24= x ³ - 3x² - 4x - 6x² - 18x - 24= x³ - 9x² - 22x - 24As a result, the required product of the two expressions supplied is x3 - 9x2 - 22x - 24.To learn more about multiplication refer::
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A zero correlation
O proves that one factor could not have caused the second factor.
O is dismissed by researchers as having no value.
O results from a computational error.
O indicates that there is no relationship between 2 variables.
O is dismissed by researchers as having no value.
Answers
A zero correlation indicates that there is no relationship between 2 variables.
What is correlation?The relationship between variables is described by correlation. It can be either strong or weak, as well as positive or negative. Correlation is a statistical measure that expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a common tool for describing simple relationships without stating a cause and effect relationship. A correlational study can yield three outcomes: a positive correlation, a negative correlation, or no correlation. A positive correlation is a two-variable relationship in which both variables move in the same direction.
Here,
A correlation of zero indicates that no relationship exists between two variables.
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I need 2 and example 3 please help I am desperate
Answers
The point at which the triangle's three interior angle bisectors intersect appears to be the incenter.
What is an incenter and it angles?The incenter of a triangle seems to be the point at which the triangle's three interior angle bisectors intersect. This point is equidistant from the triangle's sides.
∠ARU angle = 40°
AU length = 20°
∠QPA = 35°
A diagram is included here.
AR is the angle bisector of angle URK.
As a result, ∠ARU = ∠ARK = 40°.
Because the incenter point is equidistant from the triangle's sides.
As a result, AT = AU = AK = 20.
Because PA is the angle bisector of angle QPU.
As a result, ∠QPA = ∠UPA.
3x + 2 = 4x - 9
4x - 3x = 9 + 2
x = 11
Changing the value of x in the angle 3x + 2
We obtain ∠QPA = 3(11) + 2 = 35°.
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What is the quotient of 154,504 divided by 28 with long division
Answers
5518 is the quotient of 154,504 divided by 28.
What is Division?A division is a process of splitting a specific amount into equal parts.
The quotient of 154, 504 divided by 28 is 5518 after applying the arithmetic operation.
Long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals that is simple enough to perform by hand.
Hence, 5518 is the quotient of 154,504 divided by 28.
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A coin has heads on one side and tails on the other side. The coin is tossed 30 times to see if it lands heads or tails. The table below summarizes the results. Heads Tails 18 12 Based on these results, enter the expected probability that the coin will land with the tails side facing up the next time it is tossed. Enter your answer as a decimal.
Answers
Answer: The expected probability that the coin will land with the tails side facing up the next time it is tossed can be calculated by taking the ratio of the number of times the tails side came up to the total number of tosses. In this case, the coin landed tails 12 times out of 30 tosses. So the probability of tails is:
12/30 = 0.4
Therefore, the expected probability that the coin will land with the tails side facing up the next time it is tossed is 0.4 or 40%.
It's important to notice that this probability is based on the assumption that the coin is fair, meaning it has an equal chance of landing heads or tails each time it is tossed.
Step-by-step explanation:
A race car on a 150-metre-long track has a uniform acceleration from 10 m/s to 20 m/s travelling the full distance of the track. Each wheel of the car has a 250-millimetre radius. Which statement must be true?
A. The time the car is accelerating is 5 seconds.
B. The linear acceleration of a point on each of the wheels is
4 (m/s)^2.
C. The angular acceleration of each of the wheels is 4 (rad/s)^2.
D. The initial angular velocity of each of the wheels is 20 rad/s.
Answers
The correct statement is C. The angular acceleration of each of the wheels is 4 (rad/s)^2.
The car has a uniform acceleration from 10 m/s to 20 m/s, so the average speed is (10 m/s + 20 m/s) / 2 = 15 m/s. The time it takes to travel the 150-metre-long track at this average speed can be found using the equation:
distance = speed x time
time = distance / speed = 150 m / 15 m/s = 10 s
The linear acceleration of a point on each wheel can be found using the equation:
a = (vf - vi) / t = (20 m/s - 10 m/s) / 10 s = 1 m/s^2
The angular acceleration of each wheel can be found using the equation:
alpha = a / r = 1 m/s^2 / 0.25 m = 4 rad/s^2
The initial angular velocity of each wheel is not given in the problem, so statement D is not necessarily true.
The four 6th grade math teachers decide they want to go to McDonald's
for lunch. They each order big mac for $3.99 and a drink. If they spent
$20.32, how much was each drink? Create an equation using distributive
property and solve.
Answers
Let x be the cost of each drink.
The total cost for all four teachers' meals can be represented using the distributive property:
4(3.99 + x) = 20.32
Expanding and solving for x:
15.96 + 4x = 20.32
Subtracting 15.96 from both sides:
15.96 -15.96 + 4x = 20.32 -15.96
4x = 4.36
Dividing both sides by 4:
x = 1.09
Hence, each drink cost $1.09
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a portion selected to represent the whole is called a a. survey. b. sample. c. census. d. population.
Answers
A sample is a section of the population that has been chosen to represent the entire population.
A sample is a subset of a larger group that has been chosen to represent the entire group. A sample is supposed to represent the entire population and not exhibit any bias or distinctions based on a particular feature. Samples are employed in experimental research when a population is too big and to make sure that every member of a population is equally monitored and chosen.
a limited portion of a statistical population whose characteristics are investigated to learn more about the overall
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18. What is the equation for the relation? HELPPPPP
Answers
The line crosses the vertical axis at 400, so the equation has to be "C = something + 400".
If you pick any point and go up 100 and over 200, you get back on the line, so the slope is 100/200 or 1/2
Option C: C = 1/2 N + 400
Answer:
C. 1/2N +400
Step-by-step explanation:
So the 400 is reqiured in the equation as
x =0 , y= 400.
To find the slope you can do rise over run:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] =
[tex]\frac{500-400}{200-0} =\frac{100}{200} =\frac{1}{2}[/tex]
Which of the following graphs is described by the function given below?
y=x²-4x-12
-20
18
A. Graph A
B. Graph B
C. Graph C
D. Graph D
jy v
-20
SUBMIT
Answers
Answer:
Step-by-step explanation:
grew graph B for graph A
knowing that a centimeter is 10 times larger than a millimeter, how much more volume is a cubic centimeter (cm3) than a cubic millimeter (mm3)?
Answers
A cubic centimeter is 1000 times larger than a cubic millimeter because 1 centimeter equals 10 millimeters, and a volume is calculated by multiplying the length.
Width and height, so 1cm x 1cm x 1cm = 1cm3 and 0.1mm x 0.1mm x 0.1mm = 0.001mm3. A measure of volume in the metric system. One thousand boxy centimeters equal one liter. Also called cc, milliliter, and mL.
A cubic centimeter ( symbol cm ³ or cc)(U.S. spelling boxy centimeter) is a generally used unit of volume extending the deduced SI-unit boxy meter. It corresponds to the volume of a cell measuring 1 cm × 1 cm × 1 cm.
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A cubic centimetre is 1000 times greater than a cubic millimetre.
A volume is derived by multiplying the length, width and height.
As we know.
1 centimetre equals 10 millimetres.
Therefore 0.1mm x 0.1mm x 0.1mm = 0.001mm^3
And 1cm x 1cm x 1cm = 1cm^3.
A volumetric measurement using the metric system.
One litre is equivalent to one thousand boxy centimetres. Also known as cc, mL, and millilitre.
A cubic centimetre, often known as a boxy centimetre in the United States, is a commonly used volume measurement unit that extends the SI unit boxy metre. It is equivalent to the volume of a cell with dimensions of 1cm x 1cm x 1cm
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a climber measures the oxygen content of the air at 2,000 feet above sea level at 18%. the climber measures it again at 4,500 feet, this time at 14%. by how much does the oxygen content of the air change for every 1,000 feet of elevation?\
Answers
1.6% change in the level of oxygen for each 1000 feet of level change.
let the oxygen level at ground be x
so the oxygen level at 2000 feet above sea level is 0.18x
ans the oxygen level at 4500 feet above sea level is 0.14x
so total change = 0.04x for 2500 feet
so per feet height change = 0.04x/2500
for every 1000 feet of elevation change the percentage change is given by = (0.04*1000)/2500
=> 0.016x
so percentage change = 0.016x/x * 100
=> 1.6 %
so for every 1000 feet 1.6% change in the oxygen level is observed at that elevation.
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For every 1000 feet of elevation variation, the oxygen level changes by 1.6%.
In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.
Let the ground's oxygen level be x.
the oxygen concentration is 0.18x at 2000 feet above sea level.
ans the oxygen concentration is 0.14x at 4500 feet above sea level.
hence the overall change for 2500 feet is 0.04x.
as a result, per foot height change, 0.04x/2500
The formula is (0.04*1000)/2500, where 1000 feet of elevation change equals 1000 feet of change in percentage.
=> 0.016x
Consequently, % change = 0.016x/x * 100.
=> 1.6 %
Therefore, at that elevation, there is a 1.6% variation in the oxygen level for every 1000 feet.
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Imagine that you are a tudent in your final year at an alternative chool. Write a pot for your chool blog about your experience at the chool. Write around 200-300 word.
Answers
This post is about the author's experience at an alternative school, which they have been attending since freshman year. They have had the opportunity to explore their interests and develop their own unique learning style with the support of teachers. The atmosphere of the school is friendly and encouraging and the author is very grateful for the experience they have had. They recommend the school to anyone looking for an alternative learning experience.
My name is _________, and I'm a senior at an alternative school. I've been attending this school since my freshman year, and it has been an amazing experience.
At this school, I've been able to explore my interests and develop my own unique learning style. The teachers are supportive and caring, and they encourage students to actively participate in their education. I've had the opportunity to take classes that I'm passionate about and have even been able to design my own coursework.
The atmosphere of the school is also a great one. Everyone is friendly and willing to help each other out. There's no judgement or pressure. We all come from different backgrounds, but that doesn't stop us from working together and having a great time.
I'm so grateful for the experience I've had at this school. It has been an incredible journey, and I am so proud of what I have accomplished. I have grown so much as a person and have had so many opportunities to explore my interests.
I would highly recommend this school to anyone looking for an alternative learning experience. It has been a great place to learn, and I will miss it when I graduate.
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A museum groundskeeper is creating a semicircular statuary garden with a diameter of 22 feet. There will be a fence around the garden. The fencing costs $8. 75 per linear foot. About how much will the fencing cost altogether? Round to the nearest hundredth. Use 3. 14 for π
Answers
As per the circumference of circle, the fencing cost altogether is $604.45
The term circumference in math is defined as the distance around a circle or any curved geometrical shape
Here we have know that a museum groundskeeper is creating a semicircular statuary garden with a diameter of 22 feet.
Here we have also know that there will be a fence around the garden and the fencing costs $8. 75 per linear foot.
Here we have the diameter then the value of radius is calculated as,
=> radius = 22/2 = 11
Then the circumference of the circle is calculated as,
=> C = 2 x π x 11
Apply the value of π as 3.14, then we get,
=> C = 2 x 3.14 x 11
=> C = 69.08
Then the cost for fencing is calculated as,
=> 69.08 x 8.75
=> $604.45
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Select the correct answer. Given: Prove: Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (O, b) at (0, 6) and blue line s intercepts (c, O) at (2, 0) and (O, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality The table and corresponding image show the proof of the relationship between the slopes of two parallel lines. What is the missing statement in step 2? A. B. C. D.
Answers
Answer: its A
Step-by-step explanation:
Answer:
step 6
Step-by-step explanation:
Solve the inequality. x0.5>4.5
Answers
[tex]0.5x > 4.5[/tex]
Divide both sides by 0.5:
[tex]\dfrac{0.5x}{0.5} > \dfrac{4.5}{0.5}[/tex]
Answer:
[tex]x > 9[/tex]
Write the pair of fractions as a pair of fractions write a common denominator 1/8 and 2/6
Answers
Solve the iniquality below. Use the drop - down menus to describe the solution and it’s graph. -7x+13>41
Answers
Step-by-step explanation:
-13 on both sides
/ by -7 on both sides
flip the ineq sign bcus u divided by a negative
x < -5.86
John needs 23 boards to build rafters for his house. He can use 16-foot or 20-foot length boards. He needs seven fewer 16-foot boards than 20-foot boards. Write and solve a system of equations to determine how many of each board John needs
Answers
The equation which is required to solve how many of each board John needs is x + x - 7 = 23.
The number of 20-foot boards is 15.
The number of 16-foot boards is 8.
As per the given data, John needs 23 boards to build rafters for his house.
He can use 16-foot or 20-foot length boards.
He needs seven fewer 16-foot boards than 20-foot boards.
Here we have to determine how many of each board John needs.
Let the number of 20-foot boards be x.
Then the number of 16-foot boards be x - 7.
Total number of boards are 23.
Equation to determine how many of each board John needs:
x + x - 7 = 23
2x - 7 = 23
2x = 23 + 7
2x = 30
x = 15
The number of 20-foot boards are 15.
The number of 16-foot boards are x - 7
= 15 - 7
= 8
The number of 16-foot boards are 8.
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the 2 digit number which becomes 5/6th of itself when its digits reversed
Answers
The 2 digit number is 45 which becomes 5/6th of itself when its digits reversed.
What is number?
A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples.
Let the two digits of the number are x and y.
So, the number is 10x + y.
When its digits reversed: the number becomes: (10y + x)
According to the question:
(10y + x) = 5/6 (10x + y)
60y + 6x = 50x + 5y
60y - 5y = 50x - 6x
55x = 44y
x/y = 44/55
x/y = 4/5
Hence, the two digits of the number are 4 and 5 and the number is 45.
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there are five boys to every six girls in an introductory geology course. if there are 374 students enrolled in the course, how many are boys?
Answers
The total number of boys enrolled in the course is 170.
Here are 374 children, are there are 5 boys to every 6 girls.
If the ratio of boys to girls is 5 to 6, then 5 out of every 11 students are boys and 6 out of every 11 students are girls.
Set up a proportion for the boys, where b = the total number of boys.
5/11 = b/374
11b = 1870
b = 1870/11
b = 170
There are 170 boys.
The total number of student is 374, so the number of girls, is 374 -b.
There are 374-170= 204 girls.
Finding a proportionality constant would be another algebraic solution to this issue. The total number indicated by the ratio is 5 + 6 or 11, which is equal to the total number of children when multiplied by the proportionality constant.
Let x = the proportionality constant
11x=374
x=34
The number of boys is 5x and the number of girls is 6x.
5x=5×34 =170 boys
6x=6×34 =204 girls.
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What is the length of line segment AB?
Answers
Answer:
7units
Step-by-step explanation:
Step by step
Using Pythagorean theorem a^2 + b^2 = c^2
Measure leg 1 = 6
Measure leg 2 = 8
Leg c is the line or the hypotenuse
6^2 + 8^2 = c^2
36 + 64 =c^2
100 = c^2
√ 100 = √ c^2
10 = c
Your line segment is 10 units
A student weighs 565 N, She climbs 3. 25m vertically up a flight of stairs. It takes her 12. 6 s what is her power output?
Answers
The work done by student is 145.9 W.To calculate the work done by the student:
Work = Force x Distance = 565 N x 3.25 m = 1841.25 J
Calculate the power output:
Power = Work/Time = 1841.25 J/12.6 s = 145.9 W
Power is the quantity of energy that is transported or transformed per unit of time in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.
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You are throwing a party and you need 7 liters of soda for every 12 guests. If you have 90 guests, how many liters of soda do you need?
Answers
Using proportion, the number of liters of soda needed would be 52.5 liters.
How to Use Proportion to Solve Word Problem?Proportion can be described as an equation that relates two equal ratio to each other.
If you need 7 liters of soda for every 12 guests, and you have 90 guests, you can use the proportion:
7 liters / 12 guests = x liters / 90 guests.
To find the number of liters of soda you need, you can cross-multiply and solve for x:
12x = 7(90)
12x = 630
x = 630/12
x = 52.5
So, you need 52.5 liters of soda for 90 guests.
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Please help me ASAP please please please
Answers
The quadrilateral is parallelogram because the opposite sides are parallel and congruent
What is a parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
Since WZ and XY are congruent and XW and YZ are congruent and Also, WZ and XY are parallel and XW and YZ are parallel, we can therefore say that the quadrilateral obeys the property of a parallelogram.
parallel lines are two straight lines that can not meet at a point.
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in the 54th super bowl kansas city chiefs quarterback patrick machines completed 26 passes for 286 yards how many yards per completed pass did he average
Answers
The average number of yards per completed pass is 11.
What is the average number of yards per completed pass?In order to determine the number of yards per completed pass, divide the total yards completed by the total number of passes.
Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
Number of yards per completed pass = total number of yards / total number of passes = 286 / 26 = 11
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Find the one with ?.
Answers
Answer:
? is 59 degrees
Step-by-step explanation:
the two angles created by the intersecting lines are vertical angles and are equal
also, we know there are a total of 180 degrees in a triangle, so
180 - (21 + 49) = 100
this will help us find '?' because we can add 21 and 100, to get 121, then deduct 121 from 180 to get the value of ? which is 59
Which of the follow is a solution set for the following graph
Answers
The solution set for the given graph is (2,1). The solution has been obtained using linear equations.
What is a linear equation?
It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.
We are given two lines on the graph
The points of the red line are (3,0) and (0,3)
So, the equation of the line comes out to be
y=−x+3 ...(1)
The points of the blue line are (3,2) and (-1,-2)
So, the equation of the line comes out to be
y=x−1 ...(2)
To find the solution set, we need to solve the equations
Substituting (1) in (2), we get,
⇒−x+3 = x−1
⇒−2x = -4
⇒x = 2
So, y = 1
Hence, the solution set for the given graph is (2,1).
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7/10c=4 1/5 Solve for C
Answers
7/10c=21/5
multiply both sides of the equation by 10/7
c=6