NO LINKS!! Please help me with this polynomial function activity 6. Also make a graph.
Answers
Answer:
x-intercepts: -4, -2, 1 and 3
y-intercept: 24
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]y=(x+4)(x+2)(x-1)(x-3)[/tex]
The x-intercepts are the points at which the curve intersects the x-axis, so when the function equals zero.
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Therefore, to find the x-intercepts, set each factor of the given polynomial equal to zero and solve for x:
Therefore:
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-3)=0 \implies x=3[/tex]
Therefore, the x-intercepts are -4, -2, 1 and 3.
The y-intercept is the point at which the curve intersects the y-axis, so when x is zero.
To find the the y-intercept, substitute x = 0 into the given polynomial:
[tex]\implies y=(0+4)(0+2)(0-1)(0-3)[/tex]
[tex]\implies y=(4)(2)(-1)(-3)[/tex]
[tex]\implies y=(8)(-1)(-3)[/tex]
[tex]\implies y=(-8)(-3)[/tex]
[tex]\implies y=24[/tex]
Therefore, the y-intercept is 24.
To find the other points on the graph, substitute each value of x into the polynomial and solve for y:
[tex]\begin{aligned}x=-5 \implies y&=(-5+4)(-5+2)(-5-1)(-5-3)\\&=(-1)(-3)(-6)(-8)\\&=(3)(-6)(-8)\\&=(-18)(-8)\\&=144\end{aligned}[/tex]
[tex]\begin{aligned}x=-3 \implies y&=(-3+4)(-3+2)(-3-1)(-3-3)\\&=(1)(-1)(-4)(-6)\\&=(-1)(-4)(-6)\\&=(4)(-6)\\&=-24\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=(2+4)(2+2)(2-1)(2-3)\\&=(6)(4)(1)(-1)\\&=(24)(1)(-1)\\&=(24)(-1)\\&=-24\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=(4+4)(4+2)(4-1)(4-3)\\&=(8)(6)(3)(1)\\&=(48)(3)(1)\\&=(144)(1)\\&=144\end{aligned}[/tex]
Therefore:
[tex]\large\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x&-5&-3&0&2&4\\\cline{1-6}y&144&-24&24&-24&144\\\cline{1-6}\end{array}[/tex]
Related Questions
about 310 000 t of atlantic cod were caught in 1991. in 2001 the mass of the cod caught was 87% less. HOw much cod was caught in 2001
Answers
Number of Atlantic cods caught in the year 2001 is; 40300 t
How to solve percentage word problems?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;
Percentage = (value / total value) * 100%
Now, we are told that;
Number of Atlantic cods caught in 1991 = 310000 t
We are told that in the year 2001, there were 87% less caught. Thus;
Number by which it was reduced = 310000 * 87% = 269700
Thus;
Number of Atlantic cods caught in the year 2001 = 310000 - 269700
Number of Atlantic cods caught in the year 2001 = 40300 t
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A student was asked to name all values of n that make the relation a function. Correct the error.
{(2,8), (6,0), (4,2), (2n,n)}
n can be any value except 2,6, or 4
Answers
The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.
The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.
The known elements of the set A in the question are; 2, 6, and 4
The elements of the set A are known as the domain of the function.
The known element of the set B are 8, 0, and 2
The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)
To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4
Therefore;
n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2
The correct statement is therefore;
n can be any value except 1, 3, or 2
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If you roll a die three times, how many different sequences are possible? a. 6 cubed = 216 b. 3 superscript 6 baseline = 216 c. 3 superscript 6 baseline = 729 d. 6 cubed = 729
Answers
Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex] =216
What is outcome of an event?
Suppose an event is happening. The result of the event is called outcome of the event.
For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die
Number of outcomes of rolling a die first time = 6
Number of outcomes of rolling the die second time = 6
Number of outcomes in rolling a die third time = 6
Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]
= [tex]6^3[/tex]
= 216
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Solve the equation or formula for the variable indicated.
X-2y=1
Answers
Answer:
Step-by-step explanation:
-2y = -x -1
2y = x+1
y = 1/2x+1/2
necesito saber como se resuelve
Answers
La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.
¿Cómo resolver un ecuación exponencial?
Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.
Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:
f(x) = 9ˣ⁺¹ - 28.3ˣ - 3
g(x) = 0
La solución es todo punto tal que f(x) = g(x).
A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.
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Mrs. Dellett took up archery as a hobby. On her first attempt, she only scored 18 points.
Every attempt after that, she increased her score by 24 points. How many points did she score on her 9th attempt?
OA. 24
OB. 198
O C. 200
OD. 210
Answers
The points scored by Mrs. Dellett on her 9th attempt is 210.
Given, Mrs. Dellett took up archery as a hobby.
On her first attempt she scored 18 points.
then every attempt after that, she increased her score by 24 points.
first attempt = 18 points
after this her score increased to 24 points on every attempt.
second attempt = 18+24 = 42
third attempt = 42+24 = 66
fourth attempt = 66+24 = 90
fifth attempt = 90 + 24 = 114
sixth attempt = 114 + 24 = 138
seventh attempt = 138 + 24 = 162
eight attempt = 162 + 24 = 186
ninth attempt = 186 + 24 = 210
Hence the option D is correct.
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e trigonometry to work out the size of
angle x.
Answers
Check the picture below.
[tex]tan(x) =\cfrac{\stackrel{opposite}{10}}{\underset{adjacent}{4}}\implies tan(x)=\cfrac{5}{2}\implies x=tan^{-1}\left( \cfrac{5}{2} \right)\implies x\approx 68.20^o[/tex]
Make sure your calculator is in Degree mode.
Please help me Find the slope of the line
Answers
Answer:
Step-by-step explanation:
d- down four then right three
(3s+2f=18)
(2s+3f=15.75)
Answers
Answer:
(s, f) = (4.5, 2.25)
Step-by-step explanation:
You want the solution to the simultaneous equations ...
3s+2f = 182s+3f = 15.75SolutionWriting these in general form, we have ...
3s +2f -18 = 0
2s +3f -15.75 = 0
Using the "cross-multiplication method" for solution, we find ...
∆1 = (3)(3) -(2)(2) = 5
∆2 = (2)(-15.75) -(3)(-18) = 22.5
∆3 = (-18)(2) -(-15.75)(3) = 11.25
s = ∆2/∆1 = 22.5/5 = 4.5
f = ∆3/∆1 = 11.25/5 = 2.25
The solution is (s, f) = (4.5, 2.25).
__
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Math help needed (grade 9)
Answers
Step-by-step explanation:
volume = base area × height
= (1/2×12×16)×10
=960cm3
surface area:
1. triangle area = 1/2×12×16=96cm2
2.bottom area = 12×10=120cm2
3.side area = 16×10=160cm2
4.slope area = 10×20=200cm2
5.add everything and remember you have two triangle
surface area= 96×2+120+160+200 =672cm2
Jaylan makes limeade using
3
4
cup water per
1
5
cup lime juice. Wanchen makes limeade using
3
5
cup water per
1
2
cup lime juice. Find the unit rates of water (cups) per lime juice (cups). Whose limeade has a weaker lime flavor? Enter your answer as a proper fraction or a mixed number. jaylans contains how many cups of water per lime juice
Answers
The unit rate of the number of cups of water per cup of lime juice are;
Jaylan;
Unit rate is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juiceWanchen;
Unit rate is 2.91.[tex]\overline {6}[/tex] cups of water per cup of lime juiceWhat is a unit rate?Unit rate indicates the rate of an item for a quantity of one of another item such that when the quantitative relationship is expressed as a ratio, the denominator will be one.
The content of limeade Jaylan makes are;
34 cup water for every 15 cup lime juiceThe ingredient of the limeade Wanchen makes are;
35 cups of water per 12 cups of lime juiceThe unit rate of water (cups) per lime juice (cups) is therefore;
Jaylan; 34 cups of water for every 15 cups of lime juice
Therefore;
34/15 cups of water for 1 cup of lime juice
34/15 = 2.2[tex]\overline 6[/tex]
The unit rate of the drink Jaylen makes is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juice
Wanchen; 35 cups of water per 12 cups of lime juice
Therefore;
35/12 cups of water per cup of lime juice
35/12 = 2.91[tex]\overline{6}[/tex]
The unit rate is 2.91[tex]\overline 6[/tex] cups of water per cup of lime juice
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the population of a city increases by 4,000 people each year. in 2005 the population is projected to be 450,000 people. what is an equation that gives the city's population p (in thousands of people) x years after 2010
Answers
Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
As given in the question,
Let 'p' represent the population in thousands of people.
Let x represents the number of years.
Population projected in 2005 = 450,000 people
= 450 ( in thousand people)
Population increases by 4000 people each year that is equal to 4 (in thousand of people)
Required equation to represent the population in x years ( in thousand of people ) is given by:
p = 4x + 450
Population in 2010 is equal to :
p = 4 ( 2010 - 2005) + 450
= 4(5) + 450
= 20 + 450
= 470 ( in thousand of people)
= 470,000 people
Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
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Choose the equation that represents the graph shown
Answers
Answer:
[tex]y=|x|-4[/tex]
Step-by-step explanation:
The vertex of the graph is at (4, 0).
This eliminates all of the options except for [tex]y=|x|-4[/tex].
There are 100 items in a garage sale. 30% of the items are sold during the first hour of the sale. If 10 items are sold during the second hour, what percent of the items have not been sold?
Answers
The percentage of items that have not been sold is: 60%
In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.
Percent in itself stands for out of 100.
Let the total number of items= i
Let the percentage be represented as= p
Then,
i=100 (Given in the question)
Let the number of items sold in the first hour be= a
Let the number of items sold in the second-hour be= b
Since,
p= Given Value/Total value x100
thus,
a/100x100=30%
The hundreds cancel out.
Thus, a=30 -(i)
The number of items sold in the second hour= b
b=10 (provided in the question) -(ii)
Let the total number of items sold be=T
The total number of items sold= a+b
From (i) and (ii)
Total number of items sold=30+10
Thus,
Total number of items sold=40 -(iii)
Number of items that have not been sold(n)=100-(a+b)
=100-T
= 100-40
From (iii)
n = 60 -(iv)
Then,
Percentage of items that have not been sold = n/100x100
From -(iv)
= 60/100x100
Canceling hundred by hundred
= 60%
Thus,
Answer: The percentage of items that have not been sold is: 60%
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Type the missing number to complete the proportion.
18 orders in 2 days = 9 orders in
days
Answers
Answer:
18 orders in 2 days 9 orders in 1 day
Answer:
Step-by-step explanation:
9x2=18 which is 2 days so 9x1= 9 which is one day
Use grouping symbols to make each statement true 31.) 25 - 8 x 3 = 51 32.) 9 + 4 x 5 - 3 = 17
Answers
Answer:
31. (25 - 8) x 3 = 51
32. 9 + 4 x (5 - 3) = 17
Step-by-step explanation:
grouping symbols
31.) 25 - 8 x 3 = 51
(25 - 8) x 3 = 51
Do the parentheses first
17 * 3 = 51
51=51
32.) 9 + 4 x 5 - 3 = 17
9 + 4 x (5 - 3) = 17
Parentheses first
9 + 4 * 2 = 17
Multiply
9+8 = 17
Add
17=17
Mrs Tan worked at a jewellery shop and sold a gold bracelet. If she wanted to make a profit of 52%, she would need to sell the bracelet at $1216. How much profit would she get if she sold it at $2012?
Answers
If she sold the gold bracelet at $2012, the profit would be $1212
Let original price of the gold bracelet be x
Mrs Tan wanted to make a profit of 52%
The selling price would be $1216
Selling price = x + 52% of x
1216 = x + (52/100)x
1216 = 152/100x
x = 1216(100/152)
x = 800
The original price is $800
The price at which she sells the gold bracelet is 2012
Profit = selling price - original price
= 2012 - 800
= 1212
Therefore, if she sold the gold bracelet at $2012, the profit would be $1212
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there is a line whose slope is 1 and whose y-intercept is -9, what is its equation in slope-intercept form?
Answers
A taxi ride cot a cutomer a total of \$13. 73$13. 73dollar ign, 13, point, 73, which included 4\%4%4, percent ale tax and then a \$1$1dollar ign, 1 urcharge. What wa the ubtotal before the urcharge and ale tax?
Answers
The subtotal before the surcharge and the sales tax is $12.25 .
In the question ,
it is given that ,
the total amount paid for the taxi ride = $13.73
sales tax percent charged = 4%
amount of surcharge = $1 .
let the subtotal before the tax and surcharge be "x"
the amount paid by the customer can be represented by the equation ,
total amount = cost + 4% of cost + surcharge
Substituting the values from above , we get
13.73 = x + 4% of x + 1
4% of x + x = 13.73 - 1
0.04x + x = 12.73
1.04x = 12.73
x = 12.73/1.04
x = 12.24038
x ≈ 12.25
Therefore , The subtotal before the surcharge and the sales tax is $12.25 .
The given question is incomplete , the complete question is
A taxi ride cost a customer a total of $13. 73, which included 4% , percent sales tax and then a $1dollar surcharge. What was the subtotal before the surcharge and sales tax ?
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A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. What is the length of the third side of the triangle?
x + 13
2x + 13
5x − 5
12x + 3
Answers
The length of the third side of the triangle is 2x+13.
According to the question,
We have the following information:
A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.
We know that perimeter of triangle is the sum of all three sides of triangle.
Let's take its third side to be y.
So, we have the following expression:
3x+2x-5+y = 7x+8
5x-5+y = 7x+8
Adding 5 on both the sides:
5x+y = 7x+8+5
5x+y = 7x+13
Subtracting 5x from both the sides:
y = 7x-5x+13
y = 2x+13
Hence, the correct option is B.
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Answer:
B. 2x+13
Step-by-step explanation:
I got it right on the test
A rectangle is 25 cm on one side and 6 cm on another side. What is the perimeter?
Answers
Answer:
31
Step-by-step explanation:
Select the type of cross section formed when a triangular pyramid is cut parallel to its
base.
Answers
a multiple choice test consists of six questions, each of which has five choices. each question has exactly one correct answer. william guesses randomly at each answer. what is the probability that he gets four or fewer questions correct? (round your answer to four decimal places.)
Answers
The probability that he gets four or fewer questions correct is 0.9984
Let p be probability of getting correct answer and q be probability of getting in correct answer.
Number of trails : n = 6
Number of Successes : x = 4
By using binominal distribution ,
P(x≤4) = 1 - P(x>4)
= 1 - [P(x = 5) + P(x = 6)]
= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]
solving combination ,
= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]
= 1 - (24 + 1 / 625)
= 1 - 25 / 625
= 624/625 = 0.9984
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4) A pizza shop sells pizzas that are 12 inches (in diameter) or larger. A 12 inch cheese pizza costs $9. Each additional inch costs $1.75, and each additional topping costs $0.50. Write an equation that represents the cost of a pizza. Be ure to specify what the variables represent.
Answers
The equation to represent the cost is C = 8 + 1.50x + 0.75y.
To write an equation that represents the cost of a pizza.
An equation that represents the cost of a pizza will be
C = 9 + 1.75x + 0.50y
Fixed cost = $9
Cost of additional inch = 1.75x
Cost of additional topping = 0.50y
Total cost (C) will then be:
= 9 + (1.75 × x) + (0.50 × y)
C = 9 + 1.75x + 0.50y
Hence the answer is, the equation to represent the cost is C = 8 + 1.50x + 0.75y.
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Pls help me thank you
Answers
The value of y is x/2 + c/5
Given,
In the question:
5x - 7y = 3y - 2c
To find the value of y.
Now, According to the question:
The equation is given as:
5x - 7y = 3y - 2c
Combine the like terms:
-7y - 3y = -5x - 2c
Calculate the sum or difference:
-10y = -5x - 2c
y = -5x/-10 - 2c/-10
Calculate the product or quotient :
y = x/2 + c/5
Hence, The value of y is x/2 + c/5
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The rectangular floor of a classroom is 26 feet in length and 28 feet in width. A scale
drawing of the floor has a length of 13 inches. What is the perimeter, in inches, of the
floor in the scale drawing?
Answers
length = 26 ft
width = 28 ft
You need to convert ft into inches; 1 foot = 12 inches. Converting ft into inches, gives us:
length = 26 ft*12 = 312 inches
width = 28ft*12 = 336 inches
Now, knowing that the length of the classroom in the scale drawing is 13 inches, we can divide the actual length by the scale length to get:
312 inches/13 inches = multiple of 24
Taking the multiple of 24, we divide the width to get:
336 inches/24 = 14 inches
Finally to get perimeter, we add the sides of the rectangular floor together (length 13 inches and width 14 inches) to get:
Perimeter of the rectangular floor = (2*13 inches)+(2*14 inches)
Final answer = 54 inches
a coin is flipped eight times. each result is either a heads or a tails. how many possible outcomes contain at least 33 tails ?
Answers
The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.
The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:
[tex]\frac{8!}{3!5!} + \frac{8!}{4!4!} + \frac{8!}{5!3!} + \frac{8!}{6!2!} + \frac{8!}{7!1!} + \frac{8!}{8!0!}[/tex]56 + 70 + 56 + 28 + 8 + 1= 219Hence, the possible outcomes that contain at least three tails are 219.
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Evaluate the expression for the given value of the variable. 52+1/5(-1/2)
Answers
The simplified form of the expression 52 + 1/5(-1/2) is [tex]\frac{519}{10}[/tex]
What is a fraction?A fraction is a ratio of two integers.
The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.
52 + 1/5(-1/2)
Multiply out the fraction
we have
52 + (-1/10)
52 - 1/10
to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes
520/10 - 1/10
simplifying the numerator we have,
[tex]\frac{520 - 1}{10}[/tex] = [tex]\frac{519}{10}[/tex]
In conclusion the solution to 52+1/5(-1/2) is [tex]\frac{519}{10}[/tex]
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Please help pleaseee
Answers
According to the Pythagoras theorem, the value of x is 13.76
Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.
Given,
Here we have the triangle with the side values.
Now, we have to find the value of x through this given values.
In order to calculate the value of x,
First, we need the value of the side KM.
Let us consider the value of KM is y.
Then according to the concept of Pythagoras theorem,
The value of y is calculated as,
=> (12.3)² = y² + (5.4)²
=> 151.29 = y² + 29.16
=> y² = 122.13
=> y = 11.05
Therefore, the value of the hypotenuse x is calculated as,
=> x² = (11.05)² + (8.2)²
=> x² = 122.13 + 67.24
=> x² = 189.37
=> x = 13.76
Therefore, the value of x is 13.76.
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pls give answer pls pls
Answers
Answer:
k = 13
Hope this helps : )
Step-by-step explanation:
To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.
1. Divide 7 on both sides of the equal sign.
7k = 91
7 7
2. Answer.
The 7 cancels out so we are left with k = 13 since
91 ÷ 7 = 13
k = 13
3. Check.
Plug in the variable "k."
7(13) = 91
91 = 91 ✓