to
5.2.2 Guided Instruction: Solutions to the
Products and Quotients of Polynomials on a
Graph
Graphs can be used to determine the products and
quotients of polynomials similarly to using graphs when
adding and subtracting polynomials.
The functions a(x) and b(x), and their product, a(x) b(x),
represented by c(x), are shown on the coordinate plane.
35A
(10, 34)
-10
-30
-25-(-0,24)
MATH
20
(0.805, 105)
10
(1.5, 6)
0
(0-3)
b(x10
-15
(8,13)
C(x)
(6.5, 10)
5
(0-8)
(10, 17)
(8.695-10)
3. Find the value of c(10).
2. What is the product of a(10) · b(10)?
10, 2
15
(8,0)
-20
1. Describe how to use the graph to determine the value
of a (10) b(10).
20
25
Answers
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
Definition of the cubic function .f(x)=ax3+bx2+cx+d, where 0 and the coefficients a, b, c, and d are complex numbers, and where the variable x has real values. In other words, it is both a three-degree polynomial function and a real function.
Here,
Our role in this situation is:
y = ∛(x - 5) (x - 5)
so the cubic root is given.
In this case, we see that when x = 0, we have:
The y-intercept is y = -5.
And if x = 5, we get:
Because of the sign change, the x-intercept and inflection point are both equal to y = ∛0 = 0
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
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Related Questions
Alberts double number line worked example find mistake
Answers
Albert has made mistake in double number line in step 3 and 4.
The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).
Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.
Albert has made mistake in step 3 and step 4,
Firstly he has written wrong units for the respective number line,
If ratio of 2 parts of blue and 5 parts of red is used(2:5)
The equivalent ratio will be 10:25
We get the desired output by multiplying (2:5) by 5.
The Correct units will be 5 instead of 20
And the number corresponding to 25 will be 10.
The correct double number line is drawn below.
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20 POINTS!!! HELP ASAP!! What are the domain and range of the function graphed below?
Answers
PLease help and the right answer gets marked brainliest!!!!!!!!!!!
Answers
The answer is 382.5! Also I rounded to the nearest tenth. I hope this helps, have a beautiful day!
ILL BRAINLIEST YOU PLEASE HELP ME
Answers
Answer:
x = 28
Step-by-step explanation:
A team of scientists is developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time. Which variable would most likely affect the temperatures that the model predicts
Answers
Scientists are developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time.
These variables include:
Carbon dioxide emissions from human activity (x) - This variable is considered to have the greatest impact on temperature predictions as human activities have significantly increased the amount of carbon dioxide in the atmosphere, which is a major greenhouse gas that causes global warming. Carbon dioxide emissions from activities in nature (y) - This variable also plays a role in temperature predictions as it contributes to the overall amount of carbon dioxide in the atmosphere.Global sea level (z) - The time interval is sufficiently large for the global sea level to have a greater impact on temperature predictions as rising sea levels can affect coastal regions and weather patterns.Global rates of photosynthesis (p) - Changes in the Earth's orbital path can affect the global rates of photosynthesis, which in turn can affect temperature predictions.The acidity of ocean water (q) - While the acidity of ocean water is an important variable, it is considered to have a less significant impact on temperature predictions compared to the other variables listed above.In summary, the variables are ranked in order of their likely impact on temperature predictions, with carbon dioxide emissions from the human activity being the most significant variable, followed by carbon dioxide emissions from activities in nature, global sea level, global rates of photosynthesis, and acidity of ocean water.
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Logan has 4 2/3 cup of peanuts and 3 2/3 cup of cashews if you combine some nuts how much will he have
Answers
Answer: He will have 8 1/3 nuts
Step-by-step explanation:
Amount of peanuts=4 2/3 cups
Amount of cashews=3 2/3 cups
Combing the nuts will give Total amount of nuts ( peanuts and cashews)
=4 2/3 +3 2/3
=7 4/3
7 + 1 1/3
8 1/3 nuts
What composition of rigid motions maps ΔPQR to ΔXZY?
Answers
Answer:
it is C.
Step-by-step explanation:
it is C.
The transformation is 6 units left and 2 units down and reflection about x = -2 thus option (C) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As the given XYZ.
Take coordinate of Y(4,3)
Now, take it back 6 units and 2 units down as,
R(4 - 6,3 - 2) = R(-2,1)
Now, reflect the entire image about x = -2 gives the same image as OQR.
Hence "The transformation is 6 units left and 2 units down and reflection about x = -2"
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Is P 3 2 and Q 2 3 represent the same point justify?
Answers
It is Justified that P and Q are different point.
What is cartesian coordinate plane?The coordinate plane where a location of a point is represented in the form of X and Y coordinate pair, is termed as cartesian plane. In this plane two reference axes are used which are perpendicular to each other.
What is the location of two point stated above?In the question, two-point P (3, 2) and Q (2, 3) are given. As per the cartesian coordinate system a location of a point is represented by a pair of numerical terms. The first numerical terms denote the X coordinate of the point, and the next terms refers the Y coordinate of that point.
Therefore, P and Q are two different points on the cartesian plane. The point p (3, 2) where 3 is the X coordinate and the distance from Y axis is 3 and 2 is the Y coordinate and distance from X axis is 2.
Similarly for the point Q (2, 3), 2 denotes the X coordinate of the point Q and 3 is the Y coordinate.
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PLEASE HELP f(x)=x^2-12x+35 g(x)=x−5, find(f⋅g)(x)
Answers
Step-by-step explanation:
this is a multiplication dot, right ?
so,
(f.g)(x)
or
(f×g)(x)
any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.
(f×g)(x) = (x² - 12x + 35)(x - 5) =
= x³ - 5x² - 12x² + 60x + 35x -175 =
= x³ - 17x² + 95x - 175
Step-by-step explanation:
(f.g)(x) = f(x) . g(x)
= (x² - 12x + 35)(x - 5)
=x(x²-12x+35) - 5(x²-12x+35)
= x³-12x²+35x-5x²+60x-175
(f.g)(x)=x³-17x²+95x-175
If a dog is tied to a stake in the center of the yard and the chain is 20 feet long, what is the maximum area that the dog has to play in?
A
314 ft sq
B
125.6 ft sq
C
5,024 ft sq
D
1,256 ft sq
Answers
Answer:
Its 125.6
Step-by-step explanation:
20 times Pi is 62.8 and then you multiply this by 2.
what is the answer
A
B
C
D
Answers
At what point does the graph of the linear equation 2x 3y =- 15?
Answers
The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.
The linear equation
2x - 3y = -15
can be written in the form
y = mx + b,
where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us
y = (2/3)x - 5.
This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us
y = -5.
Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.
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Ashley is selling handmade jewelry to earn money for camp. Bracelets sell for $7.62 and
necklaces sell for $15.67, and she needs to make at least $450 in revenue to cover the cost
of camp.
Write the inequality in standard form that describes this situation. Use the given numbers and
the following variables.
X
= the number of bracelets
V
= the number of necklaces
Answers
Equation for the sentence's inequality are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
let X = the number of bracelets
let Y = the number of necklaces
The inequality equation = 7.62x + 15.67y >= 450
Equation for the sentence's inequality She needs to generate at least $450 in revenue because bracelets are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.
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14π
18π
36π
12π
00000000
Answers
What is the vector equivalent to the directed line segment from the point?
Answers
The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.
The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.
The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.
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1. You find that of your simplified responses to A through E match to a simplified response among F through J. List the matches by letter and write what the simplified response is to each matched pair.
Answer:
2. Determine the modulus of each of the complex numbers in the matching pairs. List these moduli in order from smallest to largest. Use the letters of the matching pair in your listing.
Answer:
3. Suppose m = 2 + 6i, and║m+n║= 3√10 , where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.
Answers
Answer:
F.(8-√-11)(8+√-11)
8²-11²i²
8²-121×-1
64+121
=185
G.
(3+i)(2+i)
6+3i+2i+i²
6-1+5i
5+5i
H.
(4+6i)+(-7-7i)
5+6i-7-7i
-2-i
i.
i^24
(i^2)^12
=1
J.
(-3+10i)-(-5+4i)
-3+10i+5-4i
2+6i.
The simplified form of the expressions are 185, G. 5 + 5i, H. -2 - i, I. 1, j. 2 + 6i.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
F. (8-√-11)(8+√-11)
[tex]8^2 - 11^2 i^2\\8^2 - 121 \times -1\\64+121\\=185[/tex]
G.
(3+i)(2+i)
[tex]6+3i+2i+i^2\\6-1+5i\\5+5i[/tex]
H.
[tex](4+6i)+(-7-7i)\\5+6i-7-7i\\-2-i[/tex]
i.
[tex]i^24(i^2)^12=1[/tex]
J.
[tex](-3+10i)-(-5+4i)\\-3+10i+5-4i\\2+6i.[/tex]
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For what value of k the equation 4x2 2 K 1 )= 0 has real and equal roots?
Answers
The values of k are 3 and −1.
Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0
Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.
⇒b2−4ac=0
[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]
For given equation, a=4, b=2(k+1),c=(k+1)
(2(k+1))^2 −4.4(k+1)=0
⇒(2k+2)^2−16(k+1)=0
⇒4k2+8k+4−16k−16=0
⇒4k2−8k−12=0
⇒4(k2−2k−3)=0
⇒k2−2k−3=0
⇒k2−3k+k−3=0
⇒k(k−3)+1(k−3)=0
⇒(k−3)(k+1)=0
⇒k−3=0 and k+1=0
⇒k=3 and k=−1
So, the values of k are 3 and −1.
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solve (2+2)+(4-1). ASAP, it's test
Answers
??
¯\_(ツ)_/¯
4+3
7
the answer is 7.
Answer:
[tex] \huge \boxed{\displaystyle 7}[/tex]
Step-by-step explanation:
we would like to simplify the following expression:
[tex] \displaystyle (2 + 2) + (4 - 1)[/tex]
in order to do we can consider the order of PEMDAS which is the abbreviation of Parentheses, Exponent, Multiplication,or Division, Addition or substraction
since Parentheses come first we'll simplify parentheses:
[tex] \displaystyle 4 + 3[/tex]
simplify addition:
[tex] \displaystyle 7[/tex]
and we are done!
I will mark 1st correct answer as brainliest
Let f(x) = log base 3 of x and g(x) = 3^x.
What is the value of
[f(g(f(f(f(g(27))))))?]
I will mark 1st correct answer as brainliest
Answers
The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1
How to evaluate the composite functionFrom the question, we have the following parameters that can be used in our computation:
Let f(x) = log base 3 of x and g(x) = 3^x.
Express the equations properly
So, we have the following representations
f(x) = log₃(x) and g(x) = 3ˣ
Calculating the composite function [f(g(f(f(f(g(27))))))], we have
[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]
Next, we have:
[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]
This gives
[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]
For f(27), we have
[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]
For f(3), we have
[f(g(f(f(f(g(27))))))] = [f(g(1))))]
Calculating g(1), we have
[f(g(f(f(f(g(27))))))] = f(3)
Lastly, we have
[f(g(f(f(f(g(27))))))] = log₃(3)
Evaluate
[f(g(f(f(f(g(27))))))] = 1
Hence, the solution is 1
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I neep help asap deadline 4:00pm
Answers
Answer:
x = -2 to x = 1
Step-by-step explanation:
A function is constant when the y value does not change (i.e. the graph is a horizontal line). This is true between x = -2 and x = 1.
Answer:The Funcation is Constact from x=-5 to x=8
Step-by-step explanation:
What is the value of the "x"?
O x = 180
O x = 45
O x = 135
O x = 90
Answers
Answer:
45
Step-by-step explanation:
its going to be the same as the other corner then on the top you have to times by 2 cause it double the size of the bottom
Help me please!!! …..
Answers
Answer:
7/25= 14/50 3/10= 15/50 common denominator: 50 so, 7/25 < 3/10
For questions 3 – 4, use the table to answer the questions.
This table shows the high schools in a metro district and whether they offer hockey and golf.
High school Hockey Golf
East Valley ✔
Central
Lincoln ✔ ✔
Davis
West Pine ✔ ✔
Adams ✔
North River ✔ ✔
A high school is chosen at random from this list.
Let event A = The high school has a hockey team.
Let event B = The high school has a golf team.
3. Which high schools offer both hockey and golf?
What is P(A ∩ B)?
4. Which high schools offer hockey or golf or both?
What is P(A ∪ B)?
Answers
We have P(A ∩ B) is 2/5 and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.
P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)
East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.
P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)
Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5 and P(A ∪ B) is 5/5.
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In Mrs. Trainer's math class, Siobhan's first five math quiz scores are 76, 96, 81, 69, and 41. Siobhan takes the sixth math quiz and scores an 85. How will the mean change if the sixth score is added to the list?
Answers
Answer:
the median will go up 2.5 points from 76 to 78.5
Step-by-step explanation:
You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.
MedianThe median is the middle value when the list is sorted into order. The ordered list is ...
41, 69, 76, 81, 96
The median is 76.
New MedianWhen 85 is added to the list, the sorted list becomes ...
41, 69, 76, 81, 85, 96
There are two middle scores, so the median is their average:
(76+81)/2 = 78.5
The median increases 2.5 points from 76 to 78.5 when the score is added.
18) If you invest $2400 at an annual interest rate of 4.5% that is compounded quarterly, how much will your investment be
worth in 12 years?
Answers
The amount of interest a single deposit earns for the period of one year is equal to your initial investment multiplied by this yield.
What is the formula for calculating investment interest?Compound interest may be computed using the formula FV = P*(1+R/N)(N*T), where FV is the loan or investment’s future value, P is the original principle amount, R is the yearly interest rate, N is the number of times interest is compounded each year, and T is the period in years.
The amount of interest earned on a single deposit over a year is equal to your initial investment multiplied by this return. As an example: After a year, $1,000 invested at a 5.00% annual effective return yields $50.00 in interest. $1,000.00 x 5.00% = $50.00.
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Becky is able to run up a 3. 00 m high flight of stairs in 2. 5 s if she has a mass of 50 kg how much power did she develop during her run up the stairs how long will it take becky in question 6 to run up a flight of stairs 4. 5 m high?
Answers
With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.
How do you calculate power going up stairs?Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)
Given that mass of Becky is 50 Kg
gravity of earth is 9.8 m/s²
height of stairs is 3.0 m
time taken to run up in stairs is 2.5 s
Power = work done/ time taken
P = (50*9.8*3.0)/2.5
P = 1470/2.5
P = 588 watt
Becky is able to run up a 3.0 m high flight of stairs in 2.5 s
She is able to run up a 4.5 m high flight of stairs in t = (2.5 * 4.5)/3
t = 11.25/3
t = 3.75 s
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If the acceleration is 6m/s/s and the mass is 3kg, calculate the force? Include the UNIT
Answers
Answer:
[tex]f = m \times a = 3 \times 6 = 18 \: n[/tex]
is -(-3) = 3 . i know its simple but I need it
Answers
Answer:
Yes
Step-by-step explanation:
[tex] - ( - 3)[/tex]
[tex] - 1 \div - 3[/tex]
[tex]3[/tex]
Hope it is helpful....What is the value of 3/4- (-3) +(-3/4)
Answers
Answer: 3
Step-by-step explanation:
Answer:
What is the value of A?
–4
–3
3 <<< CORRECT
4
Step-by-step explanation:
Edge 2022
number of faces?
number of edges?
number of vertices?
Answers
Answer:
no of face 8
no of vertices 16
no of edges 24