Answers
The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -1A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 2y-intercept = -12A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 1)(x - 1)(x - 2)^2
The y-intercept is -12
So, we have
a * (0 + 1)(0 - 1)(0 - 2)^2 = -12
This gives
a = -4
Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2
Read more about polynomial at
brainly.com/question/7693326
#SPJ1
Related Questions
Aida is 15 years old. Brice is five years younger than Aida. Henry is three years younger than Aida. How old is Brice?
Answers
Answer:
Bryce is 10 years old
Step-by-step explanation:
The age of Brice is given by B = 10 years old
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as B
Now , the value of B is
Substituting the values in the equation , we get
The age of Aida = 15 years
The age of Brice = 5 years younger than Aida
On simplifying the equation , we get
So , age of Brice = 15 - 5 = 10 years
The age of Henry = three years younger than Aida
So , the age of Henry = 15 - 3 = 12 years
Hence , the age of Brice is 10 years old
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options
Answers
The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
(3/5) (30x - 15) = 72
Solve the linear equation with a single variable for 'x', then we have
(3/5) (30x - 15) = 72
3(6x - 3) = 72
18x - 9 = 72
18x = 81
x = 4.5
The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.
More about the solution of the equation link is given below.
https://brainly.com/question/22613204
#SPJ9
Help with questions pls?
Answers
Find GI, AGI, TI...
Given:
Wages : $145,000
Interest : $2500,
Contribution towards the retirement: $3000
Exemptions: $4100
Deductions: $2800
-Thanks!
Answers
The GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.
What is Interest?
Interest is the income that is returned to the holder of capital. Different kinds of interest include gross interest and net interest.
To find GI (Gross Income), we add wages and interest:
GI = Wages + Interest = $145,000 + $2500 = $147,500
To find AGI (Adjusted Gross Income), we subtract the contributions towards retirement from GI:
AGI = GI - Contributions towards Retirement = $147,500 - $3000 = $144,500
To find TI (Taxable Income), we subtract exemptions and deductions from AGI:
TI = AGI - Exemptions - Deductions = $144,500 - $4100 - $2800 = $137,600.
Therefore, the taxable income is $137,600.
Hence, GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.
To learn more about the Interest visit:
https://brainly.com/question/30393144
#SPJ1
Help please I don’t understand it at all
Answers
Answer:
Both of them are correct.
Step-by-step explanation:
Let's review both of their methods and check their validity.
Kaylee's Method:This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.
Ariel's Method:While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.
Please help bro I need help solving this polynomial and terms
Answers
The expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.
What is a polynomialA polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.
For the polynomial expression, (1/2)x⁵ - 6 - x⁴ - 5x⁴
There are 4 terms which are: (1/2)x⁵, - 6, - x⁴, and - 5x⁴.
The constant term is -6
The leading term is (1/2)x⁵
The coefficient of the leading term is 1/2.
In conclusion, the expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.
Know more about polynomials here: https://brainly.com/question/24729294
#SPJ1
Answer:
quadrinomial, 4, -6, 1/2x^5, 1/2
Step-by-step explanation:
quadrinomials are polynomials with 4 terms
constant is the number with no variable
leading term is the term at the beginning
leading coefficient is the number at the beginning
what is the solution set to the inequality -4x - 2 ≤ - 14
Answers
Answer:
x[tex]\geq[/tex] 3
Step-by-step explanation:
-4x -2 ≤ -14
-4x ≤ -12
x ≥ 3
Move the constant to the right-hand side and change its sign: -4x<_ -14+2
Calculate the sum: -4x<_-12
Divide both sides of the inequality by and flip the inequality sign: x>_3
A local high school has 1,152 students with 391 freshmen, 351 sophomores, 208 juniors, and 202 seniors. What is the
relative frequency of sophomores at this high school?
Answers
The relative frequency of sophomores at this high school is 39/128.
How to find the relative frequency?
Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
We are given that;
Total students=1152
Freshmen=391
Sophomores=351
Juniors=208
Seniors=202
Now, to find frequency of sophomores
=number of sophomores/total number of students
=351/1152
=117/384
=39/128
Therefore, the relative frequency will be 39/128.
Learn more about conditional relative frequency here:
https://brainly.com/question/8358304
#SPJ1
For the function
f(x)
given in the table, find the average rate of change over each specified interval.
x
0 2 2.5 3 3.8 4 5
f(x)
24 13 17 18 16 13 29
(a) [2, 5]
Incorrect: Your answer is incorrect.
(b) [3.8, 4]
Answers
The average rate of change over each specified interval is 8/3 and -10.
What is an average rate?The average rate shows the change in the function per unit, over an interval.
Given that, find the average rate of change over each specified interval.
The average rate of change is given by
f(b)-f(a) / b-a
a) [2, 5] :-
To find the average rate of change we will take the change in the function over the change in x,
f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3
Therefore, the average rate of change in interval [2, 5] is 8/3
b) [3.8, 4] :-
Similarly,
f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2
= -10
Therefore, the average rate of change in interval [3.8, 4] is -10
Hence, the average rate of change over each specified interval is 8/3 and -10.
Learn more about average rate, click;
https://brainly.com/question/28739131
#SPJ9
(Q) John has 25 red marbles, 15 blue marbles and 10 yellow marbles. He wants to make similar groups using all the marbles.
(a) Work out the highest number of groups he can make.
(b) Also work out how many, of each color marble, will be in each group.
Answers
Answer:
(a) highest number of groups = 5
(b) out how many, of each color marble, will be in each group.
5 red
3 blue
2 yellow
Step-by-step explanation:
The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers
GCF of 25, 15 and 10 can be found as follows by finding factors of each number:
25 = 5 x5
15 = 5 x 3
10 = 5 x 2
Choose the highest number that is common in each group and this is 5
So John can make a maximum number of 5 groups
Divide each number by the GCF to find how may in each group
25/ 5 = 5 red marbles
15/5 = 3 blue marbles
10/5 = 2 yellow marbles
So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles
Use the Negative Area approach to depict the centroid of the section in Figure 2 beloW.
Use the reference ofigin O shown.
8cm
2cm
8cm
X
2cm
2cm
3cm
3cm
3cm
k
*
*
Figure 2
b) i. State any two (2) ways in which a structure may be deemed to lack Structural
Integrity.
(9 marks)
ii. Structural system refers to the load-resisting sub-system of a structure which transfers
loads through interconnected structural components or members. With the aid of
annotated sketches describe any two (2) of the basie types of structural systems.
Answers
A structure may lack structural integrity if it experiences overloading and material degradation.
How to explain the structureA structure may lack structural integrity if it experiences:
Overloading, where the loads placed on the structure exceed its design capacity, leading to failure of some structural components or members.
Material degradation, where the structural materials lose their strength and stiffness over time due to environmental factors such as corrosion or excessive temperature.
ii. The basic types of structural systems are:
Frame Structures, where the structural components are arranged in a series of interconnected frames that can resist lateral and gravity loads. Examples include steel frames and concrete frame structures.
Load-Bearing Wall Structures, where the structural components are arranged in a series of interconnected walls that bear the weight of the structure and transfer loads directly to the foundation. Examples include masonry and concrete walls.
Learn more about structures on:
https://brainly.com/question/1226557
#SPJ1
Help me with this worksheet pls
Answers
The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.
What is exponential function?The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The given function is:
y = 5(2)ˣ
The value of y from x= 0 to x = 3 is:
y = 5(2)⁰ = 5
y = 5(2)¹ = 10
y = 5(2)² = 20
y = 5(2)³ = 40
The most rapid rate of change as x increases beyond 0 is:
y = 7ˣ
This is observed as the graph increases rapidly with change in value of x.
3. y = (1.20)ˣ
The constant 1.20 is greater than 1 thus, the function is exponential growth.
Learn more about exponential function here:
https://brainly.com/question/15352175
#SPJ1
The temperature in burr town starts at 21 F at midnight when H=0 for the next few hours the temperature drops 4 degrees every hour which equation represents the temperature at hour h
Answers
Answer:
t = 21 + (-4)h
Step-by-step explanation:
t = temp. at hour h
h = # of hours past midnight
t = 21° + (-4°/hr)h
PLEASE HELP ME AS QUICK AS POSSIBLE !!
Answers
Answer:
1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0
Step-by-step explanation:
You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.
SimplificationThe expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.
[tex]\dfrac{1}{a^2+ab}+\dfrac{1}{ab+b^2}=\dfrac{1}{a^2+ab}\cdot\dfrac{b}{b}+\dfrac{1}{ab+b^2}\cdot\dfrac{a}{a}=\dfrac{b+a}{a^2b+ab^2}\\\\=\dfrac{a+b}{ab(a+b)}=\boxed{\dfrac{1}{ab}\quad a\ne0,b\ne0,(a+b)\ne0}[/tex]
The given conditions ensure the denominator(s) will not be zero.
1. Find the semester GPA for the following. Show or explain your work.
Class Credit Hours Grade
MAT 171 4 C
HEA 112 2 A
ENG 111 3 B
ACA 111 1 D
BIO 112 4 A
2. Annie is a junior at a local university. She has 80 credit hours and a GPA of 2.1.
She wants to raise her GPA for a scholarship this semester.
She takes 16 credit hours and makes all A's, earning a 4.0 for this semester.
Annie averages the previous GPA of 2.1 and the current semester GPA of 4.0. She adds 2.1 + 4.0, then divides by 2, obtaining 3.05.
She believes she should now have a GPA of 3.05.
Is her reasoning correct? Justify your answer with 2 - 3 sentences.
Answers
Answer:
aiaiiwakkaoajdjsjzjhsjaj
Number 1 solve use counting principle
Answers
The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.
What are factorials?Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.
Given that, three men and three women line up at a checkout counter in a store.
a) Number of ways = 6!
= 6×5×4×3×2×1
= 720 ways
b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on
There are 3 number of ways for woman standing in the odd position and for men standing in the even position.
So, number of ways = 3!×3!
= 3×2×1×3×2×1
= 36 ways
c) There are 3 men and 3 women.
Probability first is a woman is 3/6
Probability second is a man is 3/5
Probability third is a woman is 2/4
Probability fourth is a man is 2/3
Probability fifth is a woman is 1/2
Probability sixth is a man is 1/1
Multiply all these probabilities together and you get:
3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05
Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.
Learn more about factorials here:
brainly.com/question/25997932
#SPJ1
A polynomial function can be written as (x − 2)(x − 3)(x + 5). What are the x-intercepts of the graph of this function?
Answers
The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.
What are the x-intercepts of a polynomial function?The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.
On this note, the x-intercepts of the polynomial function which is as described in this scenario are;
x - 2 = 0; x = 2.
x - 3 = 0; x = 3.
x + 5 = 0; x = -5.
Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.
Read more on x-intercepts of polynomial functions;
https://brainly.com/question/29136444
#SPJ1
Determine if the point (-6, 3) is a solution to the system.
y =1/2x+6
2y = -x-3
The point (-6, 3)
is a solution to the system of equations.
is not a solution to the system of equations.
Answers
Answer:
is not a solution to the system of equations.
Step-by-step explanation:
Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:
Substitute the x and y values into the first equation:
y = 1/2x + 6
3 = 1/2(-6) + 6
Simplify the right side of the equation:
3 = -3 + 6
Solve for the value of y:
3 = 3
The first equation is satisfied, so now let's substitute the x and y values into the second equation:
2y = -x - 3
2 * 3 = -(-6) - 3
6 = +6 - 3
Simplify the right side of the equation:
6 = -3
The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.
Whats the correct answer answer asap for brainlist
Answers
A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.
The option (a) is correct.
What is quote?Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.
The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.
The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.
As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.
Learn more about on quotation here:
brainly.com/question/1228787
#SPJ9
Drag each tile to the correct box.
Put the numbers in order from greatest to least.
3.406
V
305
100
A
99 X
100
Answers
The order of the numbers from greatest to least are 3.406 > 305 / 100 > 99 × 1/100
What is descending order?Descending order refers to the arrangements of numbers from the greatest to the least.
On the other hand, ascending order is the arrangement of numbers from the least to the greatest.
3.406
305 / 100
= 3.05
99 X 1/100
= 99 × 0.01
= 0.99
Therefore, the arrangements from greatest to least is 3.406, 305 / 100, 99 × 1/100
Read more on ascending order:
https://brainly.com/question/1094377
#SPJ1
An entire 6 inch personal pizza has 620 calorie. Estimate the number of calories in a
16 inch pizza
Answers
Answer: 1,652.8 calories
Step-by-step explanation:
620 divided by 6 = 103.3 calories per inch
103.3 times 16 inches = 1,652.8 calories
A group of students stood in a circle to play a game. The circle had a diameter of 22 meters. Which measurement is closest to the area of the circle in meters?
Answers
The measurement closest to the area of the circle in meters is 379.94 sq. meters.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.
Given that,
diameter = 22m
radius = 22/2 = 11m
The area of the circle is:
A = πr²
Substituting the value of π = 3.14 and r = 11 we have:
A = (3.14)(11)²
A = 379.94
Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.
Learn more about area here:
https://brainly.com/question/27444262
#SPJ1
The probability that someone files their taxes late is 0.351. If you are questioning 10 people, what is the probability
that 6 of them filed their taxes on time.
Answers
Answer:
0.209.
Step-by-step explanation:
The probability that someone files their taxes on time is 1 - 0.351 = 0.649.
To find the probability that 6 out of 10 people file their taxes on time, we can use the binomial distribution. The binomial formula for the probability of k success in n trials is given by:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
Where (n choose k) is the number of combinations of n items taken k at a time, and p is the probability of success in a single trial.
So, for the problem at hand:
P(6) = (10 choose 6) * 0.649^6 * (1 - 0.649)^(10 - 6) = 0.209
Therefore, the probability that 6 out of 10 people file their taxes on time is approximately 0.209.
Given: AABC, CD 1 AB, AC = BC Area of AABC = 32 cm?. • M
Answers
The value of CD is 9.92 cm
How to find this value?Given:
∆ABC,CD ⊥ AB,AC = BC,Area of ABC = 32 cm2,m∠A = 72°Find: CD
Triangle ABC is an isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,
m<A = <mB = 72°
The sum of the measures of all interior angles is 180°, thus
m<C = 180° -72° - 72° = 36°
The area of the triangle ABC is
AABC= 1/2AC.BC.sin<C
If we expand,
AC = 10.43cm
Consider right triangle ACD. In this triangle,
sin <A = CD/AC
sin 72° = CD/10.43
therefore,
CD = 9.92 cm.
Read more about geometry here:
https://brainly.com/question/24375372
#SPJ1
Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°
Find: CD
The rectangle is framed find the area of shaded region if the frame is 2 unit wide
Answers
The area of the shaded region is 20 square units for the given rectangle frame.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Dimensions of the inside rectangle, are as follows:
Length L₁ = 5 units
Width W₁ = 3 units
Since the frame is 2 units wide,
So, the dimensions of the outside rectangle, are as follows:
Length L₂ = 5 + 2 = 7 units
Width W₂ = 3 + 2 = 5 units
The area of the shaded region = area of the outside rectangle - area of the inside rectangle
The area of the shaded region = L₂ x W₂ - L₁ x W₁
The area of the shaded region = 7 x 5 - 5 x 3
The area of the shaded region = 35 - 15
The area of the shaded region = 20 square units
Thus, the area of the shaded region is 20 square units.
Learn more about the Area of the rectangle here:
https://brainly.com/question/26889212
#SPJ9
The question seems incomplete, the missing figure is attached below.
Step 1: 3 - 5 = √√4x + 6
Step 2: 3x - 5-6 = √4x+6-6
Step 3: 3x 11 = √/4x
Step 4: (3x - 11)² =(√4x)
What is the next step in the solution to this equation?
Answers
The next step in the solution to this equation is to evaluate the exponents
How to determine the next step in the solution to this equationFrom the question, we have the following parameters that can be used in our computation:
The steps 1 to 4
Using the above as a guide, we have the following:
Step 4: (3x - 11)² =(√4x)²
At this point,, we open the bracket
This is done by evaluating the exponents
So, we have
9x² - 66x + 121 = 4x
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
Determine which consecutive integers do not have a real zero of f(x)=x²-4x²-4x+15 between them.
a. (4, 5)
C. (-2,-1)
b.
(1, 2)
d.
(-3,-2)
Answers
Answer:
option
Step-by-step explanation:
f(x)=-3x²-4x+15
if (-3,-2) is substitute
x=-3 x=-2 is substitute in above given equation we get real zero.
How to identify outliers in a set of data? Explain how to and answer my question.
Minimum: 1
Q1: 5
Median: 19.45
Q3: 31.5
Max: 41.6
Answers
The outliers in a set of data is the maximum value 41.6.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
Given that Minimum: 1
Q1: 5
Median: 19.45
Q3: 31.5
Max: 41.6
Range = Maximum - minimum
Range =41.6 -1
= 40.6
Since Mean not including the outlier.
The outliers in a set of data is 41.6.
Learn more about median;
https://brainly.com/question/17060266
#SPJ1
Find the value of x.
(4x+12) 64°
OA. 19
OB. 3.5
O c. 26
OD. 13
Answers
In this case, we can set n = 8, since the figure is an octagon. Therefore, the measure of each interior angle is equal to (8-2)*180/8 = 64°.
Substituting this into the equation (4x+12) = 64°, we get 4x = 52. Solving for x, we get x = 13. Therefore, the answer is OD. 13.
Answer: OD. 13
Step-by-step explanation:
For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets.
{10, 15, 14, 20, 11}
...
Answers
Step-by-step explanation:
A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.
To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.
To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.
Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.
