(x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15 as there is no remaider.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial function f(x) = x³ - x² - 17x -15.
If (x - 5) is it's factor then f(5) = 0.
∴ f(x) = x³ - x² - 17x -15.
f(5) = 5³ - 5² - 17(5) - 15.
f(5) = 125 - 25 - 85 - 15.
f(5) = 0.
So, the remainder is zero hence (x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15.
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I need help Solving this
Answer:
51°
Step-by-step explanation:
5555555555555555555555555555 X 342232323232232323232323222222
Answer: 1.90129068E57
Step-by-step explanation:
Answer:1.9012907e+57
Step-by-step explanation:
Find the accumulated value if the money is compounded quarterly?
Part b.
In this case, the money is compounded quarterly, this means that n=4 (4 times per year). So, by substrituting the given values into the compound interes formula, wer have
[tex]A=15000(1+\frac{0.045}{4})^{4\times5}[/tex]which gives:
[tex]A=18761.26[/tex]Compute the diameter of a circle with a circumference of 34 feet
Answer:
d ≈ 10.8 feet
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( where d is the diameter )
given C = 34 , then
πd = 34 ( divide both sides by d )
d ≈ 10.8 feet ( to 1 dec. place )
Answer:
The diameter of circle is 10.82 feet.
Step-by-step explanation:
Given :Circumference of circle = 34 feetTo Find :Radius of circle Diameter of circle Using Formulas :[tex]\longrightarrow\sf{Circumference_{(Circle)} = 2 \pi r}[/tex]
[tex]\longrightarrow\sf{Diameter_{(Circle)} = 2r}[/tex]
Where
π = 3.14r = radiusSolution :Finding the radius of circle by substituting all the given values in the formula :
[tex]\longrightarrow\sf{Circumference_{(Circle)} = 2 \pi r}[/tex]
[tex]\longrightarrow\sf{34 = 2 \pi r}[/tex]
[tex]\longrightarrow\sf{34 = 2 \times 3.14 \times r}[/tex]
[tex]\longrightarrow\sf{34 = 6.28 \times r}[/tex]
[tex]\longrightarrow\sf{ r = \dfrac{34}{6.28}}[/tex]
[tex]\longrightarrow\sf{\underline{\underline{ r \approx 5.41}}}[/tex]
Hence the radius of circle is 5.41 feet
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the diameter of circle by substituting the given value in the formula :
[tex]\longrightarrow\sf{Diameter_{(Circle)} = 2r}[/tex]
[tex]\longrightarrow\sf{Diameter_{(Circle)} = 2 \times r}[/tex]
[tex]\longrightarrow\sf{Diameter_{(Circle)} \approx 2 \times 5.14}[/tex]
[tex]\longrightarrow\sf{Diameter_{(Circle)} \approx 10.82}[/tex]
Hence, the diameter of circle is 10.82 feet.
————————————————using technology how do you calculate a weighted average ROR of investments
A weighted average of the share amount paid for the shares may be calculated by the investor. To achieve this, multiply the total number of shares purchased by each price, add those numbers, and then divide the total by the number of shares purchased.
This is further explained below.
What is the weighted average ROR?The total sum of the product (or multiplication) of the weights that are associated with various investment alternatives and their corresponding results is the weighted average return. This is also known as the weighted mean return.
The total of these weights is equivalent to one hundred percent.
Generally, The investor has the ability to compute a weighted average of the share prices at which the shares were purchased.
To do this, first, multiply the number of shares bought at each price by that price, then add up the values obtained from steps one and step two, and then divide the entire value by the total number of shares.
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River needs to buy a shade for a window in his house. He measured the width
of the window as 27 inches. The actual measurement is 24 inches. What is the
percent of change or the percent error
Answer: 12.5%
Step-by-step explanation:
Actual measurement of the window = 24 inches
Measured measurement of the window = 27 inches
We need to find the Rivers percent error. It can be calculated as follows :
% = (|actual value-measured value|)/actual value × 100
% [tex]=\frac{27-24}{24} \times 100\\\\[/tex]
%= 12.5%
So, River's percent error is 12.5%.
What kind of slope is this please help!
Type: Positive
Answer: y = 3/2x + 4
Formula: Rise | up = positive | down = negative
------
Run | right = positive | left = negative
Make sure to find 2 perfect points
aight i dont know what I did, but did it helped?
Simplify negative 3 and 1 over 4 minus 6 and 2 over 3.
negative 119 over 12
negative 33 over 12
negative 9 and 3 over 12
9 and 11 over 12
We need to know about mixed fractions to solve the problem. The simplified answer is -119/12.
Mixed fractions is a fraction that is represented by it's quotient and remainder. Mixed fractions are solved by multiplying the denominator with the number in front and then adding the numerator to it, to get the numerator of the simple fraction, the denominator of the simple fraction remains same. In the given question we need to simplify the mixed fractions and then solve it.
[tex]-3\frac{1}{4} -6\frac{2}{3}[/tex] = -13/4-20/3=-39-80/12=-119/12
Therefore the simplified answer is -119/12, option (a) is the correct answer.
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Answer:
119 over 12
Step-by-step explanation:
If you are counting the number of customers visiting your store on a given day, you are working with continuous data.
a. True
b. False
Answer:
b. False
Step-by-step explanation:
The number of costumers that visit your store is a DISCRETE variable because is the set of countable costumers. We count a whole person not parts of a person.
For a continuous variable we are allowed to take any value in an interval. In our case we can not say we had 3.4 costumers. We can say the costumer bought 3.4 gallons of gas for their car.
number or costumers →discrete variable
number of gallons of gas →continuous variable
b. False
urgent please look at the picture
Answer: x = 72 degrees
Step-by-step explanation:
A Pentagon has 540 degrees in total
Divide 540 by the number of angles you have
540 / 5 = 108 degrees
The x angle is on a flat line with the other angle, when you add them you will get 180
So subtract 108 from 180
180 - 108 = x = 72 degrees
heelp mee with thisssss
4. The cube of 4 in expanded form is: 4 × 4 × 4 = 64.
5. Four times three is not the same thing as cube of a number, but rather 4 × 3 = 12.
What is the Cube of a Number in Expanded Form?The cube of a number means the number multiplied by itself three times. With the knowledge of this, we can write the cube of any number in expanded form.
For example, given a number y, the cube of y is = y³
This means that y multiplied by itself three times, which can be written in expanded form as: y × y × y = y³
If y is 2, the cube of 2 would mean: 2³ = 2 × 2 × 2 = 8.
Therefore:
4. Four cubed is 4³
In expanded form, it is: 4 × 4 × 4, which is evaluated as = 64.
5. Four times 3 in numbers is: 4 × 3, which is evaluated as = 12.
Our answer in #5 is different from our answer in #4 because cube of 4 is 4 times itself in 3 places.
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Which graphs show functions with direct variation? Select three options. A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4). A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5). A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).
The graphs which show functions with direct variation include the following:
B. A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).
C. A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).
E. A coordinate plane showing Euro to U.S Dollar Conversion with Euros on the x-axis and U.S Dollars on the y-axis with a line passing through points at (1, 1.4) and (5, 7).
What is a graph?A graph is a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship (direct variation) is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis decreases or increases, the values on the y-axis decreases or increases simultaneously.
In conclusion, the graphs representing direct variation are shown in the image attached below.
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Complete Question:
Which graphs show functions with direct variation? Select three options.
A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).
A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).
A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).
A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).
E. A coordinate plane showing Euro to U.S Dollar Conversion with Euros on the x-axis and U.S Dollars on the y-axis with a line passing through points at (1, 1.4) and (5, 7).
a traffic light at a certain intersection is green 55% of the time, yellow 10% of the time, and red 35% of the time. a car approaches this intersection once each day. let y denote the number of days up to and including the third day on which a red light is encountered. assume that each day represents an independent trial.
The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479
As per the question statement, assuming that "Y" denotes the number of days pass up to and including the first day on which the car encounters a red light, a traffic light at a certain intersection is green 55% of the time, yellow 10% of the time, and red 35% of the time and a car approaches this intersection once each day.
We are required to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)
Here, Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.
And "Y" is the number of days that pass up to and including the first time the car encounters a red light, i.e.,
The distribution here is a geometric one, where
P(Y = 3)
= P(Not red light in initial 2 lights) * P(red light in third light)
= [(1 - 0.35)² * 0.35]
= 0.1479
Probability: It is a branch of Mathematics, that deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.
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Find a polynomial of the specified degree that satisfies the given conditions. degree 4; zeros -1, 1, square root 5; integer coefficients and constant term 10
The polynomial of specified degree is 2x²-8x²+6
Before attempting to answer a polynomial problem, write it out in standard form. Factor it, then when each variable factor reaches zero, set them all to zero. The answers to the derived equations are the solutions to the original equations. Polynomial equations are not always amenable to factoring as a solution.
Polynomials are the sums of terms of the form kxn, where k is any number and n is a positive integer. a description of polynomials, such the polynomial 3x+2x-5. This video covers the ideas of degree, standard form, monomial, binomial, and trinomial.
If √3 is a root
so is -√3
thus, the polynomial is c(x-1)(x+1)(x-√3)(x+√3) = c(x²-1)(x²-3) = c(x⁴-4x²+3)
As the constant term is 6, 3c = 6, so c = 2
2(x4-4x2+3) = 2x⁴-8x²+6
Hence The polynomial of specified degree is 2x²-8x²+6
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2. Find the amount of compound interest earned when $5,000 is invested at 3% for 5 years when
compounded annually.
If the area of quadrilateral SODA is 60, find the value for a.
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=a+5\\ w=a-2\\ A=60 \end{cases}\implies 60=(a+5)(a-2) \\\\\\ 60=\stackrel{F~O~I~L}{a^2+3a-10}\implies 0=a^2+3a-70 \\\\\\ 0=(a+10)(a-7)\implies a= \begin{cases} -10\\\\ 7 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]
notice, we didn't use the negative value, valid though as it is, because in this case "a" can't be negative.
the cost c in dollars of producing v video games is represented by c=6.8v^2 how many video games are produced if the cost is $979.20
Answer:
12 video games
Step-by-step explanation:
[tex]6.8 {v}^{2} = 979.20[/tex]
[tex] {v}^{2} = 144[/tex]
[tex]v = 12[/tex]
Consider each of the households living in your county.
Family 1: A married couple with one child: Due to the high cost of childcare, one parent stays home to care for the child while the other works 40 hours per week making $18 per hour. They also receive a monthly stipend of $50 to cover work related expenses.
Family 2: A married couple with two children who are in school. Both adults are working 40 hours per week with one making $16 per hour while the other makes minimum wage. One of these workers pays $25 per month in union dues.
Family 3: A fulltime student who only has the time to work 20 hours per week making $2 more than the minimum wage. They have a gerbil as a pet.
Part 1: Equations
Write an equation for the monthly wages of each family, including any bonuses or wage reduction.
Minimum wage = 11.50
Family 1: _____________________________
Family 2: _____________________________
Family 3: _____________________________
Part 2: Graph
Graph each equation on the same grid, using different colors to represent each family.
Answer:
Family 2: A married couple with two children who are in school. Both adults are working 40 hours per week with one making $16 per hour while the other makes minimum wage. One of these workers pays $25 per month in union dues.
Step-by-step explanation:
Which of the following represent the solutions to | 4x + 9|> 11 ?
Answer:
x <-5 or x> 1/2
Step-by-step explanation:
I hope this helps! If it does would you please mark me brainliest?
For f(x) = 4x + 1 and g(x) = x2 - 5, find (f- g)(x).
Answer: (f - g)(x) = -x^2+4x+6
Work Shown:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = (4x+1) - (x^2-5)
(f - g)(x) = 4x+1 - x^2+5
(f - g)(x) = -x^2+4x+(1+5)
(f - g)(x) = -x^2+4x+6
Triangle ABC is congruent to triangle A'B'C'. Describe a sequence of rigid motions
that takes A to A', B to B', and C to C'.
The transformations that take triangle ABC to triangle A'B'C' are given as follows:
Reflection over the line y = B.
Translation up and right.
These following categories are used to group transformations on a function's graph.
Translation: The figure's position can be changed by moving to the left, right, or up/down.
Reflections: These can occur over a line or on one of the axes, shifting the direction that the figure is facing.
Rotations: Changing the figure's inclination across a degree measure.
Dilation: The scale factor is multiplied by the coordinates of the original form's vertices, affecting the side lengths of the figure.
The modifications brought about by these transitions are particularly significant in the context of this issue.
For this issue, the triangle's orientation altered, causing a reflection to take place. Since B was the bottom vertex of ABC and is now at the top of A'B'C', the line of reflection is y = B.
B and B' would be in the same place if it weren't for the reflection. A translation up and right was also utilized because A'B'C' lies above and to the right of the line of reflection.
There were no rotations or dilations because the inclination and side lengths were constant.
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The table represents an absolute value function f(x).
x f(x)
−5 2
−4 1
−3 0
−2 1
−1 2
0 3
1 4
2 5
3 6
What are the vertex and range of the function?
Vertex (−3, 0), Range: {y | 0 ≤ y < ∞}
Vertex (−3, 0), Range: {y | −3 ≤ y < ∞}
Vertex (0, 3), Range: {y | 0 ≤ y < ∞}
Vertex (0, 3), Range: {y | 3 ≤ y < ∞}
Answer:
Vertex (−3, 0), Range: {y | 0 ≤ y < ∞}
Step-by-step explanation:
See attached graph.
Enter the correct answer in the box.
Linear function f is shown in the graph. Write
the slope-intercept form of the equation representing this function.
The equation describing the function f(x) = y = 4x - 8
We have a linear function f(x) as shown in the graph.
What is the Slope - intercept form of the equation of a straight line?The Slope - intercept form of the equation of a straight line exists as follows:
y = mx + c
where m is the slope of the line
c be the intercept of the line on the y-axis.
Let c = - 8 be the intercept of the line on y - axes.
Intercepting coordinates on y - axes = (0, -8).
Intercepting coordinates on x - axes = (2, 0).
Slope = m = = 4
Therefore, the equation representing the function f(x),
y = 4x - 8.
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Given m || n, find the value of x and y.
Answer:
see my picture, bro. hope it can help
Answer:
x = 15
y = 50
Step-by-step explanation:
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
The angles (8x + 10)° and y° form a linear pair.
Therefore, equate the sum of these angles to 180° and isolate y:
⇒ (8x + 10)° + y° = 180°
⇒ 8x + 10 + y = 180
⇒ 8x + 10 + y - 10 = 180 - 10
⇒ 8x + y = 170
⇒ 8x + y - 8x = 170 - 8x
⇒ y = 170 - 8x
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
The angles y° and (3x + 5)° are corresponding angles and are therefore congruent:
⇒ y° = (3x + 5)°
⇒ y = 3x + 5
Substitute the second equation for y into the first equation for y and solve for x:
⇒ 3x + 5 = 170 - 8x
⇒ 3x + 5 + 8x = 170 - 8x + 8x
⇒ 11x + 5 = 170
⇒ 11x + 5 - 5 = 170 - 5
⇒ 11x = 165
⇒ 11x ÷ 11 = 165 ÷ 11
⇒ x = 15
Substitute the found value of x into one of the expression for y and solve for y:
⇒ y = 170 - 8x
⇒ y = 170 - 8(15)
⇒ y = 170 - 120
⇒ y = 50
Final solution:
x = 15y = 50a farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. the orchard is divided into equally sized square plots. he has 10 trees of each variety and randomly assigns each tree to a separate plot in the orchard. what are the experimental unit(s) in this study?
The plots are experimental units in this study, then the farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. So ,the answer is the plots.
Based on the given conditions.
First a farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard.The orchard is divided into equally sized square plotsHe has 10 trees of each variety and randomly assigns each tree to a separate plot in the orchard.Since the plots are the things being measured, they serve as the experimental units. The explanatory variable is the type of apple trees because they induce change in the experimental unit by undergoing two distinct treatments. The experiment is being run by the farmer, and the outcome is the quantity of apples. Since each plot is being investigated separately, the orchard as a whole has no bearing on the experiment.Therefore,
The plots are experimental units in this study, then the farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. So ,the answer is the plots.
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To read 8 pages, Shirley needs 40 minutes. At that rate, how many minutes does she need to read each page
She need 5 minutes to reach each page.
What is constant rate?In mathematics, the absence of acceleration is referred to as a constant rate. A function that has a constant rate typically has a second derivative of 0.
The function would be plotted as a straight line on a piece of graph paper if the change in y (or rate) were constant. When anything moves at a fixed, steady pace or at an average speed, it is said to be moving at a constant rate, also known as a uniform rate. For instance, 3 hours pass while driving. In the first hour, it travels 30 miles, in the second hour, 45 miles, and in the third hour, 75 miles.
Given,
time she needs to read 8 pages = 40 minutes
time she needs to read 1 pages = 40/8
=5 minutes
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Name each of the following angles in three different ways.
Recall that the angles can be named:
1) The same as the vertex.
2) With 3 points being the middle point the vertex.
3) A symbol is placed at the angle.
Answer:
1) NML, M, and 3.
2) HGF, G, and 9.
What is the slope of the line that passes through the points (2, -6) and (6, -12)? Write your answer in simplest form.
Answer:
4/-18 or 2/-9
Step-by-step explanation:
The slope of a straight line is a number that indicates how steep the line is. You can calculate the slope of a line by dividing the vertical change, called the rise, by the horizontal change, called the run, between two distinct points on the line.
Slope = change in y divided by change in x or rise divided by run
6 - 2 = 4
-12 - 6 = -18
Answer would be 4/-18
I slept through class now I feel like skinning myself
7. Explain why a+b=d.
Answer:
c + d = 180 (property of 2 angles on a line), we can say that d = 180 - c
a + b + c = 180 (property of a triangle), we can say that a + b = 180 - c
therefore a + b = d
Step-by-step explanation:
If f(x) is a linear function, what is the value of n?
-4
-1
n
02
O
O 9
f(x)
-25
-10
20
Solving the QuestionDetermining the slope
In linear functions, there is a constant difference between the y-values on a table. This means that it increases or decreases by the same amount per every equal interval.
For instance: 2, 4, 6, 8 ⇒ Constant difference of 2 every 1 term
To find the constant difference for this set of values, determine the constant difference (y), and by what interval this difference occurs (x).
Looking at the first two rows of the table, we now know that for every increase in 3 in the x-values yields an increase of 15 in the y-values.
difference between -4 and -1 = 3difference between -25 and -10 = 15We can write it like a fraction, with difference in y on top and difference in x at the bottom:
[tex]\dfrac{15}{3}[/tex] ⇒ [tex]5[/tex]
Congratulations! We have now found the slope of the line.
Solving for nLinear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptPlug in our slope, and solve for the y-intercept by using one of the given points from the table:
[tex]y=5x+b\\-10=5(-1)+b\\-10=-5+b\\b=-5[/tex]
Plug this back into the equation:
[tex]y=5x-5[/tex]
To find n, plug in 20 as y and solve:
[tex]20=5n-5\\25=5n\\n=5[/tex]
Answern = 5
