Answer:
She will run a distance of 1095.78 miles per year.
Explanation:
Number of days in a year = 365.25
Number of days in a week = 7
Number of weeks in a year = 365.25/7 = 52.18 weeks.
Tomika plans to run 84 miles in 4 weeks.
Distance run by Tomika in 1 week = 84/4 = 21 miles.
Distance run by Tomika in 1 year = 21*52.18 = 1095.78 miles
So she will run a distance of 1095.78 miles per year.
If Tomika continues the pattern, she will run approximately 1,092 miles in a year.
How to get the miles ranThere are 52 weeks in a year, so you can divide 52 by 4 to find out how many 4-week periods there are in a year:
Number of 4-week periods in a year = 52 weeks / 4 weeks/period = 13 periods
Now, multiply the miles she runs in each 4-week period (84 miles) by the number of 4-week periods in a year (13 periods):
Total miles in a year = 84 miles/period × 13 periods
Total miles in a year = 1,092 miles
So, if Tomika continues the pattern, she will run approximately 1,092 miles in a year.
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Apply the distributive propertyto create an equivalent expression. 1/2(6e-3f-3/4)
3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]
multiply each of the terms in the parenthesis by [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] (6e - 3f - [tex]\frac{3}{4}[/tex] )
= 3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]
Answer:
[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{1}{2}(6e-3f-\frac{3}{4})[/tex]
To find an equivalent expression, we need to use the distributive property, that is, we have to multiply [tex]\frac{1}{2}[/tex] with each term that's inside the parenthesis.
[tex]\frac{1}{2}(6e-3f-\frac{3}{4})\\\frac{6e}{2}-\frac{3f}{2}-\frac{3}{2(4)}\\ 3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Therefore, the equivalent expression is
[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Remember that when we multiply fractions, we have to do it in a linear way, that is, numerators multiply each other, and denominators multiply each other. That means you CAN'T multiply a numerator with a denominator.
If the height of a right triangle is 24 inches and the the area of the triangle is 120 square inches, what is the length of the base?
At a peanut butter factory, the daily production cost, C, for j jars of peanut butter is modeled by the graph below. What are the domain and range of the function C(j)?
A. Domain: All Real Numbers
Range: C>5,000
B.domain: all real numbers
Range: C>2,500
C.domain: J>0
Range:C>5,000
D.domain:j>0
range:C>2,500
Answer:
Option D
Step-by-step explanation:
From the graph we find that the graph runs only in the I quadrant.
Hence x,y are positive only
Next is y intercept = 2500 and y increases continuously after that.
This implies y >=2500
Hence range is C>2500
Domain is the no of jars of peanut butter.
Hence j>0
In other words, 2500 is the fixed cost even when there is no production and cost cannot be less than 2500 at any time.
Production can be any number of jars from 0 onwards.
Hence option D
(-4-7i)-(5-6i)
Simplify.
Answer is: −4−7i−(5−6i) = −9−i
The given complex expression is (-4-7i) - (5-6i). The simplification would give −9−i.
What are complex numbers?Any complex number can be written as
z = a + ib
The given complex expression is
(-4-7i) - (5-6i)
The simplification will be
= −4−7i−(5−6i)
= −9−i
Therefore, The simplification would give −9−i.
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Does this table represent a function ?why or why not ?
(C) is correct answer. The values in the table assign to each x only one y value.
Answer:
c is the best answer for the question
Step-by-step explanation:
Find the measure of
<D = 360 - (80 + 115 + 100)
<D = 360 - 295
<D = 65
Answer
<D = 65°
A cylinder has a radius of 12 cm and height of 16 cm. What volume for the solid/
The volume of a cylinder is given by the multiplication of the base area and the height.
The base is a circle, so its area is given by
[tex] A = \pi r^2 = 144\pi [/tex]
If we then multiply this by the height, we have
[tex] V = A\cdot h = 144\pi \cdot 16 = 2304\pi[/tex]
What is 6,000 in a whole number multiplied by ten
Multiplying a number by 10 simply means to add a 0 at the end of the number, or to shift the decimal separator one unit to the right. So, for example,
[tex] 3 \cdot 10 = 30,\ -152 \cdot 10 = -1520,\ 25.467 \cdot 10 = 254.67 [/tex]
So, in your case, you have to add a 0 at the end of 6000, obtaining
[tex] 6000 \cdot 10 = 60000 [/tex]
You and three friends start a small business the total income is 1,820 and the total expenses are 360 you share the profit evenly how much do each of you get
Answer:
Each of them get 365.
Explanation:
Total income = 1820
Total expense = 360
Total profit = Total income - Total expense = 1820 - 360 = 1460
Number of persons sharing the profit = 4
Profit got by each person = Total profit/ number of persons sharing profit
= 1460/4 = 365
So each of them get 365.
Eva brick makes and sells her own cranberry apple juice in jug a s
The domain of y = 1/x - 10 is all real numbers except x = 10
TRUE or FALSE?
TRUE
because if we substitute the value of x = 10 to the equation, then we have quotient with divide by zero!
[tex]y=\dfrac{1}{x-10}\to f(x)=\dfrac{1}{x-10}\\\\f(10)=\dfrac{1}{10-10}=\dfrac{1}{0}\ !!!![/tex]
Are my answers correct? Precalculus!!
Answer:
Unfortunately, your answer is not right.
Step-by-step explanation:
The functions whose graphs do not have asymptotes are the power and the root.
The power function has no asymptote, its domain and rank are all the real.
To verify that the power function does not have an asymptote, let us make the following analysis:
The function [tex]y = x ^ n[/tex] , when x approaches infinity, where does y tend? Of course it tends to infinity as well, therefore it has no horizontal asymptotes (and neither vertical nor oblique)
With respect to the function [tex]y= \frac{1}{x}[/tex] we can verify that if it has asymptote horizontal in y = 0. Since when x approaches infinity the function is closer to the value 0.
For example: 1/2 = 0.5; 1/1000 = 0.001; 1/100000 = 0.00001 and so on. As "x" grows "y" approaches zero
Also, when x approaches 0, the function approaches infinity, in other words, when x tends to 0 y tends to infinity. For example: 1 / 0.5 = 2; 1 / 0.1 = 10; 1 / 0.01 = 100 and so on. This means that the function also has an asymptote at x = 0
The question involves precalculus, a High School or College level Mathematics topic, focusing on the accuracy and reasonableness of answers related to engineering principles. Students must consider significant figures, units of measure, and logical consistency within their mathematical processes.
Explanation:The student's question pertains to the subject of Mathematics, specifically within the realm of Precalculus, which is typically taught at the High School or College level. The inquiry involves reviewing the process of answering questions in mathematics and science as it relates to engineering. This includes checking whether an answer is reasonable in terms of units, magnitudes, and mathematical consistency. For instance, in the context of a precalculus class, students are expected to pay close attention to significant figures, units of measure, and ensuring answers are logically consistent with the problem presented.
The data set provided from Susan Dean's spring precalculus class can be used as an example for various statistical calculations. When dealing with such data, students need to organize it in a clear format, identify central tendencies (like mean, median, mode), and ensure that final answers are expressed with the proper significant figures and units. These practices are crucial for nd are rerced in a variety of STEM courses.
When it comes to the review questions mentioned, while specific questions are not provided, it is clear that students are encouraged to identify all correct answers to demonstrate their understanding of how mathematics and science connect with engineering. This holistic approach reflects real-world problem-solving where multiple solutions or considerations often exist.
Misty and Yesenia have a group of Base Ten Blocks. Misty has six more blocks than Yesenia. Yesenia's blocks represent 17. Together they have 22 blocks, and the total numbers of blocks represent 85. What blocks could each girl have? What is the value?
Answer:
Yesenia has qty 1 of 10s and qty 7 of 1s
Misty has qty 6 of 10s and qty 8 of 1s
Step-by-step explanation:
Note that there are two different types of blocks: 1s and 10s. Let x represent the number of 10s and y represent the number of 1s.
Value of the blocks Number of blocks
Yesenia: 1x + 7y 8
Misty:
Total: 8x + 5y 22
Start with the number of blocks that Misty has: 22 - 8 = 14
Next, how many 1s can be added to Yesenia's to make 5? 15 - 7 = 8
How many blocks are left over from Misty's 14? 14 - 8 = 6
********************************************************************************************
Fill in the information:
Value of the blocks Number of blocks
Yesenia: 1x + 7y 8
Misty: 6x + 8y 14
Total: 8x + 5y 22
Efren leaves home at 9am and walks 4 miles per hour. His brother, gregory leaves half an hour later and runs 8.5 miles per hour in the same direction as efren. Predict the time at which gregory will catch up to efren
Answer:
Gregory will catch up Efren after 26 minutes 40 seconds.
Explanation:
Distance traveled = Speed x Time
Speed of Efren = 4 mi/h
Speed of Gregory = 8.5 mi/h
Let the time of catch up be t hours.
Time of journey of Efren before catch up = (t+0.5)hours, since he starts before half hour.
Distance traveled by Efren = 4 x (t+0.5) miles
Time of journey of Gregory before catch up = t hours.
Distance traveled by Gregory = 8.5 x t miles
If they catch up the distance traveled by them is same, so equating both distances.
4 x (t+0.5) = 8.5 x t
4.5t = 2
t = 0.44 hours =26.67 minutes = 26 minutes 40 seconds.
So Gregory will catch up Efren after 26 minutes 40 seconds.
Gregory will catch up to Efren approximately at 9:56am.
To find out when Gregory will catch up to Efren, we need to set up an equation based on their speeds and the time they travel.
Calculate the head start distance: Efren leaves at 9am and walks at 4 miles per hour.
Gregory leaves at 9:30am, so Efren has a 0.5-hour head start. Distance head start = speed × time = 4 miles/hour × 0.5 hours = 2 milesDetermine their relative speed: Gregory runs at 8.5 miles per hour while Efren walks at 4 miles per hour.
Relative speed = Gregory's speed - Efren's speed = 8.5 miles/hour - 4 miles/hour = 4.5 miles/hourCalculate the time for Gregory to catch up: We need to divide the head start distance by their relative speed.
Time = Distance / Relative speed = 2 miles / 4.5 miles/hour ≈ 0.444 hours (which is roughly 26.67 minutes)Find the catch-up time: Gregory leaves at 9:30am, so add the catch-up time to this.
Catch-up time ≈ 9:30am + 26.67 minutes ≈ 9:56amTherefore, Gregory will catch up to Efren at approximately 9:56am.
Use Remainder Theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5 - 7x^3 -
11x^2 + 2
Answer:
(x - 2) is not a factor of f(x) = 3x^5 - 7x^3 - 11x^2 + 2
Step-by-step explanation:
According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).
So first we will divide f(x) by (x - 2) using long division to get:
(3x^5 - 7x^3 - 11x^2 + 2) / (x - 2)
= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)
= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)
= [tex]\frac{-2 + 3x^{5} - 7x^{3} - 11x^{2} + 2x}{x - 2} - 2[/tex]
Therefore the remainder is -2.
Now check x = 2 for 3x^5 - 7x^3 - 11x^2 + 2:
3(2)^5 - 7(2)^3 - 11(2)^2 + 2 = -2
The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.
So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .
Answer:
Answers to the Complex Zeroes of a Polynomial Function Quiz Part 1 (I tried to signify each question)
Step-by-step explanation:
1. C, f(x) is a polynomial function. The degree is 5... -7
2. A, f(x)=7x^9-3x^2-6
3. C,D
4. Written
5. Rational Zero Theorem, B
6. Written
7. B, -5,-2, 3
8. A, (4 + 6i, -2 -11i)
9. D, (2,3, plus minus sqrt 5i)
find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.
1. (4.1) slope = 6
2. (6,-3) slope= -5
3. (-8, 2) slope = -1/2
4. (-7,-1) slope = 0
The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
The slope-intercept form of a line:
[tex]y=mx+b[/tex]
1.
[tex]m=6,\ (4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute
[tex]y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}[/tex]
2.
[tex]m=-5,\ (6,\ -3)[/tex]
Substitute
[tex]y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}[/tex]
3.
[tex]m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}[/tex]
4.
[tex]m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}[/tex]
3/4(8x-4)=7x-5x+6
Solve this answer
Debi walks laps around the mall for exercise during the winter months. The table represents the number of steps recorded on her meter as she walks laps around the mall one day. Which statement is true about the graph of the line representing Debi’s data?
a. Debi walks 1,875 steps per lap around the mall.
b. One lap around the mall is equal to about 2,425 steps.
c. One lap around the mall is equal to 4,300 steps.
d. Debi walks 6,175 steps per lap around the mall.
Laps / Steps
0 / 1,875
1 / 4,300
2 / 6,725
3 / 9,150
4 / 11,575
Answer:
The correct option will be: b. One lap around the mall is equal to about 2,425 steps.
Step-by-step explanation:
Here, we will just find the slope of the line representing Debi’s data. For that, we will take any two data from the table in form of point like [tex](x,y)[/tex]
Lets take two points as [tex](0, 1875)[/tex] and [tex](2, 6725)[/tex]
Formula for finding the slope is: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] are two given points.
Here, [tex]x_{1}= 0 , y_{1}= 1875 , x_{2}=2 , y_{2}=6725[/tex]
So, plugging these values into the above formula, we will get......
[tex]m= \frac{6725-1875}{2-0}=\frac{4850}{2}=2425[/tex]
That means, one lap around the mall is equal to about 2,425 steps.
Answer:
One lap around the mall is equal to about 2,425 steps.
Step-by-step explanation:
Find the area of the rectangle below by multiplying its length and width.
(7x-1) units
(3x-2) units
Hello!
When multiply binomials together, we should use the FOIL method.
The FOIL method is an acronym for First, Outer, Inner, and Last.
First, let's set up the expression.
(7x - 1)(3x - 2)
Now, we can multiply in accordance with the FOIL method.
First: 7x · 3x = 21x²
Outer: 7x · -2 = -14x
Inner: -1 · 3x = -3x
Last: -1 · -2 = 2
Now, we simplify the inner terms.
21x² - 14x - 3x + 2
21x² - 17x + 2
Therefore, the area of the rectangle is 21x² - 17x + 2.
The area of the rectangle is (21x² - 17x + 2) units².
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Given the length of the rectangle is (7x-1) units, while its breadth is (3x-2) units. Therefore, the area of the rectangle is,
Area of rectangle = (7x-1) units × (3x-2) units
= 21x² - 14x - 3x + 2
= 21x² - 17x + 2 units²
Hence, the area of the rectangle is (21x² - 17x + 2) units².
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On his fruit stand, Mr. Roberts has 13 papayas 23 fruit stares 35 mangoes and 19 strawberries. What is the ratio of the number of mangoes to the total number of pieces of fruit?
Answer: [tex]\frac{7}{18}[/tex] = 7:18
Step-by-step explanation:
[tex]\frac{35(mangos)}{13(papayas)+23(stares)+35(mangos)+19(strawberries)} = \frac{35(mangos)}{90(total fruit)}[/tex]
[tex]\frac{35}{90}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{7}{18}[/tex]
At the start of 2014 Tim's house is worth ?100000. The value of the house increase by 10% every years work out the value of his house at the start 2018
Answer:
Worth of Tim's house in 2018 = 146410 $
Explanation:
Worth of house in 2014 = $100000
Raise in worth per year = 10 % = 0.1
Worth of house in 2015 = 100000 + 0.1 * 100000 = 110000 $
Worth of house in 2016 = 110000 + 0.1 * 110000 = 121000 $
Worth of house in 2017 = 121000 + 0.1 * 121000 = 133100 $
Worth of house in 2018 = 133100 + 0.1 * 133100 = 146410 $
So, worth of Tim's house in 2018 = 146410 $
Easy Method;
No of years considering = 4
Initial worth = $100000
Rate of increase = 0.1
Final worth [tex]=100000(1+0.1)^4=146410$[/tex]
Worth of Tim's house in 2018 = 146410 $
The value of Tim's house at the start of 2018 will be $ 146,410.
Given that at the start of 2014 Tim's house is worth $ 100000, and the value of the house increase by 10% every year, to determine the value of his house at the start of 2018 the following calculation must be performed:
100,000 x 1.10 ^ (2018 - 2014) = X 100,000 x 1.10 ^ 4 = X 100,000 x 1,4641 = X 146,410 = X
Therefore, the value of Tim's house at the start of 2018 will be $ 146,410.
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Writing a Polynomial Function of a Graph:
use the fact that the graph passes through (0,36) to find the coefficient a in f(x)=a(x+3)(x+1)(x-2)(x-3)
a=???
we can see that
zeros are at x=-3 , x=2 , x=3
now, we can set up function
[tex]f(x)=a(x+3)(x-2)(x-3)[/tex]
now, we can select any one point and then we can find 'a'
(0,36)
x=0 and f(x)=36
we can plug it and then we can find 'a'
[tex]36=a(0+3)(0-2)(0-3)[/tex]
[tex]a=2[/tex]
now, we can plug it back
and we get
[tex]f(x)=2(x+3)(x-2)(x-3)[/tex]
now, we can multiply it
we get
[tex]f(x)=2x^3-4x^2-18x+36[/tex]............Answer
Select the expression that represents a rational function
the answer is b f(x)=-4/x-5
What is the LCM of 8x2y2 and 10x2y3?
A.40x2y3
B.40x4y5
C.80x2y3
D.80x4y6
The multiples of 8 are: 0, 8, 16, 24, 32, 40, 48, ...
The multiples of 10 are: 0, 10, 20, 30, 40, 50, ...
LCM(8, 10) = 40
LCM(x²y², x²y³) = x²y³
Therefore
LCM(8x²y², 10x²y³) = 40x²y³The LCM of 8x²y² and 10x²y³ is Option A: 40x²y³.
Identify the LCM of the numerical coefficients.
For 8 and 10, the LCM =40.
Determine the highest power of each variable present in the terms,
For x2 from both terms, the highest power is [tex]x^2[/tex].
For y2 and y3, the highest power is [tex]y^3.[/tex]
Therefore, the LCM of [tex]8x^2y^2[/tex] and [tex]10x^2y^3[/tex]is [tex]40x^2y^3[/tex].
The correct answer is Option A: [tex]40x^2y^3.[/tex]
Kate wants a bicycle that normally costs $360 but there a sale in which all bicycles costs 5/6 of the regular. What is the price of the bicycle.
What are the domain and range of the function below?
Answer:
Domain ={0,infinity)
Range = (-infinity, 4]
Step-by-step explanation:
Given a graph with curve which has y intercept 4.
It passes x axis at 4 and extends fully
The domain is the set of values x can take
In the graph horizontal axis is x axis.
Hence from the graph we see that x can take values from 4 including 4 upto infinity.
Hence domain is x>=4
For range, we consider the values of y as per graph.
WE find that y is not taking values >4
Hence Range = (-infty, 4]
Answer:
[tex]Domain=[0,\infty)[/tex]
[tex]Range=(-\infty,4][/tex]
Step-by-step explanation:
We need to find the domain and range of the function.
Domain : It is the set of input values or x values. In a graph, domain of the function represented by the x-axis.
Range : It is the set of output values or y values. In a graph, range of the function represented by the y-axis.
From the given graph it is clear that it is defined for [tex]0\le x<\infty[/tex] and [tex]-\infty <y\le 4[/tex].
We have closed circle at (0,4). It means, 0 is included in the domain and 4 is included in the range.
[tex]Domain=[0,\infty)[/tex]
[tex]Range=(-\infty,4][/tex]
Therefore, [tex]Domain=[0,\infty)[/tex] and [tex]Range=(-\infty,4][/tex].
Options are
A. 110
B. 410
C. 502
D. 775
Answer:
502
Step-by-step explanation:
4560/x=100/11
(4560/x)*x=(100/11)*x - we multiply both sides of the equation by x
4560=9.09*x - we divide both sides of the equation by (9.09) to get x
4560/9.09=x
501.6=x
x=501.6
why hello there
Your answer is c i was gonna give a better answer but the other dude did it
The play director spent 190190190 hours preparing for a play. That time included attending 353535 rehearsals that took varying amounts of time and spending 93 \dfrac{3}{4}93 4 3 ? 93, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+93\dfrac{3}{4}=19035x+93 4 3 ? =19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?
Answer:
The equation [tex]35x+93\frac{3}{4} =190[/tex] gives average time spent on 35 rehearsals.
Step-by-step explanation:
We are supposed to find that what question does the equation [tex]35x+93\frac{3}{4} =190[/tex] finds answer of.
We can see that 35x represents time spent on 35 rehearsals and [tex]93\frac{3}{4}[/tex] is time spent on other responsibilities related to play. The sum of these times equals to total time spent on preparing the play.
Now let us solve our equation step by step.
[tex]35x+\frac{375}{4} =190[/tex]
After subtracting [tex]93\frac{3}{4}[/tex] hours from 190 hours we will get time spent on 35 rehearsals.
[tex]35x =190-\frac{375}{4}[/tex]
[tex]35x =\frac{760-375}{4}[/tex]
[tex]35x =\frac{385}{4}[/tex]
Time spent on 35 rehearsals is 96.25 hours and we are told that each rehearsal took different amount of time. Dividing 96.25 by 35 we will get average time spent on each rehearsal.
[tex]x =\frac{96.25}{35}=2.75[/tex]
Therefore, equation [tex]35x+93\frac{3}{4} =190[/tex] finds average time spent on 35 rehearsals.
Answer:
What was the average length of each rehearsal?
Step-by-step explanation:
Khan Academy
If cosx is approximately 0.9511, what is the measurement of x to the nearest degree? Approximately, what is the sine of the angle that is complementary to x?
Answer:
Using the calculator angle whose cos is 0.9511 is 18 degrees
Sine of the complementary angle = 0.9511 also
Step-by-step explanation:
The sine of the complementary angle( which is 90-18 = 72 degrees) is same value 0.9511
Answer: 18 degrees and 0.9511
Step-by-step explanation:
18°; 0.9511
Cos-1(0.9511) = 18°
The complement of 18° is 72°. The sine of 72° is the cos of 18°, which is 0.9511.
Which of the following is the correct expansion of (y + 1)(y2 + 2y + 3)?
y3 + 3y2 + 5y + 3
y3 + y2 + y + 3
y3 + 6y2 + 5y + 9
y3 + 5y2 + 6y + 3
Answer:
y3 - 4 y2 + 2 y - 5
Step-by-step explanation:
The correct expansion of (y + 1)(y² + 2y + 3) is y³ + 3y² + 5y + 3, achieved through the FOIL method and combining like terms.
The correct expansion of (y + 1)(y² + 2y + 3) is obtained by multiplying each term in the first polynomial by each term in the second polynomial and then simplifying the result. This process is known as FOIL (First, Outer, Inner, Last), which is an acronym that stands for multiplying the first terms, the outside terms, the inside terms, and the last terms of each binomial.
To expand (y + 1)(y² + 2y + 3), we perform the following steps:
Multiply the first terms: y * y² = y³Multiply the outside terms: y * 2y = 2y²Multiply the inside terms: 1 * y² = y²Multiply the last terms: 1 * 2y = 2yMultiply the last terms of the polynomials: 1 * 3 = 3Now, add up all the products: y³ + 2y² + y² + 2y + 3.
Combine like terms to simplify: y³ + (2y² + y²) + (2y) + 3
The final answer is y³ + 3y² + 5y + 3.