There’s t h r e e different functions that I have to match with the ones that are on the box
Answers
Since function A has 2 zeros, A has the form:
\(A(x)=f(x)(x-2)(x-4)\)Then, if we divide it by (x-2), we get:
\(\frac{A(x)}{(x-2)}=f(x)(x-4)\)And the remainder is zero.
Additionally, we know that A has 2 unique zeros: then, it cannot have a repeated factor of (x-4).
If we plot function A, we get:
The graph seems to be a polynomial of grade 3, and the leading term is negative.
Notice that
\(\lim _{x\to\infty}A(x)=-\infty\)According to the graph we got. On the other hand:
\(\lim _{x\to-\infty}A(x)=\infty\)Then. Function A matches:
1. When I am divided by (x-2) the remainder is 0.
2. f(4)=0
3. One of my end behaviors is: As x->-infinite, f(x)->infinite
As for function B.
The graph indicates that there are 3 unique zeros: x=1,2,4. That it represents a polynomial of grade 4 and the leading term is positive since the function grows when x->infinite and x->-infinite.
Thus, function B matches:
1. When I am divided by (x-2) the remainder is 0.
2. I have a positive leading coefficient.
3. f(4)=0
4. I have 3 roots
5. One of my end behaviors is: As x->infinite, f(x)->infinite
6. (x-1) is one of my factors
7. I am a Quartic
8. One of my end behaviors is: As x->-infinite, f(x)->infinite
Finally, regarding function C.
\(C(x)=x^3+4x^2-3x-18=(x-2)(x+3)^2\)Then, C(x) is a polynomial of grade 3, and its limits are:
\(\lim _{x\to\infty}C(x)=\infty,\lim _{x\to-\infty}C(x)=-\infty\)Then, the answers for function C are:
1. When I am divided by (x-2) the remainder is 0.
2. I have a positive leading coefficient. (leading coefficient is 1)
3. I have 3 roots
4. One of my end behaviors is: As x->infinite, f(x)->infinite
Related Questions
Which expression is equivalent to 25 x 1/5?
Answers
Answer:
The answer would be E.
When you solve 25 x 1/5, you get 5.
When you solve 25 ÷ 5, you get 5.
The equivalent expression is 25 ÷ 5.
Option E is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example.
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
25 x 1/5
= 25 x 1/5
= 5 x 5 x 1/5
= 5
Now,
1/25 x 5
= 1/5
1/25 x 1/5
= 1/125
1/25 ÷ 1/5
= 1/25 x 5
= 1/5
5 ÷ 25
= 5/25
= 1/5
25 ÷ 5
= 5
We see that,
25 x 1/5 and 25 ÷ 5 have the same value.
Thus,
The equivalent expression is 25 ÷ 5.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
Learn more about the surface area of revolutions here:
https://brainly.com/question/32268747
#SPJ1
Which of these would earn the same interest as a $150 principal at 4% annual interest for 2 years? Select all that apply.
A.$300 at 2% for 2 years
B.$150 at 6% for 18 months
C.$400 at 3% for 1 year
D.$100 at 1% for 8 years
E.$50 at 48% for 6 months
Answers
Answer:
A, C, E are your answers
Step-by-step explanation:
The solution is Option A , Option C and Option E.
The simple interest at a principal of $150 and annual rate of 4 % for 2 years is $ 12
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Given data ,
Let the principal be P = $ 150
Let the annual rate be R = 4 %
Let the time be T = 2 years
Now , the simple interest is calculated as SI = PRT / 100
Substituting the values in the equation , we get
Simple Interest = ( 150 x 4 x 2 ) / 100
Simple Interest = ( 150 x 2 ) / 25
Simple Interest = $ 12
So , the value of Simple Interest is $ 100
Now ,
a)
$300 at 2% for 2 years
Simple Interest = PRT / 100
Substituting the values in the equation , we get
Simple Interest = ( 300 x 2 x 2 ) / 100
Simple Interest = $ 12
c)
$400 at 3% for 1 year
Simple Interest = PRT / 100
Substituting the values in the equation , we get
Simple Interest = ( 400 x 3 x 1 ) / 100
Simple Interest = $ 12
e)
$50 at 48% for 6 months
Simple Interest = PRT / 100
Substituting the values in the equation , we get
Simple Interest = ( 50 x 48 x ( 1/2 ) ) / 100
Simple Interest = 48 / 4
Simple Interest = $ 12
Therefore , the Simple Interest is $ 12
Hence , The solution is Option A , Option C and Option E.
The simple interest at a principal of $150 and annual rate of 4 % for 2 years is $ 12
To learn more about Simple Interest click :
https://brainly.com/question/17282817
#SPJ2
A park walkway surrounds a fountain as shown. Find the area of the walkway. Round to the nearest foot.
Answers
The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.
From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.
The area of the rectangle is;
\(\begin{gathered} \text{Area}=l\times w \\ \text{Area}=30\times42.5 \\ \text{Area}=1275ft^2 \\ \text{The area of the semicircle is,} \\ \text{Area=}\frac{1}{2}(\pi\times r^2) \\ \text{The diameter is 18 ft, and therefore the radius is 9 ft} \\ \text{Area}=\frac{1}{2}(3.14\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=\frac{1}{2}(254.34) \\ \text{Area}=127.17ft^2 \end{gathered}\)Therefore, the area of the shaded region would be,
Area = 1275 - 127.17
Area = 1147.83
Next step is to calculate the other half of the figure (the right side), as follows;
Observe that the outer semi-circle is the shaded region while the inner one is the white portion.
The area is
\(\begin{gathered} \text{Shaded region;} \\ \text{Area}=\frac{1}{2}(\pi\times r^2) \\ \text{Area}=\frac{1}{2}(3.14\times15^2) \\ \text{Area}=\frac{1}{2}(3.14\times225) \\ \text{Area}=\frac{1}{2}(706.5) \\ \text{Area}=353.25ft^2 \\ \text{White region;} \\ \text{Area}=\frac{1}{2}(\pi\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=127.17ft^2 \end{gathered}\)The area of the shaded region is;
Area = 353.25 - 127.17
Area = 226.38
Therefore the total area of the walkway surrounding the fountain is;
Area = 1147.83 + 226.38
Area = 1374.21
Area = 1,374 feet squared (rounded to the nearest foot)
1PLSSSSS, NEED HELP, will give brianlist, I don't have too long.
It's 4 questions.
Answers
Step-by-step explanation:
The rule given:
(x, y) → (x + 2, y - 4)New coordinates of the vertices of ΔABC are:
1) A( - 3, 8) → A'( - 1, 4)2) B(5, 1) → B'(7, - 3)3) C( - 5, 3) → C'( - 3, - 1)4) Point (4, 9) is translated by the rule (x, y) → (x + 42, y - 17)
The image is:
(4 + 42, 9 - 17) = (46, - 8)PLEASE HELP!! What is the surface area of the cone?
Answers
Hope this helped
4*(5-2+3)+3*(9-4+2)+4*(1+2+4)
Answers
Answer:
73
Step-by-step explanation:
You would use PEMDAS...
Parentheses first:4*6+3*7+4*7 No ExponentsMultiply:24+21+28No Division Add:73No SubtractionHOPE THIS HELPS!!!
In ΔTUV, v = 77 cm, u = 72 cm and ∠U=69°. Find all possible values of ∠V, to the nearest 10th of a degree.
Answers
The value of angle V in ∆TUV is 87.4°( nearest tenth)
what is sine rule?Sine rule states that if t, u and v are the lengths of the sides of a triangle, and T, Uand Vare the angles in the triangle; with T opposite t, etc., then t/sinT=u/sinU=v/sinV
sine rule can be used to find one unknown side or angle of a triangle
u/sinU= v/SinV
72/sin69= 77/SinV
SinV = sin69×77÷72
SinV = 0.999
V= sin^-0.999
therefore angle V= 87.4°
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
If EF || DG, and S and T are midpoints, then DG= ? Ef=13 ST=19
Answers
Answer: 25
Step-by-step explanation:
QUICK HELP HURRY! Simplify the expression. \(10^{-2} +10^{-1}\)
Answers
Answer:
11/100 or 0.11
Step-by-step explanation:
10^-2 is also equal to 1/100
10^-1 is also equal to 1/10
Simply add them now:
1/100+1/10
= 1/100+ 10/100
= 11/100=0.11
Hope this helped!
Kelsey had 8 entries in her science journal. Last week, she wrote x more entries. How many entries are in her science journal now?
Answers
Answer:
Kelsey has 8 plus more entries
8 + x
123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.
Answers
Answer:
The nearest whole is 122.99 repeated
Step-by-step explanation:
please help need this done by tomorrow [PHOTO]
![please help need this done by tomorrow [PHOTO]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/DXzMMB4RuAlNOvby44Je0FszF3oJCGyj.jpeg)
Answers
Answer:
15
Step-by-step explanation:
8x-3+4x+3=180
12x=180
x=180/12
x=15
Step-by-step explanation:
The Straight angle is an angle equal to 180 degrees.
So (8x - 3) + (4x + 3) = 180
8x - 3 + 4x + 3 = 180
12x = 180
x = 15
please give me a brainliest answer
noise levels at 3 volcanoes were measured in decibels yielding the following data:142,113,135construct the 90% confidence interval for the mean noise level at such locations. assume the population is approximately normal.step 1 of 4 : calculate the sample mean for the given sample data. round your answer to one decimal place.
Answers
The t critical value and confidence interval must be determined.
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.
For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.
The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.
Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.
According to our question-
At a confidence level of 90%, we have α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05.
Degree of freedom = 4-1 = 3
When we look this up in the t critical value table,
t critical = 2.353
Learn more about confidence interval click here:
https://brainly.com/question/15712887
#SPJ4
Which method is used in elimination to find the solutions of 4a - 7b = 9 and 8a - 7b = 13?
Answers
Explanation:
First off I believe that it should be set up like so: 4a - 7b +9 = 8a -7b + 13 if you don’t know already he first step before we eliminate is to combine like terms that are on the same side which unfortunately for this problem there are none so we go straight to eliminating. The best way to eliminate is to find what’s smallest such as -7b which we switch to +7b and add to the -7b on her other side or right side of the problem which gives us 0. Now let’s do 4a and 8a, we first should turn 4a into -4a and subtract that from 8a to get 4a. Now lastly we are left with 9 and 13 which we will turn he 9 into -9 and subtract from 13 getting us 4 and 4a=4 which is the same as 4a divided by 4 is one
The circumference of a circle is 51.496 kilometers. What is the circle's radius?
Use 3.14 for a.
Answers
Answer:
Circle's radius is 6.26 km
Step-by-step explanation:
circumference = 2*pi*radius
radius = circumference / (2*pi)
taking pi as 3.14
radius = 51.496 / (2*3.14)
radius = 6.26 km
write and solve your own word problem for 1.3 x 2.79? solve without using a calculator
Answers
Answer:
The answer is 3.62
Step-by-step explanation:
Here is a word problem that you can use.
Jimmy has exactly 2.79 points. His other friend Robert has 1.3 times his points. How many points does Robert have?
(And yes, I wrote this problem myself and I do not mind you using it! )
Hopefully this helped!
Answer:
You buy 1.3 pounds of cheese, and 2.79 is the price for this cheese, how much to do you spend for cheese.
Find the product 4 2/3 x 3 3/4
Answers
Answer:
45.6
Step-by-step explanation:
trust me bro(don't)
Answer:
17 1/2
Step-by-step explanation:
The quickest way is to put it as it improper fraction and then multiply it like normal.
what would be your first step in completely factoring 6a^2-15a+6
Answers
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
for similar questions on factoring.
https://brainly.com/question/28260513
#SPJ8
7 1/2 pt = ______________ qt pleasesssss
Answers
photomath
Step-by-step explanation:
just use photomath
3.75 Quarts
Step-by-step explanation:
That is the exact answer I believe.
I checked many websites and they gave me the same answer
leo
toring
29
Due Dec 6 by 11:59pm
Question 13
Ch. 9 Quadratics Homework (Copy)
Score: 12/17 12/17 answered
▼
The width or short side is
The length or long side is
Points 20
Submit Question
The length of a rectangle is 6 feet longer than it is wide. If each side is increased 6 feet, then the area is
multiplied by 2. What was the size of the original rectangle?
<
Submitting an external too
Answers
The width or short side is 12 feet
The length or long side is 18 feet
What is Area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.
Let Width= x feet
so, as per question Length = x+6 feet
Area = Length x Width = x(x+6) = \(x^{2} +6x\)
According to the question each side is increased 6 feet
New Length = x+12 feet
New Width = x+6 feet
New Area = Length x Width\(= 2x(x+6)\) <the area is multiplied by 2>
Length x Width=\((x+6)(x+12) = 2x(x+6)\)
x+12=2x
x=12 feet
so, original width = 12 feet
original length = 18 feet
Learn more about Area from the ink below
https://brainly.com/question/27683633
#SPJ1
PLS HELP ME
Write 3.94 x 10-2 in standard form.
Answers
Aladder is leaning against a building so that the distance from the ground to the top of the ladder is 1 foot less than the length of the ladderFind the length of the ladder the distance from the bottom of the ladder to the building is 5 feet
Answers
Answer:
13
Step-by-step explanation:
5²+x²=(x+1)²
25+x²=x²+2x+1
2x=24
x=12
ladder = x+1 = 12+1 = 13
A truck is carrying passion fruit juice, cherry juice, and mango juice bottles in a ratio 1:2;7. If there are 34 cherry juice bottles, then how many mango juice bottles are there?
Answers
Answer:
119 bottles
Explanation:
The given ratio is:
\(\text{Passion Fruit juice: Cherry juice: Mango juice=1:2:7}\)There are 34 cherry juice bottles.
Let the total number of mango juice bottles = y.
Then, comparing cherry juice and mango juice:
\(\begin{gathered} \frac{2}{7}=\frac{34}{y} \\ 2y=34\times7 \\ y=\frac{34\times7}{2} \\ y=119 \end{gathered}\)There are 119 bottles of mango juice.
Find the surface area of the right triangle prism(above) using the net (below)
Answers
Answer:
144
Step-by-step explanation:
2( 1/2 × 3 × 4 ) + ( 11 × 5) + ( 11 × 4 ) + ( 11 × 3)
= 12 + 55 + 44 + 33
= 144
Solve.
Determine how many Hamilton circuits a complete graph with 23 vertices has.
Options:
22!
23!
23
232
Answers
Answer:
22!
Step-by-step explanation:
A complete graph with N vertices has (N-1)! Hamilton circuits. Half of the circuits are mirror images of the other half, so if you're looking for unique circuits, there are actually only half this many.
N = 23
Number of Hamilton circuits = (N-1)! = (23-1)! = 22!
solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
Answers
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
For more references on expression, click;
brainly.com/question/14083225
#SPJ1
4x
Store A $25 for a 45 minute lesson
Store B. $30 for a 1 hour lesson
Store C $45 for a 1.5 hour lesson
Store D. $80 for three 1 hour lessons
Julle wants to purchase swim lessons for her son. There are four different stores that offer swim lessons. Based on the lowest cost per minute, which store has the BEST dea
4x A
4x B
x
C
4x D
Store B
Store A
Store D
Store C
Answers
The store with the best deal is given as follows:
Store D.
How to obtain the store with the best deal?The store with the best deal is obtained applying the proportions in the context of the problem.
The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.
Hence the hourly cost for each store is obtained as follows:
Store A: 25/0.75 = $33.3 per hour. (45 minutes = 45/60 hour = 0.75 hour).Store B: $30/1 = $30 per hour.Store C: $45/1.5 = $30 per hour.Store D: $80/3 = $26.7 per hour -> best deal.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Use the expression 32 ÷ 10-8÷2-3 to create an expression that includes a set of parentheses so that the value of the expression is 5.
Answers
The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:
32 ÷ (10 - (8 ÷ 2) - 3)
First, we evaluate the expression inside the parentheses:
8 ÷ 2 = 4
10 - 4 - 3 = 3
So now the expression becomes:
32 ÷ 3
=10.67
This is not equal to 5.
To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:
32 ÷ (10 - (8 ÷ (2 - 3)))
Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:
8 ÷ (-1) = -8
So now the expression inside the parentheses becomes:
10 - (-8) = 18
So the entire expression becomes:
32 ÷ 18 = 1.78
This is still not equal to 5.
Another way to make the value of the expression equal to 5 is:
(32 ÷ (10 - 8)) ÷ 2 - 3
Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:
32 ÷ 2 - 3 = 13
So the entire expression becomes:
13
And this is equal to 5.
Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:
(32 ÷ (10 - 8)) ÷ 2 - 3
To know more about algebraic expressions visit:
brainly.com/question/17499155
#SPJ9
I need a little help here please
Answers
Answer:
Plot points at (0,1) and (-3,3) and draw a line going through both points.
Step-by-step explanation:
Let's start by graphing the y intercept.
y=mx+b
m is the slope. b is the y intercept. Since the equation is y=-2/3x+1, we can conclude the y intercept is 1. We graph a point at (0,1).
If you didn't know the y intercept is where the line intercepts the y-axis.
Now, from the point (0,1) we go up 2 and to the left 3 as it is a negative slope. We reach (-3,3). Plot a point there. Then draw a line going through both points. There's your line!