Answers
Answer:
a) f(x) = (x-5)/((x-3)(x-10))
b) f(x) = (x-4)/((x+4)(x^2+1))
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4))
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5))
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9))
Step-by-step explanation:
Ordinarily, we think of a horizontal (or slant) asymptote as a line that the function nears, but does not reach. Some of these questions ask for the horizontal asymptote to be zero and for a function zero at a specific place. That is, the actual value of the function must be the same as the asymptotic value, at least at one location.
There are several ways this can happen:
add a vertical asymptote on the same side of the zero as the required vertical asymptote. The function will cross the horizontal asymptote and then approach from the new direction.add a vertical asymptote on the other side of the zero from the required asymptote. The function zero will then be between the asymptotes, and the function will approach the asymptote in the expected way. (See the attachment)add complex zeros in the denominator. The function will cross the horizontal asymptote and approach it from the new direction. This does not add any asymptotes to the function.To make the horizontal asymptote be zero, the degree of the denominator must be greater than the degree of the numerator. That is, there must be additional real or complex zeros in the denominator beyond those for the required vertical asymptotes.
__
a) f(x) = (x-5)/((x-3)(x-10)) . . . . vertical asymptote added at x=10 to make the horizontal asymptote be zero
__
b) f(x) = (x-4)/((x+4)(x^2+1)) . . . . complex zero added to the denominator to make the horizontal asymptote be zero
__
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4)) . . . . factor of 2 added to the numerator to make the horizontal asymptote be 2. Numerator and denominator degrees are the same. (See the second attachment.)
__
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5)) . . . . similar to problem (c)
__
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9)) . . . . similar to the previous two problems (See the third attachment.)
_____
You remember that the difference of squares factors as ...
a² -b² = (a-b)(a+b)
so the factor that gives zeros at x=±3 can be written (x²-9).
To write a rational function with specific characteristics, define the characteristics and use factors to create the desired asymptotes and holes.
Explanation:To write a rational function with specific characteristics, we need to define the characteristics first. For example, let's say we want a function with a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a hole at x = -3. We can write the rational function as:
f(x) = (x + 3)(x - 2) / (x - 2)
In this function, the factor (x - 2) in both the numerator and denominator creates the vertical asymptote at x = 2. The (x + 3) factor in the numerator creates the hole at x = -3, and the horizontal asymptote at y = 0 is determined by the highest power of x in the numerator and the denominator being the same, which is x^1.
Learn more about Rational Functions here:https://brainly.com/question/27914791
#SPJ3
Related Questions
4\sqrt(2)+10
Is this rational or not?
Answers
Answer:
not rational
Step-by-step explanation:
√2 is irrational. Any arithmetic operation (addition, subtraction, multiplication, division) performed on that number and any rational number will result in an irrational number (except for multiplication by 0).
Answer:
Step-by-step explanation:
Because of that sqrt, this expression is irrational. A rational expression is one that can be expressed as the ratio of two integers.
In the figure below, if angle ZYX measures 23 degrees, then arc XY measures 45 degrees.
Answers
Answer:
FALSE
Step-by-step explanation:
Assuming ZY is a tangent, the measure of the arc will be twice the measure of the angle. If the angle ZYX is 23°, the measure of arc YX will be 46°.
A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total number of hours worked by this person was
Answers
Final answer:
The total number of hours worked by the person is calculated by adding the working times from two segments of the day. The morning session contributes 3 hours and 15 minutes, and the afternoon session adds 4 hours and 45 minutes. The combined total working hours are 8 hours.
Explanation:
To calculate the total number of hours worked by the person, we need to break down their workday into segments and sum up the time they spent working.
Morning session: From 8:30 AM to 11:45 AM
Afternoon session: From 12:30 PM to 5:15 PM
Calculating each session separately, we get:
Morning session: 11:45 AM - 8:30 AM = 3 hours and 15 minutes
Afternoon session: 5:15 PM - 12:30 PM = 4 hours and 45 minutes
Adding both sessions together:
3 hours and 15 minutes + 4 hours and 45 minutes = 8 hours total
Final Calculation:
3 hours 15 minutes + 4 hours 45 minutes = 7 hours 60 minutes = 8 hours
Therefore, the total number of hours worked by this person was 8 hours.
In your drawer you have 10 white socks, 6 black socks, 4 brown socks and 2 blue socks. Your roommate is still asleep, and you cannot turn the light on while you get dressed. You reach in blindly and grab two socks. What is the probability of pulling out a matching pair of black socks?
Answers
Answer: Required probability is,
[tex]\frac{36}{231}[/tex]
Step-by-step explanation:
Given,
White socks = 10,
Black socks = 6,
Brown socks = 4,
Blue socks = 2,
Total socks = 10 + 6 + 4 + 2 = 22,
Thus, the total ways of choosing any 2 socks = [tex]^22C_2[/tex],
Now, the ways of choosing a black socks = [tex]^6C_1[/tex]
Thus, ways of choosing a pair of black socks = [tex]^6C_1\times ^6C_1[/tex]
Hence, the probability of pulling out a matching pair of black socks
= [tex]\frac{^6C_1\times ^6C_1}{^{22}c_2}[/tex]
= [tex]\frac{36}{231}[/tex]
MAJOR HELP!
Imagine you are at home watching television. You are sitting 6 feet away from your TV which is hung on the wall and the top of it is 8 feet off the ground. Which of the following functions correctly represents the angle θ that you make with the top of your television?
Answers
Answer: Option A
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Step-by-step explanation:
We can model the situation by means of a right triangle.
Where the angle [tex]\theta[/tex] is the angle that you make with the top of the TV.
Then the horizontal distance of 6 feet is the adjacent side and the vertical distance of 8 feet is the opposite side to the angle the.
By definition of the [tex]tan(\theta)[/tex] function we know that:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Therefore:
[tex]tan^{-1}(\frac{8}{6})=\theta[/tex]
[tex]\theta=tan^{-1}(\frac{8}{6})[/tex]
Answer:
CORRECT
Step-by-step explanation:
n a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills. If Frank picks one bill from the bag, the expected value of the bill he chooses is ____$. If one more $20 bill and one more $10 bill are added to the bag, the expected value will change to _____$.
Answers
Answer:
Initial expected value = 7.3 $
If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $
Step-by-step explanation:
a) Total number of bills = 2 + 1 + 4 + 3 = 10
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3[/tex]
Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$
b)If one more $20 bill and one more $10 bill are added to the bag
Total number of bills = 3 + 2+ 4 + 3 = 12
[tex]\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25[/tex]
Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$
Answer:
$7.30 for the first one and $8.58 for the second one
Step-by-step explanation:
ANSWER FOR PLATO
Find the volume and surface area of the composite figure. Give four answer in terms of π.
Answers
Answer:
V = 99π in³; S = 81π in²
Step-by-step explanation:
Volume is that of a hemisphere of radius 3 in together with that of a cylinder of radius 3 in and height 9 in.
V = (2/3)πr³ +πr²h = (πr²)(2/3r +h)
= 9π(2 +9) = 99π . . . . in³
__
The area is that of a hemisphere, the side of the cylinder, and the circular bottom of the cylinder.
S = 2πr² +2πrh +πr² = πr(2r +2h +r)
S = 3π(6+18 +3) = 81π . . . . in²
Which graph shows an even function?
Answers
Answer:
A.Step-by-step explanation:
The graph of even function is symmetrical about the y-axis.
The graph of odd function is symmetrical about the origin.
A. even
B. odd
C. odd
D. neither
(look at the picture)
Answer:
I would be A
Step-by-step explanation:
It has symmetry across the y axis
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer :
22.5 is the answer
MARK ME AS BRANILIST
Answer: 90
Step-by-step explanation:
Basically you reflect twice and then rotate it
Please help me with this problem
Answers
Answer:
g(x) = -5x
Step-by-step explanation:
If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right. That point will be reflected through the x-axis to land at (1, -5). That means that the equation of the new line would be
g(x) = -5x
A reflection across the x -axis would have the opposite value of the output.
If the value is a positive value, the mirrored value would be a negative value.
The function of g(x) would be g(x) = -5x
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season.
What is Sandra’s expected value of points awarded for a race?
Integer Value Points Awarded Frequency
1-8 3 20
9-15 2 12
16-9 1 6
20 0 2
Answers
Answer:
2.25
Step-by-step explanation:
The total frequency is:
20 + 12 + 6 + 2 = 40
Calculate the probability of each score:
P(X=3) = 20/40 = 0.50
P(X=2) = 12/40 = 0.30
P(X=1) = 6/40 = 0.15
P(X=0) = 2/40 = 0.05
So the expected value is:
E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)
E = 2.25
Finley's mother bought soda for her slumber party that has 10 people. Her mother bought 6 liters of soda. How many milliliters of soda can each child have?
Answers
Answer:
Step-by-step explanation:
5/3lit
Answer:young boy
Step-by-step explanation:two two
Solve the system of equations.
6d + 3f = 12
2d = 8 - f
a. d= 3, f = 2
b. d = 3, f = 14
c. no solution
d. infinite solutions
Answers
Answer:
c. no solution
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Multiply the second equation by 3
3*2d = 3(8-f)
6d = 24-3f
Substitute into the first equation for 6d
(24-3f) +3f = 12
Combine like terms
24 =12
This is never true, so there are no solutions
Answer:
c. No Solution.
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Rearranging the second equation:
2d + f = 8 Multiply this equation by 3:
6d + 3f = 24
Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.
CAN SOMEONE HELP ME WITH THIS MATH QUESTION ITS ABOUT TRANSLATION
Answers
Answer:
(- 4, 1 )
Step-by-step explanation:
A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.
B = (- 5, 4 ), thus
B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )
[tex]B=(-5,4)\\\\B'=(-5+1,4-3)\\B'=(-4,1)[/tex]
An elevator starts at the main floor and goes up 8 floors. It then goes back fown 5 floors. What integer represents elevator final position with respect to the main floor?
Answers
Answer:
integer 3 represents elevator final position with respect to the main floor.
Step-by-step explanation:
Given : An elevator starts at the main floor and goes up 8 floors. It then goes back down 5 floors.
To find : What integer represents elevator final position with respect to the main floor.
Solution : We have given
Elevator starts at the main floor and goes up floors = + 8 ( for up).
Then goes back down floor = - 5 ( - sign for down).
Final position : 8 - 5 = 3 .
It will reach at 3 floor from the main floor .
Therefore, integer 3 represents elevator final position with respect to the main floor.
PLEASE HELP MEOWT!!!
Rewrite sin^(4)xtan^(2)x in terms of the first power of cosine.
Answers
Step-by-step explanation:
[tex] { \sin(x) }^{4} { \tan(x) }^{2} [/tex]
[tex] { \sin(x) }^{4} \frac{ { \sin(x) }^{2} }{ { \cos(x) }^{2} } [/tex]
[tex] \frac{ ({ {1 - \cos(x) }^{2} })^{3} }{ { \cos(x) }^{2} } [/tex]
hopefully this helps, I'm rusty with my trig identities
Answer:
sin⁴(x)tan²(x) = (10 -15cos(2x) +6cos(4x) -cos(6x))/(16(1 +cos(2x))
Step-by-step explanation:
The relevant identities are ...
[tex]\sin^4{x}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\\\\\tan^2{x}=\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\\cos{(a)}\cos{(b)}=\dfrac{\cos{(a+b)}+\cos{(a-b)}}{2}[/tex]
Then your product is ...
[tex]\sin^4{(x)}\tan^2{(x)}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\cdot\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\=\dfrac{3-4\cos{(2x)}+\cos{(4x)}-3\cos{(2x)}+4\cos^2{(2x)}-\cos{(4x)}\cos{(2x)}}{8(1+\cos{(2x)})}[/tex]
Collecting terms and using the identity for the product of cosines, we get ...
[tex]=\dfrac{3-7\cos{(2x)}+\cos{(4x)}+4\dfrac{1+\cos{(4x)}}{2}-\dfrac{\cos{(6x)}+\cos{(2x)}}{2}}{8(1+\cos{(2x)})}\\\\=\dfrac{10-15\cos{(2x)}+6\cos{(4x)}-\cos{(6x)}}{16(1+\cos{(2x)})}[/tex]
What is the correct value of b?
Answers
Answer:
b = 6Step-by-step explanation:
[tex]cosecant=\dfrac{hypotenuse}{opposite}\\\\\text{We have}\ opposite=3b,\ \text{and}\ hypotenuse=22.5,\ \text{and}\ \csc x=\dfrac{5}{4}.\\\\\text{Substitute:}\\\\\dfrac{5}{4}=\dfrac{22.5}{3b}\qquad\text{cross multiply}\\\\(5)(3b)=(4)(22.5)\\\\15b=90\qquad\text{divide both sides by 15}\\\\b=6[/tex]
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
Answers
a.
a^2 + b^2 = c^2
The legs are a and b. c is the hypotenuse.
Let a = 6x + 9y; b = 8x + 12y; c = 10x + 15y
The equation is:
(6x + 9y)^2 + (8x + 12y)^2 = (10x + 15y)^2
b.
Now we square each binomial and combine like terms on each side.
36x^2 + 108xy + 81y^2 + 64x^2 + 192 xy + 144y = 100x^2 + 300xy + 225y^2
36x^2 + 64x^2 + 108xy + 192xy + 81y^2 + 144y^2 = 100x^2 + 300xy + 225y^2
100x^2 + 300xy + 225y^2 = 100x^2 + 300xy + 225y^2
The two sides are equal, so it is an identity.
Answer:
see below
Step-by-step explanation:
a The pythagorean theorem is a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + b^2 = c^2
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
b solve
(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2
(6x+9y)(6x+9y) + (8x+12y)(8x+12y) = (10x + 15y)(10x+15y)
Factor out the common factors
3(2x+3y)3(2x+3y) + 4(2x+3y)4(2x+3y) = 5(2x+3y)5(2x+3y)
Rearrange
9 (2x+3y)^2 +16 (2x+3y)^2 = 25(2x+3y)^2
Divide each side by(2x+3y)^2
9 (2x+3y)^2/ (2x+3y)^2 +16 (2x+3y)^2/(2x+3y)^2 = 25(2x+3y)^2/(2x+3y)^2
9 + 16 = 25
25=25
This is true, so it is an identity
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily. The amount per $1.00 is 1.221386. What is the interest earned to the nearest cent?
Answers
Answer:
The total interest earned is $1,439.
Step-by-step explanation:
Consider the provided information:
Florence Tyler invests $6,500 in a 4-year certificate of deposit that earns interest at an annual rate of 5% compounded daily.
Now, Use the formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where, A is the total amount (after adding interest), P is the principal (investment or loan), r is the interest rate, n is compound, and t is the time (in years).
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=6500(1+\frac{0.05}{365} )^{4(365)}[/tex]
[tex]A=6500(1.00014)^{1460}[/tex]
[tex]A=6500(1.22139)[/tex]
[tex]A=7939.00918[/tex]
Therefore total interest earned is:
$7,939.00 - $6500 = $1,439.00
Hence, interest earned is $1,439.
What is the square footage for this property described by the metes-and-bounds method? Beginning at the point of the southerly side of Smith Street, 200 feet easterly from the corner formed by the intersection of the southerly side of Smith Street and the easterly side of Johnson Street; then east 200 feet; then south 100 feet; then west 200 feet; then north 100 feet to the POB.
A. 20,000 square feetB. 10,000 square feetC. 5,000 square feetD. 15,000 square feet
Answers
Answer:
A. 20,000 square feet
Step-by-step explanation:
The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:
area = (200 ft)(100 ft) = 20,000 ft²
The correct option is option A.
Area of a rectangle:The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.
The formula to finding the area of the rectangle is,
[tex]A=l\times b[/tex]
It is given that,
Length=100 ft
Breadth=200 ft
[tex]A=l\times b[/tex]
Now, substituting the given values into the above formula we get,
[tex]A=200 \times 100\\A=20000[/tex]
The required area is 20,000 square feet.
Learn more about the topic area of the rectangle:
https://brainly.com/question/11202023
Help with these questions!
Answers
Step-by-step explanation:
An inscribed angle is half the arc angle.
m∠MNQ = 80°/2
m∠MNQ = 40°
The angle between two chords is the average of the arc angles.
m∠AMB = (80° + 85°) / 2
m∠AMB = 82.5°
PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
Rx-axis (P) is (-4 , 1)
Step-by-step explanation:
* Lets revise the reflection
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
* Lets solve the problem
∵ The point P is (-4 , -1)
∵ Rx-axis (P) means reflect point P across the x-axis
∵ The reflection of a point (x , y) across the x-axis is (x , -y)
- That means we will change the sign of the y-coordinate of point P
∵ P = (-4 , -1)
∴ The y-coordinate of point P is -1 will change to 1
∴ The image of point P after reflection is (-4 , 1)
* Rx-axis (P) is (-4 , 1)
Answer:
P is -4 , 1
Step-by-step explanation:
What is the solution set of y = x2 + 2x + 7 and y = x + 7? A. {(0, 7), (-1, 6)} B. {(0, 7), (-7, 0)} C. {(0, 7), (1, 8)} D. {(-2, 0), (4, 0)}
Answers
Answer:
A.
Step-by-step explanation:
If
[tex]y=x^2+2x+7[/tex] AND
y = x + 7, then by the transitive property of equality:
[tex]x^2+2x+7=x+7[/tex]
We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:
[tex]x^2+x=0[/tex]
We can factor out the common x to get:
x(x + 1) = 0
which tells us by the Zero Product Property that either
x = 0 and/or x + 1 = 0 and x = -1
We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y
y = 0 + 7 so
y = 7 and the coordinate is (0, 7)
y = -1 + 7 so
y = 6 and the coordinate is (-1, 6)
The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side
Answers
Answer:
(7.5-2.1) /2
If the shortest side measures 2.1 m.
7.5-2.1 =5.4. Then divide by 2 each side is 2.7m
Answer:
The equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
Step-by-step explanation:
Perimeter of the isosceles triangle = 7.5 m
Length of the shortest side = 2.1 m
Let the length of each of the other sides of the triangle = x meter
Then the equation for the perimeter of the triangle becomes:
Sum of 3 sides f the triangle = 7.5 m
=> 2*x + 2.1 = 7.5
=> 2*x = 7.5 - 2.1 = 5.4
=> x = 5.4/2 = 2.7 m
So the relevant equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.
BRAINLIEST HURRY!
the griffins bought a netbook for$250.if the small computer depreciates at a rate of 25%a year,what will it be worth afer 3 years
Answers
Answer:
[tex]\$105.47[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$250\\r=25\%=25/100=0.25\\x=3\ years[/tex]
substitute
[tex]V=250(1-0.25)^{3}[/tex]
[tex]V=250(0.75)^{3}[/tex]
[tex]V=\$105.47[/tex]
Answer and Step-by-step explanation:
After three years the worth of it will be [tex]$105.47[/tex]
We know that each year, it's worth 75% of what it was, giving us :
[tex]=0.75*W[/tex] (Note that "W" means "Worth")
Now we calculate it in three years time so,
The first year is :[tex]250*0.75 = $187.50[/tex]
The second year is :[tex]187.5*0.75 = $140.625[/tex]
The third year is :[tex]140.625*0.75 = $105.47[/tex]
Now, we have our answer :
After three years time the worth of it is [tex]$105.47[/tex]
Natasha places an online order for plate holders to display her antique plates. She chooses a specific site because it has a promotional offer of 15% off on all purchases. She orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each. There is no sales tax on her purchase, but she must pay a flat rate of $5.35 for shipping and handling. What is the total of Natasha?s online purchase?
Answers
Answer:
Total online purchase is $26.473 .
Step-by-step explanation:
As given
Natasha places an online order for plate holders to display her antique plates.
Natasha orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each.
Thus
Total purchase of Natasha = Number of large holders × Cost of each large holder + Number of medium holders × Cost of each medium holder + Number of small holders × Cost of each small holder .
Put all the values in the above
Total purchase of Natasha = 3 × $4.95+ 2 × $3.25 + 2 × $1.75
= $14.85 + $6.5 + $3.5
= $ 24.85
As given
Site has a promotional offer of 15% off on all purchases.
15% is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Discount amount = 0.15 × Total purchase of Natasha .
= 0.15 × $24.85
= $ 3.7275
Thus
Total purchase of Natasha after discount = Total purchase of Natasha - Discount amount .
= $24.85 - $3.7275
= $ 21.1225
As given
Natasha must pay a flat rate of $5.35 for shipping and handling.
Thus
Total online purchase of Natasha = Total purchase of Natasha after discount + Flat rate for shipping and handling .
Total online purchase of Natasha = $21.1225 + $5.35
= $ 26.4725
= $26.473 (Approx)
Therefore the total online purchase is $26.473 .
Answer:
the order Natasha places is as follows;
3 large holders - $4.95 each - 4.95*3 = 14.85
2 medium holders - $3.25 each - 3.25*2 = 6.5
2 small holders - $1.75 each - 1.75*2 = 3.5
Total value for purchases is - 14.85 + 6.5 + 3.5 = 24.85
she gets 15% for all purchases therefore she has to pay only 85% of the purchase value
$24.85 * 85% = $21.1225
She has to pay an additional $5.35 for shipping and handling
therefore the total amount she has to pay is = 21.1225 + 5.35
total amount = 26.4725 this rounded off to second decimal place,
correct answer
C - $26.47
What are the discontinuity and zero of the function f(x) = x^2+5x+4/x+4
Answers
Answer:
The zeros of our function f is at x=-1.
The discontinuity is at x=-4.
These are correct if the function is [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] .
Please let know if I did not interpret your function correctly.
Step-by-step explanation:
I imagine you mean [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] but please correct me if I'm wrong.
The zero's of a rational expression occur from it's numerator.
That is, in a fraction, the only thing that makes that fraction 0 is it's numerator.
So we need to solve [tex]x^2+5x+4=0[/tex] for x.
The cool thing is this one is not bad to factor since the coefficient of x^2 is 1. When the coefficient of x^2 is 1 and you have a quadratic, all you have to do is ask yourself what multiplies to be c and adds to be b.
[tex]x^2+5x+4[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=5,c=4[/tex].
So we are looking for two numbers that multiply to be c and add to be b.
We are looking for two numbers that multiply to be 4 and add to be 5.
Those numbers are 1 and 4 since 1(4)=4 and 1+4=5.
The factored form of [tex]x^2+5x+4[/tex] is [tex](x+1)(x+4)[/tex].
So [tex]x^2+5x+4=0[/tex] becomes [tex](x+1)(x+4)=0[/tex].
If you have a product equals 0 then at least one of the factors is 0.
So we need to solve x+1=0 and x+4=0.
x+1=0 when x=-1 (subtracted 1 on both sides to get this).
x+4=0 when x=-4 (subtracted 4 on both sides to get this).
The zeros of our function f is at x=-1 and x=-4.
Now to find where it is discontinuous. We have to think 'oh this is a fraction and I can't divide by 0 but when is my denominator 0'. If the value for the variable is not obvious to you when the denominator is 0, just solve x+4=0.
x+4=0 when x=-4 (subtracted 4 on both sides).
So we have a contradiction at one of the zeros so x=-4 can't be a zero.
The discontinuity is at x=-4.
Answer:
This function is discontinuous at x = 4, and has a zero at x = -1.
Step-by-step explanation:
If x = -4, the denominator will be zero and thus the function will be undefined. Thus, the discontinuity is at x = -4.
To find the zero(s): Set the numerator = to 0, obtaining
x^2+5x+4 = 0. Factoring this, we get (x + 4)(x + 1) = 0. Thus, we have a zero at x = -1.
Notice that f(x) can be rewritten as
x^2 + 5x + 4 (x+4)(x+1)
f(x) = -------------------- = ---------------- = x + 1 for all x other than x = -4.
x + 4 (x+4)
This function is discontinuous at x = 4, and has a zero at x = -1.
MAJOORRRR HELPPPP!!!
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
It takes hours for the number of bacteria to increase to 300.
Answers
It takes 24 hours for the number of bacteria to increase to 300.
We have given that,
A scientist running an experiment starts with 100 bacteria cells.
These bacteria double their population every 15 hours.
Find how long it takes for the bacteria cells to increase to 300.
Use the formula, where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.
[tex]P_0=100[/tex]
[tex]d=15[/tex]
What is the formula?[tex]P_t=P_02^{\frac{t}{d} }[/tex]
[tex]Pt=300=100\times2^{\frac{t}{15} }[/tex]
[tex]3=2^{\frac{t}{15}}[/tex]
[tex]\frac{t}{15} =1.6[/tex]
t=24
It takes 24 hours for the number of bacteria to increase to 300.
To learn more about the population increase visit:
https://brainly.com/question/11608113
#SPJ2
Select all the exponential functions that have a percentage rate of change of 19%
A) f(x)=3182(0.9)^2x
B) f(x)=1.74(0.81)^3x
C) f(x)=0.2(0.38)^x/2
D) f(x)= 156(1-0.19)^x
Please Help
Answers
Answer:
B) f(x)=1.74(0.81)^3x
and
D) f(x)=156(1-0.19)^x
Step-by-step explanation:
The percentage will always be where the b is, or inside the parentheses. You just have to make sure that, when not greater than 1, you must find out WHAT SUBTRACTS FROM 1 TO GET THAT RESULT. So ask yourself, what decimal number subtracts from 1 to get 0.81?
0.81 is the equivalent to (1-0.19) because (1-0.19) = 0.81.
0.19 is 19%, which is what we're looking for!
The exponential function with a percentage rate of change of 19% is option D) f(x)= 156(1-0.19)ˣ, because it reflects a 19% decrease with the base 0.81 (which is equal to 1 - 0.19).
Exponential functions have a percentage rate of change of 19%, we need to identify the function where the base of the exponent reflects this rate of change. The percentage rate of change can be represented as a decimal where a 19% increase is 1.19 and a 19% decrease is 0.81 (since 1 - 0.19 = 0.81).
Now, let's analyze the given functions:
A) f(x) = 3182(0.9)²ˣ does not represent a 19% rate of change.
B) f(x) = 1.74(0.81)³ˣ does not represent a 19% rate of change as it involves 0.81 to the power of 3x, not x.
C) f(x) = 0.2(0.38)ˣ/² does not represent a 19% rate of change.
D) f(x) = 156(1-0.19)ˣ does represent a 19% rate of change because the base is 0.81 which is equivalent to 1 - 0.19.
Therefore, the correct answer is option D).
Factor a number, variable, or expression out of the trinomial shown below:
6x2 – 12x + 9
A. 2(3x2 – 9x + 6)
B. 2(3x2 – 4x)
C. 3(2x2 – 4x + 3)
D. 3(2x2 – 4x + 9)
Answers
Answer:
C. 3(2x2 – 4x + 3)
Step-by-step explanation:
6x^2 – 12x + 9
We can factor out a 3
3(2x^2 -4x+3)
Answer:
c. 3(2x^2-4x+3)
Step-by-step explanation:
The numbers 6, 12, and 9 are all multiples of 3. Divide everything by three, move it to the outside. There are no more common factors between all 3 terms so the trinomial is completely factored. Hope this helped, if not then I apologize.