Answers
Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)
Given, the y-intercept is at (0, 0.2).
From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.
Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.
So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).
For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)
Put f(0) = 0.2
f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2
a = - 0.6
∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).
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Related Questions
[tex]x^{2 + 5x+6[/tex]
Answers
The resulting factors on factorizing the expression is (x+2)(x+3).
Factorizing quadratic expressionQuadratic equations are equation that has a leading degree of 2.
Writing a number or other mathematical object as the sum of several factors typically smaller or simpler things of the same kind—is known as factorization or factoring.
Given the quadratic equation below:
x^2 + 5x + 6
Factorize to have:
x^2 + 2x + 3x + 6
Group
(x^2+2x)+(3x+6)
Factor out the common variable or value
x(x + 2) + 3(x + 2)
Find the factors
(x+3)(x+2)
Hence the factored form of the expression in its simplest form is (x+2)(x+3)
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Complete question
Factorize x^2 + 5x + 6
Write an equation of a parabola that passes through the points (-3,-5) , (-1,3) , and (0,4)
Answers
Hence the equation of the parabola is y = -x² + 4
In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of points in that plane that are equally spaced apart from the directrix and the focus. Another definition of a parabola is a right circular conical surface intersected by a plane parallel to another plane tangential to the conical surface, resulting in a conic section.The general equation of a parabola is given by y = ax² + bx+ c
The parabola passes through (-3,-5) , (-1,3) , and (0,4).
Now substituting the values in the parabola we get :
-5 = a(-3)² + b(-3)+ c
or , -5 = 9a -3b + c
again:
3 = a(-1)² + b(-1)+ c
or, 3 = a -b + c
again
4 = a(0)² + b(0)+ c
or, c =4
Solving the equation we get :
9a - 3b = -9 and a-b = -1
a= -1 and b = 0
Hence the equation of the parabola is
y = -x² + 4
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Identify the missing statement or reason
A. Definition of midpoint
B. Definition of angle bisector
C. Reflexive property
D. Alternate interior angles Theo
Answers
Answer:Definition of Midpoint-A
Step-by-step explanation:
Kevin earns $6 for 4 polished rocks. The equation y = 1.5x can be used to represent this situation. What is the constant of proportionality?
Answers
The constant of proportionality in the equation y=1.5x is 1.5 .
The Constant Of Proportionality(k) in the equation can be defined as the constant value of the ratio between the two proportional quantities .
In Direct proportionality y=kx , where k is the constant of proportionality
means that if x increases then y also increases at the same rate ,
and if x decreases then y also decreases at the same rate .
For Example : constant of proportionality in y=6x , will be 6 .
In the question ,
it is given that
Kevin earns $6 for 4 polished rocks ,
the equation to represent the situation is y=1.5x
So 1.5 is the constant of proportionality .
Therefore , the constant of proportionality in the equation y=1.5x is 1.5 .
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Solve 12-ln(3-X) = 0
Answers
Answer:
[tex]x = 3 - {e}^{12} [/tex]
Step-by-step explanation:
first let's isolate the logarythm:
[tex]ln(3 - x) = 12[/tex]
at this point we can apply the definition of logarythm to obtain
[tex]3 - x = {e}^{12} [/tex]
which, with some simple algebra returns
[tex]x = 3 - {e}^{12} [/tex]
Use the Distributive Property to simplify.
4(3+2)
Answers
With distributive property, you multiply both terms inside the parentheses with the term outside the parentheses.
So 4•3=12 and 4•2=8
12+8=20
Therefore the answer is 20
I need help with this pls
Answers
STEP - BY - STEP EXPLANATION
What to find?
Determine how much greater the average rate of change over the interval [ 7, 9] than the interval [4, 6].
Given:
Step 1
Calculate the average rate of change over the interval [ 7, 9] using the formula below:
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]a= 7 f(a)=1852
b=9 f(b)=3878
Substitute the values into the formula and simplify.
[tex]Average\text{ rate of change=}\frac{3878-1852}{9-7}[/tex][tex]=\frac{2026}{2}=1013[/tex]Step 2
Calculate the average rate of change over the interval [4, 6] using the same formula in step 2.
a=4 f(a)=358
b=6 f(b)=1178
[tex]average\text{ rate of change=}\frac{1178-358}{6-4}[/tex][tex]=\frac{820}{2}=410[/tex]Step 3
Compare the average rate of change over the two intervals.
Clearly, the average rate of change over the the interval [7, 9] is greater than the average rate of change over the interval [4, 6].
ANSWER
T
Which of the following sets of rational numbers
is ordered from least to greatest?
|-35| 18 |0.58|
Answers
The most appropriate choice for modulus of a number and ascending order will be given by-
|0.58|, 18, |-35| is in ascending order.
What is Modulus of a number and ascending order?
Modulus of a number returns the absolute value of the number.
Modulus of positive number is positive and modulus of negative number is also positive.
If the numbers in a series are arranged in increasing order of their value, then the series is arranged in ascending order
Here,
|-35| = 35
18 = 18
|0.58| = 0.58
As, 0.58, 18, 35 is in ascending order,
So, |0.58|, 18, |-35| is in ascending order
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Use the exponential decay model, A=A o e^kt. The half-life of thorium-229 is 7310 years. How long will it take for a sample of this substance to decay to 20% of its original amount? Round six. decimal places
Answers
The time it will take for a sample of this substance to decay to 20% of its original amount
t=16973.294years
This is further explained below.
What is half-life?The amount of time needed for a quantity to decrease to half of its original value is referred to as its half-life.
In nuclear physics, this word is often used to define the rate at which unstable atoms undergo radioactive decay or the amount of time stable atoms are able to persist.
Additionally, the phrase may be used in a broader sense to define any form of exponential decline.
Generally,
A = A0e^{-kt}
Therefore
A(t) = A0e^{[ln(0.5) / 7310 t}, t in years
0.20 = e^{ln(0.5) / 7310 ]t}
Solve for t.
ln(0.20) = [ln(0.5) / 7310 ]t
t = 7310 [ln(0.20) / ln(0.5)]
t=16973.294years
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Ms. Jacobs gave her class the number 45.692 to round. Three students rounded correctly. Which place did each student round to.
Answers
HURRYYY WILL GIVE BRAINLIESTTTT!!!
1. A player throws a basketball toward a hoop, and it
follows a parabolic path through the points (2,10)
(4,12) and (10,12). Find a quadratic model, and if
the hoop is at (12,10) will the ball pass through the
hoop?
Answers
The answer is given below
credits brainly
Answer please. Need help, 20 points
Answers
Using it's concept, there is a 0.3913 = 39.13% probability of picking a non poisonous animal or a spider.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
In the context of this problem, we have that:
There are 14 + 3 + 6 = 23 animals in total that can be picked, which is the denominator of the calculus of the probability.Of those, 3 are non poisonous snakes and 6 are poisonous spiders, hence the number of desired outcomes is of 9, which is the numerator of the calculus of the probability.Applying it's concept, of desired outcomes divided by total outcomes, the probability of picking a non poisonous animal or a spider is given as follows:
p = 9/23 = 0.3913 = 39.13%.
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A factory produce 11,650 gallon of lemonade 4,950,fewer gallons of ice tea than lemonade
Answers
Factories produce a total of 21550 gallons in a calendar year.
The gallon is used as a unit of volume in both imperial and US customary measurements.
Eight pints make up a gallon, which is a unit of measurement for liquids. It is equivalent to roughly 4.546 litres in Britain. It is roughly equivalent to 3.785 litres in America.
Lemonade, it has been stated, equals 11,650 gallons.
Lemonade = 4,950 fewer than ice tea.
Ice tea: 3,500 fewer than Root beer.
Using the formula Ice tea = 11,650 - 4,950
6700 gallons of iced tea
Root beer = 6700 - 3,500
3200 gallons equals root beer.
Total manufacturing output for a year is equal to 11,650 + 6700 + 3200
Thus, 21550 gallons are produced in total by factories each year.
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Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A? Use the law of cosinus.
Answers
Given data,
[tex]\begin{gathered} \angle B=62 \\ a=14\text{ } \\ c=16 \end{gathered}[/tex]Use the law of cosines.
[tex]\begin{gathered} b^2=a^2+c^2-2acCos(B) \\ b^2=14^2+16^2-(2\times14\times16\times Cos(62)) \\ b^2=196+256-210.32 \\ b^2=241.68 \end{gathered}[/tex]Thus, the value of b is
[tex]b=15.54[/tex]The cosines formula for angle A isThus, angle A will be
[tex]a^2=b^2+c^2-2bcCos(A)[/tex][tex]\begin{gathered} A=cos^{-1}\lbrack\frac{b^2+c^2-a^2}{2bc}\rbrack \\ A=\cos ^{-1}\lbrack\frac{15.54^2+16^2-14^2}{2\times15.54\times16}\rbrack \\ A=52.67 \end{gathered}[/tex]Therefore, angle A is 52.67 degrees.
y
=
−
2
x
+
8
x
-intercept:
Enter as a coordinate: such as
(
a
,
b
)
.
y
-intercept:
Enter as a coordinate: such as
(
a,
b
)
.
Answers
Answer:
234
Step-by-step explanation:
How do you answrt? I'm aknskwnwekene
Mrs. Byers rents a water trampoline for her son's birthday party. The delivery fee for the trampoline is $75, plus a rental fee of $8 per hour. She wants to spend less than $125 on the trampoline. Find h, the number of hours Mrs. Byers could rent the trampoline?
Answers
Answer:
h= 6
Step-by-step explanation:
To find out the value of h, start by forming an equation for the cost of renting a trampoline:
Cost of renting= $(75 +8t), where t is the rental duration.
When the cost is $125,
75 +8t= 125
Subtract 75 from both sides:
8t= 125 -75
8t= 50
Divide both sides by 8:
t= 50 ÷8
t= 6.25
Since she wants to spend less than $125, let's round the value down to the nearest hour.
∴ h= 6
Thus, she could rent it for 6 hours.
Let's check!
Total cost of renting for 6 hours
= 6(8) +75
= $123
Total cost of renting for 7 hours
= 7(8) +75
= $131
Hence, 6 hours is indeed the maximum number of hours she can rent the trampoline for, such that the total cost is less than $125.
A sub shop ordered 40 pounds of tomatoes. If the tomatoes are evenly distributed into 12 tubs, how many pounds will go into each tub?
Answers
Using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.
In this question, we have been given a sub shop ordered 40 pounds of tomatoes.
The tomatoes are evenly distributed into 12 tubs.
We need to find the number of pounds of tomatoes will go into each tub.
Let x be the number of pounds of tomatoes will go into each tub.
By unitary method,
x = 40 / 12
x = 3.33 pounds
Therefore by using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.
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Please answer with if the slope is positive or negative and what the slope is.
Answers
The slope of the line is 60 and speed of the bus is 60 miles per hour
The slope of the line is the measure of the steepness. In other words the slope of the line is the change in y coordinate with respect to the change in x coordinate.
Here the points are
(1,60) and (2,120)
The slope of the line m =[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the points
Substitute the values in the equation
The slope of the line m = [tex]\frac{120-60}{2-1}[/tex]
= 60
The speed = Distance / Time
Take one point (2,120)
The distance = 120 miles
Time = 2 hours
The speed = 120/2
= 60 miles per hour
Hence, the slope of the line is 60 and speed of the bus is 60 miles per hour.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
it is just a matter of definition that can be easily looked up.
the domain is the interval or set of all valid x values.
while the range is the interval or set of all valid y (function result) values.
so, the domain here is every value of x used in this function.
e.g. does x = -6 have a functional (y) value in the curve ?
no, it does not.
x = - 4 ? no.
x = -2 ? no.
x = -1 ? ah, yes, this is just the left-most point of the curve.
and then all x values further to the right of -1 are covered. as the arrows indicate : into all eternity ("to infinity and beyond !")
so, the domain is [-1, +infinity).
and you need to use B.
please note, the round bracket indicates that that ends of the interval is not included or undefined (after all, infinity is not a number we can work with, it is basically undefined and only represents a principle).
for the range this is tricky, as the graph does not really show us the limit. it could be y = -1 or 0 down to y = -9 or -10.
Solve the systems of equations
-8x + 2y = -4
x^2 + 2y = 5
Answers
x=1, y=2
What is the probability that a person who is alive at age 10 will not be alive at age 70 if the following is true? (Enter your probabilities as fractions.)
(a) The person is male.
b) The person is female.
Answers
The probability that a person who is alive at age 10 will not be alive at age 70 if the following is true for males and Female is
P(not alive at age 70 | male) =26999/99065P(not alive at age 70 | female) =17284/98983This is further explained below.
What is probability?Generally, A number that expresses the possibility or likelihood that a certain event will take place is referred to as its probability. Both proportions and percentages with values ranging from 0 to 1 may be used to indicate probabilities. Proportions can range from 0 to 1, while percentages can range from 0 to 100.
Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.
A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.
The characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.
In conclusion,
P(not alive at age 70 | male)
=(99065-72066)/99065
=0.273
As fraction
=26999/99065
P(not alive at age 70 | female)
=(99228-81944)/98983
0.17461
As fraction
17284/98983
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if x=3 and y=5 what is 2x squared+3y squared
Answers
Answer:
the answer is 93
Step-by-step explanation:
I'm very sure....
Answer: I really wish I could help you but I don't know the answer either
Step-by-step explanation:
JK
which of these expressions is equivalent to 15C3? a) 15C12 b)12C15 c) 15C18 d) 18C15
Answers
Answer: Choice A
15C12
=============================================
Reason:
Imagine there are 15 students and we wish to form a committee of three people, where order doesn't matter. The answer to this problem is 15C3 using the nCr formula. Here n = 15 and r = 3.
The 15C3 represents the number of ways to pick the three people on the committee, while 15C12 is the number of ways to not pick a person for the committee. We can think of it like two separate committees if you want.
So 15C3 = 15C12
The numbers after the "C" add to the value of n
The identity is [tex]_nC_r = _nC_{n-r}[/tex]
The r and n-r add to n.
You want to buy a 28,000 car. You can make a 10% down payment, and will finance the balance with a 2% interest for 48 months. What will your monthly payment be
Answers
The monthly payment when you want to buy a 28,000 car is $567.
How to calculate the value?It should be noted that when the 10% down payment is made, the amount left will be:
= $28000 - (10% × $28000)
= $28000 - $2800
= $25200
The interest will be:
= PRT / 100
P = $25200
R = 2%
T = 48 months = 4 years
Interest = (25200 × 2 × 4)/100
= $2016
Total amount to be paid:
= $25200 + $2016
= $27216
The monthly payment will be:
= Amount / 48 months
= $27216 / 48
= $567
The monthly payment is $567.
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Answer:
$546.72
Step-by-step explanation:
My dinner at San Felipe cost $15.20 before tax and $15.96 after tax. What was the sales tax?
Answers
Answer:
Step-by-step explanation:
Answer
I hope this is not the tip!
Total Cost of the meal 15.96
Menu Cost 15.20 Subtract
Tax .76
The tax on the meal is 76 cents or 0.76 dollars.
Olivia bought snacks for her team's practice. She bought a bag of chips for $2.25 and a 8-pack of juice bottles. The total cost before tax was $11.69. Which equation could be used to determine j, how much each bottle of juice costs?
Answers
Please hurry due today I will give you brainlest
Which numbers are solutions of 4p+6<3p? Choose exactly two answers that are correct
Answers
Answer: -12 and -9
Step-by-step explanation:
4p + 6 <3p
4p - 3p < -6
p < -6
So, -12 < -6 is CORRECT
-9 < -6 is CORRECT
-6 is not less than -6 SO THIS IS INCORRECT
6 is not less than -6 so this is INCORRECT
If 539 is invested at 17%, how much money will be in the account after 21 months
Answers
Step-by-step explanation:
[tex]i = prt \div 100[/tex]
p=539
r=17%
t=21
I=?
[tex]i = 539 \times 17 \times 21 \div 100[/tex]
Roberto's Club has a secret knock for its Clubhouse door that only its members know. The members remember to knock on the door exactly n times in a row, were five more than three times n and is equal to the difference between 21 and n . How many times in a row do members knock on the clubhouse door?
Answers
Answer:
[tex]\text{ They knock 4 times on the clubhouse door.}[/tex]Step-by-step explanation:
Let n be the times that they knock on the door.
If five more than three times n and is equal to the difference between 21 and n;
[tex]3n+5=21-n[/tex]Solve for n, using inverse operations to solve equations:
[tex]\begin{gathered} 3n+n=21-5 \\ 4n=16 \\ n=\frac{16}{4} \\ n=4\text{ } \\ \text{ They knock 4 times on the clubhouse door.} \end{gathered}[/tex]June has 72 gallons of punch for a party. June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Answers
If June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
The bigger cooler is five times as large as the smaller cooler
Consider the capacity of smaller cooler as x
The capacity of bigger cooler=5x
June has 72 gallons of punch for a party
Then the linear equation will be
x+5x=72
6x=72
x=12
Then the capacity of bigger cooler=5x
=5×12
=60
Hence, if June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
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