If the equation be y = x² + 4 then the inverse function be [tex]f^{-1} (x)=[/tex] ± [tex]\sqrt{x - 4[/tex].
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.
Let the equation be y = x² + 4
then the function be f(x) = x² + 4
y = x² + 4
⇒ x = y² + 4
simplifying the above equation, we get
x - 4 = y²
√y² = √x - 4
The value of y = ± √x - 4
Therefore, the inverse function be [tex]f^{-1} (x) =[/tex] ±√x - 4
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The equation y=(-16t-4)(t-2) represents the height in feet of a beach ball thrown by a child Find the zeros of the functionWhat do the zeros tell us in this situation? From what height is the beach ball thrown ?
Answer:
See below
Step-by-step explanation:
To find zeroes:
0 = (-16t-4)(t-2)
so -16t-4 = 0 t = -1/4
or t-2 = 0 t = 2
when the ball is thrown, t= 0
put t= 0 in the equation to find the initial height
y = ( -16t -4)(t-2)
= ( -16(0)-4)(0-2) = (-4)(-2) = 8 ft
there are 30 people in student council that are running for the offices of president and vice president. in how many different ways can those offices be assigned?
Answer: Assuming that it matters which one is president and which is vice president, and the same person cannot be assigned both posts, the answer is 30*29, or 870.
Step-by-step explanation:
Write the first four terms of a sequence given the recursive rule below:
f(n)=2\cdot f(n-1)+3\;for\;all\;n\geq2\;and\;f(1)=7f(n)=2⋅f(n−1)+3foralln≥2andf(1)=7
The first four terms of the sequence are 7, 17, 37 and 77, respectively.
How to determine the first four terms of a sequence by a recursive formula
Sequences can be generated by using recursive formulas, that is, formulas that are in terms of the previous elements of a sequence. Herein we find a case of sequences by using recurrence formulas, whose procedure is shown below:
n = 1
f(1) = 7
n = 2
f(2) = 2 · f(1) + 3
f(2) = 17
n = 3
f(3) = 2 · f(2) + 3
f(3) = 37
n = 4
f(4) = 2 · f(3) + 3
f(4) = 77
The first four terms of the sequence are 7, 17, 37 and 77, respectively.
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what is the outlier for the nmbers 2 4 6 8 10 and 12
The outliers of the given data set are 2 and 12.
The given data set is 2, 4, 6, 8, 10 and 12.
What is the outlier of numbers?Outliers are extreme values that stand out greatly from the overall pattern of values in a dataset or graph
A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. For example in the scores 25,29,3,32,85,33,27,28 both 3 and 85 are "outliers".
In the given data set 2, 4, 6, 8, 10 and 12.
2 is the lowest observation and 12 is the highest observation.
So, 2 and 12 are two extreme values and these two are outliers.
Therefore, the outliers of the given data set are 2 and 12.
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Alma is choosing a new smartphone and cellular service plan. let p be the phones price in dollars, m be the cost of the selected plan in dollar per month, and c be alma's total cost in dollars after time t, measured in months of service. write an equation that expresses c in terms of p, m, and t. then solve your equation for t.
The equation which expresses c in terms of p, m and t as in the task content is; c = mt + p and the solution of the equation for t is; t = (c -p)/m.
What is the equation of the situation such that c is expresses in terms of p, m and t?It follows from the fact that the rate of change, m is constant in the situation described. Hence, the equation is a linear equation.
On this note, the required equation which represents total cost, c in terms of p, m and t can be written as;
C = mt + p.
Hence, to solve the equation above for t;
Subtract p from both sides so that;
c - p = mt
Divide both sides by m;
(c - p)/m = t.
Ultimately, The equation which expresses c in terms of p, m and t as in the task content is;
c = mt + p
and the solution of the equation for t is;
t = (c -p)/m.
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What is each expression in simplest form?
a. (8 x¹⁵)⁻¹/³
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squaresInput
(8 x^15)^(-1/3)
Value
1/(2 (x^15)^(1/3))
1/(2x^5)
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How many solutions does this equation have?
7q–20= –10q+20+19q
Answer:
q = -20
Step-by-step explanation:
The solution of the equation will be negative 20. Then the number of solutions to the equation will be one.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
7q – 20 = – 10q + 20 + 19q
Simplify the equation, then we have
7q – 20 = – 10q + 20 + 19q
– 19q + 10q + 7q = 20 + 20
– 2q = 40
q = 40 / (–2)
q = – 20
The solution of the equation will be negative 20. Then the number of solutions to the equation will be one.
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A Scale drawing of a school bus has a scale of 1/2 inch to 5 feet. If the length of the school buss is 4 1/2 inches on the scale drawing, what is the actual length of the bus?
Explain or show your reasoning.
45 feet
Im writing this extra because the app said the answer was to short :)
33) Create a word problem that can be represented by the quotient -45÷5.
Answer:
molly is baking cookies. she baked 45 cookies and she needs to put a certain amount in 5 different boxes so that way everyone has an equal amount. how much cookies need to be in each box
Step-by-step explanation:
Answer:Joe is feeding cows and he has 45lbs of grass and there are 5 cows how much does each cow get fed?
Step-by-step explanation:
What is the answer to this problem?
Answer:
inequality
Step-by-step explanation:
P(x) = 4x³ – x² − 6x + 9
What is the value is 1/a+1/b+1/c
When a, b and c are the polynomials roots
Answer:
2/3.
Step-by-step explanation:
α + β + γ = -b/a
αβ + βγ + γ α = c/a
αβγ = -d/a
These are the relation between the roots α, β and γ and the coefficients of the cubic equation:
P(x) = ax^3 + bx^2 + cx + d
Our equation is:
P(x) = 4x³ – x² − 6x + 9
So, for the above equation:
a + b + c = -(-1)/4 = 1/4
ab + ac + bc = -6/4 = -3/2
abc = -9/4.
1/a + 1/b + 1/c
= (bc + ac + ab) / abc
So, plugging in the above values:
this = (-3/2) / (-9/4)
= 3/2 * 4/9
= 12/18
= 2/3.
please solve this with steps
Answer:
-13/18
Step-by-step explanation:
You have here a multiplication and a division in your expression. You need to multiply and divide in the order that they appear from left to right, according to the order of operations. So multiply first.
To multiply two fractions, you just multiply the top×top and bottom×bottom.
You could simplify it at this point but I waited to the end to simplify. See image.
Next, divide. If you have one or two fractions in a division problem, rewrite the division as a multiplication using Keep-Change-Flip! Keep the first term. Change divide to multiply. And Flip the second term (use the reciprocal is the math word for it.) See image.
Last, simplify.
For the coordinates A(5,8) and M(9,14), A is an endpoint of AB and M is the midpoint. Find the coordinates of endpoint B.
Answer:
(13, 20)
Step-by-step explanation:
Please help I need this
Answer:
11 inches
Step-by-step explanation:
The sides of the teacher's model are 110 inches
Henry's model should be 10 times shorter.
110 ÷ 10 = 11
Make Closing statement on why crocs should be allowed in school
Reasons
1.stability
2.breathable
3.Waterpfroof
Use the following setup and given equation to find your solution:
1st integer = x
2nd integer = x+2
3rd integer = x+4
Equation: x+(x+2)+(x+4)=267
Solve the equation above. What is the largest integer?
The largest integer in the set of number is 91
How to use the given equation to determine the largest integer?The given parameters are
1st integer = x2nd integer = x+23rd integer = x+4Equation: x+(x+2)+(x+4)=267So, we have
x+(x+2)+(x+4)=267
Open the brackets
x + x + 2 + x + 4 = 267
Evaluate the like terms
3x = 261
Divide both sides by 3
x = 87
Substitute x = 87 in 3rd integer = x+4
3rd integer = 87 + 4
Evaluate
3rd integer = 91
Hence, the largest integer is 91
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Prior to an election, 6,504 people vote in the advance polls for a riding. On election day, thepolling stations for that riding record an average of 407 voters per hour. How long were thepolls open on election day, if a total of 10,167 people voted in that riding?
**USE LET STATEMENTS, AND THEREFORE STATEMENTS**
The number of hours the polls open on the election day was 9 hours
From the question, we are to determine how long the polls opened on the election day
From the given information,
6,504 people vote in the advance polls for a riding prior to the election
and
A total of 10,167 people voted in that riding
Thus,
The number of people that voted on the election day = 10167 - 6504
Number of people that voted on the election day = 3663
Also, from the given information
The polling stations for the riding record an average of 407 voters per hour
Then,
Number of hours the polls open on election day = Number of people that voted on the election day ÷ Average number of voters per hour
Number of hours the polls open on election day = 3663 ÷ 407
Number of hours the polls open on election day = 9 hours
Hence, the number of hours the polls open on the election day was 9 hours
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what do the numbers 1 through 10 add up to
After adding the numbers from 1 to 10, we get the result as 55.
We are given the numbers from 1 to 10
We need to find the sum of the numbers.
Adding these numbers, we will get that:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
= 3 + 7 + 11 + 15 + 19
= 10 + 26 + 19
= 29 + 26
= 55
Therefore, we get that, after adding the numbers from 1 to 10, we get the result as 55.
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32 is the sum of a number z and 9 write the word as an equation then solve (HURRY DUE TOMORROW!!!!)
Answer: z = 23
Subtract 32 and 9, which equals 23
So your equation is 23 + 9 = 32
Step-by-step explanation:
when dividing the polynomials one factor is the quotient
When dividing with polynomials one factor becomes the dividend and the other factor becomes the quotient. This is false.
What is a polynomial?It should be noted that a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, as well as non-negative integer exponentiation of variables
Dividing polynomials simply requires that a particular factor becomes the divisor and the other factor becomes the quotient.
Therefore, it's false.
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When dividing with polynomials one factor becomes the dividend and the other factor becomes the quotient.
Simplify each rational expression. State any restrictions on the variables.
2x / 4 x²-2 x}
According to the question, the given rational expression is as follows:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}[/tex]
To simplify the given expression by performing factors on denominator:
[tex]4x^{2}-2x = 2x(2x-1)[/tex]
Substituting these factors in the final expression, we get:
Rational expression = [tex]\frac{2x}{4x^{2} -2x}=\frac{2x}{2x(2x-1)}=\frac{1}{2x-1}[/tex]
Therefore, the final answer for the given expression is [tex]\frac{1}{2x-1}[/tex].
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A kitten has 5 claws on its paw, a chicken has 4. there are 57 kittens and chickens in the yard and they all have 768 claws. how many kittens and chickens are in the yard?
Using algebraic expressions and equation, there are 26 kittens and 31 chickens in the yard.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that there are 57 kittens and chickens in the yard, we can express this as:
x + y = 57 ⇒ x = 57 - y (equation 1)
where x = number of kittens
y = number of chickens
If a kitten has 5 claws on each of its 4 paws, and a chicken has 4 claws in each of its 2 feet, and they all have 768 claws, then
5(4)x + 4(2)y = 768 ⇒ 20x + 8y = 768 (equation 2)
Substitute equation 1 to equation 2 and solve for y.
20(57 - y) + 8y = 768
1140 - 20y + 8y = 768
-12y = -372
y = 31
number of chickens = 31
Substitute the value of y in either of the two equations and solve for x.
x = 57 - y
x = 57 - 31
x = 26
number of kittens = 26
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Is |a + b] = |a| + [b] for all rational numbers a and b? Give reasons for your answer. Is |a - b| = |a| - |b| for all rational numbers and b ? Give reasons for you
Not all rational numbers a and b satisfy the equation |a+b|=|a|+|b|.
As a result, |a+b|=|a|+|b|.
If |a+b|=|a|+|b| for all rational numbers a and b, we must verify this.
A rational number is what?P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).
Now,
a=-3 and b=5
|-3+5|=|-3|+|5|
⇒2≠8
A = 2 and B = 4
|2+4|=|2|+|4|
⇒6=6
As a result, we realized from the examples above that |a+b|=|a|+|b| isn't always true.
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Select all of the true comparisons.
Answer: A, D, B
Step-by-step explanation:
Answer:A,B,D
yw :):):)
Kallie thinks that each double
problem will have an even sum.
Do you agree or not?
Since Kallie thinks that each double problem will have an even sum. in my response, it is Yes, I do not agree with her.
Why do i not agree with her?The reason why i agree with her is that the odds that is double will also give you an odd double and get an even double.
What happens when you double an odd number?An odd number is known to be one that be looked at as an even number and this is one that happens if one added to it .
For example 5 is 4+1.
Therefore, if you add two odd numbers together, there is the probability that a person may get an even number.
For example is 3 + 5 = 8
Therefore, Since Kallie thinks that each double problem will have an even sum. in my response, it is Yes, I do not agree with her.
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the number of pigs: the number of goats = 11:3
If there are 12 goats in the field, how many pigs are there?
Answer:
44pigs
Step-by-step explanation:
12/3=4.
4*11=44
The ratio shows how many times one value is contained in another value.
The number of pigs is 44.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The number of pigs: the number of goats = 11:3
Let the number of pigs = 11x
Let the number of goats = 3x
The number of goats = 12
This means,
3x = 12
Divide 3 on both sides.
x = 12/3
x = 4
Now,
The number of pigs:
= 11x
= 11 x 4
= 44
Thus,
The number of pigs is 44.
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In 2010, the population of a city was 228,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.2%. To the nearest 100 people, what was the population in 2020?
The population in the city in 2020 to the nearest 100 is 235242.65.
The population of the city was 228,000 in the year 2010.
From 2010 to 2015, the population grew by 7.7%.
The population decreases by 4.2 % from 2015 o 2020.
Initially, the population of the city is 228,000.
From 2010 to 2015,
The city's population increased by 7.7%.
7.7% of 228,000 = ( 7.7 / 100) × 228,000 = 17556
The population of the city from 2010 to 2015 = 228,000 + 17556 = 245556
From 2015 to 2020,
Now, the city's population decreases by 4.2%.
4.2% of 245556 = ( 4.2 /100) × 245556 = 10313.352.
Therefore,
The population of the city in the year 2020 = 245556 - 10313.352 = 235242.648
Therefore, the population in the year 2020 to the nearest 100 is 235242.65.
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Answer:
235200
Step-by-step explanation:
Need some assistance with this question
The equation is y = 30x +3000
$ 10500 is the rent for 250 guests.
What is slope intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b.
Given:
(100, 4350) and (155, 6000)
So, slope = 6000- 4350 / 155-100
slope = 1650/55
slope= 30
So, the equation is
y-6000 = 30( x- 100)
y - 6000 = 30x - 3000
y = 30x +3000
Now,
and, for 250 guests the rent would be
y= 30 * 250 + 3000
y = 7500+3000
y= $ 10500
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SAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
D is the correct answer!!
What is (−11)^4 when evaluated?
Answer:
14641
Step-by-step explanation:
Exponent rule
[tex]\mathrm{(-a)^n=a^n(when~n~is~even)}[/tex]
[tex]\left(-11\right)^4=11^4[/tex]
Multiply
[tex]11^4 = 11 \times 11 \times 11\times 11 = 14,641[/tex]