√ x/4 + 4 is the inverse of the function f(x)=4x^2-16
How to find the inverse of a functionWhat is inverse function?
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f
Given f(x)=4x²-16
Let f(x) = y
So we can say y =4x²-16
We will then make x the subject:
Since y = 4x²-16
4x² = y + 16
x² = y + 16/4
x = √ y/4 + 4
since x = f⁻¹(y) = √ y/4 + 4
Thus f⁻¹(x) = √ x/4 + 4
Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4
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A)y= 160.5 (2.3^x) + 20.5B)y= 99.8 (1.5^x) - 80.8C)y= 120.4 (0.8^x) – 209.1D)y= 147.3 (1.2^x) – 221.4Using technology, find the exponential function of best fit for the data.
The plot of the data in the table is shown below.
And the plot of the answer choices is plotted in the following figure.
As we can clearly see, the exponential function of choice D best fits the data in the table,
Hence, choice D is the correct one.
how many cups needed to make 3 dozen rolls
surpriya makes papadums to sell in her food truck. she uses 12oz of dough to make each batch. She had 60oz of dough.and wants to know how many batches she can make
Answer:
5 batches
Step-by-step explanation:
60÷ 12=5 batches
Solve the inequality. Check the numbers that represent solutions.
-8x + 19 < -13
5
3
4
2
6
Answer:
x equals four
Step-by-step explanation:
collect like terms
then it will be minus 8 x equals minus 13 minus 19 which gives minus 32. Divide both sides by the coefficient of x i.e minus 8
Then x is less than 4
Because you divided with minus so the sign will change
A t-shirt and two pairs of shorts cost $53.50. At the same store, two t-shirts and three pairs of shorts cost $84.
Assuming that all shirts are sold for the same price, and all shorts cost the same, too, which statement is true?
A)A t-shirt is $7.50 and a pair of shorts is $23.
B)A t-shirt is $30.50 and a pair of shorts is $3.75.
D)A t-shirt is $3.75 and a pair of shorts is $30.50.
E)A t-shirt is $23 and a pair of shorts is $7.50
First option is correct. A t - shirt cost $7.50 and a pair of shorts cost $23
Simultaneous linear equation: what is it?First, it's crucial to understand linear equations.
Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between them.
Linear equations are those with one degree.
Simultaneous linear equations are two or more linear equations that can be solved simultaneously to find a common solution.
Let the price of one t-shirt be $x and price of one pair of shorts be $y
A t-shirt and two pairs of shorts cost $53.50
So, x + 2y = 53.50 .................... (1)
Two t-shirts and three pairs of shorts cost $84.
So, 2x + 3y = 84 ................ (2)
Multiplying (1) by 2,
2x + 4y = 107 .............(3)
Subtracting (2) from (3),
4y - 3y = 107 - 84
y = 23
Putting the value of y in (1)
x + 2[tex]\times[/tex]23 = 53.50
x = 53.50 - 46
x = 7.50
A t shirt cost $7.50 and a pair of shorts cost $23
First option is correct
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38. the graph of g is a horizontal shrink by a factor of 1/5 of the graph of f.
Help soon please
Answer:
g(x) = f(5x)
Step-by-step explanation:
We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).
Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...
g(x) = f(x/(1/5))
g(x) = f(5x)
Find the measure of angle C.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 360 ~~ = ~~ (7x+19)+(15x-1)+(4x-3)+(12x+3) \\\\\\ 360~~ = ~~38x+18\implies 342=38x\implies \cfrac{342}{38}=x\implies \boxed{9=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle C}{15x-1}\implies 15(9)-1\implies 135-1\implies \stackrel{\measuredangle C}{\text{\LARGE 134}}[/tex]
PLEASE HELP!!!
The number of shirts an associate at a local department store can fold and restock, r, varies directly with the amount of time the associate spends folding and restocking, t. If Rebecca spends 2 h folding and restocking, she can fold and restock 129 shirts.
Which direct linear variation equation models the information?
A. r = 64.8t
B. r = 127t
C. r = 64.5t
D. r = 131t
The equation for the direct linear variation that models the given information is: C. r = 64.5t.
How to Write the Equation of a Direct Linear Variation?The equation of a direct linear variation can be modelled as y = kx, where the variables are x and y, while the value of k is the constant of proportionality between the variables, x and y.
Given that:
r = number of shirts that can be fold and restock t = amount of time spent folding and restockingWe are told that r varies directly with t. Where k is the constant of proportionality, the equation of the direct linear variation between r and t can be expressed as r = kt.
Constant of proportionality, k = r/t
Number of shirts Rebecca can fold and restock (r) = 129
Amount of time she would spend (t) = 2
Find the constant of proportionality, k:
k = r/t = 129/2
k = 64.5
To write the equation for the direct linear variation, substitute k = 64.5 into r = kt:
r = 64.5t
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Part Brom least toBlair purchases the T-shirts from Company B. She needs to add a 759markup to her total cost to make a profit when she sells the shirts at thcarnival. How should Blair determine the selling price of each T-shirt atthe carnival?st CostDrag a number into each box to make the statements true.В B.She canThe total cost Blair paid for one T-shirt is $calculate the markup by multiplying her total cost by:Blair will sell each T-shirt at the carnival for $Finish LaterIISubmit
First step
We want to find the cost of each shirt Blair paid. In order to find it we want to find the total price Blair paid for the whole order and then divide it by 150 (total number of shirts).
She chose Company B.
They charge $3.10 per shirt, plus 4% of the total order for shipping.
There are 150 shirts, then the total order for shipping is:
150 · $3.10 = $465
we want to add the 4%. The 4% of $465 is
$465 · 4/100 = $465 · 0.04
= $18.60
If we add it to the total order for shipping:
$465 + $18.60 = $483.60
Second step
Now we divide the total price of 150 into 150: this is the cost for one shirt.
$483.60/150 = $3.224
If we round it to the nearest hundredth:
$3.224 ≅ $3.22
Answer- The total cost Blair paid for one T-shirt is $3.22
Mark upWe know that she needs to add 75% to the total cost.
Let's remember that every percentage is equivalent to it divided by 100: for example 100% is equivalent to 1. For 75%:
75% = 75/100 = 0.75
Then 75% is equivalent to 0.75.
This means that if we want to find the 75% of something we multiply it by its equivalent: 0.75.
Answer- She can calculate the markup by multiplying her total cost by 0.75
Sell price
Based on the previous parts, we know that we want to add the 75% (0.75) of the cost of each T-shirt Blair paid ($3.22).
We first find the 75% of $3.22 and then add it to it: it will be the cost of sell.
First step
The 75% of the total cost of each shirt ($3.22) is:
0.75 · $3.224 = $2.418
Second step
Adding the 75% to the total price:
$3.224 + $2.418 = $5.642
If we round it to the nearest hundredth:
$5.642 ≅ $5.64
Answer- Blair will sell each T-shirt at the carnival for $5.64.
Enter an equivalent expression for (4.5)−5 ·
·
(4.5)11.
4.5
The expression which is equivalent to the given expression as in the task content is; 4.5⁶.
Which expression is equipped to the expression given in the task content?It follows from the task content that the expression which is equivalent to the given expression is to be determined.
Since the given expression is;
(4.5)-⁵ • (4.5)¹¹
Hence, it follows from the product of exponents law of indices that we have;
(4.5)^(-5 + 11)
= (4.5)⁶
Therefore, the expression which is equivalent is; 4.5⁶.
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x+y+z=4
x = -2y
z = -3y
We're given : x+y+z = 4
x = -2y
z = -3y
So, we replace x = -2y and z = -3y in the original equation.
-> -2y + y + -3y = 4
-> -4y = 4
-> y = -1
Now we have the value of y, we substitute it into x and z
x = -2y = -2(-1) = 2
z = -3(-1) = 3
due now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A major weakness of the Articles of Confederation is that: B. States could ignore laws passed by the Congress.
What are the Articles of Confederation?The Articles of Confederation can be defined as the first written documents that were regarded as the Constitution of the United States of America, which was agreed upon by the thirteen (13) original states.
Under the Articles of Confederation, the national government was unable to raise revenue due to lack of enforcement powers of the confederate Congress.
In conclusion, we can reasonably infer and logically deduce that one of the limitations of the Articles of Confederation was the inability of Congress to enforce the laws it made because they can be ignored by states.
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Complete Question:
What was one major weakness of the Articles of Confederation?
A. State governments lost most of their political power.
B. States could ignore laws passed by the Congress.
C. The national government could not negotiate treaties.
O D. There was no way for new territories to become states.
Graph the lines with the given description: (Note: Question a) might be already solved.)
The graph of each equation is attached below each showing the point of intersection to the y-axis.
Graph of a Straight LineTo solve this question, we have to use a graphing calculator to plot the coordinates as well as show the point of intersection.
A line graph is a graphical representation of information that changes over a period of time. It is a chart made by joining points using line segments.
The graph of equation is attached below.
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the value of x is referring to the hypotenuse of the triangle and not the arc that the x is under
Given that the length of one of the sides of the triangle is the radius, the length of the other leg of the triangle is also 6 units.
Therefore, this is an instance of a 45-45-90 triangle. The value of x can now be solve by
Given that the side length of the 45-45-90 triangle is 6 units, the length of the hypotenuse x is
[tex]x=6\sqrt[]{2}[/tex]
Crayons manufactory product 36,552 crayons each hour if the crayons containing 24 crayons each how many boxes of crayons are produced each hour 
After calculating basic arithmetic we have come to find that, 1523 boxes of crayons are produced in each hour if crayons manufactory produces 36,552 crayons in an hour.
What is arithmetic?Arithmetic ((arithmós) 'number', 'art, craft') is a fundamental branch of mathematics that focuses on the properties of traditional operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Giuseppe Peano, an Italian mathematician, formalized arithmetic in the nineteenth century with his Peano axioms,[disputed - discuss], which are still very important in the field of mathematical logic today.
The prehistory of arithmetic is limited to a few artifacts that may indicate the concept of addition and subtraction, the best-known of which is the Ishango bone from central Africa, which dates from somewhere between 20,000 and 18,000 BC, though its interpretation is disputed.
We have given that
crayon manufactory produces 36,552 per hours
Each box contain 24 crayons
No. of boxes manufactured in 1 hour = 36,552/24
= 1523
Thus, 1523 boxes of crayons are produced in each hour if Crayons manufactory produces 36,552 crayons in an hour.
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2 of 35 Question 12 Review When the binomial 27x² - 300 is factored, the result is 3(3x - b)(3x + b). What is the value of b? a.10 b.20 c.50 d.150
In elementary algebra, the binomial expansion defines the algebraic expansion of powers of a binomial. The binomial equation be 27x² - 300 exists 3(3x + 10)(3x - 10).
What is meant by binomial equation?In elementary algebra, the binomial theorem (or binomial expansion) defines the algebraic expansion of powers of a binomial. According to the theorem, it exists possible to extend the polynomial [tex]$(x+y)^n$[/tex] into a sum involving terms of the form [tex]$a x^b y^c$[/tex], where the exponents b and c exists nonnegative integers with b + c = n, and the coefficient a of each term exists a specific positive integer depending on n and b.
Let the binomial equation be 27x² - 300
Factor out common term 3:
[tex]$\quad 3\left(9 x^2-100\right)$[/tex] [tex]$=3\left(9 x^2-100\right)$[/tex]
simplifying the above equation, we get
Factor [tex]$9 x^2-100: (3 x+10)(3 x-10)$[/tex]
= 3(3x + 10)(3x - 10)
If 3(3x - b)(3x + b) then we get
= 3(3x + 10)(3x - 10)
b = 10
The value of b = 10.
Therefore, the correct answer is option a. 10.
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the sampling distribution of the sample sum is normally distributed if thirty or more observations are taken from a population that is beta distributed.
According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.
What exactly does "normal distribution" mean?A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.Because the probability density graph of the normal distribution resembles a bell, it is frequently referred to as the bell curve. In honor of the German mathematician Carl Gauss, who initially characterized it, it is often referred to as the Gaussian distribution.The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.
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not sure how to work it out
Answer:
u hv to do middle terms ig
Suppose the area of a rectangle is 9x3 + 27x2 + 36x + 18 and the length is 3x + 3. What is the width of the rectangle?• Width:
We know that the area of a rectangle is the width multiplied by its length, basically
[tex]A=b\cdot h[/tex]But here, we have the area, which is a polynomial, same for the length, then, to find out the width we must do a division of polynomial, I'll call the unknown polynomial as P, we have
[tex]\begin{gathered} A=P\cdot l \\ \\ P=\frac{A}{l} \\ \\ P=\frac{9x^3+27x^2+36x+18}{3x+3} \end{gathered}[/tex]So now we got to solve
[tex]P=\frac{9x^3+27x^2+36x+18}{3x+3}[/tex]There is a lot of ways to solve it, first, I'll factor 3 in the denominator
[tex]P=\frac{9x^3+27x^2+36x+18}{3(x+1)}[/tex]As well the numerator
[tex]P=\frac{3(3x^3+9x^2+12x+6)}{3(x+1)}[/tex]Then we can already simplify 3, and get an easier expression
[tex]P=\frac{3x^3+9x^2+12x+6}{x+1}[/tex]Now I'll factor using the grouping method, I want the numerator to be something like (x+1)*(another polynomial), doing that we can "cut" the (x+1).
One way to do it is to expand it in some simple sums, look at 3x³, we want a 3x² to match with him, but look that 9x² is 3x²+6x², let's write that way
[tex]P=\frac{3x^3+3x^2+6x^2+12x+6}{x+1}[/tex]It doesn't seem to help us at all, but look that now we can factor 3x², then
[tex]P=\frac{3x^2(x+1)+6x^2+12x+6}{x+1}[/tex]Look, we have our first (x+1) in the numerator. Let's use the same idea but now for the term 6x², we want a 6x to match with him, we have 12x, so let's write it as 6x + 6x.
[tex]P=\frac{3x^2(x+1)+6x^2+6x+6x+6}{x+1}[/tex]Similar to what we did before, factor 6x, and again
[tex]P=\frac{3x^2(x+1)+6x(x+1)+6x+6}{x+1}[/tex]Now we have one more (x+1).
Now the easiest one, factor 6
[tex]P=\frac{3x^2(x+1)+6x(x+1)+6(x+1)}{x+1}[/tex]As we can see we have (x+1) multiplied by something in all terms in the numerator, then we can factor (x+1) now
[tex]P=\frac{(x+1)(3x^2+6x+6)}{x+1}[/tex]Now we can cancel (x+1), and our final expression will be
[tex]P=3x^2+6x+6[/tex]Therefore, the width is
[tex]3x^2+6x+6=\text{ width}[/tex]Is (
–
4,
–
5) a solution to this system of equations?
y=
–
2x–13
y=
–
x+1
Answer:
Step-by-step explanation:
solution = (4 , 5)
y = 5 / x = 4
y = 2x - 13
5 = 2(4)- 3
5 = 8 - 3
5 = 5
the equation does make sense
y = x + 1
5 = 4 + 5
5 = 5
the equation does make sense
However, the questions asks if the solution works for both equations, and the solution does work for the first equation and the second one as well. The answer is yes, the solution does work for this system of equations.
Write an equation of the line that passes through the given point and is parallel to the graph of the given equation (-8,6);x+4y=20
The equation of the line that passes through the point (-8,6) is x + 4y = 16.
What is a slope?
A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given:
point = (-8,6)
equation : x+4y=20
x+4y=20
=> 4y = -x + 20
=> y = - x/4 + 5
Here the slope m is -1/4.
Now as the lines are parallel therefore the slope will be equal.
Therefore from the slope intercept form,
y - y1 = m (x - x1)
=> y - 6 = -1/4 ( x + 8 )
=> y - 6 = -x/4 - 2
=> x/4 + y = 4
=> x + 4y = 16
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Lesson 3 Practice Problems
1. Noah is running a portion of a marathon at a constant speed of 6 miles per hour.
Complete the table to predict how long it
would take him to run different distances
at that speed, and how far he would run in
different time intervals.
time
in hours
1
11/2012
13
miles traveled at
6 miles per hour
1/1/2012
9
4/1/2
The complete table when Noah is running a marathon at a constant speed of 6 miles per hour is mentioned below:
Time Distance
1 6
1/2 3
[tex]1\frac{1}{3}[/tex] 8
[tex]1\frac{1}{2}[/tex] 9
9 54
[tex]4\frac{1}{2}[/tex] 27
The running speed of Noah is 6 mph.
The formula for distance is given as:
D = v × t
Where D is the distance, v is the speed and t is the time.
Now,
When t = 1 hour,
D = 6 × 1 = 6 miles
When t = 1/2hour,
D = 6 × 1/2 = 3 miles
When t = [tex]1\frac{1}{3}[/tex] hour,
D = 6 × [tex]1\frac{1}{3}[/tex] = 6 × 4/3 = 8 miles
When t = [tex]1\frac{1}{2}[/tex] hour,
D = 6 × [tex]1\frac{1}{2}[/tex] = 6 × 3/2 = 9 miles
When t = 9 hours,
D = 6 × 9 = 54 miles
When t = [tex]4\frac{1}{2}[/tex] hour,
D = 6 × [tex]4\frac{1}{2}[/tex] = 6 × 9/2 = 27 miles
Therefore, the table will be:
Time Distance
1 6
1/2 3
[tex]1\frac{1}{3}[/tex] 8
[tex]1\frac{1}{2}[/tex] 9
9 54
[tex]4\frac{1}{2}[/tex] 27
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The weight, in pounds, of a certain type of adult squirrel is normally distributed with a mean of 4. 1 pounds and a standard deviation of 0. 5 pounds. What is the probability that a randomly selected squirrel has a weight less than 3 pounds? round your answer to four decimal places.
The percentage of squirrels that have a weight between 3 and 5 pounds is; 95.017%
What is percentage?In mathematics ,a percentage is a number that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. If you need to convert a decimal number like 0.57 to percent just multiply by 100 So 0.57 x 100 = 57. So as a percentage, 0.57 equals 57%. Percentage can be calculated by dividing the value by the total and multiplying the result by 100. The formula used to calculate the percentage is (value/total) x 100%.To learn more about percentage from the given link :
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Question 11 (1 point)
Find the slope between the two given points.
Answer:
Step-by-step explanation:
i would say a
2/3 ( 3/5 - 3/4) + 1/2÷1/4
Answer:
1.9
Step-by-step explanation:
Which expression is equivalent to the given expression?
-2x² + 8x 9 + 4x + 7x² + 2
A. -9x²
OB.
c.
-
D.
12x + 11
-5x² + 4x + 11
-9x² + 4x - 7
5x² + 12x - 7
Answer:
[tex]5x^{2} +12x-7[/tex]
Step-by-step explanation:
first, we need to simplify the expression: [tex]-2x^{2} +8x-9+4x+7x^{2} +2[/tex]we know that [tex]-2x^{2}[/tex] and [tex]7x^{2}[/tex] have the same exponent ([tex]x^{2}[/tex]) so we can combine them[tex]-2x^{2} +7x^{2} =5x^{2}[/tex]now we have left is [tex]+8x-9+4x+2[/tex]we also see that 8x and 4x have the same exponent (x). now we combine them8x+4x=12xnow we have left is -9+2-9 and 2 can be combined together-9+2=-7now we put each exponent in order (x^power biggest to least)(ex; [tex]x^{6}x^{5} x^{3}[/tex]) then just x then numbers without xit should be[tex]5x^{2} +12x-7[/tex]Algebra 1-Semester 1
What is the value of x in this equation
3(2x - 5)- 4x + 8 = -1.
Answer: x=3
Step-by-step explanation:
6x-15-4x+8=-1
2x-7=-1
2x=6
x=3
Given that points A, B, and Care the midpoints of their respective sides, which of the
following is true about the figure?
A) 1/2YZ = AC
B) BC | AB
C) ZX || AX
D) 2YZ = AC
Given that points A, B, and C are the midpoints of their respective sides, A) 1/2YZ = AC is true about the figure according to SSS congruent rule.
What is congruent rule?Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and angles have the same measure. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "."
When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general.
However, all six dimensions must be discovered. In light of this, it is possible to determine the congruence of triangles using just three of the six values. Triangles that are congruent have equal corresponding sides and angles.
YX = 2 × AX (A = midpoint of YX)
ZX = 2 × CX (C = midpoint of ZX)
∠X and ∠X are congruent as the Reflexive property rule.
Therefore, triangle XAC is congruent to triangle XYZ (SAS similarity theorem)
Since 2AX = XY and 2XC = XZ Then 2AC = YZ which SSS congruent rule.
So, the correct option is A) 1/2YZ = AC
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How many 5-digit numbers can you form using the digits 8, 9, and 0?
Number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162
The numbers are 8, 9 and 0
Combination is the one of the method to show the number of arrangements the from collection of objects or numbers
Here we have to form 5 digits numbers using the digits 8,9 and 0
The ten thousand's place can be only filled with 8 or 9, we cant fill the digit 0 on the ten thousands place,
In remaining places we can fill all three digits
Therefore the number of combination = 2 × 3 × 3 × 3 × 3
= 162
Hence, number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162
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Find the new price on a $14.50 shirt marked up 35%
Show Work.
Answer:$19.575
Solution
135/100of $14.50
=$19.575
or 35/100 of $14.50
=$5.075
$14.50+5.075
=$19.575
