Answer:
1/16
Step-by-step explanation:
F(-4) = 2^-4
= 1/(2^4) = 1/16
2. Graph the inverse of the function, then determine if the inverse is a function.
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of
the inverse of F(x). (2 points)
Part II: Is the inverse a function? Explain your answer. (3 points)
The inverse of the function f(x)= x^2 is a function.
The graph of the inverseThe equation of the function is
f(x)= x^2
Rewrite as:
y = x^2
Swap x and y
x = y^2
Make y the subject
[tex]y = \sqrt x[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt x[/tex]
So, the inverse of f(x)= x^2 is [tex]f^{-1}(x) = \sqrt x[/tex]
See attachment for the graph
Is the inverse a function?The inverse is a function.
This is so because it passes the vertical line test
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What are the first five terms, a1, a2, a3, a4, a5, of the sequence defined by a Subscript n = StartFraction n squared minus 9 Over n cubed + 3 EndFraction, and how can the sequence be described?
PLEASEEE HELP !!
Answer:
Step-by-step explanation:
So if you look at the numerator the degree is 2, and if you look at the numerator of the denominator, it's 3. This means that the value of the denominator will grow faster than the numerator, so it will diverge.
To find the first 5 terms simply plug in 1, 2, 3, 4, and 5 as n
[tex]a_1=\frac{1^2-9}{1^3+3} = \frac{-8}{4} = -2}\\a_2 = \frac{2^2-9}{2^3+3} = \frac{-5}{11} = -\frac{5}{11}\\a_3 = \frac{3^2-9}{3^3+3} = \frac{0}{30} = 0\\a_4 = \frac{4^2-9}{4^64+3} = \frac{7}{67} = \frac{7}{67}\\a_5 = \frac{5^2-9}{5^3+3} = \frac{16}{128} = \frac{1}{8}[/tex]
It should converge to a limit of 0, since the denominator is growing faster than the numerator
Answer:
C
Step-by-step explanation:
One hundred riders from several countries participated in a bicycle race. Only eighty riders, including Juan and Charlie, finished the race. Juan finished 5th and Charlie was the winner. All the riders' countries of origin and finishing times were recorded on the race register. No two riders who finished had the same time and those who did not finish were recorded as DNF.
Based on this information, determine if each set is well-defined. Yes or No
The set of riders who finished minutes or more after the winner (Yes or No)
The set of the three least tired riders at the end (Yes or No)
The set of riders with the best-looking bicycles (Yes or No)
The set of riders who finished the race (Yes or No)
The set of countries of origin of the riders that didn't finish (Yes or No)
Answer:
Finished minutes or more: Yes
Three least tired: No
Best looking bikes: No
Finished the race: Yes
Countries of origin of riders who didn't finish: Yes
Step-by-step explanation:
Things displayed on the board: name of rider, country of origin, finishing time
Finished minutes or more: anyone who finished who wasn't in first
Three least tired: subjective information, not on the board
Best looking bikes: subjective information, not on the board
Finished the race: everyone who doesn't have DNF next to their name
Countries of origin of riders who didn't finish: countries of anyone with DNF next to their name
Solve the following systems of equations
y= 3x^2 + 6x + 4
Y= -3x^2 + 4
show all work and solutions
Answer:
[tex](-1;1)[/tex] and [tex](0;4)[/tex]
Step-by-step explanation:
First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.
The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.
[tex]3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0[/tex]
which tells us that either [tex]x=0[/tex] or [tex]x=-1[/tex]
Now we can replace these value of x in one of the two to finish our work: [tex]x=0\rightarrow y= 4[/tex]
[tex]x=-1 \rightarrow y= -3+4=1[/tex]
8. In AABC, LA is a right angle and mzB = 45°. Find BC.
11√2 ft
√22 ft
2√11 ft
11 ft
Answer:
BC = 11[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin 45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{11}{BC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
BC = 11[tex]\sqrt{2}[/tex]
what statement is true
Answer:
D. Both graphs are exponential functions.
Step-by-step explanation:
Hope it helps :)
THE QUESTION IS DOWN BELOW.
major points when given branliest
The ratios are Surface area ⇒ 4 : 25 Height ⇒ 2 : 5 and Volume ⇒ 8 : 125
How to determine the ratios?The scale factor is given as:
m : n = 2 : 5
For the area, we take the square of the ratios.
i.e.
Area = 2^2 : 5^2
Evaluate
Area = 4 : 25
For the volume, we take the cube of the ratios.
i.e.
Volume = 2^3 : 5^3
Evaluate
Volume = 8 : 125
The given scale factor can be used for the height of the model and the original bicycle
Hence, the ratios are
Surface area ⇒ 4 : 25
Height ⇒ 2 : 5
Volume ⇒ 8 : 125
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Please help need answers
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\frak{Good\;Morning!!}[/tex]
[tex]\pmb{\tt{Question\;1}}[/tex]
[tex]\star\boldsymbol{\rm{Given-:}}[/tex]
Side length = 7 cm,Side length = 5 cm.[tex]\star\boldsymbol{\rm{We're\;looking\;for-:}}[/tex]
Side length = xThis is how it's done.
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.
The formula is. [tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.
Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!
[tex]\boldsymbol{\rm{7^2+5^2=c^2}}[/tex] | 7^2 simplifies to 49, and 5^2 simplifies to 25
[tex]\boldsymbol{\rm{49+25=c^2}}[/tex]. | add
[tex]\boldsymbol{\rm{74=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm{8.6=c}}}[/tex]. | the answer is given to 1 decimal place, as the problem required
[tex]\orange\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;2}}[/tex]
Once more, we're given two sides, and asked to find the third one,
which is still the longest side.
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex] is still the formula used here
Put in 5 for a and 3 for b.
[tex]\boldsymbol{\rm{5^2+3^2=c^2}}[/tex] | 5^2 simplifies to 25, and 3^2 simplifies to 9
[tex]\boldsymbol{\rm{25+9=c^2}}[/tex] | add
[tex]\boldsymbol{\rm{34=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm 5.8=c}}[/tex] | once again it's given to one decimal place
[tex]\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;3}}[/tex]
This problem is solved the exact same way
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{8.2^2+4.7^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{67.24+22.09=c^2}}[/tex]
[tex]\boldsymbol{\rm{89.33=c^2}}[/tex]
[tex]\boldsymbol{\rm{9.5=c}}[/tex], rounded to one D.P.
[tex]\orange\hspace{300pt}\above2[/tex]
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\pmb{\tt{Question4}}[/tex]
Here we have the longest side and one side length-:
[tex]\boldsymbol{\rm{4^2+b^2=7^2}}[/tex] | 4^2 simplifies to 16 and 7^2 simplifies to 49
[tex]\boldsymbol{\rm{16+b^2=49}}[/tex] | subtract 16 from both sides
[tex]\boldsymbol{b^2=33}[/tex] | square root both sides
[tex]\boldsymbol{\rm{b=5.7}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;5}}[/tex]
[tex]\boldsymbol{\rm{3.8^2+b^2=7.9^2}}[/tex]
[tex]\boldsymbol{\rm{14.44+b^2=62.41}}[/tex]
[tex]\boldsymbol{\rm{b^2=47.97}}[/tex]
[tex]\boldsymbol{\rm{b=6.9}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;6}}[/tex]
[tex]\boldsymbol{\rm{a^2+6.1^2=7.3^2}}[/tex]
[tex]\boldsymbol{\rm{a^2+37.21=53.29}}[/tex]
[tex]\boldsymbol{\rm{a^2=16.08}}[/tex]
[tex]\boldsymbol{\rm{a=4.0}}[/tex]
[tex]\pmb{\tt{done~!!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
John owns a clothing store that sells graphic T-shirts and shorts. He sells the
T-shirts for $6 each and the shorts for $14 each. He is limited to the
constraints show by the set of inequalities below. Which of the points (s, t)
will maximize John's profit?
A. (12,0)
B. (0, 13.33)
C. (25,5)
100
s≤ 40-30
s2 12-t
s≤ 30-t
s20
t≥ 0
The points (s, t) that will maximize John's profit is; (12, 0)
How to use Inequality Constraints?We are given the inequality constraints;
s ≤ 12 - 0.5t
s ≥ 10 - t
s ≤ 20 - t
s ≥ 0
t ≥ 0
We are told that John sells the T-shirts for $6 each and the shorts for $14 each. Since the coordinate point is (s, t), when we look at the options and compare with each of the constraints, it is clear that the points (s, t) that will maximize John's profit is; (12, 0)
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Two people are packing equal numbers of small boxes into large boxes.
One person has 3 large boxes that are full of smaller boxes and 24 small
boxes that are not yet packed. The other person has 5 large boxes that are
full of smaller boxes and 10 small boxes that are not yet packed. Each large
box holds the same number of small boxes. How many small boxes can
each large box hold? What is the total number of small boxes each person
will pack? How many large boxes will each person need in order to pack all of his or her small boxes?
Please answer as quickly as possible and as detailed as possible!!! Thanks!!!!!!
Answer:
29 small boxes
Step-by-step explanation:
Without actual calculating the cubes, evaluate using identities:
[tex]-11^3+8^3+3^3[/tex]
Answer:
-792
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{-11^3 + 8^3 + 3^3}[/tex]
[tex]\mathsf{= -11\times -11\times -11 + 8\times8\times8 + 3\times3\times3}[/tex]
[tex]\mathsf{= 121\times -11+ 64\times8+9\times3}[/tex]
[tex]\mathsf{= -1,331 + 512 + 27}[/tex]
[tex]\mathsf{= -819 + 27}[/tex]
[tex]\mathsf{= -792}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{-792}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which line has the same slope as the line passing through (-4, -1) and (-1, 5)
A line which has the same slope as the line passing through the given points is: C. y = 2x + 8.
Given the following data:
Points on x-axis = (-4, -1).Points on y-axis = (-1, 5).How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope = \frac{5\;-\;(-1)}{-1\;-\;(-4)}\\\\Slope = \frac{6}{3}[/tex]
Slope = 2.
Therefore, y = 2x + 8 is a line which has the same slope as the line passing through the given points.
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Complete Question:
Which line has the same slope as the line passing through (-4, -1) and (-1, 5)?
A. y = 3
B. 9x - 3y = 5
C. y = 2x + 8
D. the line passing through (1, 4) and (1, 7)
Twice the sum of two consecutive integers is 22. What are the two integers?
The consecutive two integers are 5 and 6
Linear equations
Let the two consecutive integers be (x+1) and (x). If twice the sum of two consecutive integers is 22 then;
2(x+1+x) = 22
x+x+1 = 22/2
2x + 1 = 11
Subtract 1 from both sides
2x = 11 - 1
2x = 10
x = 5
Hence the consecutive two integers are 5 and 6
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The radius of a car’s tire is 47.1 cm. Find the circumference of the tire. (This is the distance that the car must drive to rotate the tire exactly once.)
The circumference of the tire as described in the task content is; 295.8cm.
What is the circumference of the tire?It follows from the task content that the tire in discuss is circular and has radius; 47.1cm.
Hence, by the circumference formula; we have;
Circumference = 2πr = 2 × 3.14 × 47.1
Circumference = 295.8cm.
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Solve the inequalities by graphing. Select the correct graph. 2x - y > 4 2x - y < -2
The solution will be the point of intersection of the lines and since the lines are parallel to each other, there is no solution
System of inequality
Inequality are expressions not separated by an equal sign. Given the following inequalities
2x - y > 4
2x - y < -2
The lines for both inequality must be dashed since they do not include equal sign. The first line will be shaded in the upper part while the second in the lower portion
The solution will be the point of intersection of the lines
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Based on the family the graph below belongs to, which equation could represent the graph?
Answer:
the first option I believe
find x and y
pls help
Answer:
x = 14
Step-by-step explanation:
110 + 5x = 180
-110 -110
5x = 70
divide by 5 on both sides
x = 14
to find y add 70 + 40 + missing angle = 2y
missing angle is 70 because 70+40+70 = 180
so 2y = 110
y = 55
Answer:
x=14
y=55
Step-by-step explanation:
5x and 110 form a straight line so they add to 180
5x+110 =180
5x = 180-110
5x = 70
Divide by 5
5x/5 = 110/5
x = 14
We know the exterior angle of a triangle is equal to the sum of the two opposite interior angles
40 + 5x = 2y
Substitute in 14 for x
40 +5(14) = 2y
40 + 70 = 2y
110 = 2y
Divide by 2
110/2 =2y/2
55 = y
Fill in the blank with letter of the word that completes the sentence.
The sides of an angle are
Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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I need help ASAP! I need this within an hour from now!
Answer:
Definition of circle
Explanation:
1st - Given2nd - Definition of radius3rd - Distance formula4th - Definition of circle5th - Distance formula6th - Definition of circleAll the points that lies on the circle must be same distance from the center.
This is given by the definition of a circle.
AdditionalRadius is the length from the center to the points lying on the circle.
Distance formula: [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Diameter of circle is from one end point to another end point lying on circle.
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1. She paid $ 20 for both items. What fraction of the price of the first item is the price of the second item?
The fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1.
Total money Roxanne paid = $20
First item price = 20 - 1 = $19
The fraction of the price of the first item = 1/19
Thus, the fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
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the cost of 15kg of apples is 262.50. find the cost of 25kg of apples
Answer:
437.50 is the cost of 25kg of apple's.
In the parallelogram above what is the value of x?Please explain for brainlest
E.36
F.18
G.6
H.5
Answer:
[tex]\boxed{E.~36}[/tex]
Step-by-step explanation:
Supporting drawing in the attachment.
The sum of the measures of two consecutive angles is equal to 180°.
3x° + 2x° = 180°
5x° = 180° I ÷ 5
x° = 36°
E. 36Answer:
36
Step-by-step explanation:
I also did this for shsat
Listed below are measured amounts of caffeine obtained in one can from each of 14 brands. Find the variance, for the given sample data and leave the answer to the nearest hundredths.
57, 34, 30, 44, 33, 41, 60, 47, 56, 41, 31, 22, 12, 40.
Answer:
And here's your answer: 39.14
Step-by-step explanation:
First, add all the numbers up
then divide them all by 14
For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8. What is the fourth term?
Answer:
a₄=8n+1= -39.
Step-by-step explanation:
1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then
2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.
3) if n=-5, then the 4th term is:
[tex]a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;[/tex]
or a₄=-39.
Which transformation is not an isometry
From the shapes given, the third transformation is not an isometry.
What is an isometry?An isometry is a mathematical function used to describe the process of moving a geometric object without a changing its size or shape from one point to another.
Thus, from the shapes given, the third transformation is not an isometry.
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Pls help! Geometry
What is the area of the new rectangle?
Answer:
Step-by-step explanation:
Since the ladybug is [tex]3.3cm[/tex] far from each edge of the rectangle, it follows that the length of the new rectangle is [tex]3.3cm+9.5cm + 3.3cm = 16.1cm[/tex] and the width is [tex]3.3cm+7.5cm + 3.3cm = 14.1cm[/tex].
Recall a formula for the area of a rectangle: [tex]A = l \cdot w[/tex], where [tex]l[/tex] is a length and [tex]w[/tex] is a width of the rectangle.
Substitute [tex]l=16.1cm[/tex] and [tex]w=14.1cm[/tex] into the formula:
[tex]A=16.1cm\cdot 14.1cm[/tex]
Multiply the numbers:
[tex]A=[/tex] [tex]227.01cm^{2}[/tex]
Therefore, the required area is equal to [tex]227.01cm^{2}[/tex].
came across this question on my home work can some one please show how to sketch it correctly?
Answer:
Step-by-step explanation:
Martina runs 3/1/2 miles every day for 7 days . How many miles does she run altogether
Answer:
24.5
Step-by-step explanation:
All you have to is Multiply 3 1/2 by 7
3 1/2 x 7= 24.5
if a 20 ft tree casts a 15ft shadow, how long a shadow is cast
Answer:
25 ft
Step-by-step explanation:
c = √a^2 + b^2 = √20^2 + 15^2 = 25ft
Hooke me up with a 5 star and a thanks :)