Answer:
b) [tex]f^{-1}(x) = \frac{4x+5}{3}[/tex]
Step-by-step explanation:
b) To find the inverse function, switch the [tex]x[/tex] and [tex]y[/tex] variables and solve for [tex]y[/tex]:
[tex]f(x) = \frac{3x-5}{4}\\y = \frac{3x-5}{4}\\x = \frac{3y-5}{4}\\4x = 3y-5\\4x+5 = 3y\\\frac{4x+5}{3} = y\\f^{-1}(x) = \frac{4x+5}{3}[/tex]
Verify Answer:
[tex]f(1) = \frac{3(1)-5}{4} = -0.5\\f^{-1}(-0.5) = \frac{4(-0.5)+5}{3} = 1[/tex]
Out of all 252 twelfth graders, how many rode in a car to school? 11 74 111 114
Out of all 252 twelfth graders, 114 rode in a car to school
How to determine the number of students?The proportion of students that rode in a car is given as:
p = 45.24%
So, the number of students that rode in a car is:
Students = 45.24% * 252
Evaluate the product
Students = 114.008
Approximate
Student = 114
Hence, 114 rode in a car to school
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A picture frame can hold a photograph that is 16 inches long and 12 inches wide.
What is the area of the photo that fits the frame?
Answer: The area of the photo that fits the frame is 192 square inches.
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Area of a rectangle (A) = Length x width
Replacing with the values given and solving for A (area):
A = 16 x 12 = 192 in2
The area of the photo that fits the frame is 192 square inches.
Feel free to ask for more if needed or if you did not understand something.
What is x, the height of the tree?
Answer:
21 feet
Step-by-step explanation:
It increases by a rate of 2.33333333,we know this by doing 14 divided by 6. 9 x 2.33333333 is 21
(although this might be incorrect)
Answer:
21 feet
Step-by-step explanation:
Ratio between height and distance from point on ground :
9 ft / 6 ft1.5Taking ratio between x and 14 :
1.5 = x/14x = 14 × 1.5x = 21 feetTo get from home to her friend Rhianna's house, Grace would have to walk 1 mile due north.
To get from home to her friend Elise's house, Grace would have to walk 3 miles due east.
What is the straight-line distance between Rhianna's house and Elise's house? If necessary,
round to the nearest tenth.
Answer: All you would do is 3 miles north 4 miles east
Step-by-step explanation:
That is what gogle said lol
help asap pls pls pls
Answer:
the answer is 13, all you had to do was substitute 5 for N, so all you had to do was 3 + 2(5) which is 13
Right triangles below, find the values of the lengths d and h. Round your answers to the nearest tenth 
Answer:
Here is the answer...hope it helps
What is the answer? I need help
Answer:
10
Step-by-step explanation:
Square root of 74 is 8.6.
Using the pythagoras theorem,
7²+x²(half)=8.6²
49+x²(half)=74
x²=25, x=5
Now we found the half of x, we are going to add the other side which is 5+5=10
Can this please be worked out so I can have a better understanding?
Given the equation (picture 1)
and using the formula(picture 2)
find A, B, and C
Please if take your time to break it down for me so I can use it as a guide for the rest of the test!!! Thx <3 :)
Step-by-step explanation:
no, no, you use the equation to identify a, b and c.
then you use the formula with these values to get the solutions to the equation (the values of x for which the equation delivers 0).
always remember, a quadratic equation always has 2 solutions. sometimes at least one of them are not a real number, sometimes the 2 springs are equal, ...
x² - 4x - 2 = 0
a, b, c are the factors of the terms in x and the constant term.
so,
a = 1
b = -4
c = -2
x = (-b ± sqrt(b² - 4ac))/(2a)
x = (4 ± sqrt((-4)² - 4×1×-2))/(2×1) =
= (4 ± sqrt(16 + 8))/2 = (4 ± sqrt(24))/2 =
= (4 ± sqrt(4×6))/2 = (4 ± 2×sqrt(6)) / 2 =
= 2 ± sqrt(6)
x1 = 2 + sqrt(6)
x2 = 2 - sqrt(6)
Answer:
x = 4.45 and x=-0.45
Step-by-step explanation:
A = 1
B= -4
C = -2
= [tex]\frac{-(-4) \sqrt{ (-4)^{2} -4 (1)(-2) } }{2(1)}[/tex]
= [tex]\frac{4\sqrt{16+8} }{2}[/tex]
= [tex]\frac{4\sqrt{24} }{2}[/tex]
X = 4 + [tex]\sqrt{24}[/tex] / 2
x = 4.45
For x2
x= 4 - [tex]\sqrt{24}[/tex] / 2
x=-0.45
The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?
Answer:
Length: 18 inches
Width: 6 inches
Step-by-step explanation:
l+w=24
l=3w w=1w
3w+w=24
w=6
Length: 3*6=18 inches
Width: 6 inches
what is the approximate value for 683 divided by 19
Answer:
Your answer is: 36!
Step-by-step explanation:
Hope this helped :)
A bag contains 5 black marbles, 7 blue marbles, 3 green marbles, 4 red marbles, and 1 white marble. A marble is selected and then replaced. What is the probability of selecting a black marble?
Answer:
1/4
Step-by-step explanation:
5 black marbles out of 20 total is 5 /20 = 1/4
Consider the following shape. Find the value of x. Round your answer to two decimal places.
Answer: 7.81
Step-by-step explanation:
find the unit vector in the direction of v= 2i+ j + k
What shape does the net form
Answer:
The correct answer is cone.
Step-by-step explanation:
Hope this helps:) Goodluck!
Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.
Car 1 (value in dollars)
Year 1: 18,500
Year 2: 17,390
Year 3: 16,346.60
Car 2 (value in dollars)
Year 1: 18,500
Year 2: 17,500
Year 3: 16,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer.
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years.
Part C: Baxter wants to purchase a car that would have the greatest value in 10 years. Will there be any significant difference in the value of either car after 10 years? Explain your answer, and show the value of each car after 10 years.
Car 1: It is an exponential function that is given as P = 18,500 (0.9595)ⁿ and the price after 10 years is $12,235.5.
Car 2: It is a linear function that is given as 2000x + 3y = 55500 and the price after 10 years is $11,833.33.
And Yes, there is a significant difference.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.
Car 1 (value in dollars)
Year 1: 18,500
Year 2: 17,390
Year 3: 16,346.60
Car 2 (value in dollars)
Year 1: 18,500
Year 2: 17,500
Year 3: 16,500
The exponential function describes car 1.
Then the function will be
[tex]\rm P = 18500\times (0.95995)^n[/tex]
The linear function describes car 2.
[tex]\rm y \ - \ 18500 = \dfrac{-2000}{3}(x - 0)\\\\\\3y - 55500 = -2000x\\\\\\2000x +3y = 55500[/tex]
Then the value of the car 1 after 10 years will be
[tex]\rm P = 18500\times (0.95995)^{10}\\\\\\P = \$ \ 12,235.5[/tex]
Then the value of the car 2 after 10 years will be
[tex]\rm 2000 \times 10 +3y = 55500\\\\y = \$ \ 11,833.33[/tex]
Yes, there is a significant difference.
More about the function link is given below.
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what is the surface area of this solid?
_______ square meters
o 101
o 107
o 116
o 131
Answer:
The surface area of this solid is:
b. 107
Step-by-step explanation:
To understand this answer we need to analyze it. First, we have different geometric figures composing the solid. A pyramid and a rectangular prism. We need to obtain the surface, not the volume so we need to obtain the area of all the figures composing the pyramid and the prism without the hidden part of the pyramid base. We need to obtain the following areas:
2 rectangles with the following measures= W=2 L= 8
1 rectangle with the following measures= W=3 L=8
1 rectangle with the following measures= W=3 L 5
2 rectangles with the following measures= W=2 L=3
4 triangles with the following measures= B=3 H=4
Following the formula for the rectangles W x L we obtain a total area for them of 83 square meters.
Following the formula for the triangles b x h / 2 we obtain the following area: 24 square meters. Then we add both and obtain 107 square meters.
question on similar triangles attatched
Answer:
h = 24 cm
Step-by-step explanation:
The triangles are similar.
Their dimensions are proportional.
Finding scale factor :
DC/AE10/201/2Finding h :
h + h/2 = 363h/2 = 363h = 72h = 24 cmlength of a rectangular garden is 9m and breadth is 6m calculate it's area in mm2
Given
Length =9 m
Breadth =6 m
Area of the rectangle= (length × breadth) sq. units
=(9×6) m
2
=54 m
2
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You are planting a vegetable garden on a plot of land that is a sector of a circle, as shown below.
You want fencing along only the curved edge of the garden.
a. Use the figure to find the length of fencing you will need.
15 ft
75°
b. How much area will be available for planting?
Answer:
(a) 19.63 ft
(b) 147.26 ft^2
Step-by-step explanation:
(a) 75/360 degrees . 2 . pi . 15 = 19.63
(b) 75/360 degrees. pi . 15^2 = 147.26
Answer:
a) 19.63 ft (2 dp)
b) 147.26 ft² (2 dp)
Step-by-step explanation:
To find the length of the curved fence, use the formula for arc length of a circle.
To find the area of the vegetable garden, use the formula for area of a sector of a circle.
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 75°r = 15 ft[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (15)\left(\dfrac{75^{\circ}}{360^{\circ}}\right)\\ & = 30 \pi \left(\dfrac{5}{24}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf ft\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{75^{\circ}}{360^{\circ}}\right) \pi (15)^2\\& = \left(\dfrac{5}{24}\right)\pi \cdot 225\\& = \dfrac{375}{8} \pi\\& = 147.26\: \sf ft^2 \:(2\:dp)\end{aligned}[/tex]
Please help asap please
Answer:
3rd one
Step-by-step explanation:
Hi, please help me out with this math question I don't understand it.
Sorry for the black
15 POINTS
Answer:
[tex]3^{6}[/tex] is the answer your looking for
Step-by-step explanation:
Simplify using basic trigonometric identities
Answer:
1.cosx×cscx
=cosx×1/sinx
=cosx/sinx
=cotx
2.cotx×secx×sinx
=1/tanx×1/cosx×sinx
=1/tanx×sinx/cosx
=1/tanx×tanx
=1
hope it helps you
Someone help me with this please
Answer:
the answer is c=34
Step-by-step explanation:
use the pythogoras therom since there is a right angle triangle c2=a2+b2
hope this helped:)
Answer:
34
Step-by-step explanation:
[tex]Formula: a^2+B^2=C^2[/tex]
[tex]30^2= 900 \\\\16^2= 256\\\\900+256= 1156\\\\[/tex]
[tex]c^2=1156[/tex]
to find the answer we have to figure out what times itself = 1156
30x30=900 greater than 30 35x35=1225 less than 35
6x5= 9x6= 8x7= 2x3= please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Write a probability model for this experiment , and use the probability model to predict how many times Stacey would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places
The value of n is 50 and probability is 1/6, and 8.33 number of times Stacey would spin a 6.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Consider getting a 6 as a success. In this example, the chance of getting a 6 in a single spin is 1/6. The number of 6s in 50 spins can be considered a binomial random variable. Then, if X is the number of trials, we receive a score of 6 out of 50. Then there's the model below.
[tex]\rm P(X = k) = \binom{50}{K}\binom{1}{6}^k\binom{5}{6}^{50-k}[/tex]
From the binomial random variable of n trials with a probability of success of p.
We will have, n = 50, p = 1/6
Number of times Stacey would spin a 6 = 8.33
Thus, the value of n is 50 and probability is 1/6, and 8.33 number of times Stacey would spin a 6.
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(20POINTS) I WILL MARK BRAINLIEST IMAGE IS BELOW
Answer:
10.6
Step-by-step explanation:
It forms a right angle traingle so use
16^2-12^2=112
and
root of 112=10.5830052443
Answer:
10.6cm is the radius
Step-by-step explanation:
1)First You square the lateral height (12cm)
=144
2)Then you square the height (16cm)
=256
3)Then you subtract height squared from lateral height squared
256-144=112
4)Then Find the square root from the result of step 3
112 squared is 10.58 (round to the nearest tenth)
10.6 is your answer!
Hope this helps BRAINLIEST PLEASE
What is the value of z, rounded to the nearest tenth? use the law of sines to find the answer. 2.7 units 3.2 units 4.5 units 5.3 units
The triangle is a shape with 3 sides and angles. The value of z from the given figure to the nearest tenth is 3.2
Sine rule of triangleThe triangle is a shape with 3 sides and angles
From the given triangle, we will use the expression below to determine the value of z
2.6/sin51= z/sin76
simplify
z = 2.6sin76/sin51
z = 2.5227/0.7771
z = 3.246
Hence the value of z from the given figure to the nearest tenth is 3.2
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Im Not Sure of this. Can I get some help?
Answer: The amount of grain it can hold can also be called it's volume. 423.9
The formula for volume is PI × Raduis² × Height
And for the radius we divide the diameter by 2.
Answer:
Option A.
V = π × r(9)² × 15 ≈ 3,817.04
Which rounds closest to
3,815.10 inches
NEED HELP QUICKLY
(please include your work)
19. Solve for the angle x.
sin²(2x) = 1
A. 45° + 360°n, 135° + 360°n
B. 45° + 360°n, 135° + 360°n, 225° +
360°n
C. 225° +360°n
D. no solution
E. 45° +360°n, 135° + 360°n, 225° +
360°n, 315° +360°n
F. 45° + 360°n, 225° + 360°n
( A is incorrect)
Answer:
Choice E.
Step-by-step explanation:
sin^2 2x = 1
sin 2x = ± 1
So 2x = 90, 270 , 450, 630 etc
x = 45, 135, 225, 315 etc
= 45 + 360n, 135 + 360n, 225 + 360n, 315 + 360n
Which of the following is a statistical question?
Select one:
How many of Mrs. Malone's students earned an A for the first nine weeks?
How many students missed question #5 on Mrs. Malone's math test yesterday?
How many of Mrs Malone's students turn in their homework each day?
the answer is b
Step-by-step explanation:
hope this helps if not let me know have a blessed day
Answer:
See below for answers and explanation
Step-by-step explanation:
A statistical question has variability in collecting the data, and doesn't have one definitive answer:
Question 1: How many of Mrs. Malone's students earned an A for the first nine weeks? This is not a statistical question because you can narrow down exactly how many.
Question 2: How many students missed question #5 on Mrs. Malone's math test yesterday? This is not a statistical question because you can easily take all the worksheets done on the math test and find an exact number.
Question 3: How many of Mrs Malone's students turn in their homework each day? This is a statistical question because not every student will consistently turn in their homework each day, so there will be variability while collecting that data.
Hence, Question 3 is a statistical question