Answers
The composite functions are listed below:
g ° f(3) = 29 g ° f(x + 1) = 2 · x² - 1 h ° g (- 3 · x) = - 36 · x - 36 f ° g (- 2 - t) = 73 + 72 · t + 16 · t² f ° g (x²) = 3 · x² + 17How to evaluate composite functions
In this problem we find five cases of composite functions, each of which has to be evaluated. A composition between the two functions f and g is defined below:
f ° g(x) = f ( g(x) )
Now we proceed to evaluate each of the five cases by using algebra properties and the definition of the composition of functions:
Case 1
g ° f(3) = g( f(3) )
g ° f(3) = 4 · (2 · 3 + 2) - 3
g ° f(3) = 4 · 8 - 3
g ° f(3) = 29
Case 2
g ° f(x + 1) = g( f(x + 1) )
g ° f(x + 1) = 2 · [(x + 1)² - 2 · (x + 1)] + 1
g ° f(x + 1) = 2 · (x² + 2 · x + 1 - 2 · x - 2) + 1
g ° f(x + 1) = 2 · (x² - 1) + 1
g ° f(x + 1) = 2 · x² - 1
Case 3
h ° g (- 3 · x) = h( g (- 3 · x) )
h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]
h ° g (- 3 · x) = 3 · (- 12 · x - 12)
h ° g (- 3 · x) = - 36 · x - 36
Case 4
f ° g (- 2 - t) = f( g (- 2 - t))
f ° g (- 2 - t) = [4 · (- 2 - t) - 2]² + 1 + 2 · [4 · (- 2 - t) - 2]
f ° g (- 2 - t) = (- 8 - 4 · t - 2)² + 1 + 2 · (- 8 - 4 · t - 2)
f ° g (- 2 - t) = (- 10 - 4 · t)² + 1 + 2 · (- 10 - 4 · t)
f ° g (- 2 - t) = 100 + 80 · t + 16 · t² + 1 - 20 - 8 · t
f ° g (- 2 - t) = 73 + 72 · t + 16 · t²
Case 5
f ° g (x²) = f( g(x) )
f ° g (x²) = 3 · (x² + 4) + 5
f ° g (x²) = 3 · x² + 12 + 5
f ° g (x²) = 3 · x² + 17
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Related Questions
Find the values of the unknown angles marked with letters. please help me- it is about alternate angles
100 points!!!
a ?
b ?
c ?
d ?
Answers
Answer:
Step-by-step explanation:
Find either c or d first. Those are easy and everything will fall into place after those 2 are found.
c: angle c is supplementary with 115. That means that they add up to equal 180; therefore, 115° + c° = 180° so c = 65°.
d: angle d is supplementary with 70. Therefore, 70° + d° = 180° so d = 110°.
a and c are same side interior, so they are also supplementary. That means that a = 115°.
b and d are also same side interior, so they are also supplementary. That means that b = 70°.
Is √ 3x² 5y is a polynomial?
Answers
Answer: yes
Step-by-step explanation:
need help asap! will give brainliest
Answers
Answer:
C. 30 ÷ 6 = 5
Step-by-step explanation:
A. incorrect
6 - 5 is not equal to 11, it is equal to 1
B. incorrect
6 × 30 is not equal to 5, it is equal to 180
C. CORRECT
30 ÷ 6 is equal to 5
D. incorrect
11 + 5 is not equal to 6, it is equal to 16
You buy a meal for 20$. You gave a 15% tip and paid 2% before the tip. What is the total for the bill?
Answers
Answer:23.4$
Step-by-step explanation:
Allison is evaluating the expression -5-(-2) using integer tiles. She begins with 5 negative tiles as shown
VX
What should Allison do next to find the value of the expression?
remove 2 negative tiles
remove 3 negative tiles
add 2 negative tiles
Add 7 negative tiles
Answers
Answer:
its B. -3
Step-by-step explanation:
Remove 3 negative tiles .
Can I get brainliest??????
Answer:
Step-by-step explanation:
its b
When 4 times the number x is added to 12, the
result is 8. What number results when 2 times x is
added to 7 ?
A) −1
B) 5
C) 8
D) 9
Answers
The value of given linear equation is 5.
What is a linear equation?Linear equation refers to a equation that has highest degree = 1 and can be expressed in the form 'ax + b'.
Given: 4 times x + 12 gives 8
To find: 2 times x + 7
With the help of the details given in the question, we get the linear equation: 4x + 12 = 8
=> 4x = 8 - 12
=> 4x = -4
=> x = -1
Now, 2x + 7 =?
For x = -1, 2 (-1) + 7 = -2 + 7 = 5
Thus, the value of given linear equation is 5.
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Jackie's Burger Place made 24 burgers. 14 of the burgers had onions. What is the ratio of the number of burgers without onions to the number of burgers with onions?
Answers
Answer:
24:14
Step-by-step explanation:
Find all values of $x$ such that 9+27/x+8/(x^2)=0
Answers
Answer:
Step-by-step explanation:
Multiply by x^2 on both sides
9x^2+27x+8=0
Factor.
The answers are -1/3, -8/3
the vertices of triangle wxy are located at w(-14,20). x(10,4) and y (-2,-4). what is the approximate length of the midsegment parallel to xy?
Answers
The approximate length of the midsegment parallel to xy is 6.63
The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.
To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.
Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.
First, let's find the midpoint of side xw:
Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)
Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )
The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Length line of midpoint xw and midpoint yw :
√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44
So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63
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PLEASE HELP, #30 and #40 !! DUE SOON
Answers
Answer:
38. x = 60
40. x = 10
Step-by-step explanation:
38.
The segment labeled 30 connects the midpoints of two sides of a triangle, so it is parallel and half the length of the third side.
x = 2 * 30 = 60
40.
Look at the big outer triangle.
Its left side has length x. It is made up of two segments that are congruent.
The right side of the big triangle is made up of two segments that are congruent and are also congruent to the segments of the left side. That makes the left and right sides of the big triangle congruent. This is an isosceles triangle, so its base angles are congruent. The left base angle measures 60, so the right base angle also measures 60. That means the top angle also measures 60. This triangle is isosceles and equilateral.
Since the segment measuring 5 has endpoints that are midpoints of two sides of a triangle, it is parallel to the third side and half its length.
The bottom side of the triangle measures 2 * 5 = 10. Since the triangle is equilateral, then x = 10.
what is the distance between 5,4 and -1,1
Answers
Answer:
3\(\sqrt{5}\)
Step-by-step explanation:
Calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 1, 1)
d = \(\sqrt{(-1-5)^2+(1-4)^2}\)
= \(\sqrt{(-6)^2+(-3)^2}\)
= \(\sqrt{36+9}\)
= \(\sqrt{45}\)
= 3\(\sqrt{5}\) ← exact value
≈ 6.71 ( to 2 dec. places )
Help me answer all of them ;-;
Answers
Answer:
2) D, 3) A, 4) A, 5) B
Step-by-step explanation:
2) We proceed to demonstrate the statement algebraically:
(i) \(3\cdot (m+2)-4\cdot (2\cdot m -9)\) Given.
(ii) \(3\cdot m + 6 + (-4)\cdot (2\cdot m) +(-4)\cdot (-9)\) Distributive property.
(iii) \(3\cdot m +6 +[(-4)\cdot (2)]\cdot m + (-4)\cdot (-9)\) Associative property.
(iv) \(3\cdot m + 6 -8\cdot m + 36\) \((-a)\cdot b = -a\cdot b\)/\((-a)\cdot (-b) = a\cdot b\)
(v) \(-5\cdot m +42\) Distributive property/Definition of addition/Result.
Answer: D
3) We proceed to demonstrate the statement algebraically:
(i) \(-2\cdot (4\cdot x -5\cdot y - 5\cdot x )\) Given.
(ii) \(-2\cdot [(4-5)\cdot x - 5\cdot y]\) Associative and distributive properties.
(iii) \(-2\cdot (-x-5\cdot y)\) Definition of addition.
(iv) \((-2)\cdot (-x) + [(-2)\cdot (-5)]\cdot y\) Distributive and associative properties.
(v) \(2\cdot x + 10\cdot y\) \((-a)\cdot (-b) = a\cdot b\)/Result
Answer: A
4) We proceed to demonstrate the statement algebraically:
(i) \(-\frac{8}{9}\cdot \left(27+\frac{2}{3}\cdot x \right)\) Given.
(ii) \(\left(-\frac{8}{9} \right)\cdot (27) + \left[\left(-\frac{8}{9} \right)\cdot \left(\frac{2}{3} \right)\right]\cdot x\) Distributive property.
(iii) \(-24-\frac{16}{27}\cdot x\) \(\frac{a}{b}\cdot c = \frac{a\cdot c}{b}\)/\((-a)\cdot b = -a\cdot b\)/Associative property/\(\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}\)/\(\frac{a\cdot c}{b\cdot c} = \frac{a}{b}\)/Result
Answer: A
5) We proceed to demonstrate the statement algebraically:
(i) \(-\frac{1}{3}\cdot \left(3\cdot x -\frac{1}{2} \right)\) Given.
(ii) \(\left[\left(-\frac{1}{3} \right)\cdot 3\right]\cdot x +\left(-\frac{1}{3} \right)\cdot \left(-\frac{1}{2} \right)\) Distributive property.
(iii) \(-x +\frac{1}{6}\) \((-a)\cdot b = -a\cdot b\)/\((-a)\cdot (-b) = a\cdot b\)/\(\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}\)/\(\frac{a\cdot c}{b\cdot c} = \frac{a}{b}\)/Result
Answer: B
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answers
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Do
this mathematics operations using the rules of precision
(9.11)+(6.232)
(7.4023)x(19)
(9.162)-(2.39)
(0.00482)x(213)
(8.73)/(5.198)
(7644)/(0.13)
Answers
Answer:
Step-by-step explanation:
Sure! I'll perform the mathematical operations using the given numbers and apply the rules of precision. Please find the results below:
(9.11) + (6.232)
The sum of 9.11 and 6.232 is 15.342.
(7.4023) x (19)
The product of 7.4023 and 19 is 140.844.
(9.162) - (2.39)
The difference between 9.162 and 2.39 is 6.772.
(0.00482) x (213)
The product of 0.00482 and 213 is 1.02786.
(8.73) / (5.198)
The division of 8.73 by 5.198 is 1.67920734.
(7644) / (0.13)
The division of 7644 by 0.13 is 58,800.
Please note that the results are rounded to the appropriate number of decimal places based on the precision rules.
Can you please help me?
Answers
Answer:
want points
Step-by-step explanation:
sorry
Triangle ABC is dilated to create triangle DEF on a coordinate grid. You are given that angle A is congruent to angle D. What other information is required to prove that the two triangles are similar?
1) Angle B is congruent to angle D.
2) Segments AB and DE are congruent.
3) Angle B is congruent to angle E.
4) Segment AC is congruent to segment DF, and segment BC is congruent to segment EF.
ITS NOT OPTION 4!!!
Answers
Answer:
The correct option is;
Angle B is congruent to angle E
Step-by-step explanation:
The given parameters are;
Triangle ΔABC, is dilated into triangle ΔDEF
Therefore, ∠A, ∠B, and ∠C of triangle ΔABC corresponds with ∠D, ∠E, and ∠F, of triangle ΔDEF
Given that ∠A is congruent to ∠D, the other information required to prove that the two triangles are similar includes;
1) ∠B is congruent to ∠E which are corresponding angles
2) ∠C is congruent to ∠F which are also corresponding angles
Therefore, the correct option is angle B is congruent to angle E
Select all terms that are like terms 5 yx2 -8 x2 1.25 x2 1/2 x2 -3.4 x3 4 x 5 3/8
Answers
please can you simplify -x+2z+x+2y
Answers
Answer:
2y + 2z
Step-by-step explanation:
-x + 2z + x + 2y
= (-1 + 1)x + 2y + 2z
= 2y + 2z
Hope this helped!
each side of a square is increasing at a rate of 7 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm2?
Answers
If each side of a square is increasing at a rate of 7 cm/s, then the rate of increasing the area of the the square when the area of the square is 64 cm square is 112 centimeter square per second
The rate of change of length with respect to the time = 7 cm per second
That is
dl / dt = 7 cm per second
The area of the square = l^2
Where l is the length of the square
The rate of change area with respect to the time is
dA / dt = 2l dl/dt
The area is given that 64 centimeter square and the side will be 8 cm
Substitute the values in the equation
dA / dt = 2 × 8 × 7
= 112 centimeter square per second
Therefore, the rate of increasing the area is 112 centimeter square per second
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Anyone know how to do this?
Answers
Answer: 21. 4 22. 5
Step-by-step explanation:
Where could point E be if BCDE and D is between E and B?
A. -1
B. 0
C. 1
D. 2
Answers
Answer:
D, 2
Step-by-step explanation:
In the question it states that the distance between B and C is the same distance between D and E.
A circular trampoline has a padded rope that goes aroumd the outside of the frame. The rope is sold for $2.75 per foot and costs $104.50 before tax this trampoline. What is the diameter of the trampoline, to the nearest foot?
Answers
Answer: The diameter is 12ft.
Step-by-step explanation:
The length of the rope will be equal to the perimeter of the trampoline.
We know that the trampoline is circular, so the perimeter of a circle can be written as
P = 2*pi*r
where r is the radius, and pi = 3.14...
Then we now should find the perimeter.
if 1ft of rope costs $2.75
now, how many times we can fit $2.75 in $104.50?
We look at the quotient
$104.50/$2.75 = 38
So 38 times, this means that the full rope is 38 times 1 ft, or 38 ft long.
Then the perimeter of the circle is 38ft.
P = 38ft = 2*3.14*r
Now we can find the value of the radius:
r = 38ft/(2*3.14) = 6.05 ft
Now, we want to find the diameter, and we know that the diameter is two times the radius, then:
d = 2*r = 2*(6.05ft) = 12.1 ft.
But we want this to the nearest foot, so we should round it down to 12ft.
The diameter is 12ft.
i have 2 pinapple farms the rayio of their perimeter is 5:8 and the perimeter of the larger farm is 80 yards fencing cost$0.50 a yard if i want to buold a fence around the smaller farm how much will it cost me
Answers
Answer:
$40
Step-by-step explanation:
If the perimeter of the larger farm is 80 yards in a 8:5 ratio, the perimeter of the smaller farm will be 50 yards.
Multiply this value by the cost of 0.50 per yard to get $40.
PLS HELP MEMEMEMEME
Determine if triangle RST and triangle UVW are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answers
The two triangles ΔRST and ΔUVW are similar to each other by the SAS property.
What is the similarity?Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.
Given that there are two triangles ΔRST and ΔUVW. ΔRST has the angle ∠T = 59° and the sides RT = 15 units and ST = 13 units. The other triangle ΔWVU has the angle ∠W = 59° and the sides WV= 52 units and WU= 60 units.
Firstly the two angles are the same,
∠T= ∠W = 59°
The two sides are dilated by a scale factor of 4,
WV / ST = 52 / 13 = 4
WU / RT = 60 / 15 = 4
So these sides are similar.
Hence, from the SAS property, the two triangles are similar.
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What is the slope of y=-4x-3
Answers
Answer:
Using the slope-intercept form, the slope is 4 .
Answer:
the slope of this is 10
Step-by-step explanation:because while you solve -4 and x-3 you have to divide then subtract to the point get to ten. hope this helps
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High frequency EM is thought to be a cause of cancer; the lower frequencies associated with household current are generally assumed to be harmless. The following table summarizes the probability distribution for cancer sufferers and their wiring configuration in the Denver area.
Leukemia Lymphoma Other Cancers
High Frequency wiring 0.242 0.047 0.079
Low frequency wiring 0.391 0.098 ???
(a) What is the missing probability (labelled ???) in the above table?
(b) What is the probability of having high frequency wiring among cancer suffers in the Denver area?
(c) Is the event "Having Leukemia" independent of the event "Having high frequency frequency wiring"? Explain.
Answers
Answer:
\(x = 0.143\)
\(P(High\ |\ Cancer) = 0.215\)
Not independent
Step-by-step explanation:
Given
See attachment for proper table
Solving (a): The missing probability
First, we add up the given probabilities
\(Sum = 0.242+0.047+0.079+0.391+0.098\)
\(Sum = 0.857\)
The total probability must add up to 1.
If the missing probability is x, then:
\(x + 0.857 = 1\)
Collect like terms
\(x = -0.857 + 1\)
\(x = 0.143\)
Solving (b): P(High | Cancer)
This is calculated as:
\(P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}\)
So, we have:
\(P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}\)
\(P(High\ |\ Cancer) = \frac{0.079}{0.368}\)
\(P(High\ |\ Cancer) = 0.215\)
Solving (c): P(Leukemia) independent of P(High Wiring)
From the attached table
\(P(Leukemia\ n\ High\ Wiring) = 0.242\)
\(P(Leukemia) = 0.242 + 0.391 =0.633\)
\(P(High\ Wiring) = 0.242+0.047+0.079=0.368\)
If both events are independent, then:
\(P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)\)
\(0.242 = 0.633 * 0.368\)
\(0.242 \ne 0.232\)
Since the above is an inequality, then the events are not independent
the graph below models the cost for installing a fence based on the length of the fence. Use the graph to awnser the following willA) find the slope of the graph B) what are the units of the slopeC) write a linear equation in slope intercept form for the total cost C in dollars of installing a fence if the length of your fence is F feet long
Answers
a. To find the slope of the graph take 2 ordered pairs and replace its values in the following equation:
\(m=\frac{y2-y1}{x2-x1}\)For example, choose (0,150) and (5,225):
\(m=\frac{225-150}{5-0}=\frac{75}{5}=15\)The slope of the graph is 15.
b. The units of the slope (since it is a rate of change) are dollars per feet.
c. We already have the slope of the graph and its y intercept which is (0,150). Use this information to find the slope intercept form equation for the situation:
\(C=15F+150\)A submarine dove from the surface at a rate of 50 meters per minute. It is now at a depth of 450 meters. Write a numeric equation using negatives to show the number of minutes it took to get to the current depth.
Answers
Explanation
Step1
let
\(\begin{gathered} \text{rate}=-50\frac{mt}{\text{sec}} \\ \text{rate}=\frac{dis\tan ce}{\text{time}} \end{gathered}\)\(\begin{gathered} y_1=initial\text{ position=0} \\ y_2=\text{ final positivion=-50} \\ \text{time}=\text{ 1 minute} \end{gathered}\)Step 2
equation
\(\begin{gathered} time=\text{ }\frac{\text{distance}}{-50}\text{ Equation(1)} \\ \\ \text{replacing} \\ \text{time}=\frac{-450\text{ mt}}{-50\text{ }\frac{mt}{\min}} \\ \text{time}=9\text{ minutes} \end{gathered}\)I hope this helps you
Solve for m
Enter only the numerical value in the box. Do not enter units.
Answers
Answer:
∠ C ≈ 73.7°
Step-by-step explanation:
using the sine ratio in the right triangle
sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AT}{CT}\) = \(\frac{48}{50}\) , then
∠ C = \(sin^{-1}\) ( \(\frac{48}{50}\) ) ≈ 73.7° ( to the nearest tenth )
Nancy's nut shop sells cashews for $5.30 per pound and peanuts for $2.80. How many pounds of peanuts must be added to 20 pounds of cashews to make a mix that sells for $3.30 per pound?
Answers
Answer:
80 pounds
Step-by-step explanation:
let 'p' = pounds of peanuts to be added
20(5.3) + 2.8p = 3.3(20 + p)
106 + 2.8p = 66 + 3.3p
40 = 0.5p
p = 80