Answer:
a
Step-by-step explanation:
Helppp
The functions f and g are defined as follows:
#a
[tex]\\ \rm\Rrightarrow f(-4)[/tex]
[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]
[tex]\\ \rm\Rrightarrow -12+2[/tex]
[tex]\\ \rm\Rrightarrow -10[/tex]
#b
#1
[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]
Interchange x,y[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]
Find y
[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]
Inverse is
[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]
#2
[tex]\\ \rm\Rrightarrow gof(x)[/tex]
[tex]\\ \rm\Rrightarrow g(f(x))[/tex]
[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]
If we factor out
[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]
[tex]\\ \rm\Rrightarrow 2x+1[/tex]
#c
[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]
[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7[/tex]
[tex]\\ \rm\Rrightarrow x=-1[/tex]
Answer:
Given functions:
[tex]f(x)=3x+2[/tex]
[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]
Part (a)
[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]
Part (b)(i)
[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]
Part (b)(ii)
[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]
Select the correct answer from each drop-down menu.
Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.
In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.
∠EIA ≅ ∠IKC and ∠GJB ≅ ∠JLD because they are corresponding angles of parallel lines cut by a transversal.
So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________
A. Subtraction of Property
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the ____
A. Vertical Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.
m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____
A. Subtraction Property of Equality
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
Therefore, ∠IKL and ∠JLD are supplementary angles.
We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL ≅ ∠DLH by the ____
A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Linear Pair Theorem.The angle is Applying the Transitive Property of Congruency and product of m∠IKL + m∠JLD = 180°.Therefore, ∠IKL ≅ ∠DLH by the Congruent Supplements TheoremWhat is the Transitive property of congruence?This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD and as such angle is Applying the Transitive Property of Congruency because if A =b, and b = c then A = c and therefore, the above is true.
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surface area of a square pyramid with side length 6 yd and slant height 7 yd
Check the picture below.
so the pyramid is really 4 triangular faces with a base of 6 and a height of 7, and a 6x6 square at the bottom.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangular faces}}{4\left[\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{7}) \right]}~~ + ~~\stackrel{square}{(6)(6)}}\implies 84~~ + ~~36\implies 120~yd^2[/tex]
Answer:
127.38
Step-by-step explanation:
The surface area formula for a square pyramid is:
A = a^2 + 2a * sqrt[ (a^2 / 4 ) + h^2 ]
So we input the base height as the a value, and the slant as H)
A = 6^2 + 2(6) * sqrt[ (6^2 / 4 ) + 7^2 ]
When using the exponents we get:
A = 36 + 2(6) * sqrt[ (36) / 4 ) + 49 ]
Then multiply/divide:
A = 36 + 12 * sqrt[ (9) + 49 ]
Then add the value in the sqrt.
A = 36 + 12 * sqrt[ 58 ]
Now, if we find the sqrt of 58, we get: sqrt[ 58 ] ≅ 7.615
A = 36 + 12 * 7.615
When multiplying we get:
A = 36 + 91.38
Finally, after adding, the surface area of the square pyramid is:
A = 127.38
Please solve this ASAP!!!
The graph represents f(x) = [x]+3.
5
44
034
2-
1
3-2-1₁
-2
-3
--4-
-5
+
you
2 3 4 5
What is f(-2.2)?
O-2
0 0
O 1
02
Answer:
[tex]\large\text{$ f(-2.2)=1 $}[/tex]
Step-by-step explanation:
Given function:
[tex]\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}[/tex]
This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.
When graphing a Ceiling Function:
open dot means "not including"solid dot means "including"The Ceiling Function gives us the nearest integer up.
So the ceiling of x = -2.2 is -2, as the greatest integer that is more than (or equal to) -2.2 is -2
Therefore:
[tex]\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}[/tex]
This is confirmed when using the graph to solve.
To find f(-2.2), locate x = -2.2 on the graph.
Trace up vertically until a step is reached.
The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.
Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.
Therefore, f(-2.2) = 1
Let's see
[tex]\\ \rm\Rrightarrow f(x)=[x]+3[/tex]
[tex]\\ \rm\Rrightarrow f(-2.2)[/tex]
[tex]\\ \rm\Rrightarrow [-2.2]+3[/tex]
[tex]\\ \rm\Rrightarrow -2+3[/tex]
[tex]\\ \rm\Rrightarrow 1[/tex]
So
f(-2.2)=1help solving the sheet
Answer:
[tex]x > - 1 \\ the \: answer \: is \: {d}[/tex]
what is an equation of the line that passes through the point (-4, -6) and is perpendicular to the line 4x+5y=25 ?
Answer:
5x -4y = 4
Step-by-step explanation:
An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.
__
new lineSwapping the coefficients gives us ...
5x +4y = c . . . . . for some constant c
Negating the y-coefficient (so the x-coefficient remains positive) gives ...
5x -4y = c
constantPutting (x, y) = (-4, -6) into the equation gives us the value of c:
5(-4) -4(-6) = c
-20 +24 = c = 4
equationThe line perpendicular to the given line and through the point (-4, -6) will have equation ...
5x -4y = 4
A skier skis CCW along a circular ski trail that has a radius of 1.9 km. She starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. Let t represent the number of hours since she started skiing. Write an expression in terms of t to represent the number of radians that would need to be swept out from the East side of the ski trail (3 o'clock position) to reach the skier's current position. Write an expression in terms of t to represent the skier's distance East of the center of the circular ski trail (in km). Write an expression in terms of t to represent the skier's distance North of the center of the circular ski trail (in km).
The expressions of the number of radians can be expressed in the ways below.
How to write the expressionsThe radius = 1.9 km
The angular speed = 3.1 radians per hour
a. The expression of t from the number of radians
θ = π/2 + 3.1t
b. Expression from the Eastx = rcosθ
= 1.9cos(π/2 + 3.1t)km
c. Expression from the north of the center= rsinθ
= 1.9sin((π/2 + 3.1t)km
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If the measure of angle 4 is 132°, what is the measure of angle 7?
32°
48°
132°
148°
The sum of supplementary angles is 180 degrees. The measure of angle 7 is 48 degrees
Supplementary anglesThe sum of supplementary angles is 180 degrees.
Let the supplement of the angle be "x", so that;
x + 132 = 180
Subtract 132 from both sides
x + 132 - 132 = 180 - 132
x =. 180 - 132
x = 48 degrees
Hence the measure of angle 7 is 48 degrees
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What is the diameter of a circle that has a circumference of 120 pi
Answer:
38.1971
Step-by-step explanation:
The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971
Translate the shape A four squares right and two squares down.What are the coordinates of the vertices of the image?.
The translated vertices are:
A' = (5, 2)B' = (5. -1)C' = (7. -1)What are the coordinates of the vertices of the image?.The vertices of the original figure are:
A = (1, 4)B = (1, 1)C = (3, 1).Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).
This means that the translated vertices are:
A' = (1 + 4, 4 - 2) = (5, 2)B' = (1 + 4, 1 - 2) = (5. -1)C' = (3 + 4, 1 - 2) = (7. -1)If you want to learn more about translations:
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At a school dance, tickets are sold at the door and each ticket is the same price. the amount of money the school makes from the dance is equal to the total amount of money collected from ticket sales minus the total cost of the dj and decorations. for this dance, the total cost is fixed and is not dependent on the number of tickets sold. if 75 tickets are sold, the school loses $150. if 100 tickets are sold, the school makes $100. what is the total cost of the dj and decorations?
Answer:
$900
Step-by-step explanation:
x = the cost of the tickets
y = the cost of dj & decorations
In the first situation, the profit of -$150 = 75x - y
In the second situation, the profit of $100 = 100x - y
Using the first situation, we isolate y as follows:
-150 = 75x - y
Add y to each side: y-150 = 75x
Add 150 to each side to isolate y
y = 75x + 150
Use this formula in the second situation in place of the y
Original formula: 100 = 100x - y
With substitution: 100 = 100x - (75x + 150)
Simplify to: 100 = 25x - 150
Add 150 to both sides: 250 = 25x
Divide both sides by 25: 10 = x
Input the 10 in for x in either formula above
-150 = 75(10) - y
-150 = 750 - y
Add y to both sides
y - 150 = 750
Add 150 to both sides
y = 900
The gutierrez family and the kim family both have pools. the gutierrez family is filling their
pool, which is modeled by the equation y = x+1. the kim family is draining their pool,
which is modeled by the equation y = -1.25x + 5. in both equations, x represents the time in
hours and y represents the depth of the water in the pool in feet. these two situations can be
described by the following system of equations:
y
22+1
= -1.25x + 5
a) what is the rate of change for the kim family's pool, and what does it represent in the
context of the problem?
b) looking at the equation for the gutierrez family's pool, what does the 1 represent in the
context of the problem?
The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The Gutierrez family and the Kim family both have pools.
The Gutierrez family is filling their pool, which is modeled by the equation
y = x + 1
The Kim family is draining their pool, which is modeled by the equation
y = -1.25x + 5
In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.
These two situations can be described by the following system of equations:
Then the rate of change for the Kim family's pool will be
Rate of change = -1.25
The negative of 1.25 represents 1.25 feet is drain every hour.
Looking at the equation for the Gutierrez family's pool.
y = x + 1
The number 1 represents 1 foot of water that is already present in the pool.
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A restaurant is analyzing its customer satisfaction level. the manager performs an observational study of customers during the lunch hour on a monday and draws the conclusion that most of the customers are satisfied with the service they receive. the conclusion drawn from the study is because the sample is . in this instance, an study was conducted.
The conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate.
How to determine the conclusion of a study?
We are told that a restaurant is analyzing its customer satisfaction level. Now, the conclusion drawn was that most of the customers are satisfied with the service they receive.
Now, we can say that the conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate as it does not deal with the actual response from the customers but only observational.
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he proportion used to find the average number of trout you would expect to live in the pond is
7
20
= x
400
.
Solve the proportion to find the expected number of trout in the population.
The expected number of trout in the population is
5 less than a number b is 16
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
Solution :-[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]
Hence,b is equal to 11 .▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional information[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
^०^
How many inches is 35 yards?
Answer:
1260 inches
Step-by-step explanation:
Calculator
Which calculation and answer show how to convert
13
16
decimal?
8.125
16) 13.0000
128
20
16.
40
32
80
80
0
1.23
13) 16.000
to a
3 of 4 QUESTIC
Answer:
The first option. See attachment.
Step-by-step explanation:
Explained on attached image.
The mean percent of childhood asthma prevalence in 43 cities is 2.16%. A random sample of 31 of these cities is selected. What is the
probability that the mean childhood asthma prevalence for the sample is greater than 2.6% ? Interpret this probability. Assume that o=1.36%.
The probability is:
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.
What is Probability ?
Probability is the measure of likelihood of an event.
For a Normal Distribution ,
the z-score formula is given by
[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]
Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .
It is the measure of the deviation of the data from its central tendency.
Each z-score has a probability value.
It is given in the question that
Mean of 2.16% = [tex]\rm \mu\\[/tex] = 2.16
Standard deviation of 1.36% means that [tex]\rm \sigma\\[/tex] = 1.36
For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]
s = 1.36/√31
s = 0.2442
Substituting the values
Z = (2.6 -2.16)/0.2442
Z =1.8
the p value from the graph of z and p , 0.9643
To determine value of probability more than X is 1 - 0.9643= 0.0357
the
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.
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2. 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 haddeposited the $2,000 at the beginning of each year (annuity due), how much
would be in the account in 25 years?
Answer:
250.000$
Step-by-step explanation:
so you multiple 2.000 by 25
A tower is 105' tall. it casts a shadow 33' long. what is the angle of depression?
If you buy a ticket, what is the
Probability that your ticket will have the winning numbers?
Axis of symmetry y=x^2-4x+1
Answer:
So for a quadratic function, the axis of symmetry is the line that divides the curved line in the middle, which is the h value, it can be found by using the formula -b/2a, so for here it would be 4/2(1) = 2, so x =2
Hope that answers your question
Step-by-step explanation:
Find the value of x. 5 8 120 120 120 5 5 x = [?]
After school, Carlos helps his mom at her cake shop, Love and Lace Cakes. Today, he is helping her bake a 3-layer wedding cake. Each layer will be 2 1/2
inches tall and shaped like a rectangular prism. The bottom layer will be 12 inches long and 10 inches wide. The middle layer will be 10 inches long and 8 inches wide. The top layer will be 8 inches long and 6 inches wide.
What will the total volume of the wedding cake be?
Write your answer as a whole number, proper fraction, or mixed number.
The total volume of the wedding cake would be 620 in³.
What is the total volume?A rectangular prism is a three-dimensional shape. It also known as a cuboid.
Volume = length x width x height
The volume of the cake is the sum of the volume of the three layers.
Volume of the first layer = 2 1/2 x 12 x 10
5/2 x 12 x 10 = 300 in³
Volume of the second layer = 2 1/2 x 10 x 8
5/2 x 10 x 8 = 200 in³
Volume of the third layer = 2 1/2 x 8 x 6
= 5/2 x 8 x 6 = 120 in³
Total volume = 300 + 200 + 120 = 620 in³
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HELP ASAP ILL MAKE YOU THE BRAINIEST!!
Find the value of x
Answer:
x=6.18
Step-by-step explanation:
[tex]sin(31) = \frac{opp}{hyp} \\ \frac{0.52}{1} = \frac{x}{12} \\ \\ x = 12(0.52) \\ x = 6.18 [/tex]
(01.07)
Solve for x: the quantity of x plus 4 over 3 = 2. (1 point)
Group of answer choices
x = −2
x = 2
x = 2 over 3
x = negative 10 over 3
Answer:B
Step-by-step explanation:
"the quantity of can be ignored".
(x+4)/3=2
(x+4)=6
x=2
Susan drinks 2 pints of milk each day. how many days does it take her to drink 1 gallon of milk?
Answer:
4 days
Step-by-step explanation:
8 pints = 1 gallon
2 pints = 1 day
1 gallon = 4 days
Step-by-step explanation:
Susan drinks milk each day = 2 pints
1 gallon = 8 pints
Now, Susan take days to drink 1 gallon of milk
= 8 ÷ 2
= 4 answer
Hence, Susan takes 4 days to drink 1 gallon of milk .
Overview Park has a picnic area and a playground, as shown in the diagram below. What is the area of the playground, in square feet?
Answer:
Hi,
Step-by-step explanation:
The playground 's area is the difference of 2 squares:
20²-10²=(20+10)*(20-10)=30*10=300 (ft²)
Write the equation of a line in slope-intercept form, that passes through the point (6,-4) and its parallel to the line y=3x-8
y=
Answer:
Step-by-step explanation:
We'll look for a line with the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).
A parallel line will have the same slope as the reference line, For y=3x-8, the slope is 3. We can write:
y =3x + b for the new line. We need a value of b that will cause the line to include point (6,-4). To find a b that will work, simple use the given point in the above equation and solve for b:
y =3x + b
-4 =3(6) + b for (6,-4)
-4 =18 + b
b = -22
The parallel line that goes through point (6,-4) is y = 3x - 22
See the attached graph.