Answers
#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]
Related Questions
Which of the following equations is quadratic?
A) (x+3)(x+4)= 5
B) 5(4x+2) = 3
C) x(x^2+ 1) = 0
Answers
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
.
Answers
∠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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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
Answers
Answer:
The first option. See attachment.
Step-by-step explanation:
Explained on attached image.
HELPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
5,6
Step-by-step explanation:
2+8=10/2=5
3+9=12/2=6
5,6
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
Answers
5 less than a number b is 16
Answers
[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^
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.
Answers
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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Please solve this ASAP!!!
Answers
If you buy a ticket, what is the
Probability that your ticket will have the winning numbers?
Answers
1. There are 46 students in the orchestra and twice that number in the band. There are 34
boys and 23 girls in the choir. If each student only participates in one group, how many
students total are there in the orchestra, the band, and the choir?
Answers
The total number of students in the orchestra, the band, and the choir is 195
Determining the number of students
From the questions, we are to determine how many students in total are in the orchestra, the band, and the choir
From the given information,
There are 46 students in the orchestra and twice that number in the band.
Thus,
Number of students in the orchestra = 46
Number of students in the band = 2 × 46 = 92
And
There are 34 boys and 23 girls in the choir
∴ Number of students in the choir = 34 + 23 = 57
Then,
The total number of students in the orchestra, the band, and the choir = 46 + 92 + 57
Total number of students in the orchestra, the band, and the choir = 195
Hence, the total number of students in the orchestra, the band, and the choir is 195
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Identify the range of the function shown in the graph.
Answers
The range of the function shown in the graph are all real numbers.
What is the range of a function?The range of a function is the set of its possible output values.
The range of a function are the dependent variables.
In other words, the range of a function is the complete set of all possible resulting values of the dependent variable (y), after we have substituted the domain or independent variable.
According to the values of y on the graph the range are all real numbers.
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(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
Answers
Answer:B
Step-by-step explanation:
"the quantity of can be ignored".
(x+4)/3=2
(x+4)=6
x=2
Fiona recorded the mean math exam grade for six random samples of students from the entire seventh-grade class. Sample Sample Mean Grade 1 65 2 92 3 78 4 45 5 95 6 70 Why is a valid prediction for the mean of the population not possible using these samples?
Answers
The reason why Fiona cannot make a valid prediction based on the mean of the population is that the variation of Fiona’s samples is too large.
Why can't Fiona use the means she recorded?Mean is quite sensitive to outliers so it is best used when the variation between variables is not too much.
In Fiona's case, there variation is quite high with high variable of 95 compared to a low value of 45.
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Answer: just confirming/
Step-by-step explanation:
Please help i will give branliest please
Answers
Answer:
The answer is 18,700
Step-by-step explanation:
if you add 9,500+ 9,000 you get 18,500 add 200 and your answer is 18,700
What is the average rate of change for this quadratic function for the interval
from x=-5 to x = -3?
-10
10
A. -16
B. -8
C. 8
D. 16
x4
Answers
The average rate of change of the function at the interval is -8
How to determine the average rate of change?The table that completes the question is added as an attachment
From the table, we have:
f(5) = -26
f(3) = -10
The average rate is then calculated as:
Rate = (f(5) - f(3))/(5 -3)
This gives
Rate = (-26 + 10)/(5 -3)
Evaluate
Rate = -8
Hence, the average rate of change of the function is -8
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Jun 07, 7:1
What is the volume of a cylinder, in cubic centimeters, with a height of 11 centimeters
and a base diameter of 6 centimeters? Round to the nearest tenths place
Answers
Answer:
311.0
Step-by-step explanation:
pi3^2(11)
pi r^2 (h)
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?
Answers
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
find the value of a 3a+2b=8 and b=-2
Answers
Answer:
The value of a in the given equation is '4'
Step-by-step explanation:
The given equation is: 3a + 2b = 8 and b = -2
Plug the value of b into the formula:
3a + 2(-2) = 8
3a - 4 = 8
We want 3a by itself so we will add +4 to both sides:
3a - 4 + (4) = 8 + (4)
3a = 12
Divide both sides by 3 so a is by itself:
3a/3 = 12/3
1a = 4
a = 4
given triangle ABC what is the measure of angle A?
Answers
Answer:
I do not know the answer but I will just waffle to you
Step-by-step explanation:
540 divided by 3 equals 180 divided by 3 equals 60 then divide it by 3 again and you'll get the answer
solve pls brainliest
Answers
Step-by-step explanation:
(−424.9) × (-0.1) = 42.49
2.7 × (−0.5) = -1.35
Answer: Heyaa! ~
Your Answers when Multiped are...
42.49 -1.35Step-by-step explanation:
-424.9(-0.1)= 42.492.7 × (−0.5) = -1.35- Multiplied. -
Hopefully this helps you! ~
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?
Answers
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)
The playground
Toby has $70 saved.He is saving $15 more each week.In how many weeks will he have $280 saved to buy the new skateboard he wants?
Answers
Answer:
14 weeks
Step-by-step explanation:
Let's create and equation to display this situation. Toby already has $70 saved, so that is not the variable and no x should go next to it. He is saving $15 more each week. Lastly, we want to end up with $280 saved. The equation will look like this, given the information:
15x + 70 = 280
To find how many weeks it will take, solve the equation!
15x = 210 Subtract 70 from 280
x = 14 Divide 210 by 15
Therefore, it will take Toby 14 weeks to save up for a new skateboard.
Hope this helps! If you have any questions about my work, please let me know down in the comments!
Someone, please help! I'm really confused
Answers
The correct pair is option E, which is:
FH ≅ FH - reflexive property
ΔGFH ≅ ΔEFH - SAS theorem
What is the SAS Congruence Theorem?The SAS theorems states that two triangles are congruent if they have two pairs of congruent sides and a pair of congruent included angles.
What is the Reflexive Property?The reflexive property of geometry states that an angle or line will always be congruent to itself.
In the two column-proof, since FH = FH using the reflexive property, then both triangles are congruent to each other by the SAS congruence theorem.
The missing pair of reasons that completes the proof are:
FH ≅ FH - reflexive property
ΔGFH ≅ ΔEFH - SAS theorem
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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=
Answers
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.
PLEASE HELP
This Box-and-Whisker Plot is based on how many points a basketball player scored in a set of games.
In what percent of games did the player score more than 25 points?
Answers
Answer:
27.778%
Step-by-step explanation:
30-12= 18
numbers greater than 25 = 5
5/18 =26.778%
Answer:
A 25%
Step-by-step explanation:
hope this helps
write the slope-intercept form of the equation of a line passing through the following two points: (-3, 7) & (6, -5)
Answers
In order to find equation, first find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2 - x_1} \quad where \ (x_1, y_1) , \ (x_2, y_2) \ are \ points[/tex]
Given points: (-3, 7) and (6, -5)
[tex]\rightarrow \sf slope : \dfrac{-5-7}{6-(-3)} =-\dfrac{4}{3}[/tex]
Equation:
[tex]\sf y- y_1 = m(x - x_1)[/tex]
insert values
[tex]\rightarrow \sf y - 7 = -\dfrac{4}{3} (x -(-3))[/tex]
[tex]\rightarrow \sf y = -\dfrac{4}{3} x - 4 +7[/tex]
[tex]\rightarrow \sf y = -\dfrac{4}{3} x +3[/tex]
Over what interval is the quadratic function decreasing?
*€ (-2,00)
*€ (-∞, -2)
Ο τε(-2,-00)
# € (-∞0,3)
Answers
Answer:
1 is e(200) . 2 is e(-2) . 3 is O te(-02) . 4is # e(30) .
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
Note: Each horizontal or vertical division represents one unit.
X=
Y=
Answers
Answer:
can u make it in a sentence cause I don't understand ur question
Answer:
i don't know
Step-by-step explanation:
Find the value of x. 5 8 120 120 120 5 5 x = [?]
Answers
In the figure, AB and CD are common tangents to two circles of radii 5 cm with centres p
and S respectively and AB = 8 cm. Calculate the length of
Answers
Answer:
24 you used to write about something else
Answer:
Step-by-step explanation: