Answers
Answer:
1. 15, 2. -23, 3. 220, 4. 4x-5
Step-by-step explanation:
f(x) = 4x + 3 g(x) = x - 2
1. f(g(5)): Put 5 in as x in g(x) 5 - 2 = 3. Now put the 3 as x into f(x) and solve. 4(3) + 3 = 15
2. g(f(-6)) 4(-6) + 3 = -21. -21 - 2 = -23
3. (f(f(7)) 4(7) + 3 = 31, 31(7) + 3 = 220
4. g(f(x)) 4(x-2) + 3 = 4x - 8 + 3 = 4x - 5
When a function is substituted into another function it is known as a composite function.
Given the following functions:
f(x) = 4x + 3
g(x) = x - 2
Determine [tex]f(g(x)) \ and \ g(f(x))[/tex]
[tex]f(g(x)) = f(x-2)\\ f(x-2) = 4(x-2)+3\\ f(x-2)=4x-8+3\\ f(x-2) = 4x - 5\\ f(g(x)) = 4x - 4 [/tex]
1) Determine the value of [tex]f(g(5))[/tex]
[tex]f(g(5))=4(5) - 4\\ f(g(5))=20-4\\ f(g(5))=16[/tex]
2) For the function [tex]g(f(-6))[/tex]
[tex]g(f(-6))=4(-6) + 1\\ g(f(-6))=-24+1\\ g(f(-6))=-23[/tex]
3) For the value [tex]f(f(7)), [/tex]we need to determine [tex] f(f(x))[/tex]
[tex]f(f(x)) = f(4x+3)\\ f(f(x))= 4(4x+3)+3\\ f(f(x))=16x+12+3\\ f(f(x))=16x+15\\ f(f(7)) = 16(7) + 15\\ f(f(7)) = 127[/tex]
4) For the function [tex]g(f(x));[/tex]
[tex]g(f(x))=(4x+3)-2\\ g(f(x))=4x+3-2\\ g(f(x))=4x+1[/tex]
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Related Questions
pls quick plsssssssss
Answers
Answer:
[tex]{ \rm{perimeter = side + side + side}} \\ \\ { \rm{perimeter = 3 \frac{1}{2} + 4 \frac{2}{3} + 5 \frac{1}{4} }} \\ \\ { \rm{perimeter = 13 \frac{5}{12} \: cm}}[/tex]
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer: C) Today's soup will taste the same
====================================================
Explanation:
The usual recipe has 9 tomatoes for every 12 bowls. This forms the ratio 9:12.
Divide both parts of the ratio by 12 to end up with 0.75:1
9/12 = 0.7512/12 = 1The ratio 0.75:1 means that there are 0.75 tomatoes for each bowl.
--------------
Then the restaurant updates the recipe to involve 6 tomatoes for every 8 bowls, leading to the ratio 6:8. Divide both parts by 8
6/8 = 0.758/8 = 1The ratio 6:8 is the same as 0.75:1
---------------
We get the same ratio (0.75:1) each time we turn that second number into a 1, which means that each bowl involves the same number of tomatoes. Therefore, the taste should be the same.
Of course the concept of taste is subjective, meaning that the taste could easily vary over time even if you involved the same number of tomatoes. Also, the taste may vary from person to person. However, there should be an objective way to measure the "tomato"ness of each bowl.
Classify the number -5
Integer
1. Whole Number
2. Irrational Number
3. Natural Number
Answers
Answer:
1. Whole number
Step-by-step explanation:
It's a negative number, but it is not a decimal, therefore it is a whole number.
Please help if it’s correct I will give brainliest :)
(–4v–5)–(v–1)
Answers
Answer:
(-4v-5)-(v-1)= -5v-4
Step-by-step explanation:
hope it helps :D
Answer:
ok you want to come then come here
help ASAP please hmmmm
Answers
Answer:
the 3rd and 4th one r correct
Step-by-step explanation:
hope this helps!!!!
Alex is feeling stressed this morning. He did not get enough sleep because a dog barked most of the night. The dog barked from 11;41p.m. until 12:09 a.m.Then it started barking again at 3:35 a.m. and didn’t stop until 4:10 a.m.How long did the dog bark in all?
Answers
Answer:
Poor Alex, I know how they feel, I got a dog myself.
The amount of time between
11:41 pm to 12:09 am is
19 minutes (to 12 am, 60 minutes to next hour) + 9
which is 28 minutes for the first dog barking session
the second time is 35 minutes,
using same method as before.
adding the two separte barking sessions we get
35+28= 63 minutes
which is equivelant to 1 hour and 3 minutes.
In conclusion the dog barks for 1 hour and 3 minutes in total.
A rectangular hotel room is 4 meters by 7 meters. The owner of the hotel wants to recarpet the room with carpet that costs $71.00 per square meter. How much will it cost to recarpet the room?
Answers
Answer:
is it $120?
Step-by-step explanation:
Answer:
1,988$
Step-by-step explanation:
4x7=28x71
do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.
Answers
Answer: No
Step-by-step explanation:
Select the equation(s) where X=5 is a solution. *
2x + 4=14
5x=55
6x + 3 =14
8 + 3x= 23
6x = 30
5x =1
Answers
Answer:
2x + 4=14
8 + 3x= 23
6x = 30
jack has $37 and saves $6.50 per week diane has $9 and saves $8.25 per week write and solve an equation to find out how many weeks it would take for jack and diane to have saved the same amount of money
Answers
-1.75x = 28
X= 16
What is the answer to X=7-3y And 2x-4y=-6
I need it
Answers
Answer:
x = − 3 y + 7
Step-by-step explanation:
Reorder 7 and − 3
Simplify.
(5³)²
its telling me to write at least 20 characters so uhm-- ignore the rest of this weeeeeeeeeeeeeeeeee
Answers
Answer:
5⁶=15625...............
When you have a power to another power, you multiply the exponents. So 3x2 is 6. The answer is 5^6
Solve the inequality . Graph solution . 1/5 > d+ 4/5
Answers
Answer:
B
Step-by-step explanation:
Answer:
b. d>-3/5
Step-by-step explanation:
L.C.M=5
5×1/5>5×d+4/5×5
1>5d+4
1-4>5d
-3>5d
-3/5>5d/5
-3/5>d
Find the area of this semi-circle with diameter,
d
= 60cm.
Give your answer rounded to 2 DP.
Answers
Answer:
3.14*15^2=706.5
706.5/2=353.25
Hope This Helps!!!
The area of the semi-circle with a diameter of 60 cm is approximately 1413 square centimeters.
What is the area of the semi-circle?A semicircle is formed by simply dividing a circle into exactly two halves.
Hence, the area of a semi-circle is half the area of a circle.
Area of semi-circle = 1/2 × πr²
Given the parameters:
Diameter d = 60 cm
Radius r = diameter/2 = 60/2 = 30 cm
Area =?
To determine the area of the semi-circle, plug the value of the radius into the above formula and simplify:
Area of semi-circle = 1/2 × πr²
Area of semi-circle = 1/2 × 3.14 × 30²
Area of semi-circle = 1/2 × 3.14 × 900
Area of semi-circle = 3.14 × 450
Area of semi-circle = 1413 cm²
The area is approximately 1413 square centimeters.
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the sum of a number and 6 is greater than 76 write an inequality
Answers
Answer:
x+6>76
Step-by-step explanation:
sum is adding
greater than is >
Please help me solve this problem ASAP
Answers
Answer:
∠ = 130°
Step-by-step explanation:
They are vertical angles: a pair of opposite angles formed by intersecting lines. These two angles are considered congruent, which means they have exactly the same measure. So, you simply solve for x when they equal each other. Remember, both angles share the same measurement.
15x -5 = 13x + 13
5 + 15x - 5 = 13x + 13 + 5
13x - 15x = 13x + 18 - 13x
2 ÷ 2x = 18 ÷ 2
x = 9
Now you must put 9 in for x to solve the measurement of the angles.
15 (9) - 5 = 130°
13(9) + 13 = 130°
Both angles equal 130°, so you know you've done the math correctly.
the ratio to boys to girls in sixth grade is 5:3 if their are 400 sixth graders how many boys are their
Answers
Answer:
250 boys
Step-by-step explanation:
sum the parts of the ratio, 5 + 3 = 8 parts
Divide the total by 8 to find the value of 1 part of the ratio
400 ÷ 8 = 50 , then
number of boys = 5 × 50 = 250
Answer : There is 250 boys in the sixth grade
Step - by - step explanation :
400 / [ 5 + 3 ] = 400 / 8 = 50
50 x 5 <-- The ratio of boys = 250
Please Help Question In Picture
Answers
Answer:
A
Step-by-step explanation:
Since Angle XYZ is equal to Angle YZX,
XY=XZ
The two triangles are congruent.So,
VW=YZ
XY=UV
XZ=UW
Thus;
XY=UV
XZ=UW
XZ=XY=UV=UW
So the permieter is 5.7 + 5.7 + 3.7 = 15.1 cm
A certain amount of money is divided among Rio, Kim and Leo in the ratio 5:7:3. If Leo gets Php 24,000.00, how much is the total amount?
Answers
Answer:
120,000
Step-by-step explanation:
Let's say Rio gets 5x, Kim gets 7x, and Leo gets 3x. In the ratio 5:7:3:1, x = 1
5x + 7x + 3x = total = 15x
3x = 24000
divide both sides by 3 to get x
x = 8000
15x = 8000*15 = 120000
5 1/4 - 2 2/3 in fraction form
Answers
Answer:
6 1/10 (6.1)
Step-by-step explanation:
2 3/5 + 3 1/2 (2.6 + 3.5= 6.1)
2 6/10 + 3 5/10
5 11/10
6 1/10 (6.1)
if 240 slices of cake are shared into the same ration 3:5 among the boys and girls how many slices will each students recieve
Answers
Ashley and Christopher want to camp on the other side of a lake at point B. They are both going to kayak to the campsite from their homes. Ashley lives at point A and is kayaking from point A to point B. Christopher lives at point C and is kayaking from point C to point B. Based on the picture below, Ashley will kayak ___ miles more than Christopher. 0.5 mi, 1.5 mi, 2.5 mi, 3.0 mi. Please help!
Answers
Applying the midsegment theorem, the distant Ashley will kayak more than Christopher is: 0.5 mi
Recall:
The midsegment of a triangle joins two sides of a triangle at their midpoint.The third side is the base of the triangle.Triangles have three midsegments.Based on the midsegment theorem, the length of the midsegment = ½(third side).The picture given shows a triangle with two midsegments: AB and BC
AB = the distance Ashley will kayak.
BC = the distance Christopher will kayak.
XY = 5 mi (base)
XZ = 6 mi (base)
Applying the midsegment theorem, find AB and BC.
AB = ½(XZ)
SubstituteAB = ½(6)
AB = 3 mi
BC = ½(XY)
SubstituteBC = ½(5)
BC = 2.5 mi
Thus, the distance Ashley will kayak more than Christopher = AB - BC
= 3 mi - 2.5 = 0.5 mi.
Therefore, applying the midsegment theorem, the distant Ashley will kayak more than Christopher is: 0.5 mi
Learn more about the midsegment theorem on:
https://brainly.com/question/12234706
Helpp with number 23 pls
Answers
Answer : Susan is correct
Susan is correct because if you get that chart and turn all the numbers to decimals and divide the chart in half you will get the answer to 1.4/0.2 because the chart has 14 slots and if you divide that by 2 you will get 7 just think of 1.4/0.2 as 14/2.
Justin took 55 minutes to get to school and his best friend Dwayne took 3/4 hours. How much time did they take to get to school altogether?
Answers
Answer:
100 mins or 1⅔ hrs
Step-by-step explanation:
¾ hr = ¾ × 60 mins
¾ hr = 45 mins
55 + 45 = 100
100 mins = 100 × hr/60
100 mins = 1⅔ hrs
Answer:
100 mins or 1⅔ hrs
Step-by-step explanation:
¾ hr = ¾ × 60 mins
¾ hr = 45 mins
55 + 45 = 100
100 mins = 100 × hr/60
100 mins = 1⅔ hrs
So it took them 1 2/3 hrs to get to school
Help please I’ll give Brainly please answer both I’ll give 5 stars and lines
Answers
Answer:
I really cant see the picture that well or, i would help.
Step-by-step explanation:
The acute angles of a right-angled triangle other than the right angle always add up to 90 degrees
So, we get
(48-x) + (3x-10) =90
48-x+3x-10=90
-x+3x-10+48=90
2x+38=90
2x+38=90
2x=90-38
2x=52
Divide both sides by 2
52 divided by 2
X=26
If I have a ramp of 8 feet in length and 4 feet in height what is the diagonal length and degree
Answers
Answer:
almost 9
Step-by-step explanation:
Please help me with this math problem!! :)
Answers
Answer:
16.67%, 50%, 16.67%
Step-by-step explanation:
There are 6 different ways that the 4 kids can be paired up, so any one of the ways is rounded to 16.67%. So a and c are 16.67%
Not Zack is any pairing that doesn't have a Z. That is 3 out of 6, which is 50%.
enter an algebraic expression for the word expression.
The quotient of -4 and y
Answers
Hey there!
Guide to follow
“Difference” means subtract
“Is” means equal to
“Product” means multiply
“Quotient” means divide
“Sum” means add
Answering your question….
“The [QUOTIENT] of [-4] and [y]
Remember we said “quotient” means divide
So we’re dividing -4 from y and that will be your answer.
Answer
-4 ÷ y
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
3.75
Word form
please help
Answers
Answer:
three and seventy-five hundredths or three point seven five
Step-by-step explanation:
John is 9 times as heavy as his dog.
Determine which of the statement's below is true.
O John weighs 900% more than his dog.
O John weighs 800% more than his dog.
O John's dog weighs 800% less than John.
sources
O John weight is 800% of his dog's weight.
Answers
Answer:
John weighs 900% more than his dog
Step-by-step explanation:
The weight of John is 8x more than his dog.
Given that, John is 9 times as heavy as his dog.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let weight of John's dog be x, then weight of John will be 9x.
Difference of weight = 9x-x
= 8x
Therefore, the weight of John is 8x more than his dog.
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