Answer:
A composite function means that you are evaluating one function into another function.
So, fog(x) can be written as:
f(g(x))
and gof(x) = g(f(x))
this means that instead of the variable "x", we are evaluating the functions with other function.
Let's solve this:
f(x) = x^2 - 3
g(x) = x + 1
then:
> gof(x) =g(f(x)) = f(x) + 1 = (x^2 - 3) + 1 = x^2 - 2
> fog(x) =f(g(x)) = g(x)^2 - 3 = (x + 1)^2 - 3 = x^2 + 2x + 1 - 3 = x^2 + 2x - 2
a grandfather purchased a brand new car in 1958 for $2500.the car depreciated $325 a year. what would the car be worth 4 years after it was bought?
Answer:
The car would be worth 1200.
Step-by-step explanation:
Okay, the way to solve this type of question is quite simple,
you would start with the amount is lost per year being $325 a year, then multiply that by the 4 years grandpa waited and then subtract the overall amount lost in worth of the car from the original price and you got your answer.
The math: 2500-(325*4)=1200
I need help... please help me through this trigonometry. I need full answer.
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan(x + y) = [tex]\frac{tanx+tany}{1-tanxtany}[/tex] , tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex], tan [tex]\frac{\pi }{4}[/tex] = 1
tan2x = [tex]\frac{2tanx}{1-tan^2x}[/tex]
Consider the left side
tan([tex]\frac{\pi }{4}[/tex] + Θ ) - tan([tex]\frac{\pi }{4}[/tex] - Θ )
= [tex]\frac{tan\frac{\pi }{4}+tan0 }{1-tan\frac{\pi }{4}tan0 }[/tex] - [tex]\frac{tan\frac{\pi }{4}-tan0 }{1+tan\frac{\pi }{4}tan0 }[/tex]
= [tex]\frac{1+tan0}{1-tan0}[/tex] - [tex]\frac{1-tan0}{1+tan0}[/tex]
= [tex]\frac{(1+tan0)^2-(1-tan0)^2}{(1-tan0)(1+tan0)}[/tex]
= [tex]\frac{1+2tan0+tan^20-1+2tan0-tan^20}{1-tan^20}[/tex]
= [tex]\frac{4tan0}{1-tan^20}[/tex]
= 2 [tex]\frac{2tan0}{1-tan^20}[/tex]
= 2 tan2Θ = right side
How does 4D shape look like?
Answer:
here you go
i hope i helped you
Step-by-step explanation:
Answer:
It would look like these shapes on the picture
Step-by-step explanation:
It is a shape with another one of it inside it, you should see it on the pictturres.
Hope this helped you
Please mark as brainlist.
Ms. Canton has a book case. On three of the shelves there are the same amount of books. On another shelf there are four of her favorite books. Write an expression to represent all of the books in Ms. Canton's book case. Explain your answer
Answer:
y=3x+4
Step-by-step explanation:
x= the equal amount of books on 3 bookshelves
+4=the other 4 books on the fourth bookshelf
y=the total amount of books
can someone turn this into slope intercept form please ?? thank you .
Answer:
1) -1 - 0 fraction on top of -4 -3
Step-by-step explanation:
(x1,y1) and the second (x2,y2)
and the formula is x2- minus x1 over as ina fraction over y2- minus y1,,,, apply this to the other questions
Answer:
Hi there!!!
just use double point formula for the equation of st.line.
(i.e (y-y1 )= y2-y1/x2-x1 times (y-y1)
I hope the answers in the pictures will help you....
Cathy is paid at a rate of $7 20 per hour for a basic hour-week of 70 hours. She is paid time-and-a-half for over-time during the week and double-time on weekends. In a fortnight she worked 160 hours, and 4 hours on Saturday and 2 hours on Sunday. What is Cathy's hours in a fortnight
Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
Here is the calculation:
Cathy's basic pay for the fortnight is 7.2 × 70 = $504.
Her overtime pay for the week is (1.5 × 7.2) × 9 = $97.2.
Her weekend pay is (2 × 7.2) × 6 = $86.4.
Her total pay for the fortnight is 504 + 97.2 + 86.4 = $687.6.
Therefore, Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
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A furniture shop refinishes cabinets. Employees use one of two methods to refinish each cabinet Method I takes 1 hour and the material costs $6. Method II takes 2 hours, and the material costs $5. Next week, they plan to spend 260 hours in labor and $986 in material for refinishing cabinets. How many cabinets should they plan to refinish with each method?
Answer:
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
Step-by-step explanation:
Let
a = number of tables refinished using method 1
b = number of tables refinished using method 2
Time equation
a+2b=260 (1)
Cost equation
6a+5b=986 (2)
a+2b=260 (1)
6a+5b=986 (2)
Multiply (1) by 5 and (2) by 2
5a+10b=1,300 (3)
12a+10b=1,972 (4)
Subtract (3) from (4)
7a=672
Divide both sides by 7
a=96
Recall,
a+2b=260
96+2b=260
2b=260-96
2b=164
Divide both sides by 2
b=164/2
=82
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
2) A furlong is 1/8 of a mile. What part of a mile is 4 furlongs?
Answer:
1/2 mile
Step-by-step explanation:
(1/8)*4 = 1/2 mile
Answer:
4/8 or 1/2
Step-by-step explanation:
becuase 4 times 1/8 is 4/8 which is 1/2
An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal AC to divide the piece of land into two parts. What will be the length of the wall? A. 65–√ units B. 6 units C. 237−−√ units D. 2 units
Answer:
[tex] 6\sqrt{5} units [/tex]
Step-by-step Explanation:
The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).
Distance formula between two points on a graph (d) = [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] A(-6, -2) = (x_1, y_1) [/tex]
[tex] C(6, 4) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(6 - (-6))^2 + (4 -(-2))^2} [/tex]
[tex] d = \sqrt{(6 + 6)^2 + (4 + 2)^2} [/tex]
[tex] d = \sqrt{(12)^2 + (6)^2} [/tex]
[tex] d = \sqrt{144 + 36} [/tex]
[tex] d = \sqrt{180} [/tex]
[tex] d = \sqrt{36*5} [/tex]
[tex] d = 6\sqrt{5} [/tex]
The length of the wall = [tex] 6\sqrt{5} units [/tex]
WILL GIVE BRAINLY!!!!!! NEED HELP ASAP!!!!!!!! what is the range of f(x)=3^x+9
Answer:
y > 9
Step-by-step explanation:
The range of a function is the interval of all possible y-values that make the function true.
Here, one way to figure this out is to look at a graph of the function (see attachment).
From the graph, we can see that y-values approach very closely the value 9 and then the line rises beyond 9 forever. Thus, we can conclude that the range for f(x) is y > 9.
~ an aesthetics lover
What is the y-intercept of the function f(x) = -2/9x+1/3
Answer:
The y-intercept is 1/3.
Step-by-step explanation:
The equation given is in slope-intercept form. Recall that in slope-intercept form:
[tex]f(x)=mx+b[/tex]
m is the slope while b is the y-intercept.
Therefore, -2/9 would be the slope while 1/3 would be the y-intercept.
Use the clues in the sentences to determine the best meaning for each bolded word
"He was a tenacious worker, and by sticking firmly to his plan, he succeeded."
"Students planning to become scientists must select a science major, such as biology, chemistry, or physics."
"I want to take a class in calligraphy, or artistic writing, at the community center."
Done
Answer:
1. Determined
2. area of study
3. artistic writing
Step-by-step explanation:
Hope this helps! <3
Answer:
✔ determined
✔ area of study
✔ artistic writing
Explanation:
Step 2 Using Proportional Relationships
Answer:
a ( 567 miles to unit)
b( looks like 2 units so i would say 1134 miles
Answ: the scale is
Step-bstep explanatio
The graph shows the first 5 terms of the arithmetic sequence, an.
Which is the 6th term of the sequence?
A.)3
B.)6
C.)9
D.)12
E.)18
Answer:
D) 12
Step-by-step explanation:
the graphs slope is 3 using the rise over run method we have found this
now since we know the fifth x value gives a y value of 9 we can add 3 and have 12
Marlye posted a story on her blog. On the first day there were 80 responses and on the second day there were 180 responses. What percent is the increase, 100, of the original number of responses, 80?
Hey there! I'm happy to help!
In our problem, 100 is a certain percent of 80. When talking about percents, the word "is" means equals. Let's represent our certain percent with p and solve for it.
100=80p
Let's flip the equation around so p is on the left side.
80p=100
We divide both sides by 80.
p=1.25
As a percent, the increase is 125%.
Have a wonderful day!
solve for m. √m-7 = n+3 It is worth like 40 points
Answer:
sqrt of (m-7) = n+3
m = (n+3)^2 + 7 or m= n^2 + 6n + 16
sqrt of (m)-7 = n+3
m = (n+10)^2 or m =n^2 + 20n + 100
Step-by-step explanation:
(2) move the constants to the other side, and square
or (1) square and move constants
then you can solve for m
Answer:
[tex]n^2+6n+16[/tex]
Step-by-step explanation:
I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not [tex]\sqrt{m} - 7 = n+3[/tex].
[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]
Hope this helped!
A teacher has 1,425 marbles to divide equally among 9 groups of students to use in an experiment. What is the least number of marbles he could have left after the marbles are distributed?
Answer:
3
Step-by-step explanation:
Basically we need to find out whats the remainder of 1425 when you divide by 9.
1425/9 = 158 R3
R3 is 3 marbles left, so the answer is 3.
Find the area of the shape shown below.
Answer
72-30=42. The answer is 42
Step-by-step explanation:
to find the area of this, we first need to add are to the missing space, so we can make a rectangle. If we multiply the dimension of this new shape, we get 72. Now we need to find the are of the triangle-shaped space I added. To do this I must multiply the base by the height, and then divide it by 2, after multiplying the base with the height, which gave me 60, I divided it by 2 which gave me 30. Then I subtracted 30 from 72, therefore giving me 42
Answer:
42cm2
Step-by-step explanation:
You can divide the shape into two parts from the length at the top and the length at the bottom. Which means you have two shapes A and B.
Area of A which is a triangle= 1/2bh
= 1/2*5(THIS IS THE BASE OF THE TRIANGLE)12
= 30CM2
Area of b which is a rectangle= L*W
= 1(LENGTH) * 12(WIDTH)
= 12CM2
So to get the total area of the shape you add the area of shape a and b
THE ANSWER IS 42cm2
PLEASE HELP!! URGENT
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° Use the
information provided and the diagram below to determine the height of the tree. Round to the nearest
whole foot.
532 it
256 ft
479 ft
231 ft
13672 ft
< Previous
Next >
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :
[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]
[tex] \tan(25.7) = \frac{h}{532} [/tex]
[tex]532 \tan(25.7) = h[/tex]
[tex]h = 256 \: feet \: (3s.f)[/tex]
The value of height of tree is,
⇒ h = 256 feet
We have to given that,
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .
Hence, By given figure we get;
By using trigonometry formula, we get;
⇒ tan 25.7° = Opposite / Adjacent
⇒ tan 25.7° = h / 532
⇒ 0.4812 = h / 532
⇒ h = 0.4812 × 532
⇒ h = 256 feet
Therefore, The value of height of tree is,
⇒ h = 256 feet
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*LAST QUESTION, PLEASE ANSWER I NEED HELP* What will be the new volume of the prism if a scale factor of 2.5 is applied to the dimensions?
Answer:
10,500 cubic inches
Step-by-step explanation:
1. Find the new lengths after the scale factor
6 · 2.5 = 15
8 · 2.5 = 20
14 · 2.5 = 35
2. Solve for the volume (length · width · height
15 · 20 · 35 = 10500
The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.
DImension for prism,
Length = 14
width = 8
Height = 6
Scale factor = 2.5
New volume to be determined.
The scale factor is defined as the ratio of modified change in length to the original length.
Applying scale factor 2.5 to the dimensions,
Length = 2.5 * 14 = 35
width = 8 * 2.5 = 20
Height = 6* 2.5 = 15
The new volume of the prism = length * width *height
= 35 * 20 * 15
= 10, 500
Thus, The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.
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Convert .23 Kiloliters to liters
what’s the answer?
Answer:
230 liters
Step-by-step explanation:
1000 liters is 1 kiloliter
Multiplying by the conversion factor
.23 kiloliters * 1000 liter/ 1 kiloliter= 230 liters
Answer:
= 230litres
Step-by-step explanation:
know that
1000liters makes 1 kilometer
if 1000liters make 1kilometer then we will multiply 0.23 by 1000litres
that is,
0.23 x 1000
= 230litres
Each half-inch of a ruler is divided evenly into eight divisions. What is the level of accuracy of this measurement tool?
Answer:
The level of accuracy of the measurement ruler measurement tool is 1/16 of an inch
Step-by-step explanation:
The accuracy of a measurement tool is determined by the ability of the tool measure the accurate value of the actual or standard measurement. The accuracy of a measurement tool depends on its ability to take small measurements
The parameter given includes;
The number of divisions on each 1/2 inch of the ruler = 8
Therefore, the smallest divisions on the ruler = (1/2) inch ÷ 8 = 1/16 inch
Therefore, the level of accuracy of the measurement ruler measurement tool = 1/16 of an inch.
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −8 feet. The highest point of the country lies at +107 feet. Which of the following statements best describes the lowest and the highest points?
The lowest point is 8 feet above sea level, and the highest point is 107 feet below sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above the lowest point.
The lowest point is 8 feet above sea level, and the highest point is 107 feet below the lowest point.
A negative value would mean it is below sea level. A positive value would be above sea level.
-8 is 8 feet below sea level
+107 is 107 feet above sea level.
The answer Is:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Answer:
Step-by-step explanation:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
(07.05 LC)
Which statement is true for the equation 4n − 3 = 4n − 2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answer:
The answer is (A); there is no solution.
Step-by-step explanation:
It doesn't require any calculations, really, just logic. Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value. However, if you subtract both values by different numbers, you won't get the same number:
Let's say n = 5
4n = 4n
= 4(5) = 4(5)
= 20 = 20
Now,
4n - 3 = 4n - 2
= 4(5) - 3 = 4(5) - 2
= 20 - 3 = 20 -2
= 17 ≠ 18
Hope this helps! Tell me if I was wrong!
Answer:
It has no solution.
Step-by-step explanation:
If we try and solve it we end up with nonsense, so it has no solutions:
4n - 3 = 4n - 2
4n - 4n = - 2 + 3
0 = 1
- which is, of course, absurd.
Also, just by looking at the equation we can see that the term 4n -3 cannot in any way be equal to 4n - 2.
The area of a regular hexagon is 40 in^2. What is the length of a side to the nearest tenth? A. 15.4 in. B. 9.6 in. C. 6.7 in. D. 3.9 in.
Answer:
The answer is D
Step-by-step explanation:
what is the value of x
Answer:
x = 78
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
Answer:
78 degrees
Step-by-step explanation:
According to vertical angles theorem (vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent) 78 and x are congruent
PLEASE HELP!! A 5×5×5 wooden cube was painted and then sawed into 1×1×1 cubes. How many 1×1×1 cubes have exactly two faces painted?
Answer:
36
Step-by-step explanation:
There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)
A cube has 12 edges.
12x3=36
pls help!! Consider the sequence below.
-34, -21, -8, 5...
Complete the recursively defined function to describe this sequence.
Answer:
a₁= -34
aₙ = 13n - 47
Step-by-step explanation:
This is an AP with the first term of -34 and the common difference of 13.
The nth term is:
aₙ= a₁ + (n-1)daₙ= -34 + (n-1)*13aₙ = 13n - 47This is the required formula.
how many ways can you order a sandwich if you can order it with or without ham, mustard, mayo, or cheese?
165°
145
x =
Please Help!!!!
Answer:
15°
Step-by-step explanation:
The 165° and x forms a straight line or a supplementary angle. Supplementary angles add up to 180°. Therefore:
[tex]165+x=180[/tex]
Solve for x:
[tex]165+x=180\\x=15\textdegree[/tex]
Answer:
15 degress
165 and x lie on a 180 degress.
and 180 - 165 is 15.
Bye!
Step-by-step explanation:
