Answer:
y = 1/4 x - 5/4
Step-by-step explanation:
y = 4x + 5
Switch x and y.
x = 4y + 5
Solve for y.
4y = x - 5
y = 1/4 x - 5/4
The inverse of the function y = 4x + 5 is [tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
The given function is:
y = 4x + 5
To find the inverse of the given function y = 4x + 5, follow the following steps:
Make x the subject of the formula:
[tex]y = 4x + 5\\\\4x = y - 5\\\\x = \frac{y}{4}-\frac{5}{4}[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and replace y by x.
The resulting function represents the inverse of the function y = 4x + 5
[tex]f^{-1}(x)=\frac{x}{4}-\frac{5}{4}[/tex]
Which can be further simplified as:
[tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
The inverse of the function y = 4x + 5 is [tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
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Question 1
Sione just landed a great job as an engineer where he will make $55,000 a year. The
company he will work for guarantees a 3% pay increase each year so it's employees
salaries keep up with inflation. At the end of the 1* year Slone will have made $55,000
dollars.
1. What is the recursive function that will represent this situation?
a. m(t) = m(t - 1) + 0.03, m(1) = 55000
b. m(t) = m(t-1). 0.03, m(1) - 55000
c. m(t) = m(t-1) + 1.03, m(1) - 55000
d. m(t) = m(t-1). 1.03, m(1) = 55000
Answer:
Option (d)
Step-by-step explanation:
If the current salary of Sione is represented by the function m(t - 1),
Next year his salary m(t) gets hike of 3%.
So, the next year salary of Sione will be represented by,
m(t) = m(t - 1) + 3% of m(t - 1)
= m(t - 1) + 0.03 × m(t - 1)
= m(t - 1)(1 + 0.03)
= 1.03m(t - 1)
Since, at the end of year 1 his salary was $55000,
Recursive function will be,
m(t) = 1.03m(t - 1) = 55000
Therefore, Option (d) will be the answer.
A jeweler has 160.5 centimeters of gold chain. He will use half of the chain to make a necklace. He will make 5 bracelets with the remaining chain. If each bracelet is the same length, what will be the length of each bracelet in centimeters?
9514 1404 393
Answer:
16.05 cm
Step-by-step explanation:
Each bracelet will be 1/5 of 1/2 of the chain, so is
(1/5)(1/2) = 1/10
of the original length of the chain.
1/10 × 160.5 cm = 16.05 cm . . . length of each bracelet
How does light travel so you can see in the dark
Answer:
Step-by-step explanation:
Light travels as a wave. But unlike sound waves or water waves, it does not need any matter or material to carry its energy along. This means that light can travel through a vacuum—a completely airless space. ... It speeds through the vacuum of space at 186,400 miles (300,000 km) per second.
The M & P Pencil company that makes mechanical pencils expects to have two defective pencils for every 125 made. What is the number of defective pencils they will have in a batch of 4,375?_________
CAN YOU GUYS PLEASE HELP ME OUT!!!
Answer:70 i believe
Step-by-step explanation:
(4,375/125)=35
35*2=60
X - 6 < -4 please help
Answer:
x<2
Step-by-step explanation:
Two towns that are 5 inches apart on this map are how many actual miles apart?
Answer:
12*10=120
Step-by-step explanation:
What role early cells played in shaping life on earth?
Answer:
Present-day cells evolved from a common prokaryotic ancestor along three lines of descent, giving rise to archaebacteria, eubacteria, and eukaryotes.
Changed the composition of the oceans. Most of the iron was precipitated out by early life.
Changed the composition of the atmosphere. Oxygen became available in abundance.
Sally's soccer team played 25
games and won 17 of them.
What percent did the team LOSE?
Step-By-Step explanation please, I need to get this finished by tonight at 11:59 p.m!
Help with math. please
Answer:
B. 1 9/10 (19/10)
Step-by-step explanation:
3 4/5 is equal to 19/5
We would need to divide 19/5 by 2
Make 2 a fraction. 2/1
Flip the number: 1/2
Multiply 19/5 by 1/2
19/10
Simplify.
1 9/10
Hope I helped :)
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simplify by combining like terms. -2y + 14 - 9y + 5
Answer:
-11y+19
Step-by-step explanation:
-2y+(-9y)+14+5=-11y+19
Answer:
-11y+19
Step-by-step explanation:
-2y-9y+14+5
-11y+14+5
-11y+19
Hope this helps!
at store B the cost is given by y=2x where y is the cost in Dollars and the x is the number of pounds. what is the unit price of apples at store B
the price of an apple is how many pounds of apples time 2
If you bought a stock last year for a price of $63, and it has risen 17% since then, how much is the stock worth now, to the nearest cent?
The dot plots below show rainfall totals in the Highlands and Lowlands areas of a certain region.
When comparing the two sets of data, which is a true statement?
A. There are gaps in both sets of data.
B. The ranges are the same.
C. The two sets of data do not overlap.
D. The rainfall peaks at a lower value in the Lowlands.
Answer:
c
Step-by-step explanation:
took the test
Answer:
C
Step-by-step explanation:
i am just that good
PLEASE HELP AHHHH IS URGENT.
Complete the following statement.
Find the quotient. 7200/9 =
Answer:
800
Step-by-step explanation:
9 goes into 72 eight times, nine goes into 0 zero times
The complete statement is as follows:
The quotient of, 7200/9 = 800.
Quotient is the result which we get by dividing the one number by the other.
Where, the number which is getting divided is known as 'dividend' and the number which divides the dividend is known as 'divisor'.
So,
Quotient = Dividend ÷ Divisor.
Or,
[tex]\text{Quotient} = \frac{\text{Dividend}}{\text{Divisor}}[/tex]
In 7200÷9, 7200 is dividend and 9 is divisor. We have to find the quotient.
Applying the division on 7200 by 9.
Since, 9 is very less than 72. Take the first 2 digits.
72÷9 = 8
There is no remainder.
Now, take three digits:
720÷9 = 80
Still no remainder is here.
Move to the last digit (0) and apply division.
7200÷9 = 800
No remainder is there.
That means the quotient of, 7200 divided by 9 is 800.
Hence, the quotient of 7200/9 = 800.
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solve for x im not good at math
the answer would be x=9
Explain! For reward!
Answer:
32 times
Step-by-step explanation:
If you can go around 54 times for $12, then you multiply the amount of money you pay by four to get the number of times you can go around the track.
Hope this helps! Please mark Brainliest!
Answer:
I would say 36 because 54 times 8 is 432 and if you divide that by 12 you get 36.
Step-by-step explanation:
10<2x+2<16
Lol yea I’m dumb and I’m honors what abt it imma disappointment
Answer:
4 and 7
Step-by-step explanation:
Answer:
4<x<7
Step-by-step explanation:
10<2x+2<16 First, we can subtract 2 on all three sides.
-2 -2 -2
8<2x<14 Divide by 2 on both sides.
/2 /2 /2
4<x<7
Hope this helped you out!!! Be more positive about yourself...I promise it will help...and if you ever need help, just ask! Have a wonderful day :3
What conjecture can you make about the sum of the first 33 positive odd numbers?
Answer:
The number series 1, 3, 5, 7, 9, . . . . , 59. Therefore, 900 is the sum of first 30 odd numbers.
The conjecture we can make is C. The sum is equal to the no. of terms squared.
According to the given question we have been asked What conjecture can you make about the sum of the first 33 positive odd natural numbers.
We know that the sum of first 'n' odd natural numbers is n².
So, the sum of first 33 odd natural numbers is (33)² which is = 1089.
Let us prove this by AP.
First term(a₁) is = 1.
common difference(d) = 2.
No. of terms (n) = 33.
∴ aₙ = a₁ + (n-1)d
aₙ = 1 + (33-1)2
aₙ = 1 + 32(2).
aₙ = 1 + 64.
aₙ = 65.
∴ S₃₃ = 33/2×[ 2(1) + (33-1)2].
S₃₃ = 33/2×[ 2 + 64].
S₃₃ = 33/2×66.
S₃₃ = 33×33.
S₃₃ = 1089.
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Based on her recipe Elana knows that 5 servings of granola have 1,750 calories. If she wants to eat 175 calories of granola how many servings should she eat
Answer:
1/2 of a serving
Step-by-step explanation:
start by dividing the 1750 calories by 5 to find out how much for one serving. than from there I divide one serving into two and got 175 calories
What is the image point of (-1,1) after a translation right 2 units and down 1 unit
Answer:
(0,1)
Step-by-step explanation:
Answer:
I think (-2,3) is
the answer
you are renting an apartment. the living room is 412 square feet. the kitchen is 337 square feet. the bedroom is 265 square feet. how much square feet are in these three rooms
Answer: 1,014
Step-by-step explanation: 412+265=677 677+337=1,014
what is the lenght of the diagonal of the rectangle
Answer:
P = 2l + 2w
Step-by-step explanation:
(−8 − 3i) − (−8 + 5i)
Answer:
-8i
Step-by-step explanation:
Answer:
(-8 - 3i) - (-8 + 5i) = −8i
Step-by-step explanation:
How do I find the missing side with the Pythagorean theorem?
Answer:
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two.
Step-by-step explanation:
How do you make (39x5) in distributive property
Answer:
Assuming you are asking the simple question of 39x5=195Step-by-step explanation:
By taking 9x5 = 45 and 3x5 = 15 add 4 to 15.Brayden wants to buy some avocados, but he only has 1 dollar. how many avocados will he be able to buy
Answer:
just one. even though he's a adult.
what is 2 plus 2
a. 3
b. 4
c. 1
d. 7
Answer:
I have to say 4
Step-by-step explanation:
2nd my MD du web mi if
Your Answer :
B. 4
Step - By - Step Explanation :
We have two digits. 2 and 2.
The value of 2 is equivalent to 1 apple next to another apple. There are two apples.
What if there were two more apples? Now you have 2 apples next to another pair of apples. Now let's count all the apples.
One apple,
Two apples,
Three apples,
Four apples.
There are 4 apples all together.
So, 2 + 2 has a sum of 4.
Jill is baking a pumpkin pie. The recipe calls for 4 ⅓ cups of flour, but Jill has 2 ⅘ cups. How many cups of flour does Jill need?
Answer:
1 8/15
Step-by-step explanation:
We need to equal the denominators. We have 1/3 and 4/5, and we need to make the bottom numbers equal to each other. The closest common factor is 15 (which we got from 3 x 5). With the denominators solved, we now need to equal out the top numbers, or the numerators. 1 x 5 gives us 5/15, and 4 x 3 gives us 12/15. Then, we need to apply these to each variable. This gives us Jill's 2 12/15th cups of flour, and the recipe's call for 4 5/15 cups. We then subtract these from each other, giving us 1 8/15 cups of flour is needed from Jill.
A pizza with a 10-inch diameter costs $6.99 and is cut into 6 slices, what is the cost per slice?
Answer:
$1.165
Step-by-step explanation:
$6.99/6 slices = 1.165