Answer:
The inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Step-by-step explanation:
The given function is
[tex]y=2x+2[/tex]
The step and shown below to find the inverse of the function.
Step 1: Interchange x and y.
[tex]x=2y+2[/tex]
Step 2: Isolate variable y.
[tex]x-2=2y[/tex]
[tex]\frac{1}{2}(x-2)=y[/tex]
[tex]\frac{1}{2}(x)+\frac{1}{2}(-2)=y[/tex]
[tex]\frac{1}{2}(x)-1=y[/tex]
Therefore the inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Answer:
The inverse of y = 2x+2 is 1/2x-1.
Step-by-step explanation:
Given equation is
y = 2x+2
let y = f(x) = 2x+2
We have to find the inverse of given function.
Adding -2 to both sides of given equation,we get
y-2 = 2x+2-2
y-2 = 2x
dividing by 2 to both sides of above equation , we have
(y-2) / 2 = 2x / 2
y/2 - 1 = x
Swapping equation, we have
x = y/2-1
put x = f⁻¹(y) in above equation ,we have
f⁻¹(y) = y/2 -1
Replace y with x , we have
f⁻¹(x) = x/2-1
Hence , the inverse of given function is 1/2x-1.
Simplify 2(x + y) + 3(x + y).
Answer:
5x+5y
Step-by-step explanation:
A farm has 75 acres of wheat . The farmer can harvest the wheat from 12 acres per day.inhow many days will all of the fields be harvested?
Answer:
i wanna say 7 days
Step-by-step explanation:
75/12 = 6.25 round up to 7
Answer:
y=12x+75
X=75/12
X=6.25
Answer will be 7
Step-by-step explanation = x=75/12= x 6.25 = technically it’s will be 7 days
Rosy waxes 2/3 of her car with 1/4 bottle of car wax. At this rate , what fraction of the bottle of car wax will rosy use to wax the entire car ?
Answer:
8/3 = 1/x or x = 3/8
Step-by-step explanation:
Set up the ratio
(2/3)/(1/4) = 1/x
solve for x
8/3 = 1/x or x = 3/8
Answer:
Wax required for entire car = 3/8 bottle of wax
Step-by-step explanation:
We have given,
1/4 bottle of car wax can wax 2/3 of her car.
We need to find the wax required to wax her car completely.
Let's derive the relation between wax bottle and car waxing rate:
2/3 of car waxing needs 1/4 of bottle of wax.
for entire car waxing, i.e 1 car waxing needs (1/4) / (2/3) bottle of wax
wax required for entire car = (1/4 )*(3/2)
=3/8 bottle of wax
Is this true or false? The following graph represents a proportional relationship:
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, and 10. The values on the y axis are 0, 6, 12, 18, 24, 30. Points are shown on ordered pairs 0, 0 and 2, 6 and 4, 12 and 6, 18 and 8, 27. These points are connected by a line. The label on the x axis is Bunches of Thyme. The title on the y axis is Price of Bunches. sorry i dont know how to put pictures in
True
False
Answer:
False that the answer
Proportional relationships occur when the ratio between two quantities is constant. The provided details of the graph suggest a proportional relationship, but there could be an error— the point (8,27) doesn't follow the same ratio. Please double-check this point.
Explanation:Based on the provided details of the graph, we can infer that we have a proportional relationship, which exists when the ratio of the values of two quantities always remains the same. For example, in the graph, every two 'Bunches of Thyme' corresponds to a $6 increase in the 'Price of Bunches'. This constant ratio (1 bunch: $3) is characteristic of a proportional relationship.
So, the graph indeed represents a proportional relationship. The coordinates of the points (2, 6), (4, 12), (6, 18), and (8, 24), etc., fit the pattern y = 3x, which is another typical sign of a proportional relationship along the axis.
But it looks like there might be a mistake in your graph details because the point (8,27) doesn't fit the pattern y=3x. For x = 8, y should be 24 instead of 27. If that's not a typo, the graph doesn't represent a proportional relationship.
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A gardener has a patch of land that measures 96 feet long and 37 feet wide. He has 4 plants in each square foot of the garden. How many total plants does the gardener have in his garden?
The garden has a total of 14,208 plants, calculated by multiplying the area of the garden (3552 square feet) by the number of plants per square foot (4).
Explanation:The student asked how many total plants are in a gardener's garden, which measures 96 feet long and 37 feet wide, with 4 plants per square foot. To determine the total number of plants, we must first find the area of the garden by multiplying the length and width.
The area of the garden in square feet is 96 feet × 37 feet = 3552 square feet. Since there are 4 plants per square foot, the total number of plants is 3552 × 4 = 14,208 plants.
A metalworker has a metal alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 52% copper alloy?
Answer:
16 kg of I type and 64 kg of II type should be mixed.
Step-by-step explanation:
Given that a metal alloy in original has 20% copper and 80% other metals.
Another mixture contains 60% copper and 40% other metals.
We have to get a new alloy of 80 kg which has 52% copper.
Let us assume that we mix x kg of I alloy and y kg of second alloy.
Then we have x+y = total weight = 80 kg.
x+y = 80 ... (i)
Next condition is that new alloy has 52% copper in it
When we mix x kg of I, and y kg of II, copper content would be
0.2x+0.6y. This equals 52% of 80 = 41.6
Or Dividing by 0.2 we get
x+3y =208 ... (ii)
(ii)-(i) gives 2y = 128 or y =64 kg
x = 16 kg
16 kg of I type and 64 kg of II type should be mixed.
Verify:
Copper in new alloy = 16(0.2) + 64(0.6) = 3.2+38.4 = 41.6
= 52% of 80
find MI if MB = x+9 and IB = 2x–7
Answer:
MI = -x+16
Step-by-step explanation:
MI + IB = MB
MI + 2x-7 = x+9
Subtract 2x from each side
MI + 2x-7 -2x = x+9-2x
MI -7 = -x+9
Add 7 to each side
MI -7+7 = -x+9+7
MI = -x+16
The length of segment MI can be found by adding the lengths of segments MB and IB together, resulting in MI = 3x + 2.
Explanation:This problem relates to the concept of line segments in geometry. Line MB and IB are parts of a straight line where M, I and B are points on the line. Given that MB = x + 9 and IB = 2x - 7, we realize that MB + IB = MI.
To solve this problem, you simply add the equations of the two line segments together because the total length segment MI would be the sum of segments MB and IB:
So, MI = MB + IB = (x + 9) + (2x - 7).
Then, simplify the equation by performing the addition:
MI = 3x + 2.
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describe and correct the error in finding the product
2/5×3/10=6/50=3/25
Answer: There is not error in finding the product. The result is: [tex]=\frac{3}{25}[/tex]
Step-by-step explanation:
1. You have the following multiplication shown in the problem above:
[tex]\frac{2}{5}*\frac{3}{10}[/tex]
2. To solve it you must multiply the numerators and multiply the denominators, as you can see below:
[tex]\frac{2*3}{5*10}=\frac{6}{50}[/tex]
3. When you simplify the product, you obtain the following result:
[tex]=\frac{3}{25}[/tex]
Translate the sentence into an equation. Two less than the product of 5 and a number is equal to 6 . Use the variable w for the unknown number.
Answer:
i think its 5w -2 =6
Step-by-step explanation:
product is 5w and 2 less than product is 5w-2 which is equal to 6
that is 5w - 2 = 6
Write a rule to describe the function shown.
x y
−3 9
−1 3
0 0
3 −9
y = 3x
y = −3x
y equals start fraction one over three end fraction x
y equals negative start fraction one over three end fraction x
Answer:
y = -3x
Step-by-step explanation:
(a) Slope
y = mx + b
Choose points (-3, 9) and (3, -9)
m = (-9 - 9)/(3 – (-3))
m = -18/(3 + 3)
m = -18/6
m = -3
=====
(b) y-intercept
y = mx +b
Choose point (0,0).
0 = 0 + b
b = 0
=====
(c) Equation of line
y = mx + b
y = -3x
I need help ASAP please!
What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 2 is also divisible by 4.
A: 32
B: 12
C: 40
D: 18
Let's go through the list of values and test the claim
Is 32 divisible by 2? Yes because 16*2 = 32. Is it also divisible by 4? Yes because 8*4 = 32. So we can cross choice A off the list
Is 12 divisible by 2? Yes because 6*2 = 12. Is it also divisible by 4? Yes because 3*4 = 12. So we can cross choice B off the list.
Is 40 divisible by 2? Yes because 2*20 = 40. Is it also divisible by 4? Yes because 4*10 = 40. Choice C is also crossed off the list.
Is 18 divisible by 2? Yes because 2*9 = 18. Is it also divisible by 4? No. We can see that by dividing 18/4 = 4.5 which is not a whole number result. Or you can list out the multiples of 4 which are 4, 8, 12, 16, 20 and we see that 18 is not on the list.
So choice D) 18 is the answer. This is a counter example to show that the claim "if number is divisible by 2, then it is also divisible by 4" is a false statement.
The required counterexample for the conjecture is 18. which is the correct answer that would be an option (D).
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
For example divisibility rule of 3 is that the sum of the digits should be 3.
A counterexample for the conjecture is 18. This is a counterexample because 18 is divisible by 2 (it is an even number), but it is not divisible by 4.
Therefore, the statement "any number that is divisible by 2 is also divisible by 4" is false, because there are some numbers (like 18) that are divisible by 2 but not by 4.
Thus, the required counterexample for the conjecture is 18.
Hence, the correct answer would be an option (D).
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What is the following product? (2 square root 7+3 square root 6)(5 square root 2+4 square root 3)
[tex](2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\qquad\text{use distributive property}\\\\=(2\sqrt7)(5\sqrt2)+(2\sqrt7)(4\sqrt3)+(3\sqrt6)(5\sqrt2)+(3\sqrt6)(4\sqrt3)\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{12}+12\sqrt{18}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{4\cdot3}+12\sqrt{9\cdot2}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt4\cdot\sqrt3+12\sqrt9\cdot\sqrt2\\\\=10\sqrt{14}+8\sqrt{21}+(15)(2)\sqrt3+(12)(3)\sqrt2\\\\=\boxed{10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2}[/tex]
Answer: The required product is [tex]10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]
Step-by-step explanation: We are given to find the following product :
P = (2 square root 7+3 square root 6)(5 square root 2+4 square root 3).
We will be using the following property of radicals :
[tex]\sqrt a\times \sqrt b=\sqrt{ab}.[/tex]
The given product can be written and evaluated as follows :
[tex]P\\\\=(2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\\\\=2\sqrt7(5\sqrt2+4\sqrt3)+3\sqrt6(5\sqrt2+4\sqrt3)\\\\=10\sqrt{7\times2}+8\sqrt{7\times3}+15\sqrt{6\times2}+12\sqrt{6\times3}\\\\=10\sqrt{14}+8\sqrt{21}+15\times2\times\sqrt3+12\times3\sqrt2\\\\=10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]
Thus, the required product is [tex]10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]
Jessica needs to make a necklace for 3 of her friends, including her. she wants to use 4.5 inches of string for each necklace. she only has 10 inches of string. How many necklaces can she make and How many more string does she need to buy?
Answer:
She can make two necklaces with 10 inches. 8 more inches
Step-by-step explanation:
Answer:
She can make 2.2 Necklaces, and needs 3.5 more inches of string.
Step-by-step explanation:
Let's carefully read the problem for information we need.
3 Friends, 4.5 Inches per friend. She only has 10 inches.
If each necklace is 4.5 inches, we need
4.5 (friend one) + 4.5 (friend 2) + 4.5 (friend 3). We can also just take 4.5 * 3 friends and get the same result. This equals 13.5.
But wait! We only have 10 inches... Jessica needs 3.5 more inches of string to be able too complete the 3rd necklace. This is the answer to "How much more string does she need to buy"
---
For "How many necklaces can she make". Well, we know she can't make a full 3 necklaces. We can find out the answer to this by dividing the 10 inches she does have, by the 4.5 inches it takes to make one necklace.
10/4.5=2.2
This means she could make 2 necklaces, and 2/10 (.2) of another necklace before she runs out of string.
A taxicab ride costs $2.50 plus $1.10 per mile. If the total cost of the trip is $21.20, how many miles did the passenger travel? Let x represent the number of miles
Answer: The passenger will travel 17 miles.
Step-by-step explanation:
Since we have given that
Cost of a taxicab ride = $2.50
Cost of per mile = $1.10
Total cost of the trip = $21.20
Let number of miles the passenger travel be x
According to equation,
[tex]2.50+1.10x=\$21.20\\\\1.10x=\$21.20-\$2.50\\\\1.1x=18.7\\\\x=\frac{18.7}{1.1}\\\\x=17\ miles[/tex]
Hence, the passenger will travel 17 miles.
Gail bought 18 buttons to put on the shirts she makes she uses five buttons for each shirt how many shirts can still make with the buttons she Bought
Answer:
18 divided by 5 is equal to 3 with a remainder of 3 so she can only make 3 T-shirts
Step-by-step explanation:
Answer:
3 shirts
Step-by-step explanation:
She has 18 buttons. 18 divided by 5 is 3.6
so she can make 3 shirts
Enter the coordinates for the solution the following system or equations
Y=3x-8
Y=-x-4
Answer:
(1,-5)
i plugged it into a graphing calc
Mr Ortiz oversees the distribution centers for a shipping company. He recently introduced new processes at 2 centers which saved the company 2.4 million Mr. Ortiz plans to introduce the same cost saving processes at all 16 of the company's aistrubution centers. What is the total amount of money that the company can be expected to save
Answer:
19.2 million.
Step-by-step explanation:
Let us find the amount of savings per center by dividing 2.4 by 2.
[tex]\text{Amount of savings per center}=\frac{2.4\text{ Million}}{2\text{ Center}}[/tex]
[tex]\text{Amount of savings per center}=1.2\frac{\text{ Million}}{\text{ Center}}[/tex]
Hence, the company saved 1.2 million per center.
Let us multiply savings of each center by total number of company's distribution centers to find the total amount of money that the company can be expected to save.
[tex]\text{Total amount of company's savings}=(1.2\times 16)\text{ million}[/tex]
[tex]\text{Total amount of company's savings}=19.2\text{ million}[/tex]
Therefore, Mr. Ortiz's company will save 19.2 million.
Rolling a number cube twice is a dependent event. True or false Asap
Answer:
False...there's nothing to depend on when you are expecting a random number out of 2 different rolls of the "number cube".
Hope this helps!! (:
1/3(m-1)=-5
Please help
Answer:
m=-14 I hope this helps u
Step-by-step explanation:
At the farm, Justin picks 3 bushels of fruits. The bushels weigh 8 1/4 pounds, 6 1/2 pounds, and 6 5/8 pounds. What is the average weight per bushel?
Solve each system by substitution. -5x + 3y = 3 and -4x + y = 1
[tex]\left\{\begin{array}{ccc}-5x+3y=3\\-4x+y=1&|\text{add 4x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-5x+3y=3\\y=4x+1&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to the first equation}\\\\-5x+3(4x+1)=3\qquad\text{use distributive property}\\\\-5x+(3)(4x)+(3)(1)=3\\\\-5x+12x+3=3\qquad\text{subtract 3 from both sides}\\\\7x=0\qquad\text{divide both sides by (-5)}\\\\\boxed{x=0}\\\\\text{Substitute the value of x to}\ (*):\\\\y=4(0)+1\\y=0+1\\\boxed{y=1}\\\\Answer:\ x=0\ and\ y=1.[/tex]
what is a piecewise function
Answer:
is a function that is defined on a sequence of intervals
Step-by-step explanation:
next time please just search it up on google.
Answer:
A piecewise function has different rules for different parts of its domain. The following situation can be modeled by a piecewise function.
Step-by-step explanation:
Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is $13.20. How many nickels does Jamie have?
Answer: 33
5x+10x+25x= 1320 or 40x= 1320
Jamie has 33 nickels.
Explanation:To find out how many nickels Jamie has, we need to set up an equation.
Let's assume Jamie has x nickels. Since Jamie has an equal number of nickels, dimes, and quarters, he also has x dimes and x quarters.
The value of x nickels is 5x cents, the value of x dimes is 10x cents, and the value of x quarters is 25x cents.
According to the problem, the total value of all the coins is $13.20, which is equal to 1320 cents.
So we can write the equation as follows: 5x + 10x + 25x = 1320.
Combining like terms, we get 40x = 1320. Dividing both sides by 40, we find that x = 33.
Therefore, Jamie has 33 nickels.
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an antelope can run at a speed of 61 miles per hour. What is this speed in yards per second? Round to the nearest hundredth.
Who’s is the graph of Y is greater than or equal to
1 - 3x?
convert the measurement 479cm
What form of measurement do we convert it to?
Convert to what? Feet? Inches? Yards? Meters? Please tell me so i can answer this!
PLEASE HURRYY!! what is this in an exponential form?
Answer:
I think it is D because 9 times 7 equals 63...
Answer:
The answer is c Hope this helps:)
Step-by-step explanation:
−2 × 32 − 8 ÷ 2 + 6?
Answer:
-62
Step-by-step explanation:do multiplication 1st then work out problem left to right.
Sally is 18 years older than her son she was three times as old as he was one year ago how old are they now
Answer:
Today Sally is 28 years old and her son is 10
Step-by-step explanation:
x= Sally's Age; y= Sally's son age
Sally is 18 years older than her son
x-y=18
And she was three times older
x=3y
Substituting and solving:
3y-y=18
2y=18
Last year they were:
y=9
x=27
This year
y+1=10 ; x+1=28
the entry fee at a small fair is $1.50 for children and $4.00 for adults . on a certain day 1900 people enter the fair and $4402.50 is collected how many children went to the fair?
150x + 400(1900-x) = 440250
150x + 760000 - 400x = 440250
250x = 319750
x = 1279
There were 1,279 children.