The function is not one-to-one function, hence the inverse doesn't exist for the whole domain of the function. But if we restrict the domain to [tex]x\in(-\infty,0][/tex] or [tex]x\in[0,\infty)[/tex], then we can give the inverse.
[tex]f(x)=x^2-4\\\\y=x^2-4\\\\x^2=y+4\\\\x=\sqrt{y+4} \vee x=-\sqrt{y+4}\\\\f^{-1}(x)=\sqrt{x+4}\vee f^{-1}(x)=-\sqrt{x+4}[/tex]
So, when [tex]D_{f(x)}:x\in(-\infty,0][/tex], the inverse is [tex]f^{-1}(x)=-\sqrt{x+4}[/tex] and when [tex]D_{f(x)}:x\in[0,\infty)[/tex], the inverse is [tex]f^{-1}(x)=\sqrt{x+4}[/tex].
The inverse of the function f(x) = x^2 - 4 is found by switching the x and y variables and solving for y. Because y is being squared, there are two solutions: y = ±sqrt(x + 4).
Explanation:The inverse of a function f(x) is found by switching the x and y variables and solving for y. For the function f(x) = x^2 - 4, let us swap x and y, it becomes x = y^2 - 4. Next, solve for y. However, because y is being squared, there will be two solutions, one for the positive square root and other for the negative square root. Therefore, the inverse of the function f(x) = x^2 - 4 is y = ±sqrt(x + 4).
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what is 8 divided by 33 show your work
Answer:
0.24 with a line over the 24. The line means that it is repeating.
Explanation,
There is not much to explain it's just simple divison.
A rectangle has a perimeter of 30 inches. Its length is one less than three times its width. What are the length and width of the rectangle?
Perimeter of a rectangle can be represented by 2* length + 2 * width
We can represent the width with the variable x
We can represent the length by the expression 3x-1
So, now we can make a forumla and solve
2(3x-1) + 2(x) = 30
6x-2+2x = 30
8x = 32
x = 4 is the width of the rectange.
Now we find the length
3(4)-1
11 = Length
The width of the rectangle is 4 inches and its length is 11 inches.
What is the formula for the Perimeter of Rectangle?A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.
The Perimeter of rectangle is -
P = 2(x + y)
The Area of rectangle is -
A = xy
We can write -
P = 2x + 2y
Py = 2xy + 2y²
Py = 2A + 2y²
2y² - Py + 2A = 0
y = ± (P² - 16A)/4
Given is a rectangle that has a perimeter of 30 inches. Its length is one less than three times its width
Assume the length to be [x] inches and width be [y] inches. Then, we can write -
[x] = 3[y] - 1
and
2(x + y) = 30
2(3y - 1 + y) = 30
2(4y - 1) = 30
8y - 2 = 30
y = 4 inches
then -
x = 12 - 1
x = 11 inches
Hence, the width of the rectangle is 4 inches and its length is 11 inches.
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Best estimate for 61/7
I would say the best estimate would be 9 because the real answer is 8.71 and if you round that to the 1 place the answer would be 9.
if the mean of a symmetrical distribution is 56, which of the values could be the median of the distribution 56,14,28,42
First you want to organize the numbers in order to find the median so it should look like this: 14, 28, 42, 56. Then you want to find the one in the middle. But oh wait there are TWO in the middle so add 42 and 28 up 70 then divide it by 2 which equals your median of 35.
Answer: 56
Step-by-step explanation: Apex
A commuter has $245 in his savings account this account changes by -$15 each week he buys a ticket.in one time period, the account changed by -$240.for hot many weeks did the commuter buy tickets?
Which of the following expressions is equivalent to 1/4(8x+12)
The equivalent expression for the given expression is 2x+3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 1/4 (8x+12).
Here, multiply 1/4 into a bracket, we get
= 8x/4 +12/4
= 2x+3
Therefore, the equivalent expression for the given expression is 2x+3.
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Will give alot of points!
A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
This is what I think:
#1: 800 - 50 = 750
#2: 800 divided by 2 = 400 - 50 = $350
i think the dryer costs 450$ and the washer 350$
the perimeter of a rectangle photograph is 22in the length of the photograph is 1 inch more than the width what are the dimensions of the photograph
Assume that the width=w
22=2w+2(w+1)
22=2w+2w+2
22=4w+2
20=4w
w=5
The dimensions are 4 by 5.
The dimensions of the rectangle photograph are 5.5 inches (width) by 6.5 inches (length), calculated by setting the given perimeter equal to twice the sum of the length and the width, and then solving for the width and length.
Explanation:The perimeter of a rectangle is the sum of all its sides. Given that the perimeter of the photograph is 22 inches, you can work out the length and width using algebra. Let's denote the width of the photograph as 'x' (in inches). Thus, the length is 'x + 1' since it is one inch more than the width. Since the rectangle has two equal lengths and two equal widths, its perimeter can be represented as 2*(length + width) or 2*(x + x + 1). Setting this equal to 22 (the perimeter), we get 2*(2x + 1) = 22. Solving for 'x' gives us the width, which is 5.5 inches. The length is therefore 6.5 inches, being 1 inch more than the width. Therefore, the dimensions of the rectangle are 5.5 inches by 6.5 inches.
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during his first year as a pilot, rob flies 6,692 miles. he flies 16,429 miles the second year and 24,211 miles the third year. he wants to estimate how many more miles he flew in the third year than the first and second year combined. which shows one way rob could estimate?
First years flies = 6,692 miles ≈7000 miles.
Second year flies = 16,429 miles ≈ 16000.
Third year flies = 24,211 miles ≈ 24000
Total number of miles flies in first and second year = 7,000miles +16,000 miles
Number of more miles he flew in the third year than the first and second year combined = Number of miles flies in third year - Total number of miles flies in first and second year
Number of more miles he flew in the third year than the first and second year combined 24,000 - (7,000+16,000)
Therefore, 24,000 - (7,000+16,000) estimation of how many more miles he flew in the third year than the first and second year combined.
What will happen to the mean if the outlier is removed?
4, 5, 5, 7, 9, 17
1. It will not change.
2. It will be the same as the median.
3. It will decrease.
4. It will increase.
Solution:
The outlier is 17
With Outlier
4 + 5 + 5 + 7 + 9 + 17 = 47
47 / 6 = 7.83333333...
Without Outlier
4 + 5 + 5 + 7 + 9 = 30
30 / 5 = 6
Mean With Outlier - 7.8333...
Mean Without Outlier - 6
Answer - 3. It will decrease
Answer:
17
Step-by-step explanation:
if 6 subs are cut into 1/5 how many subs are there
Which number sentences show how to solve the problem?
The truck driver loaded 72 crates of eggs. There are 36 eggs in each crate. The driver will make 6 deliveries and unload the same number of eggs at each delivery stop.
How many eggs will the driver unload at each stop?
Choose all answers that are correct.
72 ÷ 6 = 12 and 12 × 36 = 432
72 ÷ 6 = 12 and 12 × 12 = 144
72 ÷ 36 = 2 and 2 × 72 = 144
72 × 36 = 2,592 and 2,592 ÷ 6 = 432
72 ÷ 6 = 12 and 12 × 36 = 432 and 72 × 36 = 2,592 and 2,592 ÷ 6 = 432
Complete the synthetic division problem below 2|1 7 -18 WHATS is the quotient polynomial form? a x+7 b x+9 c x-9 d x-7
Answer:
x+9
Step-by-step explanation:
Synthetic division calc on Mathaway
The quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
What is synthetic division?In the case of dividing by a linear factor, synthetic division is a shorthand, or quicker, technique of polynomial division.
W have:
2 | 1 7 -18
2 | 1 7 -18
__________
1
2 | 1 7 -18
____2×1 = 2______
1 7+2 = 9
2 | 1 7 -18
______2___2×9=18___
1 9 -18+18 = 0
The quotient is x+9, and the remainder is 0.
Thus, the quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
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Find the area of a square piece of cardboard for which the length of the side is 8”sq root sign”
Answer:
Area of square = 64 square units .
Step-by-step explanation:
Given : length of the side is √8.
To find : Find the area of a square piece of cardboard .
Solution : We have given side length of square cardboard = √8.
Area of square = side * side .
Area of square = √8 *√8.
Area of square = 64 square units .
Therefore, Area of square = 64 square units .
Darcy and Leah are looking at some fabric selections in a store. All of the selections are marked the same price, and the amount, in yards, of each fabric is written as an improper fraction. Which amount is the greatest? A. 33⁄4 B. 22⁄3 C. 78⁄9 D. 43⁄5
The amount is written in improper fraction.
To know, which amount is greatest, we will convert these improper fraction to proper decimal form values by division method and then we will compare the values.
A. [tex]\frac{33}{4}=8.25[/tex]
B. [tex]\frac{22}{3}=7.33[/tex]
C. [tex]\frac{78}{9}=8.66[/tex]
D. [tex]\frac{43}{5}=8.60[/tex]
Hence, the greatest amount is option C. [tex]\frac{78}{9}[/tex]
Juan bought a desktop computer and a laptop computer. Before finance charges, the laptop costs $300 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 6% per year, and for the laptop it was 7% per year. The total finance charges for one year were $398. How much did each computer cost before finance charges?
Answer:
The cost of each computer before finance is:
Desktop: $2900.00, Laptop: $3200.00
Step-by-step explanation:
Lets say the cost of Desktop is 'D' dollars.
The cost of laptop is [tex]=D+300[/tex] dollars.
Total finance charge for 1 year is given by:
[tex]0.06\times D+0.07 \times (D+300)=398[/tex]
Solving for D we get:
[tex]0.06D+0.07D+21=398[/tex].......(equation 1)
[tex]0.13D=398-21=377[/tex]
[tex]D=\frac{377}{0.13} =2900[/tex]
Now the cost of laptop is D+300:
[tex]D+300=2900+300=3200[/tex]
So before finance, the cost of desktop was $2900.00 and the cost of laptop was $3200.00.
P.S: You can check if your calculation is correct by plugging the values of the cost of laptop and desktop in the equation 1.
(6,-2),(r,-6),m=4 find the value of r so that the line passes through each pair of points has a given slope
r = 5
calculate the slope m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with ( x₁, y₁ ) = (6, - 2 ) and (x₂, y₂ ) = (r, - 6)
m = [tex]\frac{-6+2}{r-6}[/tex] = [tex]\frac{-4}{r-6}[/tex] = 4
cross multiply
4(r - 6 ) = - 4
4r - 24 = 4 ( add 24 to both sides and divide by 4 )
4r = 20
r = [tex]\frac{20}{4}[/tex] = 5
The value of r so that the Slope of a line passes through the points (6,-2) and (r,-6) with a slope of 4 is 7.
In mathematics, the slope of a line through two points can be determined using the formula m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) and (x2, y2) are the coordinates of two points on the line.
In your case, the given points are (6, -2) and (r, -6) and the slope (m) is given to be 4. So, insering these values in the formula, you get: 4 = (-6 - (-2)) / (r - 6).
By simplifying the above equation, we find that r = 7.
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need help with this math
Solution
Leased cost for 3 years = $3000 + 250 *36 [ 3 years = 36 months]
= 3000 + 9000
Leased the car for 3 years cost you = $12,000
The residual value = $10,000
Assume that you bought the car and used for 3 years and sold for $10,000
Cost of the car = $24,000
Sold after 3 years for $10,000
Your expense in 3 years = $24,000 - 10, 000 = $14,000
By comparing these two options, leasing the car will benefit you since it cost only $12,000.
Therefore, lease car is less expense.
The cost for buying the car and selling it after three years would be $14,000.
That is the answer. :)
Thank you.
evaluate 15k when k=3
if k=3 than 15k (5 mutiple k) 5*3=45
The value of the expression 15k when the value of k is 3, will be 45.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The expression is given below.
⇒ 15k
If the value of the k is 3, then the value of the expression will be
⇒ 15 × 3
⇒ 45
The value of the expression 15k when the value of k is 3, will be 45.
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Please WILL GIVE BRAINLIEST!
What is this expression in radical form?
(4x^3y^2)^3/10
what is the greatest common factor of 16y^3 z^3 and 56y^4z
Answer:
8y^3z
Step-by-step explanation:
8, y^3 and z are common to both expressions. Thus, the GCF is 8y^3z.
a house is valued £210 000, correct to 2 significant figures, what is the lowest possible value of the house and the highest possible value of the house?
The lowest possible value of the house is £205000 and highest possible value is £214999.99...
Given that:
The house is valued £210000, correct to 2 significant figures.
Since its correct to 2 significant figures, thus there is error of approx 10000 range in £210000
The lowest possible number that would round up to 2 significant numbers to £210000 is £205000 since any value lower than that would look like £204..... which won't round up to £21..... but £20....
Similarly, the highest possible number that would round up to 2 significant figures to £210000 is £214999.999... since any real number bigger than that would make starting digit of the number as £215.... and thus 2 significant figure rounding will lead to £22....
Thus, the lowest possible value of the house is £205000 and highest possible value is £214999.99...
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Record the product 51 times 77
the answer is 128 because 51 + 77= 128
The product is 3927.
what's the value of y
(3y +10) /4 = 2y
Multiply both sides by 4:
4(3y +10) = 4(2y)
12y +40 = 8y
Subtract 40 from each side:
12y = 8y -40
Subtract 8y from each side:
4y = -40
Divide both sides by 4:
y = -40 / 4
y = -10
The answer is A. -10
Find the mean of the set data. -17 32 -9 0 52 12 -14??
To find the mean you must:
-17 + -14 + -9 + 0 + 12 + 32 + 52 = 56
Then divide 56 by how many numbers are in this set so there are 7 numbers so we divide 56 by 7 and I don't even have to do the work for this because it's basic multiplication.
The answer is: 8.
Answer:
Mean is 8
Step-by-step explanation:
Given observations,
-17, 32, -9, 0, 52, 12, -14
Sum of the observations = -17 + 32 + (-9) + 0 + 52 + 12 + (-14)
= 96 - 40
= 56
Number of observations = 7,
Hence,
[tex]\text{Mean} = \frac{\text{Sum of the observations}}{\text{Number of the observations}}[/tex]
[tex]=\frac{56}{7}[/tex]
= 8
Help me please , and thank you .
Remark
There is a 4 year difference between Sal and Carrie. Carrie is the older. She is going to occupy 1 side of the equation. The other side is Sal and the 4 years.
Let Sal = S
Let Carrie = C
Carrie = Sal + 4
Equation
C = S + 4
The temperature was -3 C last night. It is now -4 C. What was the change in temperature
-1 C, that's the only logical answer I can think of. Or does it have to be in F?
The change in temperature is a decrease of 1°C, which is calculated by subtracting the initial temperature from the final temperature.
The question involves calculating the change in temperature from -3°C to -4°C. To find the change in temperature, you subtract the initial temperature from the final temperature. In this case, the change would be:
-4°C - (-3°C) = -4°C + 3°C = -1°C.
So the change in temperature is a decrease of 1°C.
A speed reader can read 850 efficient words per minute. An average reader can read at approximately 1/7 that speed. How many efficient words per minute does an average reader read?
Answer:
An average reader can read 121.43 words per minute efficiently.
Explanation:
A speed reader can read 850 efficient words per minute.
An average reader can read at approximately 1/7 that speed.
Total word read by an average reader per minute is given = 850* 1/7
= 121.43 words per minute
So an average reader can read 121.43 words per minute efficiently.
Convert 6 x 10 to the power of 5 into standard form
First let's write it out with just numbers
6×[tex]10^{5}[/tex]
Now solve!
Solve exponent first
10^5 = 100,000
Now multiply
6 x 100,000 = 600,000
600,000 is your answer
The number 6 x 10^5 in standard form equates to 600000. The conversion involves moving the decimal place the same number of steps as the power of ten indicates
Explanation:The conversion of 6 x 10 to the power of 5 into standard form involves interpreting the exponent as the number of places to shift the decimal point. In this case, the decimal point will be moved five places to the right.
Thus, 6 x 10 is equivalent to 600000 in standard form.
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