Inverse of the function is -2+x
What do you mean by inverse function?
A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.
The function's inverse, represented by , [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).
Given function is y = x² + 4x + 4
To find the inverse function, we need to express x as a function of y:
Substitue y=x
⇒ x = [tex]y^{2}+4y+4[/tex]
Substract x from the above equation we get,
[tex]y^{2}+4y+4[/tex] - x = 0
Solve the above equation using quadratic formula we get,
y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex] [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex] = [tex]\frac{-4+2x}{2}=-2+x[/tex]
Similarly, y = -2-x
Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x
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In 6 years, a father wants to accumulate $110000 to pay for his daughter's college expenses. If he can get 8% interest, compounded quarterly, how much must he invest now to achieve his goal?
The amount that hw must invest to achieve the goal when it will be compounded annualy is $68750
Given Information:
Principal Amount (P) = to be calculated
Rate of Interest (r) = 8 %
Time Period (t) = 6
Amount Received (A) = $110000
Number of times the interest is compounded quarterly (n) = 4
The Formula for the amount received when the principal (P) is compounded is given by,
[tex]A = P( 1 + \frac{r}{100n} )^{nt}[/tex]
Now, putting the values, we get:
[tex]110000 =P( 1 + \frac{8}{100*4} )^{4*6}[/tex]
P = $68750
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What is the equation of a circle with a center at (-4, 0)
that passes through the point (-2, 1)?
O x² + (y + 4)² = √√5
O (x-1)² + (y + 2)² = 5
O (x + 4)² + y² = 5
O (x + 2)2 + (y - 1)² = √5
The equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.
The standard equation of a circle is given by:
(x – h)² + (y – k)² = r²
Where (h, k) is the center of the circle and r is the radius.
We are given:
The circle has a center at (–4, 0) and passes through the point (–2, 1).
Substitute (h, k) with (–4, 0) in the above equation, we will get;
(x – (-4))² + (y – 0)² = r²
(x + 4)² + y² = r²
Substitute (x, y) with (–2, 1) in the above equation to get the value of r:
(-2 + 4)² + 1² = r²
(2)² + 1² = r²
r² = 5
Put the value r² = 5 in (x + 4)² + y² = r², we will get;
(x + 4)² + y² = 5
So, the equation of the circle is (x + 4)² + y² = 5.
Thus, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.
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Determine the domain and range of the following parabola. f(x)=−3x2−30x−74
Step-by-step explanation:
1. if to rewrite the given equation, then
y= -3(x+5)²+1;
2. the vertex of the parabola is (-5;1) and it is the highest point. Then
3. domain: x is any value, x∈(-∞;+∞);
range: y not greater than 1, y∈(-∞;1].
For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).
To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.
The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).
The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.
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Hi photo is below! Please explain how you got your answer thank you
Answer:
38.88in²
Step-by-step explanation:
Area of shaded region = Area of square - Area of semi circle
First lets find the area of the square and semi circle
Area of square = s²
Where s = side length
Here we have a given side length of 8in
So s = 8
This means area = 8² = 64in²
Area of semicircle = (πr²)/2
Where r = radius
Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in
To convert from diameter to radius we simply divide by 2
So radius = 8 / 2 = 4
Now we have Area = (πr²)/2
==> plug in r = 4 and π = 3.14
Area = (3.14(4)²))/2
==> simplify exponent
Area = (3.14(16))/2
==> multiply 3.14 and 16
Area = 50.24/2
==> simplify division
Area = 25.12in²
Area of shaded region
We now subtract the two areas
Area of shaded region = Area of square - Area of semi circle
Area of square = 64in² and Area of semicircle = 25.12in²
Area of shaded region = 64in² - 25.12in² = 38.88in²
Using a calculator, work out the value of
(7.6 x 10^-4) × (8.2 × 10^11)
Give your answer in standard form.
!!PLEASE HELP!!
The path of a baseball is modeled by the equation [tex]y=-0.25x^{2} +4x+3[/tex] where x represents the time (in seconds) and y represents the height of the baseball.
- Find and interpret the y-intercept. Find the maximum height of the baseball. Then sketch a graph of the path.
(please provide steps on how to solve if you can)
Answer:
The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.
Step-by-step explanation:
The $y$-intercept is $-1$. The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$. Here is a sketch of the path.
From the $y$-intercept, we see that the baseball starts at height $y=-1$. It reaches a maximum height at $x=\ln(4)$; that is, $y=0$. From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.
Jayden took a taxi from his house to the airport. The taxi company charged a pick-up
fee of $4.10 plus $4.25 per mile. The total fare was $101.85, not including the tip.
Which equation could be used to determine m, the number of miles in the taxi ride?
Answer:10
Step-by-step explanation:
1.20 + (4.75 × x) = 48.701.20 + 4.75x = 48.70Collect like terms 4.75x = 48.70 - 1.204.75x = 47.50Divide both side by 4.754.75x/4.75 = 47.50/4.75.x = 10
Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below. E(–2, 2), F(5, 1)
Answer:
dd
Step-by-step explanation:d
Answer:
Step-by-step explanation:
a0 - x-y=3
When planning a cruise, you have a choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G); a choice of 2 types of rooms: balcony (B) or inside view (I); and a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.
The sample space in regard to the vacations is 24
Choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G) =
3C1
A choice of 2 types of rooms: balcony (B) or inside view = 2C1
And a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z) = 4C1
Choosing only one of each, the sample space in regard to the vacations
Sample space = choice of destination x choice of room x choice of water sports
= 3C1 x 2C1 X 4C1
= 3 x 2 x 4 = 24
Therefore, the sample space in regard to the vacations is 24
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Ashley and Laura are 60 miles apart, traveling towards each other. If Laura travels 12 mph
and Ashley travels 8 mph how long until they meet?
hours
The time taken by Ashley and Laura to meet each other is 3 hrs
Relationship Between Time, Speed & Distance:The speed of an object tells us how slow or fast an object moves. The formula for speed is given below
Speed = Distance/TimeThe speed of an object is directly proportional to Distance and Inversely proportional to Time. Hence,
Distance = Speed X TimeHere we have,
Ashley and Laura are 60 miles apart, traveling toward each other
This means the distance between Ashley and Laura is 60 miles
Speed of Laura = 12 mph
Speed of Ashley = 8 mph
Let us assume that Both Ashley and Laura meet after t hours
Then
The distance traveled by Laura in t hours = 12 mph × t hrs = 12t m
The distance traveled by Ashley in t hours = 8 mph × t hrs = 8t m
As we know the distance between Laura and Ashley is 60 miles
=> 12t m + 8t m = 60 miles
=> 20t miles = 60 miles
=> t = 60/20
=> t = 3hrs
Therefore,
The time taken by Ashley and Laura to meet each other is 3 hrs
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The side x of the right triangle is 235.72 units.
How to find the sides of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras theorem depending on the sides and angles given.
Hence, let find the value of x in the combine right triangles.
Therefore,
tan 28 = opposite / adjacent
tan 28 = 105 / l
cross multiply
l = 105 / tan 28
l = 105 / 0.53170943166
l = 197.479781832
l = 197.50
tan 70 = 105 / a
a = 105 / tan 70
a = 38.2168804325
a = 38.22
Therefore,
x = 197.50 + 38.22
x = 235.72 units
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what is the equation and solution please?
Answer:
y=3x+1
y=-17
Step-by-step explanation:
y=3x+1
7=3(2)+1
7=6+1
7=7
y=3(-6)+1
y=-18+1
y=-17
Hopes this helps please mark brainliest
How long will Suban need to leave a $10 000 investment in the bank at 5% per
year simple interest for it to grow to $15 000?
a. 10 years c. 5 years
b. 100 years d. 50 years
Suban need to leave $10000 investment in the bank at 5% per year simple interest for 10 years so that it grows to $15000
According to question,
Principal (P) = 10,000
Rate of interest (I) = 5%
Interest = Amount - Principal
= 15000 - 10000
= 5000
We need to find the number of years
T = ?
Interest = P * R * T / 100
5000 = 10000 * 5 * T / 100
T = 10 years
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need help???????????????????
Step-by-step explanation:
it is totally simple : you need to put the x-value into every place of the x-variable, and then we calculate.
and then the same for the next x-value. and the next. ...
-2
-2×-2 + 9 = 4 + 9 = 13
0
-2×0 + 9 = 0 + 9 = 9
2
-2×2 + 9 = -4 + 9 = 5
4
-2×4 + 9 = -8 + 9 = 1
I really do not understand these questions at all watched a video and attempted it still got it wrong
Answer:
540 cm₂
Step-by-step explanation:
Area of right triangular prism:[tex]\sf \boxed{Area = (b_1+b_2+b_3)*l + bh}\\\\[/tex]
[tex]\sf \text{where $b_1$, $b_2$ and $b_3$ are the sides of the triangle l is the length of the rectangle}\\\\ \text{and b is the base of the triangle and h is the altitude of the triangle}[/tex]
b₁ = 12 cm ; b₂ = 5 cm ; b₃ = 13 cm
l = 16 cm ; b = 12 cm and h = 5 cm
Area = (12 + 5 + 13)*16 + (12*5)
= 30*16 + 60
= 480 + 60
= 540 cm²
Using the table, what is the average daily balance of the credit card for the August 1 through August 31 billing period? Round your answer to the nearest dollar.
Day Activity Adjustment Closing Balance
1 -- -- 950
8 Payment −600 350
16 Purchase +300 650
24 Purchase +250 900
Using the table, the average daily balance of the credit card for the August 1 through August 31 billing period is $705.
What is the average daily balance?The average daily balance refers to the computed total balance divided by the number of days in the billing cycle.
The computed total balance is the sum of closing balance multiplied by the number of days covered in the billing cycle before the next credit card transaction or activity.
Day Activity Adjustment Closing Balance No. of days Total
1 -- -- 950 7 $6,650
8 Payment −600 350 8 2,800
16 Purchase +300 650 8 5,200
24 Purchase +250 900 8 7,200
Total 31 $21,850
Average daily balance = $705 ($21,850/31)
Thus, the average daily balance on the credit card is $705.
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The edge of a cube is measured to be 20 inches. If the measurement is to be correct to within 1/10 inch, use differentials to find the error in the volume of the cube.
The error in the volume of the cube is gotten as; ±120 in³
What is the volume error?
In this type of situation, there could be maximum error, relative error and percentage error.
The maximum error is gotten by differentiating the volume equation.
The relative error is gotten by dividing the change in volume by the volume likewise change in length.
The percentage error is just converting the relative error to percentage. Thus;
Thus;
Volume of a cube is given by the formula;
V = x³
dV/dx = 3x²
dV = 3x²(dx)
We are given dx = 1/10
Thus;
dV = ±(3 * 20² × (1/10))
dV = ±120 in³
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The first three terms of a sequence are given. Round to the nearest thousandth. 10, 5, 5/2. Find the 6th term
Answer:
5/16
Step-by-step explanation:
This is a geometric sequence
aₙ=a₁*rⁿ⁻¹
a₆=10*.5⁶⁻¹
a₆=10*.5⁵
a₆=10*(1/2)⁻⁵
a₆=10*1/32
a₆=10/32=5/16
solve x^2-4x+3=0 using the quadratic formula
Answer:
1 and 3
Step-by-step explanation:
discriminant = 16 - 4 * 1 * 3 = 16 - 12 = 4
x1 = (4 + √4)/2 = (4+2)/2 = 6/2 = 3
x2 = (4 - √4)/2 = (4-2)/2 = 2/2 = 1
b) Write 13 x 10 in standard form.
Answer:
130 in standard form
100+30 in expanded form
Step-by-step explanation:
standard from is writing the sentence in a number fro example
three hundred seventy two is writen as 372 in standard for
expanded form is 300+70+2
Answer:
130 in standard form
In expanded form is100+30=1300
Step-by-step explanation:
For further example 4236
In standard form is 4236
In expanded form is 4000+200+30+6=4236
Sunland Company reports the following information (in millions) during a
recent year: net sales, $11,257.9; net earnings, $327.9; total assets, ending,
$5,560.0; and total assets, beginning, $5,370.0.
(a) Calculate the (1) return on assets, (2) asset turnover, and (3) profit
margin. (Round answers to 1 decimal place, e.g. 6.2% and 6.2.)
The calculation of the required financial ratios for Sunland Company is as follows:
The return on assets is 6%.
The Asset Turnover is 2.06 times.
The profit margin is 2.9%.
What are financial ratios?Financial ratios express the numerical relationships of two or more financial statement elements.
Financial ratios are used to make comparisons of the financial performance or position of companies from one year to another (trend analysis) and between companies or the industry average.
Net sales $11,257.9
Net earnings $327.9
Total assets, ending = $5,560.0
Total assets, beginning = $5,370.0
Average assets = (Beginning total assets + Ending total assets) ÷ 2
= $5,465 ($5,560 + $5,370)/2
Return on assets = Net earnings/Average total assets x 100
= 6% ($327.9/$5,465 x 100)
Asset Turnover = Net Sales/Average total assets
= 2.06x ($11,257.9/$5,465)
Profit margin = Net earnings/Net Sales x 100
= 2.9% ($327.9/$11,257.9 x 100)
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Does anyone know what the Answer is...
45 ÷ ? = 8
Answer:
Step-by-step explanation:
Instead you do 45 divided by 8
And you will get 5.625
One year, the population of a city was 215,000. Several years later it was 206,400. Find the percent decrease.
The percent of decrease is 4%.
One year, the population of a city was 215,000. Several years later it was 206,400.
To find out the percent decrease:
A fraction with denominator equals 100 to a percentage: 4%
Based on the given conditions, formulate: [tex]\frac{215000-206400}{215000}[/tex]
Calculate the sum or difference: [tex]\frac{8600}{215000}[/tex]
Cross out the common factor: [tex]\frac{1}{25}[/tex]
Multiply a number to both the numerator and the denominator: [tex]\frac{1}{25}* \frac{4}{4}[/tex]
Write as a single fraction: [tex]\frac{4}{25*4}[/tex]
Calculate the product or quotient: [tex]\frac{4}{100}[/tex]
Rewrite a fraction with denominator equals 100 to a percentage: 4%
Hence the answer is the percent of decrease is 4%.
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Which rule applies to this equation? (6)(3 π) = 18 π
Rational x Irrational = Rational
Rational x Irrational = Irrational
Rational x Rational = Rational
Irrational x Irrational = Irrational
Answer:
Rational x Irrational = Irrational
Step-by-step explanation:
6 is a rational number. It can be written as an integer over and integer [tex]\frac{6}{1}[/tex]
[tex]\pi[/tex] is irrational. This is a number that never repeats or terminates, so it can not be written as an integer over and integer.
Answer: Choice B
Rational x Irrational = Irrational
==============================================
Reason:
6 = a rational number
3pi = an irrational number
18pi = an irrational number
Anything involving pi is irrational. The value 6 is rational because 6 = 6/1.
pi is irrational since we cannot write it as a ratio of two integers. We can get approximations like 22/7, but we can't nail down the exact value of pi with a fraction.
Add vegetable stand a person can buy two bags of apples and two bags of potatoes for $11 at a farmers market the same person by two bags of apples and three bags of potatoes for $13 assuming the prices are the same what is the price of each bag of apples in each bag of potatoes use the matrix equation to solve the system of equations
The price of each bag of apples is $3.5 and price of each bag of potatoes is $2.
Given:
a person can buy two bags of apples and two bags of potatoes for $11 at a farmers market the same person by two bags of apples and three bags of potatoes for $13.
Let x be the apples and y be the potatoes.
2x + 2y = 11
2x + 3y = 13
on solving:
2x + 2y - 2x - 3y = 11 - 13
2y - 3y = -2
-y = -2
y = 2
2x + 2y = 11
2x + 2*2 = 11
2x + 4 = 11
2x = 7
x = 7/2
x = 3.5
Therefore The price of each bag of apples is $3.5 and price of each bag of potatoes is $2.
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Answer:
Apples cost $3.50, potatoes cost $2.
Step-by-step explanation:
If you only add one bag of potatoes and the price jumps two dollars, then the potatoes cost two dollars each. We can substitute this into the equation, which can be solved to find apple price.
IXL Please Help Fast!
The lines which are skewed in the rectangular prisms shown are Line QT (↔QT) and Line WX(↔WX).
What is skew in geometry?
This refers to two lines that do not cut across (intersect) each other and are not parallel to each other. the pair of lines must also be opposite edges of the shape. The lines are not also lying or acting in the same plane. i.e non-coplanar.
How to identify skew lines?
a) Locate lines that do not intersect each other.
b)Find out if these pairs of lines are also not parallel to each other.
c) Examine if these non-intersecting and non-parallel lines are non-coplanar.
If yes then the chosen pair of lines are skew lines.
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The radius of a hula hoop is 15in what is the area of a hula hoop in terms of pi
The area of the hula hoop is equal to 450π square inches.
What is the area of a hula hoop?
A hula hoop is a toy with the form of a circle, whose area (A), in square inches, has to be found. The area of a circle is described by the following formula:
A = 2π · R²
Where R is the radius of the hula hoop, in inches.
If we know that R = 15 inches, then the area covered by the hula hoop is:
A = 2π · (15 in)²
A = 450π in²
The area is equal to 450π square inches.
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brainliest if you’re correct !!!
thanks :)))))))
Angle BCD is the same as angle FGH which is 122
Step-by-step explanation:
congruent means that they have the same angles.
so, the angle BCD = 122
What is the value of 3b - 2 when b = 5?
Answer:
13
Step-by-step explanation:
if b = 5, then 3(5) - 2 = 15 - 2 = 13
y is directly proportional to x3 When x = 10, y = 250
(a) Find a formula for y in terms of x.
The formula for y in terms of x is a cubic equation:
y = 0.25*x³
How to find the relation between x and y?We know that y is directly proportional to x³, then we can write the equation:
y = k*x³
Where k is the constant of proportionality.
In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:
250 = k*10³
250 = k*1,000
Dividing both sides by 1,000 we get:
250/1,000 = k
0.25 = k
Then the equation is:
y = 0.25*10³
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