Given that:
The function to represent the growth of Neveah hair is
\(f(x)=\dfrac{2x+4}{3}\)
where, x represents the number of months since her last hair cut.
To find:
The inverse of function and time when her hair will have grown 6 inches.
Solution:
We have,
\(f(x)=\dfrac{2x+4}{3}\)
Put f(x)=y.
\(y=\dfrac{2x+4}{3}\)
Interchange x and y.
\(x=\dfrac{2y+4}{3}\)
Isolate y.
\(3x=2y+4\)
\(3x-4=2y\)
\(\dfrac{3x-4}{2}=y\)
Put \(y=f^{-1}(x)\).
\(f^{-1}(x)=\dfrac{3x-4}{2}\)
So, the required inverse function is \(f^{-1}(x)=\dfrac{3x-4}{2}\). It represents the number of months to grow her hair x inches.
She can predict when her hair will have grown 6 inches by putting x=6 in the inverse function.
Put x=6 in the inverse function.
\(f^{-1}(6)=\dfrac{3(6)-4}{2}\)
\(f^{-1}(6)=\dfrac{18-4}{2}\)
\(f^{-1}(6)=\dfrac{14}{2}\)
\(f^{-1}(6)=7\)
Therefore, growth of her hair is 6 inches in 7 months.
What is the area of this figure?
8 m
6 m
5 m
2 m
13 m
8 m
Answer:
It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?
Step-by-step explanation:
Jake had soccer practice for 2 hours last month. Jake practiced 8 times more this month . How many hours did Jake practice this month?
Answer:
16 Hours your welcome
solve for unknown in 2x^3+6x^2-20x=0
The solution of x is x = 0, x =2 and x = -5
How to solve for the unknown?The equation is given as:
2x^3+6x^2-20x=0
Factor out x
x(2x^2+6x-20)=0
Split the equation
x = 0 or 2x^2+6x - 20=0
Solve for x in 2x^2+6x - 20=0
Expand the equation
2x^2 + 10x - 4x - 20 = 0
Factorize the equation
(2x - 4)(x +5) = 0
Split the equation
2x - 4 = 0 and x + 5 = 0
Solve for x
x =2 and x = -5
Hence, the solution of x is x = 0, x =2 and x = -5
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1. A. What is the formula for the Pythagorean Theorem? (1 point)
B. Find the missing leg of the triangle using the Pythagorean Theorem. Remember that drawings may not be to scale (Round to the nearest tenth).
Show your work. (4 points)
20 ft
18 ft
x
Answer:
side 1^2 + side 2 ^2 = hypotenuse ^ 2
18^2 + 20^2 = hypotenuse^2
324 + 400 = 724
hypotenuse^2 = 724
hypotenuse = 26.9072480941474
hypotenuse = 26.9
Step-by-step explanation:
A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.
Answer: The momentum of the truck before the collision is given by the formula:
p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.
The momentum of the truck before the collision is:
p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s
The momentum of the car before the collision is:
p_i (car) = 1000 kg * 0 m/s = 0 kg m/s
The total initial momentum of the system is the sum of the initial momenta of the truck and car:
p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s
After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:
p_f (total) = p_f (truck) + p_f (car)
Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:
p_f (truck) = 3000 kg * v_f (truck)
The final momentum of the car is:
p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s
Using the conservation of momentum, we can write an equation:
p_f (total) = p_i (total)
30000 kg m/s = p_f (truck) + p_f (car)
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s
So, the velocity of the truck immediately after the collision is 7.5 m/s.
Step-by-step explanation:
Which statement is true regarding the graphed functions?
f(0) = g(0)
f(-2) = g(-2)
f(0) = g(-2)
f(-2)=g(0)
A ladder leans against a brick wall. The foot of the ladder is 7 feet from the wall. The ladder reaches a height of 22 feet on the wall. What is the angle the ladder makes with the wall? (to the nearest tenth)
Answer: 17.7
Step-by-step explanation:
\(tan x = \frac{7}{22} \\tan x = .318181\\inverse tan of .3181818= 17. 65\)
The number of people estimated to vote in an election was 7000. The actual number of people who voted was 5600
Answer:
If you mean the percentage error then look at this
Step-by-step explanation:
% error = Estimated - Actual x 100
Estimated. 1
% error = 7000 - 5600 x 100
7000. 1
% error = 1400 x 100
7000
% error = 140000/7000
% error = 20%
wyatt earns 21$ for painting fences for 3 hours, if wyatt charges at the same rate how many hours will it take him to earn 28?
Answer:
4 hours
Step-by-step explanation:
\(\frac{28}{21} :\frac{y}{3}\)
21 · y = 3 · 28
21y = 84
21y ÷ 21 = 84 ÷ 21
y = 4
Fidgets cost $3 each and Pop Its cost $4 each. If you buy a total of 20 Fidgets and Pop
Its for $75, which system of equations could you use to determine how many of each
you bought? Let x represent the number of fidgets you bought and y represent the
number of pop its you bought.
The number of fidgets and pop bought was 15 each
How to determine the equationFrom the information given, we have that;
1 fidget costs $3
1 Pop cost $4
Let the number of Fidgets be x
Let the number of Pop be y
Then, we have that a total of 20 fidgets and Pop cots $75
We have that;
20x + y = 75
Now, substitute the value of x as 3, we get;
20(3) + y= 75
expand the bracket
y = 75 - 60
y = 15
The number of fidgets is expressed as;
20x/4 = 20(3) /4 = 15
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if 12 sec A +.5 cos A =13 prive that tan A= 12÷5
Answer:
To prove that tan A = 12/5, we can use the identity that relates the sine and cosine of an angle to its tangent:
tan A = sin A / cos A
We are given that 0.5 * cos A = 13, so cos A = 26.
Substituting this value into the identity above, we get:
tan A = sin A / 26
We are also given that 12 sec A = 13, so sec A = 13/12 = 1.083333.
The reciprocal of sec A is cosec A, so cosec A = 1/1.083333 = 0.9230769.
The sine of an angle is the reciprocal of the cosecant of the angle, so sin A = 1/0.9230769 = 1.083333.
Substituting this value into the identity tan A = sin A / cos A, we get:
tan A = 1.083333 / 26 = 12/5
Therefore, tan A = 12/5.
When entering a power, you can use a caret (SHIFT-6).
Enter
as w^5:
Use the fraction tool (fraction tool) to enter the numerator and denominator.
Enter
:
The power expression "w^5" can be entered as "w^5".
To represent a power using the caret symbol, follow these steps:
Start with the base variable or term, in this case, "w".
Type the caret symbol (^), which can be accessed by pressing SHIFT-6 on your keyboard.
Immediately after the caret symbol, enter the exponent or power value, in this case, "5".
The resulting power expression "w^5" represents the variable "w" raised to the power of 5.
Regarding the use of the fraction tool, it is not required to represent the power "w^5" as it does not involve any fraction. The fraction tool is typically used to enter fractions or rational expressions in the form of numerator/denominator.
Therefore, to represent the power "w^5", simply write it as "w^5" without using the fraction tool.
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50 points! Please help fast. I will mark brainliest. Random answers will be reported
Answer:
-2,-4
Step-by-step explanation:
How many different sums of money can be made from 4coins of different denomination
Answer:
15 different sums----------------------
There are various combinations of coins.
1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 optionIn total there are:
4 + 6 + 4 + 1 = 15 different sumsI need help with math
If the circle has a diameter of 6 feet about how long is the chalk outline
Answer:
Find the circumference,
C = 2πr
Where 'π' is pi (3.14 or 22/70, and 'r' is the radius.
To find the radius of a diameter, you must the half of the diameter:
Diameter/2 = radius
6/2 = 3 is the radius.
Plug this into our formula;
C = 2πr
C = 2 x 3.14 x 3
C = 6.28 x 3
C = 18.84 feet.
Which has a greater absolute value 10 or -9
Answer:
10
Step-by-step explanation:
10 is 10 units away from 0 on a number line
-9 is only 9 units away from 0 on a number line
The farthest away from 0 would be 10
If you want to save your total contribution for all 4 years before you start attending college, how much do you need to save each month if you have 4 years to accomplish your goal?
The solution is:
If my parents are going to pay the 5%, then, they will pay: $2979.
I will need to save $62.06 each month to accomplish my goal.
Here,
I'm going to a 4-year college that will cost $14895/year.
It means that I will need to pay: 14895*4 = $59.580
If my parents are going to pay the 5%, then, they will pay: $2979.
Now, if I want to save my total contribution for all four years, and I have four years to accomplish the goal, then:
Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.
Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.
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complete question:
You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.
How much do you need to pay for each year of attending?
If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?
What is a proportional relationship?
Answer:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality
Step-by-step explanation:
express 5.57 as a fraction in its simplest form
Answer:
i think it's 557/100, but i'm not sure that is its simplest form
Answer:557/100
Step-by-step explanation: 557 can be split into two parts: whole number(5) and decimal fraction(0.57). Therefore by expansion:
5.57=5 + 0.5 + 0.07 i.e five + five tenths + five hundredths
= 5 + 5/10 + 7/100 = 5 + (5/10 + 7/100) = 5 + 57/100 = 557/100
Both numerator and denominator have no common factor. Hence, the resulting fraction cannot be simplified further.
NO LINKS!!
Given the function: 1/(x + 1) - 4:
a. State the Domain using INTERVAL notation
b. State the Range using INTERVAL notation
c. Are there any asymptotes? If so, state their equations and draw them on the graph as dotted lines
Answer:
a) (-∞, -1) ∪ (-1, ∞)
b) (-∞, -4) ∪ (-4, ∞)
c) Vertical asymptote: x = -1
Horizontal asymptote: y = -4
Step-by-step explanation:
Given function:
\(f(x)=\dfrac{1}{x+1}-4\)
Part (a)The domain of a function is the set of all possible input values (x-values).
When the denominator of a rational function is zero, the function is undefined.
Rewrite the function as one fraction:
\(\implies f(x)=\dfrac{1}{x+1}-\dfrac{4(x+1)}{x+1}\)
\(\implies f(x)=\dfrac{1-4(x+1)}{x+1}\)
\(\implies f(x)=\dfrac{-4x-3}{x+1}\)
Set the denominator to zero and solve for x:
\(\implies x+1=0\)
\(\implies x=-1\)
Therefore, the given function is undefined when x = -1, so its domain in interval notation is:
(-∞, -1) ∪ (-1, ∞)Part (b)The range of a function is the set of all possible output values (y-values).
As the domain is restricted to (-∞, -1) ∪ (-1, ∞), the range is also restricted.
To find the range of a rational function, first solve the equation for x:
\(\implies y=\dfrac{1}{x+1}-4\)
\(\implies y+4=\dfrac{1}{x+1}\)
\(\implies (y+4)(x+1)=1\)
\(\implies x+1=\dfrac{1}{y+4}\)
\(\implies x=\dfrac{1}{y+4}-1\)
\(\implies x=\dfrac{1-(y+4)}{y+4}\)
Set the denominator of the resultant equation ≠ 0 and solve for y:
\(\implies y+4 \neq 0\)
\(\implies y \neq -4\)
Therefore, the range is the set of all real numbers other than y = -4:
(-∞, -4) ∪ (-4, ∞)Part (c)A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.
Therefore, there is a vertical asymptote at x = -1.
As the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.
\(\implies f(x)=\dfrac{-4x-3}{x+1}\)
Therefore, there is a horizontal asymptote at:
\(y=\dfrac{-4}{1}=-4\)There are no slant asymptotes as there is a horizontal asymptote.
I neead a fast answer 50pts fast (+Brainliest for right answer)!!!!
Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.
Step-by-step explanation:
Hope this helps :)
triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B
what is the FORMULA for circumferece
Answer:
Circumference = 2π(r)
So, your answer would be: C. pi x r²
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
I need 100,000,000$ for my vacation. I only have 90,000,000. How many do I need?
Answer:
10,000,000.
Step-by-step explanation:
Because 10,000,000+90,000,000=100,000,000!
and 100,000,000-90,000,00= 10,000,000! and
100,000,000-10,000,000=90,000,000!
Answer:
$ 10 000 000
Step-by-step explanation:
100 000 000-90 000 000=10 000 000
Can someone please answer this for me I’ll love you forever please ASAP
Answer:
17
Step-by-step explanation:
Using the distributive property, we can rearrange the expression into this:
-4^2+-4+5
Which when expanding, is:
16+-4+5, which gives 17.
a) What is the value of the 4 in the number 546210?
Give your answer in words.
The place value of 4 in 546210 is 40,000.
In mathematics, place value refers to the relative importance of each digit in a number. These positions begin at the unit's (or first person's) location. Ones/units, tens, hundreds, thousands, ten thousand, and so on are used to describe the order of place values of digits in a number from right to left.
For instance, 5 in 2358 has a place value of 5 tens, or 50. The place value of 5 in 5671 is, nevertheless, written as 5,000 or 5,000,000. Understanding that a digit can have the same value regardless of where it appears in the number is crucial.
In the question, we are asked to find the place value of 4 in 546210.
In the number 546210, the digit 4 is at the ten thousand place.
Thus, the value of 4 in 546210 can be shown as 4 * 10,000 = 40,000.
Thus, the place value of 4 in 546210 is 40,000.
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Crisette lives miles from the school. She rode her bike of the way and stopped to get ice cream. How far did Crisette ride to get ice cream?
Answer:
The amount is not showing
Step-by-step explanation:
If the measure of angle P is three less than twice the measure of angle Q, and angle P and angle Q are supplementary angles, find each angle measure.
The value of angle P = 119°
The value of angle Q = 61°
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of angle P be = P
Let the value of angle Q = Q
Now , the equation will be
Measure of angle P is three less than twice the measure of angle Q
Substituting the values in the equation , we get
P = 2Q - 3 be equation (1)
And , angle P and angle Q are supplementary
So ,
P + Q = 180° be equation (2)
Substituting the value of P from equation (2) in equation (1) , we get
2Q - 3 + Q = 180
On simplifying the equation , we get
3Q - 3 = 180
Adding 3 on both sides of the equation , we get
3Q = 183
Divide by 3 on both sides of the equation , we get
Q = 61°
Therefore , the value of Q is 61°
Substitute the value of Q in equation (2) , we get
P + Q = 180°
Subtracting Q on both sides of the equation , we get
P = 180° - 61°
P = 119°
The measure of angle P = 119°
Hence , The value of angle P = 119°
The value of angle Q = 61°
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Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,2)
, (2,5)
, (3,7)
, (4,2)
, (5,10)
, (6,10)
, (7,9)
The equation of the line of best fit is y = 1.19x - 0.37.
What is linear regression ?
Linear regression is a statistical method that is used to establish the relationship between two variables, usually represented as a straight line. It is used to determine the extent to which one variable is dependent on the other variable, and to make predictions based on this relationship.
Using linear regression, we want to find the equation of the line of best fit in the form y = mx + b, where m is the slope and b is the y-intercept.
First, we need to calculate some sums:
∑x = 28
∑y = 45
∑xy = 224
∑x² = 140
∑y²= 275
Using these sums, we can calculate the slope m:
m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²)
m = (7(224) - (28)(45)) / (7(140) - (28)^2)
m = 1.19
Now we can use the slope to calculate the y-intercept b:
b = (∑y - m∑x) / n
b = (45 - (1.19)(28)) / 7
b = -0.37
Therefore, the equation of the line of best fit is y = 1.19x - 0.37.
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plssss help pls thank u
The value of n(R∪S) is 11.
What is Venn Diagram?
A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groupings of objects. Circles that overlap have some characteristics, but circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different graphically. They have long been acknowledged for their value as teaching resources. Venn diagrams have been used in elementary-level lesson plans and the introduction to logic curricula worldwide Venn diagrams are helpful for displaying the relationships between several ideas or elements. They can quickly demonstrate how objects are alike or unlike as well as where and how they overlap. A Venn diagram's center, which is where two or more circles meet, frequently indicates some nexus or central concept that may be broken down into the various other circles, with the labels on the outer sections representing more abstract and separate concepts than those near the center. The overlapped regions can also be utilized to highlight the similarities between two seemingly unrelated settings. The sample diagram below, for instance, shows that while the urban and rural environments are diverse and have their own range of activities, they do share athletic events.
Here,
\(\begin{aligned}&R=\{4,8,14,16,18,24\} \\&S=\{2,6,8,10,20,22\}\end{aligned}$$\)
Here,
\(\text { - } n(R \cup S)=n(R)+n(S)-n(R \cap S)\)
so,
n(R) = 6;
n(S) = 6;
n(R∩S) = 1;
So,
n(R∪S) = 6 + 6 -1
n(R∪S) = 12-1
n(R∪S) = 11.
Hence, The value of n(R∪S) is 11.
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