The inverse and domain of the function are y = x²-9 and all real numbers.
Inverse of a functionA function's inverse is a function that reverses the action of a function, such as g(x). If and only if g(x) is bijective, then the inverse of g(x) exists, and if it exist.
If the function f(x)=√x + 9, find the inverse;
y = √x+9
x = √y+9
x² = y+9
y = x²-9
The domain of the inverse function will exist on all real numbers.
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If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle LMN is an obtuse angle then, the angle at vertex L is acute, the angle at vertex N is acute.
The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.
As ∠M is an obtuse angle
So 90° < m∠M < 180°
By the property of a triangle,
m∠L + m∠M + m∠N = 180°
m∠M = 180° - (m∠L + m∠N)
90° < 180° - (m∠L + m∠N) < 180°
90° - 180° < -(m∠L + m∠N) < 0
-90° < -(m∠L + m∠N) < 0
90° >(m∠L + m∠N) > 0
90° > m∠L and 90° > m∠N
Therefore both angles L and N are acute angles.
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Answer:
1, 2 and 5
Step-by-step explanation:
see picture
Givin f(x) = 1/x+5 and g(x)=x-2. What are the restrictions of the domain of f(g(x))?
OX≠ -5
OX≠ -3
OX≠ 2
OThere are no restrictions
Answer:
Step-by-step explanation:
x cannot be -3 or 2
Step-by-step explanation:
f(g(x)) = 1 / (( x-2) +5)
= 1/ (x+3)
g(x) cannot have x=2
The domain is restricted where
f(x) has an restriction that x cannot be 5
so g(x) cannot be -5
-5 = x-2
Add 2 to each side
-5+2 = x
-3
2/3 ÷ -5/6 yo nesecesito dividir
Answer:
-4/5
Step-by-step explanation:
2/3 * -6/5 = -4/5
:]
Make x the subject of the formula. 5d cubed= d squared (2b-3cx)
The value of x = [tex]\frac{2b-5d}{3c}[/tex] .
What is a equation?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
The given equation is
[tex]5d^{3}=d^{2}(2b-3cx)[/tex]
5[tex]d^{3}= d^{2}2b-3cd^{2}x[/tex]
3c[tex]d^{2}x = d^{2}2b-5d^{3}[/tex]
x = [tex]\frac{d^{2}(2b-5d) }{3cd^{2} }[/tex]
x = [tex]\frac{2b-5d}{3c}[/tex]
Hence, The value of x = [tex]\frac{2b-5d}{3c}[/tex] .
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1/16 - ( -7/16)
Write your answer as a fraction in simplest form.
describe five occupations you want to do, and how you prepare for your dream job. And list the average salary, and then, combine your family cost per month, make a reasonable saving plan.
architecture, invest money so that I can pay fr fees
Find the values of a,b and c that would make the statements true.
1) (ax+2)(5x+b)=10x^2+bx+c
The values of a, b and c are a = 2, b = -10 and c = -20
How to determine the values of the variables?The equation is given as
(ax + 2)(5x + b) = 10x^2 + bx + c
Open the brackets
So, we have
5ax^2 + 10x + abx + 2b = 10x^2 + bx + c
By comparing the above equation.
We have the following set of equations
5a = 10
10 + ab = b
2b = c
By solving the equations, we have
a = 2
Substitute a = 2 in 10 + ab = b
10 + 2b = b
So, we have
b = -10
Substitute b = -10 in 2b = c
2(-10) = c
Evaluate
c = -20
Hence, the values of the variables are a = 2, b = -10 and c = -20
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a $52 video game is adversited for 20% of it sales tax is 6%
Answer:
39 dollars
Step-by-step explanation: 20 perrcent of 52
The product of -2 and a number is at most 10.
Find the possible numbers.
On<-5
Ons-5
Onz-5
On>-5
Answer:
n ≥ -5
Step-by-step explanation:
-2n ≤ 10
Divide both sides by -2. Remember to flip ≤ to ≥.
-2n/(-2) ≥ 10/(-2)
n ≥ -5
7th grade students were asked to choose their
favorite color. The table shows the fraction of
students that choose each color. What DECIMAL
shows the difference between the most and least
favorite colors?
Color
Fraction
Red Yellow Blue Green
5/18
1/6
4/9
1/9
Answer:
Step-by-step explanation:
find the area under the standard normal distribution curve to the right of . use a ti-83 plus/ti-84 plus calculator and round the answer to at least four decimal places.
using calculator
Area right to the right of the 2=2.12
P(Z > 2.12)
• P(Z < -2.12)
= 0.0170
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A house has decreased in value by 35% since it was purchased. If the current value is $78,000, what was the value when it was purchased?
Answer: The value of the house when it was purchased was 120,000
Step-by-step explanation:
1) Set up the equation. Let x be the house.
x-x*35%= 78,000
First, the house decreases 35% of the cost of the original house. It now costs 78,000.
2) Solve the equation.
x-x*0.35 = 78,000
x-0.35x=78,000
0.65x = 78,000
x= 120,000
write and solve a real world problem in which you find the commission
A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?
($27,990)*(0.03) = $839.70
The Jones family will pay their insurance broker a commission of $1,750.00.
Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.
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PLEASE HELP ME ILL LITERALLY AND I PROMISE ON GOD TO RATE YOU 5 STARS AND GIVE U POINTS
Answer:
1. 12hrs
2. 2hrs
Step-by-step explanation:
4:00pm is 2 hrs from 6:00pm
5:00am is 12hrs from 5:00pm
Wilbur landed his plane.
The plane's elevation relative to the ground
(in meters) as a function of time (in seconds)
is graphed.
How high was the plane after 1000 seconds?
At 1000 seconds the graph shows the height of 3500 meter.
what is graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
The graph gives the relation between Elevation and Time.
As, if at 400 seconds the height is 6500 meters.
and, at 800 seconds the height is 4500 meters.
Thus, at 1000 seconds the graph shows the height of 3500 meter.
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A store has two types of animal feed available. Type A contains 3 pounds of oats and 3 pounds of corn per bag. Type B contains 1 pound of oats and 7 pounds of
corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 18 pounds of oats and at least 54 pounds of corn. The store
only has 11 bags of type A feed and 12 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many bags of each type should
the farmer buy to minimize her cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
Type A feed:
Type B feed:
bag(s)
bag(s)
The farmer will purchase five bags of kind A and six bags of type B.
Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.
Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.
The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.
Allow the farmer to mix type A feed = x pounds.
and feed type B = y pounds
(9x + 2y) pounds of oats when blended
Corn amount when combined: (3x + 10y) pounds
Oats equation: 9x + 2y = 57 ———— (1)
Corn equation: 3x + 10y = 75 ————- (2)
Subtract equation (2) from equation (2) by multiplying it by three (1)
3(3x + 10y) - (9x + 2y) = 75×3 - 57
9x + 30y - 9x - 2y = 225 - 57
28y = 168
y = 6 bags
derived from the equation (1)
9x + 2×6 = 57
9x + 12 = 57
9x = 57 - 12
9x = 45
x = 5 bags
Because the business has 15 bags of each sort, each bag costs $4.
As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)
= 20 + 24
= $44
The farmer intends to buy five bags of kind A and six bags of type B.
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Please help and provide an explanation for why the answer is f(x) = -1/3x - 4
What is the equation of the line that passes through Point (-6, -2) and has a Slope of -1/3.
y=-1/3-4
Step-by-step explanation:
point slope form!
y-y=m(x-x)
with the point (-6,-2) and the slope (-1/3) replace the 2nd variables of each variable and replace m with the slope
y-(-2)=-1/3(x-(-6))
then solve that normally
y-(-2)=-1/3(x-(-6))
y+2=-1/3x -2
y=-1/3x-4
I didnt use officially math symbols but i hope you can still read it!
PLS HELP ME OUT MARKING BRAINLEIST
The side x = 104 unit and angle y = 74 °
What is a parallelogram?A quadrilateral is referred to as a parallelogram in geometry.
The opposite sides of a parallelogram are parallel and of equal length.
Rhombus, rectangle, and square are a few instances of parallelograms.
The special properties of a parallelogram is that the two opposing sides are both equal and parallel. Also the opposite angles are equal. And the angles inside the parallelogram on the same side , their sum is 180 degrees .
Given : A parallelogram ABCD.
Now in a parallelogram opposite sides are both equal and parallel.
So in this parallelogram ;
97 = x - 7
⇒ x = 97 + 7
⇒ x = 104 .
Also opposite angles of a parallelogram are equal.
⇒ y = 74 °
Thus the required solution is x= 104 degree and y= 74 degrees
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Create three probability application problems of your own. Solve your problems. Explain your answers.
In the above question, we need to from 3 probability questions and then give solutions for them
Example 1 : A coin is tossed three times. What is the probability of getting at least one head?
Solution : A coin is tossed 3 times then
Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8
Favorable Cases = 7
P (A) = 7/8
OR
Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8
Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is
(i) black
(ii) not black
Solution :
Total number of balls in the bag are = 3 + 4 = 7 balls
Number of favorable outcomes or number of black balls in the bag = 4
(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]
P(black ball) = [tex]\frac{4}{7}[/tex]
(ii) Probability getting no black balls = 1 - P(black ball)
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
Example 3 : Given two dice, what is the likelihood of receiving the number 7?
Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6
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inverse of (1/4x) +2
Answer:
Inverse Function = 4x -8
Step-by-step explanation:
replace x with y and replace x with y
solve for y (meaning isolate y)
y=(1/4x) +2
x= (1/4y) +2
x-2 = 1/4y
multiply by 4 on each side to remove 1/4 from the right side
4(x-2) = y
y= 4(x-2)
y= 4x -8
Inverse Function = 4x -8
How do I solve number 4 and 5 to get the correct answer?
Answer:
4. (d)
5. (b)
Step-by-step explanation:
You want to apply the secant and chord rules to the circles given in the diagram.
The secant rule is "the product of distances from the point of intersection of secants to the two points of intersection of the secant with the circle is the same for both secants." A tangent can be considered to be a secant that has both points of intersection with the circle in the same place.
The chord rule is similar to the secant rule: "The product of distances from the point of intersection of the chords to their intersection with the circle is the same for both chords."
4.The diagram shows a tangent of length 12, so the product of distances to the two points of intersection with the circle is 12(12).
The secant has length 8 to the near point of intersection, and (x+8) to the far point of intersection. That product is the same as for the tangent:
8(x +8) = 12(12) . . . . . . matches choice D
5.One chord has lengths of 14 and x, so the product of those is 14x.
The other chord has lengths of 12 and 21, so the product of those is 12(21).
The product is the same for both chords, meaning ...
14x = 12(21) . . . . . . matches choice B
__
Additional comment
We have purposely tried to write the rules in "parallel" fashion, because we find them easier to remember that way. Considering a tangent to be a secant with the points of intersection with the circle merged means the same rule can be used for all three cases:
intersecting secants, a tangent intersecting a secant, and intersecting chords.Price-club sells a 12-ounce package of spaghetti noodles for $3.44 and Shop Mart sells a 2 1/2-pound box of spaghetti noodles for $8.35.
The unit price per ounce at Price-Club is $ and the unit price per ounce at
Shop Mart is $
0.28 0.21
0.30 0.20
0.29 0.19
The unit price per ounce at Price-Club is $0.29 per ounce and the unit price per ounce at Shop Mart is $0.21 per ounce.
What is the unit price?The unit price can be determined by dividing the total cost by the total ounce that is purchased.
Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient. Other mathematical operations include addition, subtraction and multiplication.
Unit price = total cost / total ounce sold
Unit price of Price-Club = $3.44 / 12 = $0.29 per ounce
In order to determine the unit price of Shop Mart, pounds have to be converted to ounces
1 pound = 16 ounces
To convert 2 1/2 pounds to ounces, multiply 2 1/2 by 16. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
16 x 2 1/2
16 x 5/2 = 40 ounces
Unit price of Shop Mart = $8.35 ÷ 40 = $0.21 per ounce
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What is the US GDP for the first quarter and second quarter of 2020? What is the personal consumption expenditures for the first quarter and second quarter of 2020?
The US GDP for the first quarter of 2020 was 21.54 trillion dollars, and the US GDP for the second quarter of 2020 was 19.49 trillion dollars.
The personal consumption expenditures for the first quarter of 2020 are 13.02 trillion dollars.
the personal consumption expenditures for the second quarter of 2020 are 11.82 trillion dollars.
What are the personal consumption expenditures?
Personal consumption expenditures are the price that citizens of the US pay for goods and services. This is a crucial index that indicates inflation or deflation and consumer behavior over some time.
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For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 5.2x
(3, [?])
Enter
Answer:
40
Step-by-step explanation:
5*(2^3)=40
Arnold plants a tree sapling in his yard and measures its height every year. His measurements so far are shown in the scatterplot.
The equation of the scatter plot is y = 5/3x + 2 and the tree will be 18.7 feet in ten years
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the height of the tree?The information that completes the question is added as an attachment
From the scatter plot, we have the following points
(x, y) = (0, 2) and (6, 12)
The equation of the line is calculated as
y = (y2 - y1)/(x2 - x1) * (x - x1) + y1
Substitute the known values in the above equation
So, we have
y = (12 - 2)/(6 - 0) * (x - 0) + 2
So, we have
y = 5/3x + 2
In ten years, the value of x is
x = 10
So, we have
y = 5/3 x 10 + 2
Evaluate
y = 18.7
Hence, the height of the tree is 18.7 feet
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You take a $4,500 loan to pay for a trip
to the Amazon rainforest to photograph
wild animals. If the loan's interest rate is
8% for 1 year, what is the interest for the
first payment?
A $12.58
C $30.00
Vincent Fal
B $26.00
D $80.99
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]
c.
PRT/100
4500×8×1/100=360
per month=360÷12
=30
question is in the picture
Write 41% as a fraction in simplest form.
Answer:
[tex]\frac{41}{100}[/tex]
Step-by-step explanation:
It cannot be simplified.
Ex: 50% can be simplified to [tex]\frac{1}{2}[/tex]
Hillsboro Street and Manchester Avenue intersect. If the diagonal distance across the
intersection is 73 feet and Hillsboro Street is 55 feet wide, how wide is Manchester Avenue?
The intersection's two opposing corners are 91.40 feet apart.
Since the given data are:
Width of the Hillsboro Street = 73 feet
Width of Manchester Avenue = 55 feet
When Hillsboro Street and Manchester Avenue cross, calculate the distance between the intersection's two opposing corners,
Because the junction of Hillsboro Street and Manchester Avenue created a right-angled triangle:
Using Pythagoras's Theorem,
H² = B² + P²
H² = (55)² + (73)²
H² = 3025 + 5329
H² = 8354
H = √8354
H = 91.40
As a result, the distance between the intersection's two opposing corners is 91.40 feet.
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ANSWER QUICK I WILL GIVE BRAINLIEST!
Solve k over negative 1.8 is less than negative 4.9 for k.
k < −8.82
k > 8.82
k < −6.7
k > −6.7
Answer:
k<-8.82
Step-by-step explanation:
k/1.8<-4.9
k<-8.82
Answer:k<-8.82
Step-by-step explanation: