To verify whether the function f(x) = [tex]x^{2}[/tex]- 7 has an inverse function, we need to determine if it is a one-to-one function. An inverse function or an anti function is defined as a function, which can reverse into another function
A function is one-to-one if it passes the horizontal line test, meaning that no two distinct points on the graph of the function have the same y-coordinate. In this case, f(x) = [tex]x^{2}[/tex]- 7 is a parabolic function that opens upward and has a minimum point. Since the parabola opens upward, it is not one-to-one. Therefore, f(x) = [tex]x^{2}[/tex] - 7 does not have an inverse function. Now, to find (t-1)(a), we can use Theorem 5.9, which states that if a function f has an inverse function g, then f(g(x)) = x for every x in the domain of g. Since f does not have an inverse function, we cannot directly use this theorem. Hence, we cannot find (t-1)(a) using the given function f and the real number a because f does not have an inverse function.
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Determine S9 of the series where a=6 and r=2
Hi
arithmetic serie mean that to change from a rank to an other, you add "r"
So : if 6 is S1, and 2 is pace,
then you need 8 hops to go from S1 to S9.
so you 'r going to add the reason 8 times.
so : S9 = 6 + 8 * 2 = 6 + 16 = 22
conclusion : S9 = 22
Which of the following are factor pairs for 12?
1. 1 and 12
2. 2 and 4
3. 2 and 6
3. 3 and 4
4. 3 and 5
NEED ANSWER QUICK PLEASE!!
Answer:
FACTOR pairs are a set of two integers that when multiplied together gives a particular product.FACTOR pairs of 12 are :1 and 12 because 1 x 12 = 122 and 6 because 2 x 6 =123 and 4 because 3 x 4 = 12Hope you understandHope this helps.Good luck ✅.3 + 2 x 7 - 30(^2)
help me
calculate problems one and two.
Answer:
Question 1) 2/3
Question 2) -3
Step-by-step explanation:
Question 1)
The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.
1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.
2. The slope will be 2/3.
Question 2)
In this question, we can consider n as x and f(n) as y.
1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.
2. The slope will be -9/3.
3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.
4. The final slope will be -3.
The length of tr is 17 units. what are the lengths of sv and qt? sv = units qt = units
Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.
What is a kite?A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.
The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:
TR = RV [congruent adjacent sides of the kite]
Plug in the values
17 = 3x + 2
17 - 2 = 3x
15 = 3x
15/3 = x
x = 5
SV = TS = 9x - 4 [congruent adjacent sides of the kite]
Plug in the value of x
SV = 9(5) - 4
SV = 41 units
The length of segment QT is 41 units.
QT = QV = 4x + 1 [congruent adjacent sides of the kite]
Plug in the value of x
QT = 4(5) + 1
QT = 21 units
The length of segment QT is: 21 units.
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Answer:
SV: 41
QT:21
Step-by-step explanation:
4. (06.02 MC)
Write an equation of a line that passes through the point (7,3) and is parallel to the line y =
y=-3x+3.0
x + 3. (5 points)
Answer:
Step-by-step explanation:
Givens
Line: y = 3x + 3
Point: (7,3)
Discussion
The easiest variation on line problems is one like this one. The reason is that all you need do is read the slope of the given line.
m = 3 of the given line. Also the slope of the new line.
What you have so far is
y = 3x + b
The point is used to find b -- the y intercept.
x = 7
y = 3
You are not given this, but what you want to think is that when x = 7, y = 3
Substitute into the new equation
3 = 3*7 + b
3 = 21 + b Subtract 21 from both sides.
3 - 21 = 21-21 + b
- 18 = b
Answer
y = 3x - 18
Answer:
-2/3x+23/3
Step-by-step explanation:
y= mx+c
where
m is the slope c is the y-intercept.
1-getting the slope:
we are given that the line we are looking for is parallel to the line
y=-2/3x+3
this means that the slope of the two lines are equal . comparing the general formula with the given line , we would find that the slope of the given lines -2/3.this means that the slope of the lines we are looking for is also -2/3
The equation of the line now becomes:y=-2/3x+c
2-getting the value of c
to get the value of c, we will use a point that belongs to the line (7,3),substitute in the equation and solve for c as follows:
y=-2/3x+c
3=(-2/3)(7)+c
3=-14/3+c
c=3+14/3
c=23/3
Based on the above, the equation of the line we are looking for is:
y=-2/3x+23/3
Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?
acute, because 102+122>152
acute, because 122+152>102
obtuse, because 102+122>152
obtuse, because 122+152>102
Answer:
Option (1)
Step-by-step explanation:
See attached image.
The given measures form a acute angle triangle.
What is an obtuse angle triangle?An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Given that, a triangle with side lengths 10 in., 12 in., and 15 in.
We know that,
a²+b²=c² then triangle will be right angled
a²+b²>c² then triangle will be acute angled
a²+b²><c² then triangle will be obtuse angled
Here, a=10 inches, b=12 inches and c=15 inches
10²+12²>15²
100+144>225
244>225
Therefore, the given measures form a acute angle triangle.
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You are the CEO of a corporation that makes computer hard drives. The company made $50 million dollars in annual profit this year, after struggling for the 5 previous years. About 6,000 people are working for your company and about 80% of them are directly associated with the manufacturing plant. Workers at the plant have not received a salary raise for the past 5 years, and the workers union is demanding a salary raise this year. The company has an annual payroll of about $500 million dollars, with about 70% of it for the workers in the plant. Factory managers are asking for $25 million dollars to upgrade the equipment and improve the efficiency of the plant. White-collar workers in the head office claim that it is their strategy that turned the factory around and put it on the path to profit. Due to this reason, they think they deserve to get a big bonus. How do you allocate the profits to meet all these demands? Justify your decision.
When it comes to resource allocation, it's not a one sentence answer. The explanation for how to go about this is given below. But first, lets look at what Profit Allocation means.
What is profit allocation?This simply means the process of distributing profit to various areas of the business such that all parts are (human and non-human components) are satisfied and operating at equilibrium.
So how does one allocate resources?There are five steps to aligning your budget and resource demands when planning for support resource allocation.
Recognize your financial flow.Outline your present staffing and resource requirements.Examine your present budget.Create firm growth objectives.Align your budget with your objectives.Learn more about profit allocation at;
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Please help with these problems having trouble!!
The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
How to compare both functions?The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
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Find the perimeter of a parallelogram with corner points at (2,1), (4,5), (7,5), and (5,1)
Perimeter =
THANK YOU SO MUCHHH
Answer:
14 units
Step-by-step explanation:
Oops, I was solving for the area in the picture. You can still use the picture to find the perimeter. When I change the shape into a rectangle, you can see that the top and bottom lengths are 3 and the side lengths are 4. 3+3+4+4=14
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
These two should be the points as then 2 points will remain on both sides
Slope
m=(7+2)/6+6m=9/12m=3/4Equation in point slope form
y+2=3/4(x+6)y=3/4x+6-2y=3/4x+4When x=-15
y=3/4(-15)+4y=-45/4+4y=(-45+16)/4y=--29/4Just above 7
What comes next in the following series?
The next number in the series is 30.
What is series?It should be noted that series simply means the operation of adding values together in a data set.
In this case, it can be seen that the numbers are interchangeable between 30 and 31.
In this case, since 31 was the last number, the next number will be 30.
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.
7-9p≥7 or 2p - 9> 11
Answer:
2p-9>
Step-by-step explanation:
Find the area of a circle with diameter, d = 3.3m. give your answer rounded to 1 dp.
Answer:
Step-by-step explanation:
the area of a circle is πr²
r being the radius, which is equal to half the diameter
3.3/2= 1.65
π(1.65)²=8.6m
Find the equation of the line perpendicular to 2x+3y-6=0 and passing through (-1,1)
Answer: [tex]y-1=\frac{3}{2}(x+1)[/tex]
Step-by-step explanation:
[tex]2x+3y-6=0\\\\3y=-2x+6\\\\y=-\frac{2}{3}x+2[/tex]
So, the slope of the given line is -2/3, meaning the slope of the line we want to find is 3/2.
Substituting into point-slope form, we get the equation of the line is
[tex]y-1=\frac{3}{2}(x+1)[/tex]
Drag the tiles to the correct boxes to complete the pairs.
Match the descriptions of cross sections of three-dimensional figures to their corresponding shapes.
Answer:
B, C, A
Step-by-step explanation:
Don't really know how to explain this.
a) There are 12 different varieties of flowers. How many different kinds of bouquets can be made using 5 different kinds of flowers
Total of 1820 different kinds of banquets can be made.
What is combination in mathematics?Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial. Combos' components can be chosen in any hierarchy.
[tex]$C_{12}(16)=\left(\begin{array}{l}16 \\ 12\end{array}\right)=\frac{16 !}{12 !(16-12) !}=\frac{16 \cdot 15 \cdot 14\cdot13}{4\cdot3 \cdot 2 \cdot 1}=1820[/tex]
[tex]$n=5$ $k=12$\\$x=\left(\begin{array}{c}n+k-1 \\ k\end{array}\right)=\left(\begin{array}{c}5+12-1 \\ 12\end{array}\right)=1820$[/tex]
Total of 1820 different kinds of banquets can be made
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The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them? question 5
Answer:
you would look for them 3.5 meters away from the base
Step-by-step explanation:
so u do tan 86 =50/x
and u solve from there
Rebecca filled 28 glasses with orange juice for a camp breakfast. if each glass holds 1 cup of juice, how many quarts of orange juice did rebecca use?
The number of quarts of orange juice did Rebecca use is 7
Given that 28 glasses with orange juice are filled for a camp breakfast
Each glass holds 1 cup of juice
We need to find the number of quarts of orange juice did Rebecca use
We know that a quarts has 4 cups
We need to calculate the quarts from 28 glasses
Let the number of the quarts be x
So the equation formed is
4x = 28
Where x is number of quarts and 28 are the number of glasses
x = 7
Hence the number of quarts is 7
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Volume=
Help me please!! Asap thanks so much
The volume of the oblique cylinder is 6867.18 cubic units
How to determine the volume?The given parameters are:
Height = 27
Radius = 9
The volume is calculated as:
[tex]V = \pi r^2 h[/tex]
So, we have:
[tex]V = 3.14 * 9^2 * 27[/tex]
Evaluate
V = 6867.18
Hence, the volume of the oblique cylinder is 6867.18 cubic units
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PLEASE HELP IM SO STUCK
Answer:
Slope = 7/4
Step-by-step explanation:
You are given coordinate values and a formula that tells you what to do with them. All you need to do is put the values in the formula and do the arithmetic.
PointsYou are given points (2, -3) and (6, 4). The slope formula refers to the two points as (x1, y1) and (x2, y2). It does not matter which is which.
If we use the points in the same order they are given, then we can see that ...
x1 = 2y1 = -3x2 = 6y2 = 4FormulaUsing these values in the given formula, we find the slope to be ...
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-(-3)}{6-2}=\dfrac{7}{4}[/tex]
The slope of the line through the given points is 7/4.
What is the perimeter of the given quadrilateral?
y
0000
20 units
10 units
50 units
25 units
A
D
B
C
Answer:
20 units
Step-by-step explanation:
As you know that the quadrilateral is a square, you’ll just have to find the length of one side and multiply it by four. We can count and see that one side is 5 units.
5 * 4 = 20 units
You can also add the length of each of the four sides.
5 + 5 + 5 + 5 = 20
Hope that helps you! Please let me know if you need more help with this question. Have a great day!
What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.
The roots of the polynomial equation are -1.73, 1.73 and 0
How to determine the roots?The polynomial equation is given as:
[tex]x^4 + x^2 = 4x^3 - 12x + 12[/tex]
Next, we split the equation as follows:
[tex]y = x^4 + x^2[/tex]
[tex]y= 4x^3 - 12x + 12[/tex]
Next, we plot the equations on a graphing calculator
From the graph, we have the x-coordinates of the intersection points to be:
x = -1.73, 1.73 and 0
Hence, the roots of the polynomial equation are -1.73, 1.73 and 0
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what is the solution to the system of equation -4+3y=-3
Answer:
[tex]\huge\boxed{\sf y = 1/3}[/tex]
Step-by-step explanation:
Given equation:-4 + 3y = -3
Add 4 to both sides
3y = -3 + 4
3y = 1
Divide 3 to both sides
y = 1/3[tex]\rule[225]{225}{2}[/tex]
If the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.
We are required to find the number of bacteria present after 10 weeks.
let the number of bacteria present at t is x.
So,
dx/dt∝x
dx/dt=kx
1/x dx=k dt
Now integrate both sides.
[tex]\int\limits {1/x} \, dx[/tex]=[tex]\int\limits{k} \, dt[/tex]
log x=kt+log c----------1
Put t=0
log [tex]x_{0}[/tex]=0 +log c ([tex]x_{0}[/tex] shows the population in beginning)
Cancelling log from both sides.
c=[tex]x_{0}[/tex]
So put c=[tex]x_{0}[/tex] in 1
log x=kt+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}[/tex]+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}x_{0}[/tex]
x=[tex]e^{kt}x_{0}[/tex]
We have been given that the population triples in a week so we have to put the value of x=2[tex]x_{0}[/tex] and t=1 to get the value of k.
2[tex]x_{0}[/tex]=[tex]e^{k} x_{0}[/tex]
2=[tex]e^{k}[/tex]
log 2=k
We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.
x=[tex]e^{20log 2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{0.30*2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{6}x_{0}[/tex]
x=403.42[tex]x_{0}[/tex]
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
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The given question is incomplete as the question incudes the following:
Calculate the population after 20 weeks.
A family needs to build fencing around their rectangular home and square swimming pool, depicted below.
A rectangle labeled home has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.
The total amount of fencing they need can be written as x + 10.
If x = 5;
The family needs yards of fencing for their home.
The family needs yards of fencing for their pool.
The total amount of fencing they need = 38x + 10.
Perimeter for the rectangular fencing of the home = 160 yards
Perimeter for the square fencing of the pool = 40 yards
What is the Perimeter of a Rectangle and a Square?Perimeter of a rectangle = 2(length + width)
Perimeter of a square = 4(side length).
Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10
Perimeter for the square fencing of the pool = 4(2x) = 8x
The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.
If x = 5, then:
Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards
Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.
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Answer:
38
160
40
Step-by-step explanation:
determine which two of the three given triangles are similar. Find the scale factor for the pair
Answer:
Triangles MNP and QRS
Step-by-step explanation:
This is due to each corresponding line follows the same ratio of 1.5:1
e.g.
NP=6
RS=4
6:4
1.5:1
You can verify this by dividing 6 by 4 (6/4) which is 1.5
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
m=15
Step-by-step explanation:
Oh, I think I answered this question recently, but it's m=15c
The explanation for the question was written in my other response.
Answer:
d. m = 15c
Step-by-step explanation:
Directly proportional means as one amount increases, another amount increases at the same rate.
Proportionality can be used to set up an equation.
Given variables:
m = amount of money earned (in dollars)c = number of cars washedIf m is directly proportional to c then: [tex]m \propto c[/tex]
Convert this to an equation by using a constant of proportionality, k:
[tex]\implies m=kc[/tex]
We are told that Paul washed 8 cars and earned $120.
Substitute these values into the found equation and solve for k:
[tex]\implies 120=8k[/tex]
[tex]\implies k=\dfrac{120}{8}[/tex]
[tex]\implies k=15[/tex]
Finally, substitute the found constant of proportionality (k) into the equation:
[tex]\implies m=15c[/tex]
Select the correct answer from the drop-down menu.
Jaden and his family are using a map to drive down to Napa Valley. On the map, the distance is given by the equation c = 1.3m, where c is the number of centimeters on the map and m is the corresponding real-world distance in miles.
If they cover a distance of 18 miles, that would mean a distance of
centimeters on the map.
Answer:
13.846153846
Step-by-step explanation:
Its easy Just 18:1.3=13.846153846
Which is the completely factored form of 12x4 + 39x3 + 9x2?
3x2(x – 3)(4x – 1)
3x2(x + 3)(4x + 1)
3x(x + 3)(4x + 1)
3x(x – 3)(4x + 1)
Answer:
The second option, 3x^2(x+3)(4x+1)
Step-by-step explanation:
Factor out the common term, which is 3x^2
This then becomes 3x^2(4x^2+13x+3)
Factor the inside term and it becomes
(3x^2)(x+3)(4x+1)