For the function g(x)=32/x+3, find (g^-1o g) (5)
The value of the composite function is found as 68/5.
What is meant as the inverse of the function?An inverse function is one that reverses the action of another function. A function g seems to be the inverse of a function f if and only if y=f(x) and x=g (y).The function is given as;
g(x) = 32/(x+3)
Write the function as 'y'
y = 32/(x+3)
Replace the value of x with y.
x = 32/(y+3)
Solve for y.
x(y + 3) = 32
xy = 32 - 3x
y = (32 - 3x)/x
Thus, g⁻¹ (x) = (32 - 3x)/x is the inverse of the function.
Now, find the value composite function; (g⁻¹ o g) (5).
(g⁻¹ o g) (5) = (32 - 3x)/x . 32/(x+3)
Put x = 5
(g⁻¹ o g) (5) = (32 - 15)/5 . 32/(5+3)
(g⁻¹ o g) (5) = 17×4/5
(g⁻¹ o g) (5) = 68/5
Thus, the value of the composite function is found as 68/5.
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Which of the following equations have odd products? Select all that apply.
A.4x3=?
B.6x8=?
C.3x7=?
D.3x9=?
E.1x9=?
c, d, and e. this is because c equals 21, d equals 27, and e equals 9
Graph the polygon with the given vertices and its image after a reflection in the given line.
J(2, 4), K(-4,-2), L( − 1, 0); y = 1
The coordinates of the image after reflection over line y = 1 is
preimage Image
J(2, 4 J' (2. -2)
K(-4,-2) K' (-4. 4)
L( − 1, 0) L' (-1, 2)
How to fine the coordinates of the reflected imageReflection is one of the movements in transformation that involve creation of mirror image
The reflection to be done is over line y = 1
Transformation rule for reflection over line y at origin (0, 0)) is
(x, y) → (x, -y)
However, reflection over line y = 1 which is (0, 1) is done as follows
J(2, 4) ⇒ (2, 4 - 1) ⇒ (2, 3) ⇒ (2, 1 - 3) → J' (2, -2)
from 4 to 1 = 4 - 1 = 3 units
reflecting 3 units over y = 1
1 - 3 = -2
J' (2, -2)
K(-4,-2) ⇒ (-4, -2 - 1) ⇒ (-4, -3) ⇒ (-4, 1 - -3) ⇒ K' (-4, 4)
from -2 to 1 = -2 - 1 = -3 units
reflecting -3 units over y = 1
1 - -3 = 4
K' (-4, 4)
L (-1, 0) ⇒ (-1, 0 - 1) ⇒ (-1, -1) ⇒ (-1, 1 - - 1) ⇒ L' (-1, 2')
from 0 to 1 = 0 - 1 = -1 unit
reflecting -1 unit over y = 1
1 - -1 = 2
L' (-1, 2)
see graph for more information
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stigma notation stuff
What is the slope?
A) 2/1
B)1/2
C)-2/1
D)-1/2
Answer:
The slope is 1/2, so B is correct.
Answer:B is correct
Step-by-step explanation: it goes up 1=y and right 2=x and y/x
Cecil started at the beginning again and walked 6 1/2 feet ,backed up 1 foot
Answer: 5 1/2 feet
Step-by-step explanation: 6 1/2ft - 1ft = 5 feet
Good Question! Jk
lf had his hourly salary increase from $9.25 per hour to $10.75 per hour, what's the percent increase in Jordan's salary
Answer:
16.22%
Explanation:
The percent of increase can be calculated as:
[tex]\frac{v_f-v_i}{v_i}\times100[/tex]Where vf is the final value and vi is the initial value. So, replacing vf by 10.75 and vi by 9.25, we get:
[tex]\frac{10.75-9.25}{9.25}\times100=\frac{1.5}{9.25}\times100=16.22\text{ \%}[/tex]Therefore, the percent of the increase is 16.22%
Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
a = t over delta v.
m = StartFraction v subscript 1 - v subscript 2 Over x subscript 2 minus x subscript 1 EndFraction.
a =
m = StartFraction x subscript 2 minus x subscript 1 Over v subscript 1 - v subscript 2 EndFraction.
An equation which is most likely used to determine the acceleration from a velocity vs. time graph is: B. m = (y₂ - y₁) / (x₂ - x₁).
What is a velocity vs. time graph?A velocity vs. time graph can be defined as a type of graph that is used to graphically represent the rate of change of velocity of an object with respect to time.
In Mathematics, the velocity of a physical object is plotted on the horizontal axis (y-coordinate) time is while plotted on the vertical axis (x-coordinate) of a velocity vs. time graph.
Mathematically, the acceleration of a physical object on a velocity vs. time graph can be calculated by determining the rate of change (slope) as modeled by this formula:
Acceleration, m = change in velocity/change in time
Acceleration, m = (y₂ - y₁) / (x₂ - x₁).
Where:
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Complete Question:
Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
answer choices
A. a = t/delta v
B. m = (y₂ - y₁) / (x₂ - x₁)
C. a = delta v/t
D. m = (x₂ - x₁) / (y₂ - y₁)
Answer:
B. m = StartFraction v subscript 1 - v subscript 2 Over x subscript 2 minus x subscript 1 EndFraction.
Step-by-step explanation:
Got 100% on the test. Y'all have a good day! :D
Use inverse matrix to solve the linear system. Solve #19
19)
The given system of equations is,
[tex]\begin{gathered} 4x-3y=11 \\ 5x-2y=12 \end{gathered}[/tex]The above system of equations can be written in matrix form as,
[tex]\begin{bmatrix}{4} & {-3} & {} \\ {5} & {-2} & {} \\ {} & {} & \end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix}\text{ -----(1)}[/tex]Here,
[tex]A=\begin{bmatrix}{4} & {-3} & {} \\ {5} & {-2} & {} \\ {} & {} & \end{bmatrix},\text{ X=}\begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}\text{ },\text{ B=}\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix}[/tex]Therefore, equation (1) can be written as,
[tex]AX=B[/tex]Therefore,
[tex]X=A^{-1}B\text{ -------(2)}[/tex]Now, we need to calculate the inverse of A.
(Note:
Let a 2x2 matrix P is of the form given below.
[tex]P=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {} \\ {} & {} & {}\end{bmatrix}[/tex]The inverse of the matrix P is,
[tex]\begin{gathered} P^{-1}=\frac{1}{|P|}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{ad-bc}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex])
Similar to the inverse matrix of 2x2 matrix P, the inverse matrix of A can be written as,
[tex]\begin{gathered} A^{-1}=\frac{1}{4\times(-2)-(-3)\times5}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{-8+15}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{7}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-2}{7}} & {\frac{3}{7}} & {} \\ {\frac{-5}{7}} & {\frac{4}{7}} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Now, put the values in equation (2) to find the solution to the system of equations.
[tex]\begin{gathered} X=A^{-1^{}}B \\ \begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{\frac{-2}{7}} & {\frac{3}{7}} & {} \\ {\frac{-5}{7}} & {\frac{4}{7}} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{\frac{-2}{7}\times11+\frac{3}{7}\times12} & {} & {} \\ {\frac{-5}{7}\times11+\frac{4}{7}\times12} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-22}{7}+\frac{36}{7}} & {} & {} \\ {\frac{-55}{7}+\frac{48}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-22+36}{7}} & {} & {} \\ {\frac{-55+48}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{14}{7}} & {} & {} \\ {\frac{-7}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{2} & {} & {} \\ {-1} & & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Therefore, the solution to the system of equations using inverse matrix is x=2 and y=-1.
The values of y vary directly with x, and y=425 when x=8.5 . What is the value of y when x=12 ?
The value of y when x=12 is 600
The values of y vary directly with x
y α x
y = kx
where k is the proportationality constant
The values of y=425 when x=8.5
y = kx
425 = k (8.5)
k = 50
We need to find the value of y when x=12
y = kx
y = 50 x 12
y = 600
Therefore, the value of y when x=12 is 600
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How to multiply easily big Numbers
Answer:
Step-by-step explanation:
Multiplying large numbers together is performed by multiplying the ones digit of the bottom number to the entire top number. After the ones place value has finished multiplying, move to the tens place value in the bottom number and multiply that digit by the top number.
I hope it helps!
In the figure below, when the sund angle of elevation is 50 degrees, the tree casts a shadow 80 feet long. which can be used to find the height of the tree?
A
1) In this picture, we can see clearly a triangle with an adjacent leg to an angle of 50º and an opposite leg (that tree).
2) So the trigonometric ratio to be used is the one that relates both legs:
[tex]\begin{gathered} \tan (50)=\frac{opposite\text{ leg}}{\text{adjacent}} \\ \tan (50)\text{ =}\frac{x}{80} \end{gathered}[/tex]3) Hence, the answer is A
A large glass holds 5/6 cup of water spouse you have 8 cups of water you want to fill both glasses how many of each size glass can you fill
PLEASEE HURRY
The number of large glasses that will be filled is 10 glasses.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Given that the large glass holds 5/6 cup of water and you have 8 cups of water. The number of glasses filled will be:
= 8 ÷ 5/6
= 8 × 6/5
= 48/5
= 9.6
= 10 glasses approximately
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Round the number to the place of the underlined digit. 50.633 The rounded number is
According to the rules of rounding to the nearest numbers, 50.633 rounded to the nearest whole number is equal to 51.
To round 50.633, we have to consider
The tenths’ value of the number 50.633 which is equal to 6 and it is also equal to or more than 5.
Therefore, we have to round up the part of 50.633
50, when increases by 1 results in 51
Here, the decimal point and all the following digits (.633) get removed.
Therefore, 50.633 rounded to the nearest number is equal to 51.
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which table is a probability distribution table?
Answer:
Table 1 is the only table which represents PROBABILITY DISTRIBUTION table.
Step-by-step explanation:
I really need help solving this, struggling with it this is a problem from my ACT prep guide It is trigonometry
Solution
For this case we can do the following:
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)=\frac{-\sqrt[]{3}}{\frac{\sqrt[]{2}}{2}}-(-1)=\frac{2\sqrt[]{3}}{\sqrt[]{2}}+1=-\sqrt[]{2}\cdot\sqrt[]{3}+1=-\sqrt[]{6}+1[/tex]Does anyone know how to do this ???
Answer:
8) x = 6.5, 9) x = 7, 10) x = 13Step-by-step explanation:
We have similar figures given.
The ratio of corresponding sides of similar figures is same as per definition of similarity.
Use this property and solve each question.
Question 8HG/DC = FG/BCx/13 = 13/26x/13 = 1/2x = 13/2x = 6.5Question 9WY/SU = YX/UT4/(x + 5) = 3/94/(x + 5) = 1/3x + 5 = 4*3x + 5 = 12x = 7Question 10Considering x is positive, PS and MN are longer legs of right triangles.
PS/MN = ST/ML(x + 2)/10 = (x - 1)/810(x - 1) = 8(x + 2)10x - 10 = 8x + 1610x - 8x = 16 + 102x = 26x = 13At a local print shop, 20 copies can be made for $8. At this rate, how how many copies could be made for $34?
Fill out the table of equivalent ratios until you have found the value of x.
Copies Dollars
20 8
xx 34
It would cost $34 to make
copies.
Answer:4
Step-by-step explanation:
20 times 8 =$160 which is the total price for all copies
$160:34=4.7....$ but you can't make 0.7... of copy, so we don't count it. You can make 4 copies for $34
Which of the following scenarios describes independent events from disjoint sets?1) A bag contains orange, yellow, and purple marbles. You randomly draw 2 marbles at the same time and want to know the probability that either marbleis orange.II) You roll a number cube and spin a spinner. You want to know the probability of rolling a 3 and spinning a B.ill) Lunch includes a choice of salad and a choice of vegetables. You want to know the probability of choosing a chef salad and asparagus as yourvegetableIV) A math class has 30 students. The teacher chooses 2 students at random. You want to know the probability that one of the two students will befemale
Independent events are not affected by previous events, that is, the probability of a new event doesn't change from the previous event. However, disjoint sets mean they don't have any data in common, which means the intersection of such sets is impossible. In other words, the events are exclusive, if one occurs, then the other can't occur.
Having said that, we can deduct that scenario 1 represents an independent exclusive event because the occurrence of one event excludes the other. The main reason is that there's just one orange marble.
Hence, the answer is I only.I’m so confused can someone help me solve this step by step?
Bases on the red line that represents the angle, we can see that:
[tex]\angle VRS\cong\angle RUT[/tex][tex]\angle SVR\cong\angle UTR[/tex]Therefore, they are similar by AA.
Give Triangle QRS ~= Triangle TUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV
1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:
[tex]\begin{gathered} QS=TV \\ 3v+2=7v-6 \\ 3v-7v=-6-2 \\ -4v=-8 \\ 4v=8 \\ \frac{4v}{4}=\frac{8}{4} \\ v=2 \end{gathered}[/tex]2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:
[tex]\begin{gathered} QS=3v+2 \\ QS=3(2)+2 \\ QS=6+2 \\ QS=8 \\ --- \\ TV=7(2)-6 \\ TV=14-6 \\ TV=8 \end{gathered}[/tex]As we can see these segments are congruent.
u A store is having a sale where everything is 15% off. Which expression below does not represent the cost of an item in the store? Select all that apply85/100cc-0.15c15/100c0.85cc-0.85c
Given:
Percentage discount = 15%
Let's find the expression that does not represent the cost of an item in the store.
Let c represent the original cost of an item.
To find the c
[tex]undefined[/tex]find the equation of this line.
Answer:
[tex]y=-\frac{1}{2} +1[/tex]
Step-by-step explanation:
We have to choose two points in the graph:
P₁ = (0, 1) → x₁ = 0 & y₁ = 1
P₂ = (2, 0) → x₂ = 2 & y₂ = 0
Now any of those point can be the P₀ I'll choose P₁ as P₀
P₀ = (0, 1) → x₀ = 0 & y₀ = 1
[tex]y - y_o=\frac{y_2-y_1}{x_2-x_1}(x-x_0)\\ \\y-1 = \frac{0-1}{2-0}(x-0)\\ \\y-1=\frac{-1}{2}(x) \\\\y-1=-\frac{1}{2}x\\ \\y=-\frac{1}{2}x+1[/tex]
Factor completely.
48-24x + 3x²
Answer:
3(4−x)²
Step-by-step explanation:
Answer:
3(4-x)^2
Step-by-step explanation:
factor
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
The rectangular floor of a classroom is 36 feet in length and 22 feet in width. a scale drawing of the floor has a length of 18 inches. what is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 58 inches.
Define Perimeter of the rectangle.The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
The letter "p" stands for the perimeter, which is equal to twice the width plus twice the length of the rectangle.
Given, the length of rectangular classroom is 36 feet
and the width is 22 feet.
The scale drawing has a length of 18 inches.
Here we can see that two different units are used.
So, we need to convert feet to inches.
1 foot = 12 inches
Now we will convert the length in inches,
36 feet = 36*12 inches
= 432 inches
Now we will convert the width in inches,
22 feet = 22*12
= 264 inches
Now, we will calculate by how many times the length has been scaled down:
[tex]\frac{432}{18} = 24[/tex]
So, the length has been scaled down to 24 times.
Now, we will scale down the width 24 times:
[tex]\frac{264}{24} = 11[/tex]
So, the width of the scale drawing is 11 inches.
Now, we will find the perimeter of the scale drawing:
Perimeter = 2(scale down length + scale down width)
= 2(18+11)
=2*29
=58 inches
Therefore, the perimeter of the scale down drawing is 58 inches.
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Mathew and his 3 siblings are weeding a flower bed with an area of 9 square yards. If they share the job equally, how many square yards of the flower bed will each child need to weed. write as a fraccion and whole number.
Data:
Mark and his 3 siblings: 4 persons
Area of the flower bed: 9 square yards
Job equally.
Divide the total area into the number of persons:
[tex]\frac{9^{}}{4}=2.25[/tex]100 Points + Brainliest if correct and well explained: The data in the table describes the preferred type of exercise of student athletes.
Cycling Running Row Totals
Male 0.22 0.32 0.54
Female 0.15 0.31 0.46
Column Totals 0.37 0.63 1.00
What is the conditional relative frequency that cycling is preferred by a female? Round your answer to two decimal places.
0.15
0.33
0.41
0.67
Answer:
0.33
Step-by-step explanation:
The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :
all females
all people preferring cycling
the way it was phrased I would say the reference is all females.
the conditional relative frequency is then
0.15 / 0.46 = 0.326=0.33(rounded)
Hence the conditional relative frequency that a female prefers running is 0.33
I’ve got 6 graphing questions today that I need help with please
For a given simultaneous equation,
The point at which both the lines intersect gives us the solution.
Thus,
the point A gives the solution of the system of equation.
Answer is A.
A(6,2), B(2,4) and C(8,-4) are three points in a plane. P is a point on the line BC and Q is a point in the plane such that PAQB is a rectangle. Find the:
(i) equations of the sides AP and BP,
(ii) coordinates of the point P,
(iii) area of the rectangle.
(i) The equations of the sides AP and BP are y = 0.75x - 2.5 and y = (-4/3)x + (20/3), respectively.
(ii) The coordinates of the point P are (4.4, 0.8).
(iii) The area of the rectangle is 8 square units.
A (6, 2), B (2, 4) and C (8, -4) are three points in a plane. P is a point on the line BC, and Q is a point in the plane, such that PAQB is a rectangle.
The point P lies on the line BC. The equation of the line BC will be the same as that of BC. The equation of line BP is calculated below.
(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)
(y - 4) = [(-4 - 4)/(8 - 2)]*(x - 2)
y - 4 = (-8/6)*(x - 2)
y = (-4/3)x + (20/3)
The line AP must be perpendicular to the line BP because they are the sides of a rectangle. The equation for AP is calculated below.
y = mx + c
y = (3/4)x + c
It passes through (6, 2).
2 = (3/4)*6 + c
c = 2 - 4.5
c = -2.5
The equation of AP is y = 0.75x - 2.5.
The coordinates of P are calculated by finding the intersection point of the equations of AP and BP. The coordinates of P are (4.4, 0.8).
The length of the rectangle is BP. The width of the rectangle is AP. These are calculated below using the distance formula.
BP = √[(2 - 4.4)² + (4 - 0.8)²]
BP = √(5.76 + 10.24)
BP = 4
AP = √[(6 - 4.4)² + (2 - 0.8)²]
AP = √(2.56 + 1.44)
AP = 2
The area of the rectangle is calculated below.
A = BP*AP
A = 4×2
A = 8
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