The value of y is 11/3 when the value of x = 3
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
If y varies inversely as x^2, and y=11/9 when x=9
when x =3,
y = 11/9 *x²
y = 11/3
Hence, the value of y is 11/3 when the value of x = 3
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42. HOW DO YOU SEE IT?
Write an expression in rational
exponent form that represents
the side length of the square.
Area:
x in.²
The exponent form that represents the side length of the square is √x
How to determine the side length of the square.From the question, we have the following parameters that can be used in our computation:
Area = x in.²
The area of a square is calculated as
Area = Side length²
substitute the known values in the above equation, so, we have the following representation
Side length² = x
Take the square root of both sides
Side length = √x
Hence, the expression is √x
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Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building, what is the height of the building? Show your work.
The height of the building that cast the shadow 98 feet will be 61.25 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.
Let 'h' be the height of the building. Then the equation is given as,
h / (90 + 8) = 5 / 8
h / 98 = 5 / 8
h = 98 x 5 / 8
h = 12.25 x 5
h = 61.25 feet
The height of the building that cast the shadow 98 feet will be 61.25 feet.
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row reduce the matrices in exercises 3 and 4 to reduced echelon form. circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.
Reduced matrix to its reduced echelon form Original Matrix:
[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,4)
Pivot Columns (Original): 1, 2, 4
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,4)
Pivot Columns (Reduced): 1, 2, 4
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column
4. Divide row 2 by 3 to get the coefficient 2/3 in the third column
5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column
6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column
Exercise 4:
Original Matrix:
[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,3)
Pivot Columns (Original): 1, 2, 3
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,3)
Pivot Columns (Reduced): 1, 2, 3
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract row 1 from row 3 to get the leading 1 in the third column
4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column
5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column
6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively
7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column
8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column
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E.
Carry out the following operations to the proper number of significant figures:
1. 212.45 +5.61-37.9
2. 89.001+2.50-91.50
3. 400+125= 500
4. 73.35-3.65-69.70
5. (81.7-23.456)+(78.44+2.72) =
By adding (81.7-23.456)+(78.44+2.72), we get 139.404
How does one determine the number of significant figures?Use the three rules below to calculate the number of significant figures in a number:
Non-zero digits are always meaningful.
Any zero between the first and second significant digits is significant.
Only the last zero or trailing zeros in the decimal section are important.
Numbers Have Rules INCLUDING a Decimal Point
START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.
STOP COUNTING FOR SIGNIFICANT FIGURES.
Non-zero numbers are ALWAYS meaningful.
After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.
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Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10* micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.
How can the size of transistors be known?The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.
We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.
In another sentence, we were told that the size of the transistor today is expressed as 1 × 10^-2
We can then know the difference in size will which will be
= 1 × 10^4 / 1 × 10^-2
= 1 × 10^6
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complete question:
Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
The vertices of triangle xyz are x=(-2,6), y=(4,10), and z=(14,6). Find the coordinates of the centroid of triangle xyz
The centroid of the given triangle is =(5.3 , 7.3)
What is Centroid of triangle?The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.
The centroid formula of a given triangle can be expressed as,
C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)
where,
C denotes the centroid of a triangle
x1,x2,x3 are the x-coordinates of the 3 vertices.
y1,y2,y3 are the y-coordinates of the 3 vertices
To find: Centroid of a triangle.
We are taking the Cordinates of the traiangle XYZ
as x1,y1,x1,y2,x3,andy3
so,Given parameters are,
(x1,y1)=(-2,6)
(x2,y2)=(4,10)
(x3,y3)=(14,6)
Using centroid formula,
The centroid of a triangle = ,
=-2+4+14/3 6+10+6/3
=5.3 7.3
The centroid of a triangle is ==(5.3 and 7.3)
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at a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded.
A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.
A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.
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Points A and B are 10 units apart. Points B and C are 4 units apart. Points C and D are 3 units apart. If A and D are as close as possible, then the number of units between them is
A. 0 B. 3 C. 9 D. 11 E. 17
A perimeter longer than 50 for any point, C satisfies the area requirement.
Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.
The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.
Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.
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The full question
In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?
Use the graphs of f and g to evaluate g(f(2))
I have added the photo of the graphs.
When I answered it the first two times I put -2 and then for the second time I put 4 and I got both of them wrong
Answer:
1
Step-by-step explanation:
We have g(f(2))
Working from the inside out, we start with f(2)
So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2
Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)
Now we can go to the other graph, g(x) and find where X is -2.
That's where we find the point (-2,1)
Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1
Now we can conclude g(f(2)) = 1
Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
What is the graph?
A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.
To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).
Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
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find the coordinates of point $p$ along the directed line segment $ab$ , from $a\left(-3,\ 2\right)$ to $b\left(5,-4\right)$ , so that the ratio of $ap$ to $pb$ is $2$ to $6$ . the coordinates are $p\text{(}$ , $\text{)}$ .
The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]
Let the coordinates of point p be (x,y)
The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]
We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:
[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]
We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:
[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]
Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.
Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]
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Please help!! It’s due in 10 minutes!!! Also please explain how you got the answer!
Answer: 22 vaccines
Step-by-step explanation:
first, reduce the amount that doctors leave out from the total amount of a vial
6 - 0.5 = 5.5
next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give
5.5/ 0.25 = 22 vaccines
In circle I, IJ = 2 and the area of shaded sector = . Find the length of JLK.
Express your answer as a fraction times T.
J
H
K
C
Given that IJ = 2, we know that IJ is the radius of the circle.
The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:
(x/360) * pi * 2^2 =
Solving for x:
x = (180/pi)*
We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.
Please please please please help
Can someone help me?
Answer: Maybe if you post the question
Step-by-step explanation:
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 12 miles. If the two airplanes are 20 miles apart, how far has the eastbound airplane traveled?
The eastbound airplane has traveled 16 miles.
This can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance the northbound airplane has traveled (12 miles) is one side of the triangle, the distance the eastbound airplane has traveled is the other side, and the distance between the two airplanes (20 miles) is the hypotenuse.
So, we can set up the equation as:
(distance eastbound airplane)^2 + 12^2 = 20^2
Solving for the distance eastbound airplane, we get:
distance eastbound airplane = sqrt(20^2 - 12^2) = sqrt(256 - 144) = sqrt(112) = 16 miles
how to calculate the area of a circle
Answer:
The area of a circle is pi multiplied by the radius squared (A = π r²)
The radius (r) is the distance from the center of the circle, to the edge of the circle.
Example:
if you have a circle with radius 2, the area would be:
r = 2
A = π (2)²
A = π(4)
A = 4π
Answer:
Area can be calculated by the formula = [tex]\pi r^{2}[/tex]
Step-by-step explanation:
We can calculate the area of a circle with the formula,
Area of Circle = [tex]\pi r^{2}[/tex]
Where r replicates the radius of the circle
Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation? Group of answer choices
(1)x + y = -2
x - y = -10
(2) x - y = -10
x + y = 2
(3) x + y = -10
x - y = -2
(4) x = -2
y = 5
Answer: The answer is 3
Step-by-step explanation:
the perimeter of a rectangle is 700 feet. let x represent the width of the rectangle. write a quadratic function for the area a of the rectangle in terms of its width.
The perimeter of a rectangle is 700 feet. A quadratic function for its area in terms of its width is A(w) = 350w - w²
The formula for the perimeter of a rectangle is given by:
p = 2w + 2l
While its area is:
A = w x l
Where:
w = width
l = length
Substitute p = 700 ft.,
700 = 2w + 2l
700 = 2(w + l)
w + l = 350
l = 350 - w
Substitute l = 350 - w into the formula of area:
A = w x l
A = w (350 - w)
A(w) = 350w - w²
Hence, the expression is: A(w) = 350w - w²
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Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second -- the second face of the roof. The first beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof is perpendicular to the first face?Need ANSWER ASAP
The altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.
How do you find the altitude of the second beetle?In order to find the altitude of the second beetle, let x be the altitude of the second beetle above the first beetle.
The horizontal distance between the two beetles is 72 cm.
The first beetle moves twice as fast as the second beetle, so the vertical distance between them is 2x.
Therefore, the equation for the problem is:
3x + 2x = 72
5x = 72
x = 14.4 cm
Therefore, the altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.
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find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
The equation of a line passing through the terminal point of a vector a and in the direction of vector b is r = a + λb.
In math the equation of a straight line is y = m x + c
where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,
=> r = a + λb.
Where λ refers the constant term.
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find the domain of each expression
1. y ^2+1)/(y^2-2y),
2. 25(y-9),
3. 32/y - (y+1)/Y+7)
The domain of each expression is given as follows:
1. All real values except y = 0 and y = 2.
2. All real values.
3. All real values except y = 0 and y = -7.
How to obtain the domain of the expressions?The domain of an expression is composed by the set of all the possible input values that the expression can assume.
For an expression that is a fraction, the denominator cannot be zero, hence:
Item 1: y² - 2y = 0 -> y(y - 2) = 0, hence the domain is all real values except y = 0 and y = 2.Item 3: y = 0 and y + 7 = 0 -> y = -7, hence the domain is all real values except y = 0 and y = -7.For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.
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Determine the number of lines of symmetry for the figure.
The figure has ✓line(s) of symmetry.
Select the angles of rotation, if any, that map the figure onto itself.
O 30°
O 90°
☐ 180°
dh
O 45°
O 120°
Answer:
The figure has 4 lines of symmetry.Rotating through angles 90° or 180° will map the figure to itself.Step-by-step explanation:
You want the number of lines of symmetry of the 4-leaved rose shown in the figure.
Lines of symmetryThe figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.
Rotational symmetryThe petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)
The figure maps to itself when rotated 90° or 180°.
7. Is this a leap year?
FEBRUARY
answer
no
steps
February ends on the 28th this year 2023
leap year February ends on the 29th
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
0.325
0.625
0.750
0.875
Answer:
0.750
Step-by-step explanation:
Yellow sections: section 2 and section 3
Number of yellow sections: 2
Number of non yellow sections: 6
Total sections: 8
p(not yellow) = 6/8 = 0.75
Answer:
0.750
Step-by-step explanation:
you take a quarter and then you divide and think
Two fractions with the same denominator that have numerators 5 and 7 what would the denominator be?
The denominator could be any real value
How to determine the possible denominatorFrom the question, we have the following parameters that can be used in our computation:
Fraction = same denominator
Such that the numerators are 5 and 7
This means that the fractions can be represented as
Fractions = 5/x and 7/x
There is no restriction on the possible value of x
hence, the denominator is any value
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Translate this polygon six units to the left and two units upward:
The image that gives the translation of the polygon six units to the left and two units upward is given as follows:
The fourth graph.
(which is the third graph if we consider that the first is the original image).
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the translation 5 units left, we have that:
The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.
For the translation 2 units up, we have that:
The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.
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because of the enormity of the viewing audience, firms that advertise during the super bowl create special commercials that tend to be quite entertaining. thirty-second commercials cost over $5 million for the 2017 game. a random sample of people who watched the game were asked how many commercials they watch in their entirety. Do these data allow us to inter that the mean number of commercials watch is greater than 15?
No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.
To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.
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What should go into the leaves for 11?
answer asap!!!!
Find the product of the binomial factors using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).
(x+8)2
The product of the binomial factors is x² + 16x + 64
How to determine the product of the binomial factorsfrom the question, we have the following parameters that can be used in our computation:
(x+8)2
Express properly
So, we have
(x+8)²
Using the square of a binomial sum, we have
(x+8)² = x² + 2 * x * 8 + 8²
Evaluate
(x+8)² = x² + 16x + 64
Hence, the solution is x² + 16x + 64
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match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. enter the appropriate letter (a,b,c,d, or e) in each blank.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.
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