(1) In general, switching the coordinates x and y is how an inverse is calculated.
(2) The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
(3) We can find the inverse in algebra by replacing f(x) by y and then solve for x.
In general, switching the coordinates x and y is how an inverse is calculated. Although not strictly a function, this freshly constructed inverse is a relation.
To ensure that the initial function's inverse will be a function, the major purpose must be a one-to-one function. When every second element matches the first value, a function is said to be a one-to-one function.
To determine whether a function is a one-to-one function, use the horizontal line test. The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
When a function's formula has been provided to you, follow these steps to discover its inverse:
(1) Change "f(x)" to "y".
(2) Make an effort to resolve the x= equation.
(3) Switch the xs and ys.
(3) Change y to "f1(x)"
We can find the inverse in algebra by replacing f(x) by y and then solve for x.
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if B=t+10 and A=3t^2-2 find an expression that equals 2B−3A in standard form.
The expression that equals 2B−3A in standard form is - 9t² + 2t + 14
How to determine the expression that equals 2B−3A in standard form.From the question, we have the following parameters that can be used in our computation:
B = t + 10
Also, we have
A = 3t² - 2
The expression that equals 2B−3A is calculated as
Expression = 2B - 3A
Substitute the known values in the above equation, so, we have the following representation
Expression = 2 * (t + 10) - 3 *(3t² - 2)
So, we have
Expression = 2t + 20 - 9t² - 6
Evaluate the like terms
Expression = - 9t² + 2t + 14
Hence, the expression = - 9t² + 2t + 14
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer: Adult: $20 Child: $9
Step-by-step explanation:
20 + 20 + 20 = 60
9 + 9 + 9 + 9 = 36
60 + 36 =96
State whether each figure has a line of symmetry (yes or no.) If so, draw all possible lines of symmetry. (Some may have more than one.)
Answer:
Step-by-step explanation:
What is the formula for height?
The height of the triangle is determined by the formula, 2 × Area / Base
Given,
Triangle;-
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
We have to find the formula for height of triangle;
According to theorem;
The area of the triangle = 1/2 × base × height
Then,
Height of the triangle = 2 × Area / Base
That is,
The formula for the height of the triangle is 2 × Area / Base
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Complete question is here;
What is the formula to find the height of a triangle?
|x-6|=11 solve this equation
Answer:
x = -5 or x = 17
Step-by-step explanation:
The absolute value is the number's distance from 0.
So, we need to write two equations.
x - 6 = 11
x - 6 = -11.
Next, we need to add 6 to both sides of each equations.
11 + 6 = 17
-11 + 6 = -5
So, x = 17 and x = -5.
Answer: It could be -5 or 17
Step-by-step explanation: So, it can be both, but as I see it would most likely be 17 because I see you put x-6 as an absolute value. so, to find the value of x, we could do 11 + 6 (Inverse operations), so 11 + 6 = 17. If it was NOT the absolute value of x-6, we could find it to be -5, by subtracting -6 from 11, to get -5. I hope this helps you understand now, if any questions please comment down below.
In ΔSTU, s = 3.4 cm, ∠T=165° and ∠U=13°. Find the length of t, to the nearest 10th of a centimeter.
Answer:
25.2 cm
Step-by-step explanation:
[tex]\angle S=180^{\circ}-165^{\circ}-13^{\circ}=2^{\circ} \\ \\ \frac{t}{\sin T}=\frac{s}{\sin S} \\ \\ \frac{t}{\sin 165^{\circ}}=\frac{3.4}{\sin 2^{\circ}} \\ \\ t=\frac{3.4\sin 165^{\circ}}{\sin 2^{\circ}} \\ \\ t \approx 25.2[/tex]
Answer the questions about the work below:
3x − 8 ≤5x + 6
3x ≤5x −2
−2x ≤−2
Are there any errors in the above work so far? Response area
The correct final answer is:
Answer:
Yes, there is an error in the third step of the solution. The correct result of the third step should be -2x ≤ 8, not -2x ≤ -2. The error occurred because the incorrect value was subtracted from both sides of the inequality
Step-by-step explanation:
The final answer for the inequality 3x − 8 ≤5x + 6 is x ≥ -7, and the third step is wrong, the right answer is -14 ≤ 2x.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
3x − 8 ≤ 5x + 6
Add 8 on both sides of the inequality as shown below,
3x − 8 + 8 ≤ 5x + 6 + 8
3x ≤ 5x + 14
Subtract -3x from both sides as shown below,
3x - 3x ≤ 5x + 14 - 3x
0 ≤ 2x + 14
Subtract 14 from both sides as shown below,
0 - 14 ≤ 2x + 14 - 14
-14 ≤ 2x
Divide both sides by 2 as shown below,
-14 / 2 ≤ 2x / 2
-7 ≤ x
or x ≥ -7
Thus, the final answer is x ≥ -7.
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Are all equilateral triangles congruent Why?
No, All equilateral triangles need not to be always congruent with one another .
Justification of answer:
The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .
Properties of an equilateral triangles:1. All 3 side of an equilateral triangles have same length .
2. All 3 angles of an equilateral triangles have same measure.
3. Each angles of an equilateral triangles is 60 degree .
4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]
5 . Perimeter of an equilateral triangles = 3*a
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How do you describe the graph of x is equal to 2?
The graph of x = 2 is a vertical line parallel to y-axis. Also, the slope of x = 2 is undefined and there is no y-intercept.
In this question we need to describe the graph of x is equal to 2.
To draw the graph of x = 2, firstwe find some coordinates of the points.
Consider the points (2, 1), (2, 0), (2, -1)
[As the x coordinate is fixed, we can take any value of y coordinate]
The graph of x = 2 is as shown below.
The graph of x = 2 is a straight vertical line, which is parallel to y-axis.
There is no y-intercept to the graph of x = 2.
Also the slope of line x = 2 is undefined.
Therefore, the graph of x = 2 is a straight line with Slope = Undefined
and no y-intercept.
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A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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find the area and perimeter of an equilateral triangle whose equal side is 6cm
Answer:
Area = 9√3 cm²
Perimeter = 18 cm
Step-by-step explanation:
Area of equilateral triangle ABC =
(√3/4) × 6²
= (√3/4) × 36
= 9√3 inches2
ABC is an equilateral triangle with side = 6 cm
Perimeter of an equilateral triangle = AB+BC+CA
Perimeter of an equilateral triangle = 6+6+6
Perimeter of an equilateral triangle = 18 cm
A mountain in jackson county is eroding and losing elevation at a rate of 5% every millennium. If the current elevation is 1,300 meters, how tall will the mountain be in 8 millennia?.
So the mountain will be approximately 798.02 meters tall after 8 millennia.
The mountain loses 5% of its elevation every millennium, which is the same as losing 0.05 * its current elevation. Therefore, after 1 millennium, the mountain's elevation will be 1 - 0.05 = 0.95 times its current elevation. After 2 millennia, it will be 0.95 * 0.95 = 0.9025 times its current elevation, and so on.
After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
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After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
How do I solve for x?
Step-by-step explanation:
I just answered this question. how often did you post it ?
in short again :
360 = 8x + 20 + 104 + arc angle KJP
arc angle KJP = 2× opposite angle of K and P =
= 2×(5x + 1)
so, together
360 = 8x + 124 + 2×(5x + 1) = 8x + 124 + 10x + 2 =
= 18x + 126
234 = 18x
x = 13
5
6
A curve has equation y = x³ + ax + b.
The stationary points of the curve have coordinates (2, k) and (-2, 10-k).
Work out the value of a, the value of b and the value of k.
The value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
The stationary points of a curve are those points at which the first derivative of the function f(x) becomes zero. At the stationary points, the nature of the function is neither increasing nor decreasing.
→ The stationary points of a curve can either be a local minima or a local maxima of the function.
→ If we plot the graph of the curve, then stationary points can be said to be those points at which the tangent to the curve becomes horizontal which means the tangent becomes parallel to the x-axis.
→ Therefore for a point (a,b) to be the stationary point of a function f(x): f'(a) must be equal to zero.
→ For the given question:
f(x) = y = x³ + ax + b
f'(x) = 3x² + a
(2, k) is a stationary point:
f'(2) = 0
f'(2) = 3(2)² + a = 0
a = -12
The value of 'a' comes out to be equal to -12.
→ Hence the equation of the curve is: y = x³ - 12x + b
→ The stationary points (2, k) and (-2, 10-k) must be lying on the curve, hence they must satisfy the equation of the curve:
→ Putting (2, k) in the equation of the curve:
k = (2)³ - 12(2) + b
(k - b) = -16 - Equation (i)
→ Putting (-2, 10 - k) in the equation of the curve:
(10 - k) = (-2)³ -12(-2) + b
(10 - k) = -8 + 24 + b
b = -6 - k - Equation (ii)
→ Putting the value of 'b' from the equation (ii) in equation (i):
k - (-6 - k) = -16
k + 6 + k = -16
2k = -22
k = -11
∴ The value of 'k' comes out to be equal to -11.
→ Putting the value of 'k' in equation (i):
k - b = -16
-11 - b = -16
b = 5
∴ The value of 'b' comes out to be equal to 5.
Therefore, the value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
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A clerk counted 13 small baseball caps, 36 medium baseball caps, and 27 large baseball caps on the store shelves. She also counted 10 small baseball caps and 15 medium baseball caps in the stockroom.
Organize the data in a matrix. Name the matrix B. Label the rows and columns.
Each baseball cap sells for $19. Create the matrix that shows the total value of each cap size in each location. Show your work.
The matrix B that organizes the data is given as follows:
B = [13, 36, 27,
10, 15, 0,
23, 51, 27].
The matrix that shows the total value of each cap size in each location is given as follows:
C = [247, 684, 513,
190, 285, 0,
437, 969, 513].
How to define the matrix B?The matrix B is defined considering that it will have three rows and three columns, as follows:
Row 1: Number of each type of cap on the store shelves.Row 2: Number of each type of cap on the stockroom.Row 3: Total number of each type of car -> Row 1 + Row 2.Column 1: Small caps.Column 2: Medium caps.Column 3: Large caps.Then the matrix B is defined as follows:
B = [13, 36, 27,
10, 15, 0,
23, 51, 27].
The cost of each baseball cap is of $19, thus the cost matrix is obtained multiplying the matrix B by the constant of 19.
When a matrix is multiplied by a constant, all the elements of the matrix are multiplied by the constant, hence the cost matrix is given as follows:
C = [247, 684, 513,
190, 285, 0,
437, 969, 513].
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30 points! are the volumes the same? if not which one is greater?
Answer:
i round off to two decimals
LEFT:(solve for radius)circumference = 2ñr
11 = 2(3.14)r
11 = 6.28r
r = 0.57 inches
(solve for volume)
volume = ñr²h
volume = (3.14)(0.57²)(8.5)
volume = (3.14)(0.33)(8.5)
volume = 8.81 inches³
RIGHT:(solve for radius)circumference = 2ñr
8.5 = 2(3.14)r
8.5 = 6.28r
r = 0.74 inches
(solve for volume)
Volume - ñr²h
Volume = (3.14)(0.74²)(11)
Volume = (3.14)(0.55)(11)
Volume = 18 inches
Therefore, the right side cylinder is greater than the left cylinder.
i round off to two decimals
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-2x + 5x = 3x + 16
Someone help. Can you help me figure out what x is and simplify this equation?
Answer:
Step-by-step explanation:
Rena Roosh, fun name :P so, just use your algebra skillz
2x + 5x = 3x + 16
I'm wondering if there is an extra "x" on the right hand side,
anyway
7x -3x = 16
4x = 16
x = 4
see??
Answer:
Step-by-step explanation: Perform any simplification of like terms if possible
7x=3x+16
Collect x terms on one side. Can use the left side for x terms. That means 3x must dissapear. To do this we need to take 3x from both sides.
7x-3x=3x-3x+16
4x=16
To solve for x we need to divide by 4 on both sides
4x/4=16/4
x=4
Which ordered
pair is on the line
y = -5x + 2?
Answer:
(0,2)
(1,-3)
(2,-8)
The regular price is $150 but there is a 20% off coupon. What is the sale price?
Answer:
30
Step-by-step explanation:
30
When two parallel lines cut by a transversal What do you called the four angle formed inside the parallel lines?
When two parallel lines are cut by a transversal, the four angles formed inside the parallel lines are called interior angles.
Interior angles are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. There are always four interior angles formed when two parallel lines are cut by a transversal. These angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior angles is important in geometry, as they can be used to prove the parallelism of lines.
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What is pyramid equation?
The equation of the pyramid is as follow,
Volume is equal to one by third of the Area of the base into Height.
V=(1/3) X A X H, where A is area and H is height.
The sum of a pyramid's side faces makes up the lateral surface area.
LSA of the pyramid multiplied by the base's area gives the total surface area.
A pyramid is a 3D shape that has a base made of a polygon and faces that are all triangular and linked. The conventional form of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this part, let's study more about pyramids.
Volume of a PyramidThe area encompassed between a pyramid's faces is referred to as the pyramid's volume. The formula for each pyramid varies based on the pyramid's foundation. The formula used to determine a pyramid's volume, which is expressed in cubic units, is as follows V=(1/3) X A X H.
Surface Area of a PyramidDifferent forms of pyramids have varying amounts of surface area. The following formula is used to determine a pyramid's surface area:
Surface Area = Base Area + (½ × Perimeter of the base × Slant height)
Surface Area = Base Area + Lateral Area.
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What are the 4 functions of a roots?
Four main functions of the roots of the plant is given by:
1. Anchorage
2. Absorption of water and minerals
4. Prevention of the soil erosion.
5. Transportation of food from the soil.
Four function of the roots of any terrestrial plants:
Anchorage of the plant :Due to anchorage of the plant root fix in the soil and help in growing the aerial shoot system part of the any tree or plant.
Absorption of water and minerals: It helps to absorb water and minerals from the soil to the roots of the plants .
Prevention of the Soil Erosion : Due to root of the plant soil gets binds to the roots of the plants and does not or in very less quantity get eroded by water or wind.
Transport : Roots of the plants helps to transport food , salt , mineral , and water which given or present in the soil to the shoot or leaves and flowers , fruit of the plant.
Therefore, the four functions of the roots are:
1.Anchorage of the plant
2. Absorption of water and minerals
3. Prevention of the soil erosion
5. Transportation of food.
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Solve the system of equations by substitution.
Answer:
x = -6
y = -18
Step-by-step explanation:
6x -2y = 0
x - y = 12
Times the second equation by -2!
6x -2y = 0
-2x + 2y = -24
Now add them together and solve for x first!
4x = -24
x = -6
Now put -6 back in the equation and solve for y
6(-6) -2y = 0
-36 - 2y = 0
-2y = 36
y = -18
So, x= -6
y= -18
gsuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.45. using the empirical rule, what percentage of the students have grade point averages that are greater than 1.66? please do not round your answer.
The percentage of students with GPAs greater than 1.66 is 88.22%.
To answer this question, we need to use the empirical rule, which states that 68% of the data is within one standard deviation of the mean. To calculate the percentage of students with GPAs greater than 1.66, we need to subtract the percentage of students with GPAs less than 1.66 from 100%.
The percentage of students with GPAs less than 1.66 can be calculated by subtracting 1.66 from the mean of 2.56, then dividing by the standard deviation of 0.45. This gives us 2.11 standard deviations below the mean, which corresponds to a percentile of 11.78%.
Therefore, the percentage of students with GPAs greater than 1.66 is 100% - 11.78% = 88.22%.
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a local bank needs information concerning the savings account balances of its customers. a random sample of 15 accounts was checked. the mean balance was $686.75 with a standard deviation of $256.20. find a 98% confidence interval for the true mean. assume that the account balances are normally distributed. round to the nearest cent.
Answer:
hlo bro what's up where r u from
How do you write a preimage?
Answer: The image T(V) is defined as the set {k | k=T(v) for some v in V}. So x=T(y) where y is an element of T^-1(S). The preimage of S is the set {m | T(m) is in S}. Thus T(y) is in S, so since x=T(y), we have that x is in S.
Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C. The symbol f−1(D) is also pronounced as “f inverse of D.”
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
Step-by-step explanation:
Explain the Triangle Inequality Theorem as it relates to angles.
Answer:
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, the length of one side of a triangle must always be shorter than the sum of the lengths of the other two sides. This theorem is often used in geometry to determine whether or not a given set of lines can form a triangle.
When it comes to angles, the Triangle Inequality Theorem can be used to determine whether or not a triangle can be formed given the measures of its angles. For example, if the measures of two angles in a triangle are 45 degrees and 60 degrees, the measure of the third angle must be less than 180 degrees - 45 degrees - 60 degrees, or 75 degrees. If the measure of the third angle is greater than 75 degrees, it is not possible for the three angles to form a triangle.
Overall, the Triangle Inequality Theorem is a useful tool for understanding the relationships between the sides and angles of a triangle, and for determining whether or not a given set of lines or angles can form a triangle.
Step-by-step explanation:
How many numbers are on a fair dice?
Answer:
When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.
Step-by-step explanation:
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Bonnie makes $12.40/hr and works as a server. on tuesday she worked for 6 hours and twenty minutes and made $110 in tips. how much did she make in total and what is her hourly wage?
Answer: 188.53$ in total.
$31.42 as hourly wage .
Step-by-step explanation:
Wage1 for 6hours = $12.4 * 6
Wage2 for 20minutes = $12.4 / 3
Since an Hour has three 20 minutes in it , so hourly wage $12.4 is divided by 3 to get the wage for a 20minute work.
Wage3 as Tips = $110
Total Wages for Tuesday = Wage1 + Wage2 + Wage3
= $188.53
New hourly Wage = $188.53 / 6 = $31.42
there are six balls in a box if we select three balls what is the probability of having one white ball
The probability of having one white ball is 1/20 or approximately 0.05.
To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.
Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.
The probability of selecting one white ball out of three would be:
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.
Therefore, the probability of selecting one white ball out of three would be
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Probability = 1/20
Probability = approximately 0.05.
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