Solve for X

This was on a Geometry Honors quiz

The inverse of f(x) has no restriction on the domain.

The graph of the inverse function is given below.

The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x - 3)²

The inverse of f(x).

Step 1:

Make f(x) = y

y = (x - 3)²

Step 2:

Interchange x and y

x = (y - 3)²

Step 3:

Solve for y.

square root on both sides.

x² = y - 3

y = x² + 3

So,

[tex]f^{-1}[/tex](x) = x² + 3.

a)

[tex]f^{-1}[/tex](x) = x² + 3

we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.

So,

There is no restriction on the domain.

b)

The graph is given below.

c)

The inverse equation is

[tex]f^{-1}[/tex](x) = x² + 3.

Thus,

The inverse of f(x) has no restriction on the domain.

The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.

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Matrix A is: A = [1 2 3] and Matrix B is: B = [1]

                         [2 4 6]                                 [2]

                         [1 1 1]                                    [3]

An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:

A = [1 2 3]

   [2 4 6]

   [1 1 1]

B = [1]

   [2]

   [3]

To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:

Ax = b

[1 2 3] [x1] = [1]

[2 4 6] [x2]   [2]

[1 1 1] [x3]   [3]

Ax = b

x1 + 2x2 + 3x3 = 1

2x1 + 4x2 + 6x3 = 2

x1 + x2 + x3 = 3

Dividing the second equation by 2 and subtracting it from the first equation, we get:

-x1 - x2 = -1

Solving for x2 in terms of x1 and x3, we get:

x2 = -x1 + 1 - (3/2)x3

Solving for x3 in terms of a parameter t, we get:

x3 = t

Then, x1 can be expressed in terms of t as:

x1 = -t + 1

Therefore, the solution set of Ax = b is:

x = [-t + 1]

   [-t + 1 - (3/2)t]

   [t]

which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].

A × [0; 0; 0] = [0; 0; 0]

Therefore, the origin is not on the line of solutions.

So, Matrix A is:

A = [1 2 3]

     [2 4 6]

      [1 1 1]

and Matrix B is:

B = [1]

     [2]

     [3]

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Answer:

Step-by-step explanation:

The probability that the committee has exactly two woman is 0.1758.

Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.

Given that, 4 women and 5 men are eligible to serve on a committee.

A committee of 3 is randomly selected.

Choosing 2 women out of 3 women is

³[tex]C_{2}[/tex]

= 3

Choosing 1 men out of  5 men is

5C1

= 5

Total number of eligible person is = (4+5)=9

Choosing 3 member out of 9 member is

9C3

=84

The required  probability is

=3*5/84

0.1785

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The more accurate statement is that hypotheses are only as good as the observations on which they are based.

A hypothesis is a tested assertion regarding the relationship between two or more variables or a suggested explanation for some observable occurrence in a scientific setting.

As a result, hypothesis are only as good as the observations upon which they are built.

For instance, if we stay up late, we will be fatigued the next day. Turning off your phone allows it to charge more quickly. All of them are hypotheses since they are based on observations and are only valid for as long as the observations stay true.

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Answer:

yes beacuse he have nice grapics and u can play with your friends.

Step-by-step explanation:

Answer: Yes it is very good i recommend getting it, but it takes a ton of time to get use to it.

Step-by-step explanation:

Dinner would cost $123 at either restaurant if Betty's lobster weighed 36 pounds.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In the context of this problem, the slope and the intercept are defined as follows:

Hence the functions for each restaurant are given as follows:

The costs are the same when:

y1(x) = y2(x)

51 + 2x = 15 + 3x

x = 36.

The cost is of:

y = 15 + 3 x 36

y = $123.

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1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.

2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.

Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.

A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.

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Answer:-3

Step-by-step explanation: -7 -4

Perimeter and area of the rectangle would be 2(10x² + 7xy²) and 70x²y².

What is Perimeter and area?

The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.

Given the length l = 10x² and width w = 7xy² of a rectangle, the perimeter P and area A can be calculated as follows:

1) Perimeter P:

    P = 2(l + w)

       = 2(10x² + 7xy²)

2)Area A:

A = l * w

   = 10x² * 7xy²

   = 70x²y²

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Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.

What is overtime pay?

Overtime pay is the additional compensation paid to an employee for any hours worked in excess of the standard working hours or beyond the standard workweek. The rate of overtime pay is usually higher than the regular rate of pay for an employee's normal working hours.

To determine the extra overtime pay due to Casey Na for the first quarter, we need to know his regular pay rate and the number of hours he worked each week.

Let's assume that Casey Na's regular pay rate is $20 per hour and that he worked 40 hours each week during the first quarter. This means that he worked 3 hours of overtime each week, for a total of 39 hours at his regular rate and 3 hours at his overtime rate.

To calculate his overtime pay for the first quarter, we can use the following formula:

Overtime pay = overtime hours x overtime rate

Since Casey Na worked 3 hours of overtime each week for 13 weeks, his total overtime hours for the first quarter were:

Total overtime hours = 3 hours/week x 13 weeks = 39 hours

His overtime rate is 1.5 times his regular rate, or $20 x 1.5 = $30 per hour.

Therefore, his overtime pay for the first quarter was:

Overtime pay = 39 hours x $30/hour = $1,170

Since he also earned a bonus of $975 for perfect attendance, his total extra pay for the first quarter was:

Extra pay = Overtime pay + Bonus = $1,170 + $975 = $2,145

Therefore, Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.

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Answer:

Yes

Step-by-step explanation:

length 138,435 ÷ 3 ft stride = 46,145 equally

The simplest radical form is x⁵.

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

The given radical form is [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex].

The radical and root of a number are the same thing.

Simplifying a radical eliminates the square roots, cube roots, fourth roots, etc.

In the given expression, 1/6 is the 6th root, in both numerator and denominator cancel out 6th root x.

That is,  [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex] =x⁵ ([tex]x^{\frac{1}{6} }[/tex]  in the denominator is gets cancelled with [tex]x^{\frac{1}{6} }[/tex] in the numerator)

Therefore, the simplest radical form is x⁵.

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Answer:

Step-by-step explanation:

if the sum of two consecutive even numbers is 42 find the number

42 - 2 = 40                       remove the difference (2)

40 : 2 = 20                       find the smallest number

20 + 2 = 22                      find the largest number

------------------------------------

(20 + 22 = 42)                

[tex](3x^2+5x+4)+(6x+1)~~ = ~~3x^2+11x+5 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ (3x^5+15x^3+4)+(-3x^5+2x^2-8)\stackrel{ \textit{not on all cases} }{~~ = ~~15x^3+2x^2-4} ~~ \bigotimes[/tex]

Black Beauty stands one inch taller than Thumbelina, measuring 18 inches in height compared to Thumbelina's 17-inch stature.

Black Beauty is 1 inch taller than Thumbelina.

Two or more expressions with an Equal sign is called as Equation.

Given that Thumbelina, who stands 17 inches tall

Black Beauty, who stands 18 inches tall.

Einstein, who stands 14 inches tall.

We have to find how tall is Black Beauty than Thumbelina.

To find out, we can subtract Thumbelina's height from Black Beauty's height:

Black Beauty's height - Thumbelina's height

= 18 inches - 17 inches = 1 inch

Therefore, Black Beauty is 1 inch taller than Thumbelina.

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a. The amount of copper in a bronze of 360g is 324g

b. The mass of bronze with 670.5g of copper is 745g

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The ratio of copper to Tin is 9:1. The total ratio is 10

a.therefore the amount of copper = 9/10 × 360

= 324g

b. The mass of copper = 670.5g

therefore the mass of the bronze =

= 9/10× y = 670.5

9y = 670.5 × 10

9y = 6705

y = 6705/9

y = 745g

therefore the total mass of the bronze is 745g

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Kyle: Rotation about the origin, then reflection across the x axis

Tina: Reflection over the line y = x

In geometry, reflection refers to a transformation that involves flipping a shape or object over a line, often called the "line of reflection".

This transformation preserves the size and shape of the original object, but changes its orientation by reversing the positions of all its points across the line of reflection.

Considering the image, rotation about the origin, then reflection across the x axis when compare with Reflection over the line y = x. will yield similar result.

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The two unique values of sin theta in radians are

The sine function has a range of [-1, 1], so there are multiple angles that correspond to a sine of 1/2.

The most commonly used values are π/6 (30 degrees) and 7π/6 (150 degrees), which are in the first quadrant and second quadrant and have a positive sine value of 1/2.

It's worth noting that there are an infinite number of angles that correspond to a given sine value, since the sine function has period 2π. These angles are related to the angles by adding or subtracting multiples of 2π.

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The angle of rotation that will bring Car 3 to the position of Car 18 is 11.25 degrees. The angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees. Car 3 needs to move 15 positions counterclockwise to reach Car 18.

a. We have to determine the angle of rotation that will bring Car 3 to the position of Car 18 on the London Eye, so we will first calculate the number of positions that Car 3 needs to move counterclockwise to reach Car 18.

We know that there are 32 observation cars on the London Eye, so the distance between two adjacent cars will be 360/32 = 11.25 degrees.

b. To find the angle of rotation that a car travels when it moves one position counterclockwise, we will divide the full rotation of the London Eye by the number of observation cars (i.e. 32).

360/32 = 11.25 degrees

Next, to determine the angle of rotation that would bring Car 3 to the position of Car 18, we will multiply the number of positions that Car 3 needs to move counterclockwise and the angle of rotation for each position as follows -

15 x 11.25 = 168.75 degrees

Therefore, the angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees.

c. To find the number of positions that Car 3 needs to move counterclockwise to reach Car 18, we will subtract the position number of Car 18 from that of Car 3 and then take the absolute value, as it is a cyclical rotation.

|18 - 3| = 15

Hence, Car 3 needs to move 15 positions counterclockwise to reach Car 18.

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The multiplication of the given fraction 6 × 3/5 is 15 or 3 3/5

Fraction refers to numbers which comprises of a numerator and a denominator. A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

6 × 3/5

multiply the numerator and denominator separately

= (6 × 3) / (1 × 5)

= 18/5

= 3 3/5

Therefore, 3 3/5 is the solution to the multiplication of the fraction.

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Answer: 3x + 8y

Step-by-step explanation:

Combining like terms is simply adding all the terms which are similar.

2x+6x-5x= 3x

5y+3y= 8y

Hope it helps!

Answer:

yes

Step-by-step explanation:

Answer:

Check below

Step-by-step explanation:

Number of tiger shark teeth = 6

Number of sand shark teeth = 8

    Number of tiger shark teeth : Number of sand shark teeth

                                    6                :                8

∴ 6 : 8 ratio representation

Answer:

6:8

Step-by-step explanation:

The length of the rectangular classroom will be 8 inches on the scale drawing.

What is a rectangle defined as?

Rectangles are four-sided polygons having internal angles of 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from the square in that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the other side must be 20 cm long as well.

Two diagonals cross form a rectangle. Both diagonals are the same length.

P = 2 (Length + Width) defines the perimeter.

Rectangle Area=Length*Breadth

Now,

As total length of room =36 feet

and 9 feet = 2 inch on drawing scale

then length of classroom on  drawing scale is = 36/9*2

=8 inch

Hence,

            The length of the rectangular classroom will be 8 inches on the scale drawing.

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Players A and B withdraw balls from the urn consecutively until a read ball is selected, the probability that player A selects the red ball is approximately 0.408.

To find the probability that player A selects the red ball, we can use the law of total probability and consider all the possible ways the game could end. A selects the red ball on the first draw. The probability of this is simply the proportion of red balls in the urn, which is 3/10.

A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until A finally selects the red ball. The probability of this is:

(7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7)

Notice that the probability of selecting a black ball decreases by one after each turn, since the total number of balls in the urn decreases by one and the number of black balls decreases by one.

The probability of selecting the red ball on the last turn (after all the black balls have been selected) is 3/3 = 1. We multiply all these probabilities together to get the total probability of this sequence of events.

A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until B finally selects the red ball. The probability of this is:

(7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6)

Notice that the probability of selecting a black ball decreases by one after each turn, just like in the previous case. However, the probability of B selecting the red ball on their turn is now 3/6, since there are only six balls left in the urn at this point. We multiply all these probabilities together to get the total probability of this sequence of events.

Adding up these three probabilities, we get:

3/10 + (7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7) + (7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6) ≈ 0.408

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The solution is 440 ft² because the overall size of the image is 528 sq ft, which in itself is closest approaching 440 square feet.

Parallel forms are defined as having at least two even more parallel lines. If two lines never cross, they are considered to be parallel. There are different parallel shapes, however any parallel sides require an equitable distribution of sides in the shape.

Sum of the measurements of the two main sides divided by height equals the area of a trapezoid.

Let's refer to the longer parallel side's length as "L." The figure's height is 22 feet, while the shorter parallel side's length is 16 feet.

Area = (L + 16) / 2 * 22

We also knows that the distance between a point and the vertical line formed by two studs is 4 feet and the distance between a vertex and the opposing height is 8 feet. The Pythagorean theorem may be used to determine the length of the greater parallel side, L, since these two lengths create a right triangle.

L² = (8 + 4)² = 64

L = 8

We can now calculate the overall area using the formula for a trapezoid's area.

Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528

The solution is 440 ft² because the overall size of the figures is 528 sq ft, that is closest towards 440 sq ft.

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Answer:

< 1 is acute (less than 90⁰)

<2 is acute

<BOA is obtuse (greater than 90⁰)

Answer: Jamie burned 420 calories on Tuesday

Step-by-step explanation:

Cross method is best for this question

Let x = calories burnt on tuesday
480 is 100%
x is 7/8 (or 87.5%)

∴
(480*87.5%) ÷ 100%
= 420 ÷ 100%
= 420

Therefore, Jamie burned 420 calories on Tuesday