If f (x = x-2) any y (x) = -2 x +7 what value makes f (x) =y (x) ?

After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.

You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.

Let's write the coordinates of the original figure,

A = (1, -5)

B = (6, -2)

C = (6, -5)

D = (1, -8)

Now, if we rotate it 90 degrees counterclockwise, the coordinates are:

A' = ( 5, 1)

B' = (2, 6)

C' = (5, 6)

D' = (8, 1)

Now if we rotate it again 90 degrees counterclockwise, the coordinates are:

A'' = ( -1, 5)

B'' = (-6, 2)

C'' = (-6, 5)

D'' = (-1, 8)

Now from the figure, let's write the coordinates.

A' = ( -1, 5)

B' =  (-6, 2)

C' = (-6, 5)

D' =  (-1, 8)

This is the same as the coordinates of the second 90 degrees counterclockwise rotation.

Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.

Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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To find out how many stamps Sierra and her brother each collected, we need to set up an equation and solve for the unknown variable.

Let's use "x" to represent the number of stamps that Sierra's brother collected.
According to the question, Sierra collected 3 times as many stamps as her brother. So, we can represent Sierra's number of stamps as 3x.
The total number of stamps that they collected together is 144, so we can set up the following equation:
x + 3x = 144
Now we need to solve for "x" to find out how many stamps Sierra's brother collected.
First, we'll combine like terms on the left side of the equation:
4x = 144
Next, we'll divide both sides of the equation by 4 to isolate the variable:
x = 36
So, Sierra's brother collected 36 stamps.

To find out how many stamps Sierra collected, we can plug this value back into the equation for Sierra's number of stamps:
3x = 3(36) = 108
So, Sierra collected 108 stamps.

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A. The amount of aspirin in the dose is 22.066 milligrams.

B. ƒ (60) = 7.483 milligrams
This means that 60 hours after ingesting a dose of 22.066 milligrams of aspirin, the amount of aspirin in the person's blood will be 7.483 milligrams.

C. The aspirin level will be less than 10 milligrams after approximately 45.06 hours.

a. The initial amount of aspirin in the dose can be found by evaluating f(0):

f(0) = 300 * (1/2)^(1/30) ≈ 22.066

Therefore, there are approximately 22.066 milligrams of aspirin in the dose.

b. We can find f(60) by substituting t = 60 into the equation:

f(60) = 300 * (1/2)^(1/30 * 60) ≈ 7.483

Therefore, there are approximately 7.483 milligrams of aspirin in the person's blood 60 hours after ingesting the dose. This is significantly less than the initial amount of 22.066 milligrams, indicating that the aspirin is being metabolized and eliminated from the body over time.

c. We want to solve for t when f(t) < 10:

300 * (1/2)^(1/30t) < 10

Dividing both sides by 300:

(1/2)^(1/30t) < 1/30

Taking the natural logarithm of both sides:

ln[(1/2)^(1/30t)] < ln(1/30)

Using the properties of logarithms:

(1/30t)ln(1/2) < ln(1/30)

Simplifying:

-0.6931t < ln(1/30)

Dividing both sides by -0.6931 (which is ln(1/2)):

t > ln(1/30) / (-0.6931)

t > 45.06

Therefore, the aspirin level will be less than 10 milligrams after approximately 45.06 hours.

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The solutions in radian units are:
Ω = 0.928, 2.213, 4.070, 5.355
The solutions should be entered as a comma-separated list:
Ω = 0.928, 2.213, 4.070, 5.355

The equation cos(Ω) = -cos(2Ω) can be solved by using the double angle formula for cosine. The double angle formula for cosine is cos(2Ω) = 1 - 2sin^2(Ω).

Substituting the double angle formula into the original equation gives:
cos(Ω) = - (1 - 2sin^2(Ω))

Rearranging the equation gives:
2sin^2(Ω) = 1 + cos(Ω)

Squaring both sides of the equation gives:
4sin^4(Ω) - 4sin^2(Ω) - cos^2(Ω) = 0

Using the identity cos^2(Ω) = 1 - sin^2(Ω) gives:
4sin^4(Ω) - 4sin^2(Ω) - (1 - sin^2(Ω)) = 0

Simplifying the equation gives:
4sin^4(Ω) - 3sin^2(Ω) - 1 = 0

Using the quadratic formula gives:
sin^2(Ω) = (3 ± √(9 + 16))/8

Solving for sin(Ω) gives:
sin(Ω) = ±√(7/8)

Taking the inverse sine of both sides gives:
Ω = sin^-1(±√(7/8))

The solutions in radian units are:
Ω = 0.928, 2.213, 4.070, 5.355

The solutions should be entered as a comma-separated list:
Ω = 0.928, 2.213, 4.070, 5.355

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To create a Pandas crosstab to compare the number of players in each position by foot, we first need to import the pandas library and then use the `pd.crosstab()` function with the appropriate parameters.

We can set `normalize='all'` to view the data as a percent of the total and `margins=True` to include row and column totals. Here's how we can do it:

```python
import pandas as pd

# Create a crosstab with the desired parameters
crosstab = pd.crosstab(df['Position'], df['Foot'], normalize='all', margins=True)

# Print the crosstab
print(crosstab)
```

To find the combination of footedness and position that is the rarest in our data, we can use the `idxmin()` function to find the index of the minimum value in the crosstab. Here's how we can do it:

```python
# Find the index of the minimum value in the crosstab
min_index = crosstab.idxmin()

# Print the combination of footedness and position that is rare
print('The most rare combination of footedness and position is', min_index)
```

The output of this code will show the combination of footedness and position that is the rarest in our data.

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The average percentage change in population from 2000-20009 is 1.36%.

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

a) Average percentage change

= Sum of percentage change in each year/number of years

= (1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93) / 9

= 1.36%

Therefore the average percentage change in population from 2000-20009 is 1.36%.

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Answer:

232.5 units²

Step-by-step explanation:

After evaluating using the correct order of operations, the result will become 22/9.

The correct order of operations is to perform any calculations inside parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. This order of operations is known as PEMDAS. Using this order, we can evaluate the expression as follows:

(17)/(18) + (6)/(35) ÷ (5)/(7) x (25)/(4)

Divide 6/35 by 5/7 by multiplying 6/35 by the reciprocal of 5/7.
= (17/18) + (6/35) x (7/5) x (25/4)
= (17/18) + (6/25) x (25/4)

Multiply 6/25 by 25/4.
= (17/18) + (6/4)

Finally, add 17/18 and 6/4 together.
= 22/9

Therefore, the final answer is 22/9,

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The values of the variables in the kite are:

x = 50°

y = 58°

z = 32°

Since a kite is symmetrical. Thus, it has two opposite and equal angles

Also, the line of symmetry divides the kite angle into equal angles and similar triangles. We have:

In ΔABO:

x + 90° + 40° = 180° (angle sum in a triangle)

x + 130 = 180

x = 180 - 130

x = 50°

In ΔBCO:

y + 90° + 32° = 180° (angle sum in a triangle)

y = 180 - 122

y = 58°

In ΔCDO:

z = 32°  (congruent triangles)

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Answer: A

Step-by-step explanation:

You can prove it by Pythagorean's Theorem, a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

It has to be a right triangle.

Cylinder B is taller which is 3.45 inches more than cylinder A.    

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases that are connected by a curved surface.

The formula for the volume of a cylinder is given by  

Where V is the volume of the cylinder, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

Here we have

Two cylinders have the same volume of 845π cubic inches.  

The radius of Cylinder A is 13 inches

Let 'h₁' be the height of th cylinder

By using the formula, V = π r² h₁

Volume of the cylinder A = π (13)² h₁ = 169πh₁

From the data, 169πh₁ = 845π

=> 169h₁ = 845

=> h₁ = 845/169

=> h₁ =  5  

The radius of Cylinder B is 10 inches.

Let h₂ be the height

Volume of the Cylinder B = π (10)² h₂ = 100πh₂  

From the data, 100πh₂ = 845π  

=> 100h₂ = 845

=> h₂ = 8.45

The difference between the heights of the two cylinders

= 8.45 inch - 5 inch = 3.45 inch  

Therefore,

Cylinder B is taller which is 3.45 inches more than cylinder A.  

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Using point-slope form, the coordinate of D(2, X) is 2 units away from point X(1, 1).

To find the coordinates of point D, we need to know the location of point X on the line YZ. We can use the slope-intercept form of the equation of a line to find the equation of the line passing through points Y and Z:

slope m = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 2) = -2

Using the point-slope form of the equation of a line with point Y(2, 2) and slope m = -2:

y - y1 = m(x - x1)

y - 2 = -2(x - 2)

y - 2 = -2x + 4

y = -2x + 6

Now we can substitute x = 2 into the equation of the line to find the y-coordinate of point D:

y = -2x + 6

y = -2(2) + 6

y = 2

Therefore, the coordinates of point D are (2, 2).

So, D(2, 2) is the point that lies on line YZ and is 2 units away from point X(1, 1).

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The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.

a) What is the sample? (5 points)

The sample is the set of A students sitting in the front row who stated their latest test scores.

b) What is the population? (5 points)

The population is the entire class of 105 students who took the test.

c) What is the variable of interest? (5 points)

The variable of interest is the mean test score of the students.

d) Do you think that the sample is representative of the population? Can you generalize the result that you get from the sample to the population? Why? Why not? Discuss (5 points).

The sample may or may not be representative of the population. It is difficult to say for certain without knowing the overall distribution of test scores for the population. If the sample is randomly selected and the distribution of the sample is similar to the distribution of the population, then the results from the sample can be generalized to the population. However, if the sample is not randomly selected, then the results may not be reliable for generalization to the population.

e) Suppose that the sample mean is 82.4 and assume that the test scores are normally with a population variance of 38.2. Construct a 90% confidence interval on the mean test score of the students i. Write the appropriate formula. (5 points)

The appropriate formula for a 90% confidence interval is:
Mean ± (1.645 * (Standard Error of the Mean))

ii. Find the necessary table value. (5 points)

The necessary table value is 1.645, which is the critical value associated with a 90% confidence interval.

iii. Substitute the quantities into your formula. (5 points)

Mean ± (1.645 * (Standard Error of the Mean))

82.4 ± (1.645 * (Standard Error of the Mean))

iv. Calculate the confidence interval. (10 points)

Standard Error of the Mean = (Population Variance/Sample Size)0.5

Standard Error of the Mean = (38.2/105)0.5

Standard Error of the Mean = 0.8244


Confidence Interval = 82.4 ± (1.645 * 0.8244)

Confidence Interval = 82.4 ± 1.34

Confidence Interval = (81.06, 83.74)

v. Interpret your interval. (5 points)

The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.

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The areas of section 1, 2 and 3 are  8 inches square, 80 inches square and 8 inches square respectively.

The area of the trapezium is 96 inches square.

Section 1 and 2 are right triangles.

Area of a right triangle = 1/2 x base x height

Height = 8cm

Base = (14 - 10) / 2 = 2cm

Area of a right triangle = 1/2 x 2 x 8 = 8cm²

Section 3 is a rectangle.

Area of a rectangle = length x width

8 x 10 = 80 cm²

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

= 1/2 x (10 + 14) x 8

1/2 x 24 x 8 = 96cm²

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Answer:

709

Step-by-step explanation:

473 + 236 = 709

The inverse of the statement is if two angles are vertical, then they are congruent

The statement from the question is:

if two angles are not vertical, then they are not congruent

Given a statement

If a then b

The inverse of the statement is

If not a then not b

To write the inverse statement using the above rule, we have the following statement

The inverse of the given statement is if two angles are vertical, then they are congruent

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Answer:

Let x = the price of one shirt

Since he bought 3 shirts, he will pay three times the amount. Also, there is a discount. With the discount, the total cost is $63.

We can set up an equation to represent this scenario. Assuming we have a 30% discount as David said

3(x - 0.3x) = 63

Just so you understand, (x - 0.30x) is the sales price for one shirt. We apply this discount price 3 times because the discount is added for each shirt.

Solve for x from this equation to get the price for one shirt.

3(0.70x) = 63

2.1x = 63

x = 30

Step-by-step explanation:

Refer to pic...............

It takes approximately0.082 seconds for the eraser to hit the student in the head.

The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.

First, we will set h(t) equal to 3 and rearrange the equation:

-16t^(2)+35t+6=3

Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0

Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))

Simplifying further, we get:
t= (-35±√(1417))/(-32)

Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27

Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.

Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.

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Answer:

See below.

Step-by-step explanation:

I'm sure the question is asking to solve for ∠BDC, but we'll solve for all of the angles.

We should note that we have a Given Exterior Angle.

An Exterior Angle is an angle that is formed by extended lines.

An exterior angle is equal to the combined sum of the two nonadjacent, and interior angles.

Using what we learned, ∠BCD and ∠CDB will equal ∠DBE°.

Let's turn this problem into an equation.

60° + ∠BDC = 120°
Subtract 60 from both sides.

∠BDC = 60°.

We can also identify that ∠CBD is a linear pair with ∠DBE.

A Linear Pair is 2 adjacent angles that add up to 180°. Linear Pairs are straight lines with one line intersecting in between.

Meaning that ∠CBD + ∠DBE = 180°.

∠CBD + 120° = 180°.

∠CBD = 60°.

We can identify that this triangle is an Equilateral Triangle. An Equilateral  Triangles is a triangle that has all congruent sides and angles.

Our final answers are;

∠BDC = 60°.

∠CBD = 60°.

Check the picture below.

we have three sides, let's look at the two smaller sides first, 1.9 and 2.7.

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 2.7 - 1.9 = 0.8.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 0.8.

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 1.9 + 2.7 = 4.6.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 4.6, it can't be 4.6.

So no dice.

The argument for the dilation is that: No, in order for one figure to be dilated of another, both coordinates of all points must be multiplied by the same constant

The complete question is added as an attachment

From the attached table of values, we can see that:

The coordinates of x are multiplied by 3, while the coordinates of y are multiplied by 6

This means that

The figure is not properly dilated, because these coordinates must be multiplied by the same constant value

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The value of x in the given figure of parallel lines is x = 0.89.

When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".

From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.

Thus, the two angles form a straight line.

The angle of a straight line is 180 degrees.

Thus,

x + 94 + 95x = 180

96x + 94 = 180

x = 0.89

Hence, the value of x in the given figure of parallel lines is x = 0.89.

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The correct answer is (i) and (ii). Both of the sets are subspaces of R3 because they satisfy the three criteria of a subspace. The first set, {(x,y,z)| z = (x+y)2}, is a set of all triplets (x,y,z) such that z = (x+y)2. The second set, {(x,y,z)| x=10z}, is a set of all triplets (x,y,z) such that x = 10z. Neither of the other choices are correct.

Formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.

Let 4,8,12,20,24 be the sequence's first five terms.

Let me define the terms explicit formula and recursive formula.

The generic formula to find any term in a series is known as the explicit formula.

Also, if we know the (n-1)th term of the series, we can use the recursive formula to find the nth term.

Thus, the sequence's explicit formula is,

Y equals 4 n, where n is any positive integer.

And this is the recursive formula.

Y = 4 (n-1), and we can find the nth term by using the (n-1)th term.

Initial term = 4 = 4 1

Term two = 8 = 4 2

Term three =12=43

Fourteenth term = 16 = 4 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

The universal and recursive formula is obtained by applying the straightforward technique of examining the first, second, and direction of the next term.

You stated that you did not desire a simpler sequence.

Think about the sequence's first five terms: 0, 3,8, 15, and 24.

Well stated formula =n2 + 2 n

Recursive equation: (n-1)

²+2(n-1)

If you examine the sequence, neither geometry nor arithmetic applies.

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

In the explicit formula, n is a whole number and n²+2n.

Therefore, the formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.

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Answer:

Thanks :)

Step-by-step explanation:

solution

1531-1400=113

decrease/original ×100

113/1513×100

7.46

round off to 7.5