Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 180° counterclockwise.

U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(4, 0), W′(1, 4)
U′(−1, 1), V′(4, 0), W′(1, −4)
U′(−1, 1), V′(0, −4), W′(−4, −1)

Answer:

Step-by-step explanation:

You want to identify a pair of supplementary angles, and a pair of vertical angles in the given figure.

Two angles are supplementary if they total 180°. This will be the case for any linear pair of angles. A linear pair of angles combines to form a straight line.

Supplementary angle pairs in the figure are ...

  (1, 2), (1, 3), (2, 4), (3, 4), (5, 6), (5, 7), (6, 8), (7, 8)

Two angles are vertical angles if they are formed by two intersecting lines and if their shared vertex is the point where the lines cross. The angles do not share a side, but have sides formed from opposite rays.

A pair of crossing lines forms two sets of vertical angles.

Vertical angle pairs in the figure are ...

  (1, 4), (2, 3), (5, 8), (6, 7)

Your answer will be a pair of angles from the first list, and a pair of angles from the second list. The highlighted pairs are the ones we list at the top of the answer.

__

Additional comment

Angles may be supplementary in a variety of other contexts. Adjacent angles in a parallelogram are supplementary, as are opposite angles in a quadrilateral inscribed in a circle. When parallel lines are crossed by a transversal, consecutive interior angles are supplementary, as are consecutive exterior angles. (There are no parallel lines in the given figure for this problem.)

Answer:

3r + 2b = 600 ---(1)

r + b = 225 ---(2)

We can solve this system of equations using substitution or elimination method.

Using substitution method, we can solve equation (2) for "r" in terms of "b":

r = 225 - b

Substituting this expression for "r" into equation (1), we get:

3(225 - b) + 2b = 600

Simplifying and solving for "b", we get:

675 - 3b + 2b = 600

-b = -75

b = $75

Therefore, the cost of one bag is $75.

Step-by-step explanation:

use brain

The solutions of the equation in the interval [0, 27) are: θ = π/3, 2π/3.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operators.

Starting with the given equation:

3cot²θ - 1 = 0

Add 1 to both sides:

3cot²θ = 1

Divide both sides by 3:

cot²θ = 1/3

Taking the square root of both sides:

cotθ = ± √(1/3)

Since cotθ = cosθ/sinθ, we can write:

cosθ/sinθ = ± √(1/3)

Multiplying both sides by sinθ:

cosθ = ± √(1/3)sinθ

Squaring both sides:

cos²θ = (1/3)sin²θ

Using the identity sin²θ + cos²θ = 1, we get:

sin²θ + (1/3)sin²θ = 1

Simplifying:

(4/3)sin²θ = 1

Dividing by 4/3:

sin²θ = 3/4

Taking the square root of both sides:

sinθ = ± √(3)/2

We know that θ is in the interval [0, 27). Therefore, the possible solutions are:

θ = π/3 or θ = 2π/3

However, we need to check if these solutions are in the given interval.

For θ = π/3, we have:

0 ≤ π/3 < 27

Therefore, π/3 is a valid solution.

For θ = 2π/3, we have:

0 ≤ 2π/3 < 27

Therefore, 2π/3 is also a valid solution.

Thus, the solutions of the equation in the interval [0, 27) are:

θ = π/3, 2π/3

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for the first table to find the equation of its line you need to find the gradient(m). to do that you take 2 points then subtract the first y from the second y. so 12-9=3 then do the same with the x so 5-2=3 then divide the first by the second and 3÷3=1 so the gradient(m) is 1. so the equation is in the form y=mx+c and since we know m is 1 the equation will be y=x+c. to find c we take a point on the line and replace the numbers so 9=2+c must be true and for it to be true c must be 7. so the equation of the line is y=x+7. also pls mark as brainliest answer

Result:

Mickey and Minnie Mouse will need to put $680.75 into their escrow account each month to cover the property taxes, homeowner's insurance, and flood insurance costs.

An escrow account is like a savings account that is managed by a mortgage servicer. The portion deposited into an escrow account usually covers estimated property taxes and your homeowners and mortgage insurance premiums.

To calculate the monthly amount Mickey and Minnie Mouse need to put into their escrow account for property taxes, homeowner's insurance, and flood insurance, we will first add up the total annual costs for these expenses:

Property taxes: $5,467

Homeowner's insurance: $1,440

Flood insurance: $1,262

Total annual costs = $5,467 + $1,440 + $1,262 = $8,169

Next, we divide the total annual costs by 12 to get the monthly escrow amount:

$8,169 / 12 = $680.75

Therefore, $680.75 is the amount they will need to put into their escrow account each month.

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Answer: 5 hours

Step-by-step explanation:

Since y = money, plug in 28 for y

28= 10x-22

Add 22 over to the 28 to get 50= 10x

Divide 50 by 10 to find x to be 5 which the hours

Answer: infinite

Step-by-step explanation:

infinite

you get 5=5 so ther is not x in the answer and they are equal so for any value you put in x you get a valid answer

Answer:

Only 1

Which X is 0

also can say as infinite

Step-by-step explanation:

Answer & Step-by-step explanation:

In hypothesis testing, the claim being made is called the alternative hypothesis. The null hypothesis is the opposing statement, and it is presumed to be true until sufficient evidence suggests otherwise. The wording of the claim must be specific and precise, and one must clearly state the population, the parameter of interest, and the direction of the hypothesis test (i.e., one-tailed or two-tailed).

For example, a well-worded alternative hypothesis might be "The new teaching method will result in a higher mean test score for students than the traditional teaching method." In this case, the null hypothesis would be "The new teaching method will not result in a higher mean test score for students than the traditional teaching method."

An incorrectly worded claim might be "The new teaching method is better than the traditional teaching method." This claim is too vague because it does not specify in what way the new method is better, nor does it give a direction for the hypothesis test.

In summary, when conducting a hypothesis test to support a claim regarding the mean test score under a new teaching method, the wording of the claim must be specific and precise, and the claim will become the alternative hypothesis.

Answer:

f(x)will be explained above

The value of a and b in the figure are 5 and 5√3.

We have,

From the figure,

Sin 30 = a/10

Cos 30 = b/10

Now,

Sin 30 = 1/2

Cos 30 = √3/2

Now,

1/2 = a/10

a = 5

√3/2 = b/10

b = 5√3

Thus,

The value of a and b are 5 and 5√3.

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Answer:

x = 28°

Step-by-step explanation:

Angle sum property of triangle:

             Sum of all the three angles of the triangle is 180°.

   50 + 2x + 3x - 10 = 180°

    2x + 3x + 50 - 10 = 180°

Combine like terms,

                   5x + 40 = 180°

Subtract 40 from both sides,

                           5x = 180 - 40

                           5x = 140°

Divide both sides by 5,

                             x = 140 ÷ 5

                            [tex]\sf \boxed{\bf x = 28^\circ}[/tex]

The probability that an intern had a Computer Science Major and did not get hired is 36.2%. The probability that an intern had a major other than Computer Science is 51.2%. The probability that a Computer Science Major was hired is 48.6%. The probability that an intern with a major other than Computer Science was not hired is 68.3%. So, the column A 1,2,3 and 4 matches to c, b, a and d of column B.

Conditional - 48.6% This probability represents the chance that an intern with a Computer Science Major was hired, and is calculated as the number of CS majors hired (58) divided by the total number of CS majors (160). so, 3 matches a.

Joint - 51.2% This probability represents the chance that an intern with a major other than Computer Science was not hired, and is calculated as the number of non-CS majors not hired (36) divided by the total number of non-CS majors (74). so, 2 matches b.

Conditional - 36.2% This probability represents the chance that an intern had a Computer Science Major and did not get hired, and is calculated as the number of CS majors not hired (102) divided by the total number of applicants not hired (138). so, 1 matches c.

Marginal - 68.3% This probability represents the total proportion of interns who were not hired, and is calculated as the total number of interns not hired (138) divided by the total number of applicants (234). so, 4 matches d.

Joint - 43.6% This probability represents the chance that an intern had a Computer Science Major and did not get hired, and is calculated as the number of CS majors not hired (102) divided by the total number of applicants (234).

Marginal - 31.6% This probability represents the total proportion of interns who were hired, and is calculated as the total number of interns hired (96) divided by the total number of applicants (234).

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The power series representation for function f(x) is; ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1), and the radius of convergence is infinite, R = ∞.

To find a power series representation for the function f(x) = x⁶×arctan(x³), we can use the power series representation for arctan(x);

arctan(x) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(2n+1)}[/tex] / (2n+1)

Substituting x³ for x in this series, we have;

arctan(x³) = ∑ [tex](-1)^{n}[/tex] × (x³[tex])^{(2n+1)}[/tex] / (2n+1)

= ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+3)}[/tex] / (2n+1)

Multiplying this series by x⁶, we get;

x⁶ × arctan(x³) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1)

So the power series representation for f(x) is;

f(x) = x⁶ × arctan(x³) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1)

To find radius of convergence R, we use the ratio test:

lim |[tex](-1)^{n}[/tex] × [tex]X^{(6(n+1)+9)}[/tex] / (2(n+1)+1) × (2n+1) / [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex]|

n->∞

= lim |x⁶ / (2n+3)|

n->∞

As n approaches infinity, the denominator of the fraction approaches infinity, so the limit is zero for all values of x. Therefore, the power series converges for all values of x, and the radius of convergence is infinite, R = ∞.

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The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.

We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.

Let's consider the three different locations as follows:

Attach the chain to a corner of the shed.

Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:

Area = (1/4) x π x (15 meters)²

Area = 176.71 square meters (approx)

Affix the chain to the middle of one of the shed's longer sides.

This semicircle's area is:

Area = (1/2) x π x (15 meters)²

Area = 353. 57 square meters (approx)

To the center of one of the shed's shorter sides, fasten the chain.

This circular sector's area will be as follows:

Area = (90/360) x π x (15 meters)²

Area = 176.71 square meters (approx)

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Answer: 12

Step-by-step explanation:

1. You multiply 2 x 10 = 20

2. Divide 20 / 4 = 5

3. Add 8 and 5 = 13

4. Subtract 13 - 1 = 12

Answer:

9^2 + 12^2 = c^2

81 + 144 = c^2

√15 = √c^2

c = 15

Step-by-step explanation:

The equation is solved to give 2x² -x - 22

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are;

From the information given, we have that the functions are;

g(x) = 2x² + 3x +10

k(x) = 2x +16

To determine the equation g(x) = 2k(x), we need to substitute the value into the equation, we have;

2x² + 3x + 10 = 2(2x + 16)

expand the bracket, we have;

2x² + 3x + 10 = 4x + 32

collect the like terms, we have;

2x² - x = 32 - 10

subtract the values

2x² -x = 22

2x² -x - 22

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Answer:  The cost of the scarf sweater 4 4 4 4

Step-by-step explanation:

Cost of a sweater = 4 * Cost of a scarf = 4 * $7 = $28

In this way, a sweater costs $28.

The right bar model that addresses the issue is:

Scarf 7

Sweater 4 4 4 4

The solution is,  the dimensions that could be used at a minimum cost is 17.32 ft of pine boards by 69.28 ft of galvanized steel.

SOLUTION

From the question, let the

Length of pine boards be represented as x and

Let the length of galvanized steel fencing be represented as y.

The diagram of Lucy Dog Daycare can be represented as follows

So, the Total cost C should include cost of two pine boards 2x and cost of one galvanized steel y.

So we have

C = 12x + 3y

Also the total area is 1,200 square.

That is

xy = 1200

or, y = 1200/x

Now substituting the value of y into the cost equation, we have

C = 12 x + 3600/x

Taking the derivative, we have

C = 12 - 3600/ x^2

At minimum or maximum cost, the derivative should be equal to zero,

So, C = 12 - 3600/ x^2 = 0

or, x^2 = 3600/ 12

or, x^2= 300

or, x = 17.32

Hence x = 17.32 ft

From the equation above, where y was made the subject, we have

y = 1200/ 17.32

Hence y = 69.28 ft

Hence the dimensions that could be used at a minimum cost is 17.32 ft of pine boards by 69.28 ft of galvanized steel

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The polar form of the complex number  -2√3 - 6i is r , θ = (2√24 , 60°)

The polar form of a complex number is given by  r = x + iy is r , θ where r = √(x² + y²) and θ = tan⁻¹y/x

So, to find the polar form of the complex number, -2√3 - 6i we proceed as follows. -2√3 - 6i

Since r = x + iy where

So, substituting the values of the variables into the equation, we have that the magnitude r = √(x² + y²)

= √((-2√3)² + ( -6)²)

= √(4 × 3 + 36)

= √(12 + 36)

= √48

= √(24 × 4)

= 2√24

The angle θ = tan⁻¹y/x where

So, substituting the values of the variables into the equation, we have that

θ = tan⁻¹y/x

= tan⁻¹(-6/-2√3)

= tan⁻¹(3/√3 × √3/√3)

= tan⁻¹(3√3/(√3 × √3)]

= tan⁻¹(3√3/3]

= tan⁻¹√3

= 60°

So, the polar form is r , θ = (2√24 , 60°)

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The value of Marina's height is, 100 centimeters

Given that;

The relationship between the heights can be represented by the equation,

⇒ 2x − 15 = 185

Where, Martha's height is x

Now, We can simplify as;

⇒ 2x − 15 = 185

Add 15 both side we get;

⇒ 2x = 185 + 15

⇒ 2x = 200

⇒ x = 100

Thus, The value of Marina's height is, 100 centimeters

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Answer:

so the reding of it all

Step-by-step explanation:

1: Wrong

2: Wrong

3: Wrong

4: CORRECT equal to 1369

The solutions to the radical expression √3x-5= x-8 are x = 1.146 and x = 7.854

From the question, we have the following parameters that can be used in our computation:

√3x-5= x-8

Add 5 to both sides

So, we have

√3x= x - 3

Square both sides

So, we have

3x = x² - 6x + 9

So, we have

x² - 9x + 9 = 0

When solved, we have

x = 1.146 and x = 7.854

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The sketch of the linear equation y = 2x - 2 and the curve y = x² - 2x + 1 as required is as attached and the points of intersection are; (1, 0) and (3, 4).

It follows from the task content that the graph of the line and the curve are required to be determined.

The graph is as attached.

By Observation of the graph; the points of intersection of the two graphs as required are; (1, 0) and (3, 4).

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Answer:

11

Step-by-step explanation:

7x + 33 = 10x

3x = 33

x = 11

Answer:

Step-by-step explanation:

Answer: 4/9. Based on the given conditions, formulate:: 2/3 * 3/7 / 9/14 Divide a fraction by multiplying its rec.