Given j || k and m∠8=150° What is m∠3?

Enter your answer in the box.

m∠3= ___°

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

The first one is False.

Step-by-step explanation:

If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

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

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

Answer:

38.32

Step-by-step explanation:

8% × 479

8/100 × 479

0.08 × 479

38.32

The slope of restaurant B is twice that of restaurant A

The tables of values are given as

           X(Bill)     Y(Tip)                          X(Bill)        Y(Tip)

Rest A     10           1                  Rest B      25            5    

Rest A     20          2                 Rest B      50            10

Rest A     30          3                 Rest B      75             15

The slopes are calculated using

Slope = (y2 - y1)/(x2 - x1)

Using the table of values, we have:

Rest A = (2 - 1)/(20 - 10)

Rest A = 0.1

Rest B = (10 - 5)/(50 - 25)

Rest B = 0.2

By comparing the slopes, we have:

Rest B = 2 * Rest A

This implies that the slope of restaurant B is twice that of restaurant A

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Answer:

1 + cosx   -    1 - cosx    

1-cosx            1+cosx

Multiplying by conjugate

1 + cosx * 1+cosx  -    1 - cosx * 1-cosx  

1-cosx       1+cosx        1+cosx     1 -cosx

(1+cosx)²   - (1-cosx)²

1- cos²x          1- cos²x

1 + 2cosx + cos²x -(1 - 2cosx + cos²x)

                1-cos²x

4cosx    =    4 cosx . 1          4 cotx cosecx

sin²x                sinx   sinx

Step-by-step explanation:

A single outlier does not affect the values of the quartiles.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier does not affect the values of the upper and lower quartiles. This is an advantage of the upper and lower quartiles over range.

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The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

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Answer:

\(\left \{ {{-6x-6y=12} \atop {x+6y=-32}} \right.\)

Step-by-step explanation:

note, that (-2)*(3x+3y)=(-2)*(-6) is 6x-6y=12.

Then the system

\(\left \{ {-6x-6y=12} \atop {x+6y=-32}} \right.\)

has the same roots as the system provided above.

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

Step-by-step explanation:

maybe 3.) esteem needs

....

Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.

The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:

Var(x) = (b-a)^2 / 12

For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:

Var(x) = (44 - 40)^2 / 12 = 1.155

Therefore, the variance of 'x' is approximately 1.155

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Answer:

95% = Within two standard deviations from the mean

99.7% = Within three standard deviations from the mean

68% = Within one standard deviation from the mean

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks" to help me out!

Answer:

16.4

Step-by-step explanation:

For the 66° angle, the side with length 15 is the opposite leg.

The hypotenuse is x.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

sin A = opp/hyp

sin 66° = 15/x

x * sin 66° = 15

x = 15/sin 66°

x = 16.4

The value of x and y is 5 , 7

An expression consists of variables , constants and mathematical operators , when equated by any other algebraic expression or a constant it becomes an equation.

The equation given in the question is

(x + 1)/2  -(y+4)/11 = 2

(x+3) /2 + (2y+3)/17 = 5

It has to be solved for x and y ,

The simplification of the equation has to be done

and the equation is

11x-2y = 41  -----------1

and

17x +4y = 113    -------------------2

to find the solution elimination method will be followed as

Multiplying equation 1 by 2 and adding the both equations

39x = 195

x = 5

Substituting this value in equation 1

55 -2y = 41

y = 7

The value of x and y is 5 , 7

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Answer:

-2x -8

Step-by-step explanation:

Answer:

42/5% as a decimal is 8.4

Answer:

10.9

Step-by-step explanation:

Pythagoras theorem- a² + b² = c²

Since this is a right angle with each side on the right angle's length given you can use pythagoras theorem.

7² + 8.44² = c²

= 49 + 70.56 = c²

= 119.56 = c²

∴ c = √119.56

= 10.9

Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

9514 1404 393

Answer:

  19,463 cm²

Step-by-step explanation:

The area is given by the formula ...

  A = (1/2)ij·sin(K)

Filling in the values, we find the area to be ...

  A = (1/2)(270 cm)(170 cm)·sin(122°) ≈ 19,463 cm²

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

x=−2

Step-by-step explanation:

like so:

2x+4y=−4

...subract 2x from both sides:

4y=−2x−4

...divide both sides by 4:

y=(−x2)−1

Now, the y intercept is the value of y where x = 0 -

y=0−1=−1

For the x intercept, set y = 0 and solve for x:

0=(−x2)−1

x2=−1

x=−2

so now you have your x & y intercepts. On your graph, plot points (-2, 0) and (0,-1)

And draw your line extending through these points.

graph{y = (-x/2)-1 [-10, 10, -5, 5]}

To find the x-intercept, we plug a 0 in for y.

So we have 2x + 4(0) = -4 or 2x = -4 which simplifies to x = -2.

To find the y-intercept, we plug a 0 in for x.

So we have 2(0) + 4y = -4 or 4y = -4 which simplifies to y = -1.

So this line crosses x-axis at (-2,0) and the y-axis at (0,-1).

The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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Answer:

90

Step-by-step explanation:

3/1=3

30x3=90

Answer:

30

Step-by-step explanation:

First, you need to find the original number whose 36% is 180.

To do so, you can use the generic equation below:

\(\frac{resultant}{orignalnumber} =\frac{percent}{100percent}\)

Now plug in the variables

resultant = 180 because the resulting number of the % is 180

percent = 36% because 180 is 36% of number

original number = represented by x

\(\frac{180}{x} =\frac{36}{100}\)

36 * x = 180 * 100

36x = 18000

x = 18000/36 = 500

Next, find 6% of the original number, 500

To do that, simply plug in the numbers into the generic equation used above:

resultant = represented by x

percent = 6%

original number = 500

\(\frac{x}{500} =\frac{6}{100}\)

100 * x = 6 * 500

100x = 3000

x = 3000/100 = 30

Answer:

30

Step-by-step explanation:

i think

The equation for the first option would be

Where "x" is the number of copies and y the cost.

The second equation will be

If we graph both equations we have

As we can see, they will be equal in terms of cost with 2 copies. The cost will be 50.

We can see it at the intersection of the two graphs! we can also do it with algebra, if the costs are equal (same "y") we can say

The number of copies is 2.

Answer:

\(x = 51\)

Step-by-step explanation:

\(the \: sum \: of \: the \: exterio \: angles\: a \\ \: polygon \: is \: 360. \\ \\ 64 + 60 + 69 + 42 + x + (x + 23) = 360 \\ 335 + 2x + 23 = 360 \\ x = \frac{360 - 258}{2} = 51\)