ZA and B are complementary angles. If mA = (6x + 22)° and m
ZB = (7x + 16)°, then find the measure of ZB.

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

It is the diameter of the circle

it is 7 cm

it is a chord

Explanation:

First, we notice that the line segment CB passes through the centre of the circle and its endpoints touch the circumference - this tells us that CB is the diameter.

Furthermore, any line segment whose endpoints lie on the circumference of the circle is a chord (meaning that the diameter is the longest chord), and so we deduce that CB is also a chord.

Since CB is the diamter, its length is 2 times the radius. The raduis of the circle we know is DA = 3.5 cm; therefore, the dimater is CB = 2 DA = 2 * 3.5 = 7 cm.

Hence, the correct choices are:

It is the diameter of the circle

it is 7 cm

it is a chord

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

An equation of the line in fully simplified slope-intercept form is y = -13x - 22.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data points (-2, 4), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (10 - (-3))/(-3 - (-2))(x - (-2))

y - 4 = -13(x + 2)

y = -13x - 26 + 4

y = -13x - 22

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Answer:

\(41\frac{2}{3}\)  

I hope this helps!

Answer:

41.66 repeating or 41.67

Step-by-step explanation: hope this helps

According to the identity property, the product of 3k x 1 = 3k.

Identity property:

The identity property of multiplication defined that that we multiply 1 by any number, the product is the number itself.

The standard form of the identity property is written as.

a x 1 = 1 x a = a

Where the value of a must be greater than zero.

If the value of a is zero then the resulting value is 0.

Given,

Here we need to find the product of 3k x 1.

The general form of the identity property is written as,

=> a x 1 = a

So, if we multiply anything with 1, then it will gives the same.

So, the product of

=>3k x 1 = 3k.

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The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

Step-by-step explanation:

The regular selling price of the jewelry is $253.00. The sale price for the jewelry is $189.75. And the rate of markdown is 25%.

A jewellery store paid a unit price of $250 less 40%, 16 1/3 %, for a shipment of designer watches . The store's overhead is 65% of cost and the normal profit is 55% of cost.

Overhead and Profit means those costs incurred by you and paid to a General Contractor to perform and oversee covered repairs to the insured location. “Overhead and Profit” does not apply to independent or specialty contractors including, but not limited to, roofers, plumbers, electricians and painters.

It is given that the unit price of the watch is $250 and the discount rates are 40%, 16 +2/3 or 16.666666667%, and 8%. Therefore the purchase price of watches per unit can be estimated as:

Purchase price of watches per unit = Unit price*(1- first discount %)(1-second discount %)(1-third discount %)

Purchase price of watches per unit = 250*(1-40%)(1-16.66666667%)(1-8%)

Purchase price of watches per unit =115

Now, the overhead expense is 65% of the cost. So the overhead amount is Overhead amount = 65% of the cost

Overhead amount = 115*65%

Overhead amount = 74.75

Now, the profit is 55% of the cost. So

Profit amount = Cost *profit %

Profit amount =115*55%

Profit amount =63.25

a. Thus, the regular selling price can be estimated as:

Regular selling price = Unit purchase cost + overhead + profit

Regular selling price =115+74.75+63.25

Regular selling price =253.00

Therefore, the regular selling price of the watches would be $253.00

b. The sale price to break even would be equal to the cost of the watch plus overhead. It is the amount that is required to cover only the total cost of the product. So,

Break-even price = Cost + overhead

Break-even price =115 + 74.75

Break-even price = 189.75

Therefore, the break-even price is $189.75.

c. From above, the regular selling price is 253.00 and the break-even price is 189.75. Thus,

Mark-down rate to sell at break-even price = (Regular selling price-Breakeven price)/Regular selling price.

Mark-down rate to sell at break-even price = (253-189.75)/253

Mark-down rate to sell at break-even price = 0.25 or 25%

Therefore, the mark-down rate is 25%.

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The domain of the function will be (-∞, ∞) and the range of the function will be (-∞, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The set of ordered pairs is given below.

{(-3, 2), (-2, 1), (-1,0), (0, -1)}

Then the line function will be

    y – 0 = [(– 1 – 0)/(0 + 1)] (x + 1)

          y = – x – 1

x + y + 1 = 0

Then the domain of the function will be (-∞, ∞) and the range of the function will be (-∞, ∞).

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Answer:

The function which represents this sequence will be:

\(a_n=-15n+110\)

Hence, option (A) is true.

Step-by-step explanation:

Given the sequence

\(95, 80, 65, 50, ...\)

An arithmetic sequence has a constant difference 'd' and is defined by  

\(a_n=a_1+\left(n-1\right)d\)

computing the differences of all the adjacent terms

\(80-95=-15,\:\quad \:65-80=-15,\:\quad \:50-65=-15\)

As the difference is the same, so

\(d = -15\)

as

\(a_1=95\)

Thus, substituting \(d = -15\), \(a_1=95\) in the nth term of an arithmetic sequence

\(a_n=a_1+\left(n-1\right)d\)

\(a_n=-15\left(n-1\right)+95\)

\(a_n=-15n+110\)

Therefore, the function which represents this sequence will be:

\(a_n=-15n+110\)

Hence, option (A) is true.

Answer:

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class

Step-by-step explanation:

We solve this question working with the probabilities as Venn sets.

I am going to say that:

Event A: Taking a math class.

Event B: Taking an English class.

77% of students are taking a math class

This means that \(P(A) = 0.77\)

74% of student are taking an English class

This means that \(P(B) = 0.74\)

70% of students are taking both

This means that \(P(A \cap B) = 0.7\)

Find the probability that a randomly selected student is taking a math class or an English class.

This is \(P(A \cup B)\), which is given by:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

So

\(P(A \cup B) = 0.77 + 0.74 - 0.7 = 0.81\)

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

Find the probability that a randomly selected student is taking neither a math class nor an English class.

This is

\(1 - P(A \cup B) = 1 - 0.81 = 0.19\)

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class

The equations used are:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the following expressions represent the lengths of the sides of the triangle:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

Perimeter = a + 1/2a + a - 1 = 39

a + 1/2a + a = 39 + 1

2a + 1/2a = 40

2 1/2a = 40

5/2a = 40

a = 40 x 2/5

a = 16 inches

Shortest side = 1/2 x 16 = 8 inches

Third side = 16 - 1 = 15 inches

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The Probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

There are a total of 52 cards in a regular deck, with 4 cards of each rank (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 13 cards in each suit (hearts, diamonds, clubs, spades).

To determine the probability of drawing a card higher than an 8, we need to count the number of cards that satisfy this condition and divide it by the total number of cards in the deck.

There are 4 cards of each rank that are higher than an 8: 9, 10, Jack, Queen, King, and Ace. Therefore, there are a total of 5 x 4 = 20 cards that are higher than an 8 in the deck.

So, the probability of drawing a card higher than an 8 is:

P(higher than 8) = number of cards higher than 8 / total number of cards

P(higher than 8) = 20 / 52

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

P(higher than 8) = 5 / 13

Therefore, the probability of drawing a card higher than an 8 from a regular 52-card deck is 5/13, or approximately 0.3846 (rounded to four decimal places).

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Answer:

$7.25.

Step-by-step explanation:

Given that, when Brandon went bowling, it cost $ 4.95 per game, plus a one-time fee to rent the shoes, and knowing that Brandon played 5 games and paid $ 32, to find the cost to rent the shoes the following equation must be performed :

4.95 x 5 + X = 32

24.75 + X = 32

X = 32 - 24.75

X = 7.25

Thus, the cost of renting the shoes was $ 7.25.

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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,Sandwiches = 4

Fruit = 3

Drinks = 5

His choice is = A sandwich, piece of fruit and a drink

What is the probability that Chase selects a tuna sandwich, a kiwi and a V8 for lunch?

​

Answer:

Step-by-step explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0

Step-by-step explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

Answer:

Step-by-step explanation:

The answer is, no!

Step-by-step explanation:

The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.

So, here is the given information on what we need to classify a shape as a parallelogram:-

1) Parallel Sides

2)Opposite Sides are equal.

3) Adjacent sides are not equal.

4) Opposite angles are equal.

5)Adjacent angles are not equal.

Based on this, we can classify a shape as a parallelogram.

Hope, this answer helps!

The functions are illustrations of trigonometry ratios

\(\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}\)

\(\mathbf{sin\theta = \sqrt{1 - (15/25)}}\)

Take LCM

\(\mathbf{sin\theta = \sqrt{\frac{10}{25}}}\)

\(\mathbf{sin\theta = \frac{\sqrt{10}}{5}}\)

\(\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}\)

\(\mathbf{Hypotenuse^2 = 10 + 4}\)

\(\mathbf{Hypotenuse^2 = 14}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{14}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}\)

\(\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}\)

The sine of the angles is:

\(\mathbf{sin \theta = \frac{1}{csc\theta}}\)

So, we have:

\(\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}\)

\(\mathbf{sin \theta = \frac{3}{\sqrt{15}}}\)

Rationalize

\(\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}\)

\(\mathbf{sin \theta = \frac{\sqrt{15}}{5}}\)

\(\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}\)

\(\mathbf{sin\theta = \sqrt{(1 - 9/6)}}\)

\(\mathbf{sin\theta = \sqrt{( - 3/6)}}\)

The sine of the angle does not have a real value

\(\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}\)

Start by calculating the tangent of the angle

\(\mathbf{tan\theta = \frac{1}{cot\theta}}\)

So, we have:

\(\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}\)

\(\mathbf{tan\theta = \frac{2}{\sqrt 6}}\)

Rationalize

\(\mathbf{tan\theta = \frac{2\sqrt 6}{6}}\)

\(\mathbf{tan\theta = \frac{\sqrt 6}{3}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}\)

\(\mathbf{Hypotenuse^2 = 6 + 9}\)

\(\mathbf{Hypotenuse^2 = 15}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{15}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}\)

Rewrite as:

\(\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}\)

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Answer:

A: 12.5

B: 36

C: 40

D: 88

Step-by-step explanation:

those are the answers

Answer: E

Step-by-step explanation:

X= 4 this solution is valid

X= 20 this solution is valid

1. 18

2.8

3.-1

An expression is a set of terms combined using the operations +, – , x or ,/.

Given:

1. 22 − 1 (4)

=22- 1*4

= 22-4

= 18

2. 2 + 2 (3)

=2+2*3

=2+6

=8

3. 1 − 2

= -1

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The value of x in part (a) is [-3+√21]/6 and [-3-√21]/6, the value of t in part (b) is (1/5+√11/5) and (1/5-√11/10), the value of t in part (c) is 1/5 and the value of t in part (d) is 1/5-3/5i and 1/5+3/5i.

Part a. Solving for x,

1/x - 1/(x+1) = 3

(1-x+x)/x(x+1) = 3

1/(x²+x) = 3

1 = 3x²+3x

3x²+3x-1=0

Solving the quadratic by using quadratic formula,

x = [-b±√(b²-4ac)]/2a

Here,

a = 3

b = 3

c = -1

Putting all the values,

x= [-3±√(3²-4(3)(-1)]/6

x = [-3±√21]/6

We get,

x = [-3+√21]/6 and

x = [-3-√21]/6

Part b. Solving for t;

2 =√[(1+t)²+(1-2t)²]

Squaring both sides,

4 = (1+t)²+(1-2t)²

4 = 1+t²+2t+1+4t²-4t

2 = 5t²-2t

5t²-2t-2=0

Solving the equation by using quadratic formula,

t= [-b±√(b²-4ac)]/2a

Here,

a = 5

b = -2

c = -2

Putting all the values,

t = [2±√(4-4(5)(-2))]/10

t = [2±√44]/10

We get

t = (1/5+√11/5) and (1/5-√11/10)

Part c. Solving for t;

3/√5 = √[(1 + t)² + (1 − 2t)²]

Squaring both sides,

9/5 = (1+t)²+(1-2t)²

9/5 = 1+t²+2t+1+4t²-4t

9 = 5+5t²+10t+5+20t²-20t

25t²-10t+1=0

t = [-b±√(b²-4ac)]/2a

Here,

a = 25

b = -10

c = 1

Putting all the values,

t = [10±√(100-4(25))]/50

t= [10±0]/50

t= 1/5

Part d. Solving for t;

0 = √[(1 + t)²+(1 − 2t)²]

Squaring both sides,

(1+t)² =-(1-2t)²

1+t²+2t = -(1+4t²-4t)

1+t²+2t = -1-4t²+4t

5t²-2t+2=0

Solving the equation by using quadratic formula,

t = [-b±√(b²-4ac)]/2a

Here,

a = 5

b = -2

c = 2

Putting all the values,

t = [2±√(4-4(5)(-2)]/10

t = [2±√(-36)]/10

t = [2±6√(-1)]/10

√-1 is 'iota' or i.

t = (2±6i)/10

We get,

t = 1/5-3/5i and 1/5+3/5i

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Answer:

A=115.6

Step-by-step explanation:

Hey There!

So the first step is to find the formula for area of a trapezoid

\(A = \frac{1}{2} h(b1 +b2)\)

h = height

b1 = base 1

b2 = base 2

now all we do its plug in the values

\(A=\frac{1}{2} 6.8(28.3+5.7)\)

\(6.8x26.3=192.44\\5.7x6.8=38.76\\38.76+192.44=231.2\\\frac{231.2}{2} =115.6\\A=115.6\)

Hope this helps!!

A) horizontal asymptote: y = 7 B) vertical asymptote: x = -4, 5 is the required answers for horizontal and vertical asymptotes of the curve.

The horizontal asymptote of a curve is a horizontal line that the curve approaches as x approaches infinity or negative infinity. The vertical asymptote of a curve is a vertical line that the curve approaches but never crosses as x approaches a certain value. In this case, the horizontal asymptote is found by letting x approach infinity in the fraction and observing what the value of y approaches. In the limit as x approaches infinity, the x^2 term dominates and thus y approaches 7, which is the horizontal asymptote. To find the vertical asymptote, we find the values of x where the denominator equals 0 and the numerator is not equal to 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5. Thus, the vertical asymptotes are x = -4 and x = 5. To find the vertical asymptotes, we look for the values of x where the denominator of the function equals 0 and the numerator does not equal 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5, which means that x = -4 and x = 5 are the vertical asymptotes of the function. These values of x represent the values at which the function is undefined, and as x approaches these values from either side, the value of the function approaches positive or negative infinity.

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