Nathan cut a square tile in half for his kitchen,he made one cut along a diagonal from one vertex to another,which triangles resulted from the cut

The values of five remaining trigonometric functions of θ.

sinθ = 1/√5, cosθ = 2/√5, tanθ = 2, secθ = √5/2, cosecθ = √5

We have to determine values of five remaining trigonometric functions of θ. ​Suppose θ is an angle in the standard position whose terminal side is in quadrant IV and cot θ = -9/18.

The ratio of trigonometry is:

sinθ = Perpendicular/Hypotenuse

cosθ = Adjacent Side/Hypotenuse

tanθ = Perpendicular/Adjacent Side

cotθ = Adjacent Side/Perpendicular

sec = Hypotenuse/Adjacent Side

cosec = Hypotenuse/Perpendicular

We know that;

Adjacent Side = 9, Perpendicular = 18

Now finding the value of Hypotenuse using the Pythagorean Theorem

(Hypotenuse)^2 = (Adjacent Side)^2 + (Perpendicular)^2

(Hypotenuse)^2 = (9)^2 + (18)^2

(Hypotenuse)^2 = 81 + 324

(Hypotenuse)^2 = 405

Taking square root on both side, we get

Hypotenuse = 9√5

Now finding the other trigonometry ratio:

sinθ = Perpendicular/Hypotenuse

sinθ = 9/9√5

sinθ = 1/√5

cosθ = Adjacent Side/Hypotenuse

cosθ = 18/9√5

cosθ = 2/√5

tanθ = Perpendicular/Adjacent Side

tanθ = 18/9

tanθ = 2

secθ = Hypotenuse/Adjacent Side

secθ = 9√5/18

secθ = √5/2

cosecθ = Hypotenuse/Perpendicular

cosecθ = 9√5/9

cosecθ = √5

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The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).

Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -

Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)

Now keeping the values in formula to find the total amount spent by eight people in desired format.

Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)

Performing addition to simplify the expression is -

Total amount spent by eight people = 8 × 95.8

Thus, the correct simplified expression will be 8×95.8.

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The sum of the relative frequencies for all classes will always equal option (C) 1 i.e. when all relative frequencies on a set of values are added it is always equal to one.

A relative frequency tells us the number of times a particular value for a data item has been perceived to occur in relation as compared to the total number of values for that set of data items.

It is calculated by dividing the absolute frequency by the total number of values for the set of data items. It is used to express proportions, ratios, percentages, etc.

Absolute frequency is a mathematical term used in statistics to calculate the number of times a value occurs in a trial set of values. It is used to calculate relative frequency, and display a graph to give a visual representation.

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Answer:

Slope:3/4

y-int: (0,5)

Step-by-step explanation:

Slope:

3x-4y=20

-3x        -3x

-4y=-3x+20

/-4     /-4

y=3/4x+5

So 5 would be y-int

The length of PQ in terms of MO if ∠POQ = 120° is PQ = -x * √3/3.

Let MO = x.

Since MO is perpendicular to plane α, MP and MQ form right angles with MO.

Using the Pythagorean Theorem, we have:

MP = x * tan(30°) = x * √3/3

MQ = x * tan(60°) = x * √3

Since ∠POQ = 120°, we have:

PQ = MP * 2 * cos(120°)

= 2 * x * √3/3 * -1/2

= -x * √3/3

Therefore, the length of PQ in terms of MO is PQ = -x * √3/3.

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Step-by-step explanation:

( x1 + x2 /2 , y1 + y2 / 2 )

= ( -7 + 7 / 2 , 0 + 7 / 2 )

= ( 0, 3.5 )

Answer:

x = 2

Step-by-step explanation:

2x + 8 = -3.5x+19

2x = -3.5x + 11

5.5x = 11

x = 2

Let's check

2(2) + 8 = -3.5(2) + 19

4 + 8 = -7 + 19

12 = 12

So, x = 2 is the only correct answer.

Answer:

In Explanation

Step-by-step explanation:

To solve for x in the equation log₂ 3+ log₂ (x-4)= 4, we can first use the logarithm identity: log₂ a + log₂ b = log₂ (ab)

So, we can rewrite the equation as:

log₂ (3(x-4)) = 4

Then we can use the definition of logarithm to find the value of x:

2^4 = (3(x-4)) = 3x-12

16 = 3x - 12

28 = 3x

x = 9 + 4 = 9

Therefore, x = 9 is the solution of the equation log₂ 3+ log₂ (x-4)= 4

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The two mathematical expressions can be written as:-

2) . [ 23 + ( 14 ÷ 2 ) - 20 ] = 5

3) . [ 9² - ( 8 x 4 ) + 26 ] = 75

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The two expressions will be solved as:-

For the first problem, the numbers are 23,2,14, and 20. The expression will be written as:-

[ 23 + ( 14 ÷ 2 ) - 20 ] = 5

[ 23 + 2- 20 ] = 5

[ 25 - 20 ] = 5

5 = 5

The numbers for the second expression are 8,26,9 and 4. The expression can be written as:-

[ 9² - ( 8 x 4 ) + 26 ] = 75

[ 81 - 32 + 26 ] = 75

[ 49 + 26 ] = 75

75 = 75

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A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.

It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.

A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.

Although it is not taken into account in the study, it might affect how the variables are related.

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We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.

link the points that lie on it to form a straight line.

Y = 2x - 1 is the first equation.

Calculate the corresponding values of y by substituting various values of x into the equation.

X      Y = 2x-1   point (x, y)

0           -1         (0, -1)

2            3         (2, 3)

4            7          (4, 7)

-1           -3         (-1, -3)

-3           -7         (-3, -7)

On the graph paper, place these points and draw a straight line connecting them.

Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.

In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.

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Answer:

Step-by-step explanation:

the new one will tell you be

Answer:

D is the one trust me man I do this all the time and good luck on your exam

To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.

How to find the sum of interior angles ?

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The solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

What is inequality?

An inequality is a statement that compares two expressions and asserts that one is greater or less than the other. It can be represented using mathematical symbols such as <, >, ≤, ≥, ≠.

|2x + 3| < 7 is a type of absolute value inequality. The absolute value of a number is its distance from zero on the number line, and is always positive. So, |2x + 3| is the absolute value of 2x + 3, which is always greater than or equal to zero.

To solve this inequality, we need to consider two cases:

If 2x + 3 is greater than or equal to zero, we can drop the absolute value bars and solve the inequality as is:

2x + 3 < 7

2x < 4

x < 2

If 2x + 3 is less than zero, we need to reverse the inequality sign:

-2x - 3 < 7

-2x < 10

x > -5

Hence, the solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

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The probability that exactly 14 adults have been vaccinated 0.49

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event

the national center for health statistics (nchs) reports that 70% of us adults aged 65 and over have ever  vaccination

the pneumococcal vaccination rate applies to an independent random sample of 20 us adults aged 65

the probability that exactly 14 adults have been vaccinated

(14/20)*(70/100)

0.49

The probability that exactly 14 adults have been vaccinated 0.49

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Answer:A.½ B.-½ C.2⁷/20

Step-by-step explanation:A. 5¾+(-¼) =23/4 - ¼ =22/

=5½

B. -⅔+⅙ = (-4+1)/6=-½

 C. -8/5-¾= (-32-15)/20 =47/20 =2⁷/

According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)

In math the term called graph is defined as  a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.

Here we know that the function is f(x) = 8x.

When we plot the function then we get the graph like the following.

While we looking into plotted graph, then we have identified that the y-intercept is 0.

And the horizontal asymptote is the limit as x goes to ∞.

And the range is the set of values above the horizontal asymptote (-∞, ∞).

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Answer: the second, third and fifth options.

Step-by-step explanation:

When an equation is set up in a y=mx+b format, the slope is always equal to the value m.

The single discount of 45% is better than the successive discount of 30% and 20%.

Let us assume that the Maximum retail price = 100x

As in case 1,

The percentage discount is given as 45%

So, the value of the selling price of the item will be = (100-45)% of 100x

=55% of 100x = 55x ------(i)

Now in case 2,

The successive discount of 30% and 20% is given.

So, let us assume that the Maximum retail price = 100x

So, after giving the discount of 30%

The value of the selling price will be = (100-30)% of 100x

=70% of 100x = 70x

Now again giving the discount of 20%

Then the value of new selling price will be = (100-20)% of 70x

=80% of 70x = 56x ------(2)

In case (1) the selling price is 55x while in case 2 the selling price is 56x.

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It depends on the price of the article. A 45% single discount will always result in a larger price reduction than a 30% discount followed by a 20% discount on the same price.

However, the overall savings from the two different discount schemes may be the same if the price of the article is high enough. To determine which discount scheme is better, it is necessary to know the price of the article and calculate the total savings under both schemes.

For instance: For example, if we are considering the price of an article is Rs 100, then the successive percentage would be 30% and 20% for the discount, the price falls to Rs 56, whereas with a single 45%discount, the amount comes to Rs55.

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Answer: (x + 3)^2 + (y + 8)^2 = 14pi^2

(x-h)^2 + (y-k)^2 = r^2

Answer: $4,914

Step-by-step explanation:

To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)

where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have:

P = $11,000

r = 1% = 0.01

n = 4 (because the interest is compounded quarterly)

t = 20

so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20

To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.

In this case, we have:

P = $11,000

r = 13/100 = 0.13

n = 12 (because the interest is compounded monthly)

t = 20

so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34

To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:

$27,731.34 - $22,817.20 = $4,914.14

To the nearest dollar, the difference is $4,914.

Answer:391

Step-by-step explanation:

The expression using brackets is (3x)(x⁴) + (2)(2) = 26

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

7x5-4x5+16÷4=26

Express the superscripts in the expression properly

So, we have the following representation

7x⁵ - 4x⁵ + 16 ÷ 4 = 26

Evaluate the like terms

3x⁵ + 16 ÷ 4 = 26

Divide 16 by 4

3x⁵ + 4 = 26

Factorize and use brackets

(3x)(x⁴) + (2)(2) = 26

Hence, the expression is (3x)(x⁴) + (2)(2) = 26

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Debts, or other outstanding bills or loans that must be repaid are called option B: Liabilities.

What is Debt?

Debt can be defined as the sum that the borrower owes the lender. A debt is an amount of money that has been borrowed for a set period of time and must be repaid, plus interest.

A liability is a debt that a person or business has, typically in the form of money. Through the transmission of economic benefits like money, products, or services, liabilities are eventually satisfied.

Liabilities are items that are listed on the balance sheet's right side and consist of debts including loans, accounts payable, mortgages, deferred income, bonds, warranties, and accumulated expenses.

Therefore, debts are a form of liability.

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The size of each angle to draw the pie chart is given as follows:

The size of each angle in this problem is found applying the proportions.

First we obtain the relative frequency of each item, dividing the absolute frequency by 40.

Then we obtain the angle size, multiplying the relative frequency by 360º, which is the angle measure of the entire circumference of the pie chart.

Then the angle measures are obtained as follows:

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The angular speed of the wheels is approximately 1480 / π radians per minute.

We can start by converting the velocity of the truck from miles per hour to feet per minute, since the diameter of the wheels is given in feet.

50 miles/hour = 50 x 5280 feet/hour = 264,000 feet/hour

264,000 feet/hour / 60 minutes/hour = 4,400 feet/minute

Next, we can find the circumference of the wheel and then divide it by the velocity of the truck to find the angular velocity in radians per minute:

Circumference = 2 * π * r = 2 * π * (diameter/2) = 2 * π * (3 feet / 2) = 3π feet

Angular velocity (ω) = velocity / circumference = 4,400 feet/minute / (3π feet) = 1480 / π radians/minute

So the angular speed of the wheels is approximately 1480 / π radians per minute.

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Joint and 2/3 survivor means that if the insured passes away, two of the beneficiaries will receive two-thirds of the insurance benefits, and the remaining third will be divided among all three beneficiaries.

Joint and 2/3 survivor is a settlement option for life insurance policies which means that when the insured passes away, two of the beneficiaries will receive two-thirds of the death benefits, while the remaining third will be divided equally among all three beneficiaries. This is beneficial because it ensures that two of the beneficiaries will receive the majority of the death benefits, while the remaining third will be split equally among all three. This provides a more secure financial future for the two beneficiaries receiving the most money as well as allowing the remaining third to be split equally, providing more financial security for all beneficiaries.

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[tex]2~~,~~\stackrel{2\cdot \frac{5}{2}}{5}~~\stackrel{5\cdot \frac{5}{2}}{\cfrac{25}{2}}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=2\\ n=9\\ r=\frac{5}{2} \end{cases}[/tex]

[tex]a_9=2\left( \frac{5}{2} \right)^{9-1}\implies a_9=2\left( \frac{5}{2} \right)^8\implies a_9=2\left( \cfrac{390625}{256} \right) \\\\\\ a_9=\cfrac{390625}{128}\implies {\Large \begin{array}{llll} a_9=3051\frac{97}{128} \end{array}}[/tex]