In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m

The horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.

The force can be broken down into its horizontal and vertical components using trigonometry.

Horizontal component:

cos(42) = adjacent/hypotenuse

adjacent = cos(42) * 110 N

adjacent ≈ 80.34 N

Vertical component:

sin(42) = opposite/hypotenuse

opposite = sin(42) * 110 N

opposite ≈ 74.62 N

Therefore, the horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.

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The correct option is C. mean, that is Mr. Greene should use the mean temperature, which is 77.86°F.

In mathematics, the mean value is a measure of central tendency of a set of numbers. It is also known as the arithmetic mean and is found by adding all the numbers in a set and dividing the sum by the total number of values. The mean is commonly used to represent the typical or average value of a set of data. It is a useful tool in statistics and other branches of mathematics for analyzing data and making predictions. The mean value can be affected by outliers or extreme values in a set of data, which can skew the results. However, in many cases, the mean provides a reliable and useful measure of central tendency.

Mr. Greene should use the mean temperature, which is 77.86°F, to summarize the temperatures for each day. The mean is a good measure of central tendency when the data set is approximately symmetric and has no significant outliers, which appears to be the case here. Additionally, using the mean will provide a single number that is representative of the entire data set. The interquartile range and mean absolute deviation are measures of spread and do not provide a summary of the temperatures for each day, and the maximum temperature is just one value and may not be representative of the entire data set.

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The median, mode and range for both dot plots are:

The median

This is the middle value

From the dot plots, we have the middle values to be

Group A = (7 + 8)/2 = 7.5

Group B = 5

So, we have

Median Group A = 7.5

Median Group B = 5

The mode

This is the number of books with the highest dots

From the dot plots, we have the modal values to be

Mode Group A = 7 and 8

Mode Group B = 4 and 5

The range

This is the difference between the smallest and highest number of books with the highest dots

From the dot plots, we have the range to be

Group A = 9 - 6 = 3

Group B = 10 - 3 = 7

So, we have

Range Group A = 3

Range Group B = 7

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Answer:

a) The scale factor is [tex]\frac{4}{5}[/tex]

b) [tex]t=5\frac{3}{5}[/tex]

Step-by-step explanation:

The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.

In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.

Let's start by calling our "certain value" k.

[tex]5k=4=\\k=\frac{4}{5}[/tex]

Let's check 15 to make sure k is 4/5, like so:

[tex]15(\frac{4}{5})=\\\frac{60}{5} =\\12[/tex]

Since 15 times 4/5 is twelve, our initial answer was correct.

So, the scale factor, or k, is 4/5.

Following this logic, we know that 7 multiplied by the scale factor is equal to t.

Let's set up an equation and solve for t:

[tex]7(\frac{4}{5} )=t=\\\frac{28}{5} =t=\\5\frac{3}{5} =t[/tex]

So, [tex]t=5\frac{3}{5}[/tex]

The distance from the center are equal,

x = 6

The value of x is solved using the relationship existing between chords and the bisectors.

It will be noted that the line from the center

In the figure, since the chords are equal and the line from the center are perpendicular bisectors then the line from the center are equal.

we can therefore say that x = 6

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A quadratic equation with opposite solutions can be found by multiplying a variable by its negative value. Specifically, if we start with a quadratic equation of the form:

ax^2 + bx + c = 0

We can find an equation with opposite solutions by multiplying either a or c by -1. For example, if we multiply c by -1, we get:

ax^2 + bx - c = 0

This equation will have opposite solutions if the discriminant, b^2 - 4ac, is negative. This is because the solutions of a quadratic equation are given by the formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Thus, if the discriminant is negative, then the square root term will be imaginary, which means that the solutions will be complex conjugates of each other.

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Answer:

13

Step-by-step explanation:

By counting the amount of dots there is on the graph you would end up with 13 trees.

The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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Answer:

C.

Step-by-step explanation:

because x value cannot be repeated in an ordered pair

The calculated value of sec^-1(1.4) is 44.41 degrees

The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.

In other words, if secθ = x, then sec^-1(x) = θ.

To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.

However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.

Uisng a graphint tool, we have

sec^-1(1.4) = 44.41

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The correct statement is option a) The height of the terrain can measure between 2 meters and 10 meters.

Let the base of the triangular piece of land be x meters. Then, the height of the triangular plot is (x+2) meters.

The area of a triangle is given by the formula: A = (1/2)bh, where b is the base and h is the height.

Substituting the given values:

A = (1/2)x(x+2)

Simplifying:

A = (1/2)(x² + 2x)

Since the area is less than 40 m², write:

(1/2)(x² + 2x) < 40

Multiplying both sides by 2:

x² + 2x < 80

Rearranging and factorizing:

x² + 2x - 80 < 0

(x+10)(x-8) < 0

The roots of the quadratic equation are -10 and 8. Since the coefficient of x² is positive, the parabola opens upwards and is negative in between the roots. Therefore, the inequality is true when -10 < x < 8.

However, x cannot be negative, so the base of the triangular terrain is between 0 and 8 meters.

Substituting the values in the expression for the height, the height is between 2 and 10 meters.

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Answer:

The answer to (m+3)(m-3) is m^2-9.

Step-by-step explanation:

We will use distributive law to solve this question.

m(m-3)+3(m-3)

= m^2-3m+3m-9

= m^2-9 (since, 3m-3m=0)

As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.

so, here a=m and b=3.

(m+3)(m-3)

=m^2-3^2

=m^2-9

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

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A registered investment account, or RRSP, enables you to put money aside for retirement while delaying taxes on investment gains.

An annuity is a financial product that provides regular payments over a specified period of time in exchange for a lump sum of money. It's often used as a retirement income source and comes in different types such as fixed, variable, immediate, and deferred annuities. It's important to understand the terms, fees, and charges before purchasing an annuity.

Registered Retirement Savings Plan is the full form of RRSP.

In Canada, both workers and independent contractors can save and invest during their retirement through Registered Retirement Savings Plans (RRSP).

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As per the question of trigonometry the another equation that describes the given graph is

y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.

The sine and cosine function graphs' main characteristics are:  

a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.

b. We can simplify the following equation and compare it with  [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.

We obtain this by applying the same trigonometric identity as before.

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The solution of missing sides and angle  is:  A = 60°, B = 34.8°, C = 85.2°  a = 4, b = 5, c = √21

Trigonometric functions are used to obtain unknown angles and distances from known or measured angles in geometric drawings.

Basics of Trigonometry deals with measuring angles and problems related to angles. There are six basic trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent. All  important trigonometric concepts  are based on these trigonometric relationships or functions.

Solving a triangle means determining all  its angles and sides. In this case, we are given angle A and sides a and b, and we want to find the remaining angles and sides.

First, we can use the law of cosines c to find the third side:

c² = a²+ b² - 2ab cos(A)

c² = 4² + 5² – 2(4)(5) cos(60)

c² = 16 + 25 - 40 cos (60)

c² = 41-20

c² = 21

c = √21

Now that we have all three sides, we can use the law of cosines to find the remaining angles:

cos(B) = (a²+ c² – b²) / (2ac)

cos(B) = (4²  +(√21)² – 5²) / (2(4) (√21))

cos(B) = (16 + 21 - 25) / (8√21)

cos(B) = 12 / (8√21)

B = cos⁻¹ (12 / (8√21))

cos(C) = (a²+ b² – c²) / (2ab)

cos(C) = (4² + 5² – (√21)²) / (2(4)(5))

cos(C) = (16 + 25 - 21) / 40

cos(C) = 20/40

C = cos⁻¹ (20/40)

Simplifying  trigonometric functions:

B ≈ 34.8°

C = 85.2°

Therefore, the solution is:

A = 60°, B = 34.8°, C = 85.2°

a = 4, b = 5, c = √21

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The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

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Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function.

A mathematical item called a function accepts an input and creates an output. It looks like an apparatus with an input and an output. A formula or a graph can both be used to express a function. For instance, the function f(x) = x² returns the square of an input x as output.

Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function. A(x) is not one-to-one, for instance, because a(1) and a(3) are both equal to 1.

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Answer:

4. b/c

Step-by-step explanation:

In a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle), the sine of the angle opposite side b (angle B) is given by:

Sin theta : Opposite/hypotenuse

sin(B) = b/c

Therefore, the answer is 4. b/c

Given:

[tex]\vec F_{1} =27 \ N[/tex]

[tex]\vec F_{2} =24 \ N[/tex]

[tex]\vec a_{1} = 9 \ m/s^2[/tex]

Find:

[tex]\vec a_{2} = ?? \ m/s^2[/tex]

We know that [tex]\vec F= m \vec a[/tex]. Use [tex]\vec F_{1}[/tex] and [tex]\vec a_{1}[/tex] to find mass, m.

[tex]\Longrightarrow \vec F_{1} = m \vec a_{1} \Longrightarrow 27= m(9) \Longrightarrow m= \frac{27}{9} \Longrightarrow m= \boxed{ 3 \ kg }[/tex]

We now know the mass of the moving object we can now find [tex]\vec a_{2}[/tex].

[tex]\Longrightarrow \vec F_{2} = m \vec a_{2} \Longrightarrow 24= (3) \vec a_{2} \Longrightarrow \vec a_{2}= \frac{24}{3} \Longrightarrow \vec a_{2}= \boxed{ 8 \ m/s^2 } \ \therefore \ Sol.[/tex]

The area of a parallelogram with base of 10 inches and height of 5 inches is 50 in²

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

The area of a parallelogram is the product of its base and height. It is given as:

Area = base * height

For a parallelogram with base of 10 in and height of 5 in:

Area = base * height

Area = 10 in * 5 in = 50 in²

The area is 50 in²

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A diagram that represents the expression |-5| include the following: A. graph A.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the absolute value of -5 or |-5|, an inequality that matches this graph is represented by the first diagram.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.

Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.

The Situation column should have two entries: "finding part of a total" and "difference".

The Operation column should have only one entry: "minus".

The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.

To solve for s, we can add 2.3 to both sides of the equation:

s - 2.3 + 2.3 = 6.8 + 2.3

s = 9.1

Therefore, Sam ran 9.1 kilometers.

So, the Situation entries are: "difference" and "finding part of a total".

The Operation entry is: "minus".

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The requreid, as per the given percentage condition Mia tips the movers $80.

To find the amount of the tip, we need to calculate 16% of the total cost of the services, which is $500.

16% of $500 = 0.16 x $500 = $80

Therefore, Mia tips the movers $80.

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The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

We have,

The Addition Property of Equality states that if we add the same quantity to both sides of an equation, the equation remains true.

In the given equation,

AB = CD, we can add the same quantity, EF, to both sides of the equation to obtain:

AB + EF = CD + EF

This is because if two quantities are equal, and we add the same amount to both of them, the result is still equal.

Therefore,

The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

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The value of the function when the quantity f divided by g of 8 is given by option D. 5.

The function are equal to,

f(x) = 3x + 1

g(x) = x - 3

The expression 'f divided by g of 8' means it is required to evaluate the function f(x) divided by g(x) at x=8.

First, find the individual values of function  f(8) and g(8) is equal to,

f(x) = 3x + 1

Substitute the value of x = 8 we get,

⇒ f(8) = 3(8) + 1

⇒ f(8) = 25

Now, for the function g(x),

g(x) = x - 3

Substitute the value of x = 8 we get,

⇒ g(8) = 8 - 3

⇒ g(8) = 5

Then, we can find the value of f(x) divided by g(x) at x=8 which is equal to,

f(x) / g(x)

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

= f(8) / g(8)

= 25 / 5

= 5

Therefore, the quantity function f divided by g of 8 is 5, which is option (D).

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By using the properties of logarithms, The logarithm "log₅(98)" can be written as log₅(2) + log₅(7) + log₅(7).

We use the "product' and "quotient" logarithmic identities to write log₅(98) in terms of log₅(2) and log₅(7):

⇒ logₐ(b × c) = logₐ(b) + logₐ(c)      ....(product rule)

⇒ logₐ(b/c) = logₐ(b) - logₐ(c)           ...(quotient rule)

First, we write the number "98" as the product of 2 and 7, which is :

⇒ log₅(98) = log₅(2 × 7 × 7),

Using the product rule, we can split this into three logarithms;

⇒ log₅(2 × 7 × 7) = log₅(2) + log₅(7) + log₅(7),

So, we have,

⇒ log₅(98) = log₅(2) + log₅(7) + log₅(7),

Therefore, log₅(98) is equal to log₅(2) + log₅(7) + log₅(7).

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The given question is incomplete, the complete question is

Use the properties of logarithms to write the logarithm in terms of log₅(2) and log₅(7).

The logarithm is log₅(98).

Answer:

dependent

Step-by-step explanation:

its dependent because the names getting pulled depends on the names pulled first