Explain the difference between using the trigonometric ratios (sin, cos, tan) to solve for a
missing angle in a right triangle versus using the reciprocal ratios (sec, csc, cot). You must
use complete sentences and any evidence needed (such as an example) to prove your
point of view. (10 points)

Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constant is:

k = 75/10 = 97.5/13 = 112.5/15 = 7.5.

Hence Carlos earns an allowance of $7.5 for each chore that he completes.

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The y-intercept of the linear function y = 3x - 2 is -2

The function is given as

y = 3x - 2

The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)

As a general rule, linear functions are those functions that have constant rates or slopes

Next, we set x to 0, and calculate y to determine the value of the y-intercept

y = 3(0) - 2

Remove the bracket in the above equation

y = 3 * 0 - 2

Evaluate the product of 3 and 0 i.e. multiply 3 and 0

y = 0 - 2

Evaluate the difference of 0 and -2 i.e. subtract 0 from 2

y = -2

The above means that the value of y when x is 0 is -2

Hence, the y-intercept of the linear function y = 3x - 2 is -2

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The simplification of the equation above in words is = Twelve minus thirteen X.

In mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.

The equation given is,

10 - 13x + 2

Arrange the digits without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is Twelve minus thirteen X.

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the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

Answer:

[tex]\frac{169}{49}[/tex]

Step-by-step explanation:

Square the top and bottom numbers in the fraction

13^2 = 169

7^2 = 49

169/49

Using it's concepts, we have that:

The absolute change between two values is given by the absolute value of the difference between two values.

In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:

A = 40,156 - 25,003 = $15,153 million.

The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:

(15,153/25,003) x 100% = 60.60%.

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The confidence interval expressed in the form p - E is:

(0.104 - 0.039, 0.104 + 0.039).

The mean is the mean of the bounds, hence:

p = (0.065 + 0.143)/2 = 0.104.

The margin of error is the difference between the bounds and the mean, hence:

E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.

Hence the interval in the desired format is:

(0.104 - 0.039, 0.104 + 0.039).

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Answer:

Hello,

Step-by-step explanation:

[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.

Given that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.

So, the combination for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

                                                                        =  17576000

Therefore, 17576000 license plates can be made.

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The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

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Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7

Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.

Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.

Thus in the given question, it can be deduced that;

The population of people living in White Plains =56,853

The population of people living in Elmira = 29,200

So, the difference in the population between the two cities can be determined as;

                         = 56,853 - 29,200

                         = 27,653

Thus, the number of fewer people living in Elmira than in White Plains is 27,653

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The value of csc theta is [tex]\frac{3. 61}{2}[/tex]

It is important to note that the ratio for cot is given as;

Cot theta = adjacent/opposite

cosec theta = hypotenuse/opposite

If cot theta = 3/2, then

Adjacent = 3

Opposite = 2

Using Pythagoras theorem, we have

Hypotenuse square = opposite + adjacent square

[tex]H = \sqrt{2^2 + 3^2}[/tex]

[tex]H = \sqrt{4 + 9}[/tex]

[tex]H = 3. 61[/tex]

Cosec theta = [tex]\frac{3. 61}{2}[/tex]

Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]

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Answer:

3.16/2

Step-by-step explanation:

Have a great day

Step-by-step explanation:

=fog(x)

−2x=0

x(x−2)=0

x=0,2

Answer:

Step-by-step explanation:

Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.

First, let's find the volume of each component.

If the oil is x then water is 4x according to ratio and their sum is 100 ml:

So, we have 20 ml of oil and 80 ml of water.

Now, let's added volume of oil be y. Then we have the ratio:

So, we have 40 ml of oil and 80 ml of water.

Lastly, let's added water be z. Then we have the ratio:

We must add 40 ml of water.

By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].

According to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex]     (1)

Where:

First, we find the magnitude and direction of the complex number:

[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]

r = 6

[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]

[tex]\theta = \frac{2\pi}{3} \,rad[/tex]

Now we find the four quartic roots of the complex number:

[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]

[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]

[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]

[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]

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The output voltage of the op-amp circuit shown is -5v.

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute,  it represents the unit rate of houses per minute .

The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.

36/30 = 1.2 houses per minute

The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses

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Answer:

A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION

f

(

x

)

=

b

x

An exponential function with the form

f

(

x

)

=

b

x

,

b

>

0

,

b

≠

1

, has these characteristics:

one-to-one function

horizontal asymptote:

y

=

0

domain:

(

−

∞

,

∞

)

range:

(

0

,

∞

)

x-intercept: none

y-intercept:

(

0

,

1

)

increasing if

b

>

1

decreasing if

b

<

1

Step-by-step explanation:

hope it helps you

The equations that can be used to find the lengths of the legs of the triangle are as follows:

The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

c²  = a² + b²

where

Therefore,

10²  = (x + 2)² + x²

100 = (x + 2)² + x²

Therefore, using the area of a triangle,

area of a triangle  = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × (x + 2)(x)

24 = 0.5 × (x + 2)(x)

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

x² + 2x - 48 = 0

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The value of g(3) is g(3) = 4

The function value is given as:

g(x)

The notation g(3) implies that:

We determine the value of g(x) when x = 3

From the graph, the function has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the value of g(3) is g(3) = 4

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The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

Given six equations as under:

We are required to find the quadratic equations among the above equations.

Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.

It is in form of [tex]ax^{2} +bx+c=0[/tex].

In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

5x-1=3x+8: It is not a quadratic equation as the highest power is 1.

5 x- 3 = 0:It is also a linear equation not quadratic equation.

x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.

Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

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The statements that correctly compare the sum and product of the function are:

A linear function simply means a function that represents a straight line on the coordinate plane.

In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.

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On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation =  (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 +  10 + 9 + 5+  2 +  10 + 3 + 3+  5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) +  (10 - 6)  + (9 - 6)  + (5 - 6) +  (2 - 6) +  (10 - 6)  + (3 - 6)  + (3 - 6) + ( 5 - 6) = 3.2

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Answer:

x = -3

Step-by-step explanation:

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry:  x = -3

Answer:

c. [-1, infinity)

Step-by-step explanation:

the domain the interval or set of valid x values (while the range is the same for the valid y values).

what is the smallest value of x we see for the graph ?

for x values we need to look left and right.

and the more left the value, the smaller it is.

so, in other words, what is the left-most x value e can find ?

x = -1

that is the "starting point" of the function. there is no functional value for any smaller x.

and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.

therefore the answer.

keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).

The future value of Investment A is 9511.81

The future value of Investment B is 68,351.02

The future value of Investment C is29.067.07.

When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.

The formula for calculating future value:

FV = P (1 + r)^nm

Investment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81

Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02

Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07

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Answer:

Step-by-step explanation:

hello :

 f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x        (f g)(x) = 4x......(answer : A)

Answer:

C

Step-by-step explanation:

We can use process of elimination

D is incorrect because the roots are 3 and -4 and there are no negative roots visible

B is wrong because the roots -3 and -6 are both negative

You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6

For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate