Unit 8: right triangles & trigonometry homework 4 trigonometry finding sides and angles

Answer:

m(x)=1.75

m(10)= 10x / 17.5

17.5

Step-by-step explanation:

Answer:

y=2/3x-8

Step-by-step explanation:

Answer:

y=(2/3)x-8

Step-by-step explanation:

y=mx+b

m(slope)= 2/3   b(y-intercept)= -8

plug in the given slope and y-intercept

Given: A rhombus with diagonals as 6 m and 5 m respectively.

The area of rhombus(A) is given by the formula:

Substituing p=6 and q=5,

Answer:

Step-by-step explanation:

Area of a rhombus = product of its diagonals / 2

= 6*5 / 2

= 15 m^2.

Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

\(d = \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1 })^{2} }\)

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

Answer:

6 fruits per hour.

Step-by-step explanation:

If you think of these as fraction, 2/12 is the same as 1/6. If you multiply the hours and fruit count by 7, you get 7/42. They are the same fractions. This means 1/6 represents 6 fruits every hour.

The equation of a trend line that passes through the points (7, 450) and (14, 401) is y = -7x+99.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Points are: (7, 450) and (14, 401)

Slope(m)=(401-450)/(14-7)

              = -49/7

              = -7

Equation of trend line:

(y-450)= -7(x-7)

y-450= -7x+49

y= -7x+49+450

y= -7x+499

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68 B candies

Stem leaf

The required factor each polynomial by grouping are factored.

A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.

1) \(x^3+4x^2+2x+8\)

can be factored by grouping as:

\(x^3 + 2x + 4x^2 + 8\)

= \(x(x^2+2) + 4(x^2+2)\)

= \((x+4)(x^2+2)\)

2) \(4b^3-6b^2+10b-15\)

can be factored by grouping as:

\(2b^2(2b-3)+5(2b-3)\)

=\((2b-3)(2b^2+5)\)

3)\(2m^3+4m^2+6m+12\)

can be factored by grouping as:

\(2m^2(m+2) + 6(m+2)\)

= \((2m^2+6)(m+2)\)

= \(2(m^2+3)(m+2)\)

4) \(7r^3-35r^2+6r-30\)

can be factored by grouping as:

\(7r^2(r-5)+6(r-5)\)

=\((7r^2+6)(r-5)\)

\(10a^3+4a^2+5a+2\)

can be factored by grouping as:

\(2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)\)

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Answer:

area = 254.5 m²

Step-by-step explanation:

area = πr² = (3.14159)(9²) = 254.46 m²

Background:

"As much as" means that two quantities are being compared and is a keyword for division.

Procedure:

Answer: 2

Answer:

for ponits

Step-by-step explanation:

x     4      3     2      1

f      3      5     4      2

Total number of scores in table are ∈ f =  3 + 5 + 4 + 2 = 14

According to the question, given that

x     4      3     2      1

f      3      5     4      2

Total number of scores are ∈ f =  3 + 5 + 4 + 2 = 14

Therefore, after sum of score we get total number of scores is 14

The average or computed center value of a group of values is known as the mean, and it is used to determine the central tendency of the data. The entire collection of data or distribution is identified by a single number using the statistical metric known as central tendency.

We can use the direct technique, the assumed mean method, or the step deviation method to determine the mean of grouped data. The frequency of several observations or variables that are combined together is the subject of the mean of grouped data. Let's examine each of these approaches in turn.

Direct Method

The direct approach is the most straightforward way to determine the mean of the grouped data. The mean of the data is given by, if the values of the observations are x1, x2, x3, and x4 and their associated frequencies are f1, f2, f3, and f4, respectively.

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(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

Given that Frame zero, F0 is the fixed global frame.

For each of the cases below find T1

Case (a)

F1 is rotated by an angle θ about zo.

Let O be the origin of the fixed frame F0, A be the origin of the frame F1 and α be the angle between the x-axis of the frame F0 and the projection of the x-axis of the frame F1 on the xy plane of the frame F0.

Let l, m, n be the direction cosines of the vector from O to A, expressed in F0.

The content-loaded frame zero F0 is the fixed global frame, which means that the vectors i, j, k representing the x, y, and z-axis of F0 are fixed and cannot be transformed.

Therefore, the transformation matrix T1:0

in this case is:

`T1:0 = [l1 m1 n1 0; l2 m2 n2 0; l3 m3 n3 0; 0 0 0 1]`

Case (b)

F1 is rotated by θ about xo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

Case (c)

F1 is rotated by θ about yo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Thus, the transformation matrix T1:0

for the three cases (a), (b), and (c) are given as follows:

(a) `T1:0 = [cosθ sinθ 0 0; -sinθ cosθ 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

(c) `T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Given θ = 150,

T1:0 for the three cases are:

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

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Step-by-step explanation:

exterior angle is the sum of two opposite interior angle

11x+9=3x+12+85

11x-3x=88

8x=88

x=11.

hope this helps you.

Answer:

x=11

Step-by-step explanation:

85 + 3x + 12= 11x+9

97  +3x= 11x+9

-97            -97

3x= 11x - 88

-11x    -11x

-8x = -88

/-8     /-8

x=11

To solve the equation we first squared both sides of it, that is:

Now we can use the general formula for quadratic equations, then:

Now that we found two option for x, we have to check which of them is really a solution for the original equation (we have to do this since we squared the original equation to get rid of the root), to do this we plug the values we found to see if the eqaution holds.

If x=1:

hence x=1 is a solution for the original equation.

If x=-2:

since this is not true, x=-2 is not a solution for the original equation.

Therefore, the solution for the equation is x=1.

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.

A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).

The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.

However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.

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Answer:

degree 3  zeros -1 and 1

Step-by-step explanation:

This is a third degree polynomial

f(x)=(x-1)^2(x+1)

It has an x^2 from the first term and an x from the second term for x^3

The zeros are x-1 =0  which means x=1

x+1 = 0  x=-1

Answer:

Step-by-step explanation:

(x-1)²(x+1) = x³-2x²+x+x²-2x+1

                 = x³-x²-x+1

                 = x²(x-1)-x+1

                 = x²(x-1)-(x-1)

                 = (x²-1) (x-1)

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:

6 ft

Step-by-step explanation:

Let the width = w

Then the length = 4w - 3

perimeter = 2(length + width)

perimeter = 2(4w - 3 + w)

perimeter = 2(5w - 3)

perimeter = 10w - 6 = 54

10w - 6 = 54

10w = 60

w = 6

Answer: The width is 6 ft

Age Frequency

41-45 5

46-50 9

51-55 3

56-60 10

61-65 10

66-70 6

1) Since the frequency represents how many times a given data point occurs within a Data Set. We can fill it in by counting.

2) So let's write them out (Note that in this case the least value is included as well as the greater one):

Age Frequency

41-45 5

46-50 9

51-55 3

56-60 10

61-65 10

66-70 6

And that is the answer

The slope for the relationship between the number of minutes, x, and the amount charged, y is $1.5

Given that at Beans-and-Donuts Coffee shop, they display their internet fees on a chart

We have to find the slope for the relationship between the number of minutes, x, and the amount charged, y.

Slope = $4.49-$2.99/2-1

Slope=$1.5

Hence, the slope for the relationship between the number of minutes, x, and the amount charged, y is $1.5

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If functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

A relation is a function if it has only One y-value for each x-value.

The given two functions are f(x) = 2x² + 4x - 5

and g(x) = - 6x³+2x² - 3

We need to find  (f + g)(x).

(f + g)(x)=f(x)+g(x)

=2x² + 4x - 5 - 6x³+ 2x² -3

Now add the like terms

= 6x³+ 4x² +4x-8

(f + g)(x)=6x³+ 4x² +4x-8

Hence, if functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

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Answer:

hope that helps you out.

Range is R={n^2: n is natural number} U {n(n+1) : n is natural number}

The expression ⌈y⌉⋅⌊y⌋ represents the product of the ceiling and floor functions of y.

To find the range of all possible values of y, we need to consider the possible values of the ceiling and floor functions individually.

1. Ceiling function (⌈y⌉): This function rounds y up to the nearest integer. Since y is greater than 0, the ceiling of y will always be greater than or equal to y.

2. Floor function (⌊y⌋): This function rounds y down to the nearest integer. Again, since y is greater than 0, the floor of y will always be less than or equal to y.

Now, let's consider the product of the ceiling and floor functions, ⌈y⌉⋅⌊y⌋.

The product ⌈y⌉⋅⌊y⌋ will always be greater than or equal to 0 since y > 0 and this can take only integral values.

Therefore, the range of all possible values of y such that ⌈y⌉⋅⌊y⌋ is the set R={n^2: n is natural number} U {n(n+1): n is natural number}

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Answer:

the point is located in the overlapping shaded areas

Step-by-step explanation:

solutions to systems of inequalities lie within the shaded areas graphically. solutions have to be true for both inequalities

Answer:

If the point is in the shaded area

Step-by-step explanation:

when graphing your inequalities equations you look for the points in the shaded area and that is your solution, if the point is not in the shaded area it is not a solution.

Answer:

All of the above are correct.

Using the geometric sequence, we know that the relationship between the F, G, and H is (D) h = g^2/f.

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

So, let r represent the common ratio:

f(r) = g   ...(1)

g(r) = h   ...(2)

Put "r" as the topic in both equations:

f(r) = g   ...(1)

r = g/f   ...(3)

g(r) = h   ...(2)

r = h/g   ...(4)

Since r = g/f (3), change r in (4) to g/f:

r = h/g   ...(4)

g/f = h/g   ...(5)

Equation V's two sides should be multiplied by g:

g/f = h/g   ...(5)

g/f X g = h/g X g

g^2/f = h

h = g^2/f

Therefore, using the geometric sequence, we know that the relationship between the F, G, and H is (D) h = g^2/f.

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Complete question:
A student wrote the first three values in a geometric sequence as shown below.

F, G,H...

Which of the following shows the correct relationship between these terms?

A. f-g=g-h

B. fg=gh

C.h=g/f

D.h=g^2/f

The linear equation is f(x) = 2^2 + x, while the other two functions are nonlinear functions

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

The three equations

A linear equation is any equation that has a degree of 1

From the three equations, we can see that

Degree = 1

Degree = 2

Degree = 3

Hence, the linear function is f(x) = 2^2 + x

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