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The value of the trigonometric relation cos ∠O = 0.849

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of ∠PQR = 90° and it is a right triangle

The measure of the hypotenuse PO = 53

The measure of adjacent side OQ = 45

The measure of opposite side QP = 28

Now , from the trigonometric relations ,

cos θ = adjacent / hypotenuse

cos θ = OQ / PO

Substituting the values in the equation , we get

cos θ = 45 / 53

cos θ = 0.849

Therefore , the value of cos ∠O is 0.849

Hence , the trigonometric relation cos θ = 0.849

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Answer:

x = 1

Step-by-step explanation:

2(4x + 5) - 3 = 5x(2+1)

Distribute.

8x + 10 - 3 = 10x + 5x

Subtract 8x from both sides.

10 - 3 = 10x + 5x -8x

Solve

7 = 15x - 8x

7 = 7x

1 = x

The complete question:

The stem-and-leaf plot shows the test scores for a chemistry class.

How many students had a score greater than 90 points?

A. 6

B. 7

C. 8

D. 9

Solution:

The number of students had a score greater than 90 points is 7. So option B is correct.

A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.

To the left of the vertical bar are the tens places.

As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.

To the right are 6 values - 1, 2, 3, 4, 6, and 7.

So there are six scores here higher than 90:

91, 92, 93, 94, 96, and 97.

Now we move lower to 10 in the tens place.

There is one score there - 100. (That smart kid.)

Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.

Hence, the number of students is 7

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In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.

To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.

The diagonal WX is the hypotenuse of right triangle WXY, so we have:

WX^2 = WY^2 + XY^2

Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:

YZ^2 = XY^2 + XZ^2

Substituting the given values for WY and XZ, and x = 2, we get:

WY = 24(2) - 8 = 40

XZ = -18(2) + 13 = -23

Plugging these values into the equations above and simplifying, we get:

WX^2 = 40^2 + XY^2

YZ^2 = XY^2 + (-23)^2

Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:

40^2 + XY^2 = XY^2 + (-23)^2

Simplifying, we get:

40^2 + 23^2 = 2XY^2

XY^2 = (40^2 + 23^2) / 2 = 1039

Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:

WX^2 = 40^2 + 1039 = 1679

YZ^2 = 1039 + (-23)^2 = 1598

Taking the square roots, we get:

WX = sqrt(1679) ≈ 40.97

YZ = sqrt(1598) ≈ 39.98

Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.

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_____The given question is incomplete, the complete question is given below:

Find the lengths of the diagonals of rectangle WXYZ.

WY = 24x-8

XZ = -18x+13

x= 2

The length of each diagonal is ___ units.

Answer:

75.50 + 14x - (35.50 + 9x) = 40 + 5x

Step-by-step explanation:

Answer:answer

Step-by-step explanation:because

Answer:

B, C, A.

Step-by-step explanation:

In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.

Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)

Next, we can use the perimeter equation of the triangle, which is

KL + LM + KM = 27, to find the value of x:

x - 4 + x + 4 + 2x - 1 = 27

4x = 36

x = 9

So, the lengths of the sides of the triangle are

KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.

Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)

cos A = 74 / 60

A = cos^-1 (74/60) = approximately 49.7°

Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:

B + C = 180° - 49.7° = 130.3°

B / sin B = LM / sin A

B = sin^-1 (sin B / sin A) * LM / sin A

C = 130.3° - B

The angles of triangle KLM in order from least to greatest are approximately:

B, C, A.

Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.

[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]

Here we have two fractions top and bottom

[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]

We have division in between . we reverse the second fraction and multiply it with first fraction.

[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]

Now we factor both numerator and denominator

[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]

Replace the factors,

[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]

We cancel out same factors at the top and bottom

So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]

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The missing corresponding side length of figure B is 30 meter.

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Two figures are said to be similar if the ratio of their corresponding sides are in the same proportion.

Figures A and B are similar. Figure A has a perimeter of 72 meters and one of the side lengths is 18 meters. Figure B has a perimeter of 120 meters. Find the missing corresponding side length.

Let x represent the missing side length. Hence:

Scale factor = figure B perimeter / figure A perimeter = 120/72

Hence:

scale factor = figure B side length / figure A side length

substituting:

120/72 = x / 18

x = 30 meter

The missing side length is 30 meter.

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Not sure but i think it's 6.3.

Pythagoras theorem

a²+b²=c²

6.9 is the hypotenuse (c)

2.9 is the base (b)

a is the altitude of the wall or the height of the wall (a)

a²+2.9²=6.9²

a= 6.3

Answer:

16% is the answer.

Answer:

16%

Step-by-step explanation:

$6 divided by $5.04 = 0.84

0.84 x 100 = 84%

100 - 84 = 16

6 - 5.04 = 0.96

0.96 divided by 6 = 0.16

0.16 x 100 = 16

Answer:

A ratio of 5 parts water to 1 part fertilizer for watering plants. This ratio ensures that the plants receive the proper amount of nutrients without being over-fertilized, which can harm their growth.

A ratio of 5 parts rest to 1 part exercise for a healthy lifestyle. This ratio helps to maintain a healthy balance between rest and physical activity, allowing for proper recovery and growth. It also ensures that a person does not over-exercise and become exhausted, which can lead to injury or burnout.

The total surface area of the given prism would be = 504

The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L

where a = 7

L = 14.5

Area = 2(7²) + 4 ( 7× 14.5)

= 2×49 + 4( 101.5)

= 98 + 406

= 504

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Answer:

x=-2(3-2√2), -2(3+2√2)

well, let's first off get the whole area of the circular garden, and then from it subtract the area of the squarish sculpture, thus what's leftover is simply the shaded area, or just the garden minus the sculpture.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{whole~circle}{\pi (6x)^2}~~ - ~~\stackrel{square}{(4x)(6x)}}\implies 36\pi x^2-24x^2\implies {\Large \begin{array}{llll} 12x^2(3\pi -2) \end{array}}[/tex]

well, if we use the vertex form of a parabola, we can pretty much see the parabolas all pretty much have a vertext at the origin, (0,0), now, let's take a look of a point they go by, Check the picture below.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=4 \end{cases} \\\\\\ 4=a(4-0)^2 + 0\implies 4=16a\implies \cfrac{4}{16}=a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}x^2}[/tex]

now let's do D

[tex]\begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=-1\\ y=-3 \end{cases} \\\\\\ -3=a(-1-0)^2+0\implies -3=a\hspace{5em}\boxed{y=-3x^2}[/tex]

The resulting sum function if x is equivalent to 2 is 18

Composite functions are known as function of a function

Given the following functions

f(x) = 3x + 5 and;

g(x) = 4x - 1.

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

(f+g)(x) = 3x + 5 + 4x - 1

(f+g)(x) = 7x + 4

Substitute x = 2 into the result

(f+g)(2) = 7(2) + 4

(f+g)(2) = 18

Hence the value of the sum of the function when x = 2 is 18

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The factored form of 8x^2+2x-3 is (8x-3)(x+1).

The factored form of 16x^2-1 is (4x+1)(4x-1). The expression 6x^2+1 cannot be factored further,

So the factored form of 36x^2+6 is 6(6x^2+1).

Factoring is a mathematical process that involves breaking down a complex expression into simpler terms that can be multiplied together to obtain the original word. In algebra, factoring is finding the factors or the prime numbers that multiply together to give the original polynomial.

For example, the expression x^2 + 5x + 6 can be factored as (x+2)(x+3). Factoring is a useful tool in solving equations and simplifying expressions, as it allows us to manipulate the original expression in a more manageable way. In addition, factoring is used in various fields such as cryptography, signal processing, and computer science. For instance, factoring large numbers is an important problem in cryptography and is used to secure data transmission.

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The exponential function that shows Riley's target mileage is y = 12(1.1)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent Riley target mileage x weeks after she starts training.

She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Hence:

a = 12; b = 100% + 10% = 110% = 1.1

The exponential function is y = 12(1.1)ˣ

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Answer: 5 1/4

Step-by-step explanation:

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

[tex]C = \frac{5}{9} (F- 32)[/tex]

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

power of ten

Step-by-step explanation:

Answer:

Option 1 and 5 will be your answer :)

Step-by-step explanation:

Let the equation representing number of sold is,

y - y' = m(x - x')

Where m = number of condo sold per month  

(x', y') is a point from the given table,

Slope of line passing through two points  and  =

Slope of the passing through (1, 8) and (0, 11) will be,

m =  = -3

Therefore, equation of the line passing through (3, 2) and slope (-3),

y - 2 = (-3)(x - 3)

y - 2 = -3(x - 3)

Similarly, equation of the line passing through (0, 1) and slope (-3),

y - 11 = -3(x - 0)

Therefore, Option (1) and (5) will be the answer.

Answer: 165 (look at the image for the solution)

Step-by-step explanation:

Answer:

x = 655

Step-by-step explanation:

find the pressure of x and y by using radical expressions and then solving it with the theory called x ^2+ y^2 = c^2

Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

Answer: 168 in.

Step-by-step explanation:

Feet to inches:

14ft = 168 in.

or

12 x 14 = 168.

Answer: 4 ft 3.8 inches

Step-by-step explanation:

First I converted the measurements to inches to make it easier-

Man - 74in

Tree - 240in

Tree shadow - 168in

240/168 = 74/x

x=51.8

Answer:

1.666... or 1 2/3

Step-by-step explanation:

The table needs to change number of Bags to Clementines.

And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price

Answer:

164 degree is the answer

Answer:

Step-by-step explanation:

Chord PM and PN are equal

arc PM = arc PN

164=5x+4

x=32

arc PN = 5x+4 = 5(32)+4=164