In triangle OPQ, o=700 cm, p=840 cm and q=620. Find the meaure of ide P to the nearet degree

Answers

Answer 1

The measure of side P to the nearest degree is 79 degrees.

Given:

ΔOPQ ,

O = 700 cm,

P = 840cm

Q = 620cm.

To find:

The measure of angle P.

According to the Law of Cosines:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:

                                   [tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]

Using Law of Cosines ΔOPQ, we get,

           cos P = o² +q²- p² / 2oq

       ⇒ cos P = (700)² + (620)² -(840)² /2×700×620

       ⇒ Cos P = 490000 + 384400 - 705600 / 868000

       ⇒ Cos P = 168800/868000

on further simplification, we get,

Cos P = 0.19447

P = Cos⁻¹ (0.19447)

P = 78.786236

P = 79.

∴ the measure of angle P is 79 degrees.

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Therefore, the measure of angle P is 79 degrees.


Related Questions

Write an equation in slope-intercept form of the line shown.

Answers

answer would be: y=2x-5

you first need to find the slope which is 2/1. Then you can use that slope to find the y-intercept which is b. Just go down 2 over 1 until you reach a point on the y - axis and it will land on -5

Determine the value for k in the equation k-173.54 = 294.57

Answers

Answer:

468.11

Step-by-step explanation:

k = 294.57 + 173.54 = 468.11

Answer:

k = 468.11

Step-by-step explanation:

Given equation,

→ k - 173.54 = 294.57

Now the value of k will be,

→ k - 173.54 = 294.57

→ k = 294.57 + 173.54

→ [ k = 468.11 ]

Hence, value of k is 468.11.

PLEASE HELP ME WITH THIS!!!

Answers

The composite figure has an area of 205 square feet

How to determine the area of a composite figure

In this question we find the composite figure formed by two right triangles and two rectangles, whose total area is the sum of the areas of the two right right triangles and two rectangles. Then, the area formula is shown below:

A = Σ A' + Σ A''

Where:

A - Total area, in square feet.A' - Total area of the two rectangles, in square feet.A'' - Total area of the two right triangles, in square feet.

The area formulas for right triangles and rectangles:

Right triangles

A = 0.5 · b · h

Where:

b - Base, in feet.h - Height, in feet.

Rectangles

A = b · h

Now we proceed to calculate the area of the composite figure:

A = 0.5 · (13 ft) · (20 ft) + 0.5 · (11 ft) · (4 ft) + (4 ft) · (8 ft) + (7 ft) · (3 ft)

A = 130 ft² + 22 ft² + 32 ft² + 21 ft²

A = 130 ft² + 75 ft²

A = 205 ft²

The area of the composite figure is equal to 205 square feet.

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Simplify the expression to a polynomial in standard form: (x + 1) (2x^2 - 3x - 7)

Answers

Answer:

2x^3-x^2-10x-7

Step-by-step explanation:

Distribute x to 2x^2, 3x, and -7

Then, distribute 1 to 2x^2, 3x, and -7

Hope this helps.

:)

Si tuviera 4 huevos y un ladrón me lleva 3 y el gallo que tengo pone 5 cuántos huevos tengo.

Answers

Tengo un total de 3 huevos en la última.

Los rompecabezas también son una excelente manera de pensar fuera de la caja. Resolver acertijos fortalece las conexiones entre las células cerebrales y forma nuevas células cerebrales, mejorando así la memoria. Resolver acertijos es una excelente manera de mejorar tu memoria a corto plazo.

Este acertijo viral debe leerse con atención. Su primer pensamiento podría ser que este es un problema matemático simple.

Si tuviera cuatro huevos

Un ladrón me da 3 huevos,

Mi gallo de granja pone 5 huevos,

¿Cuántos huevos tengo?

La explicación lógica de este acertijo es "Para empezar, el acertijo dice 'Si tuviera 4 huevos', pero este es solo un escenario y no tenías ningún huevo en primer lugar. Así que eso es 0 huevos.

Entonces el ladrón te dio 3 huevos.

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10 A car depreciates in value at 15% per year If the car is bought for £20,000, how much will it be worth in 5 years.​

Answers

Answer:

£8884.10625

Step-by-step explanation:

15% of £20,000:

20000x15/100=£3000

20000-3000=£17000

15% of £17000:

17000x15/100=£2550

17000-2550=£14450

15% of £14450:

14450x15/100=£2167.5

14450-2167.5=£12282.5

15% of £12282.5:

12282.5x15/100=£1842.375

12282.5-1842.375=£10440.125

15% of £10440.125:

10440.125x15/100=£1556.01875

10440.125-1556.01875=£8884.10625

Since the car loses 15% of it's value each year, it retains 85% of the value.

Value after 1 year = 85% of original value.

Value after 2 years = 85% of value after year 1

Value after 3 years = 85% of value after year 2

and so on...

We could calculate this year by year or we could do a single calculation to obtain the value.  We need to take 85% of the original value a total of 5 times, since we're wondering about the value in 5 years.

value after 5 years = 20000(0.85)(0.85)(0.85)(0.85)(0.85)

value after 5 years = 20000(0.85)^5

value after 5 years ≈ 8874.10625

So the value will be 8874.11 pounds in 5 years.

f(x) = x^2. What is g(x)?

Answers

If the function f(x) = [tex]x^2[/tex], then the function g(x) = [tex]-x^2-2[/tex]

From the given graph

The function is

f(x) = [tex]x^2[/tex]

The function is the rule the shows the relationship between one variable and another variable. If one variable is independent variable and another variable will be dependent variable. We can also says that the it show the relationship between input and output of the function

We can see that the function g(x) is the reflection of the function f(x) at y = -2

The reflection of f(x) = - f(x)

= - [tex]x^2[/tex]

The reflection of f(x) at y = -2 is

f(x) =  [tex]-x^2-2[/tex]

Then the function g(x) = [tex]-x^2-2[/tex]

Hence, If the function f(x) = [tex]x^2[/tex], then the function g(x) = [tex]-x^2-2[/tex]

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8 more than triple a number is -8

Answers

Answer:

8+3x=-8

x=-5 1/3

Step-by-step explanation:

triple a number means to multiply by 3

More than is to add

8+3x=-8

-8.      -8

3x=-16

x=-5 1/3

Hopes this helps please mark brainliest


Let's find the slope of the line containing the points (-4,1) and (2, 3).

Answers

Answer:

1/3

Step-by-step explanation:

Compute the slope of the line through the following points:

p_1 = (-4, 1) and p_2 = (2, 3)

The slope of the line through (x_1, y_1) and (x_2, y_2) is:

(y_2 - y_1)/(x_2 - x_1)

Substitute (x_1, y_1) = (-4, 1) and (x_2, y_2) = (2, 3):

= (3 - 1)/(2 - -4)

3 - 1 = 2:

= 2/(2 - -4)

-(-4) = 4:

= 2/(2 + 4)

2 + 4 = 6:

= 2/6

The gcd of 2 and 6 is 2, so 2/6 = (2×1)/(2×3) = 2/2×1/3 = 1/3:

Answer:  = 1/3

The function f={(x,y)|y =mx+c} is a. Quadratic function b. Constant function c. Cubic function d. Linear function

Answers

⇒The given function is a linear function as we know the general equation of a straight line is y=mx+c

Option d is the answer.

The function f(x) = 4x + 10 models the amount of money francis makes when babysitting for x hours. How much money will he make for 2 hours of babysitting work?.

Answers

The amount of money that he will make for 2 hours of baby sitting work is $18

The function is

f(x) = 4x + 10

The function f(x) is the amount of money Francis makes when babysitting for x hours

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will independent variable

The function

f(x) = 4x + 10

The number of hours x = 2 hours

Substitute the values of x in the function

f(2) = 4(2) + 10

f(2) = 8 +10

f(2) = $18

Hence, the amount of money that he will make for 2 hours of baby sitting work is $18

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What’s the newer to this??

Answers

Answer:point c

Step-by-step explanation:

because point c is three lines down from -1. making -1 and 3/8

Answer:

Point C

Step-by-step explanation:

Because -1 3/8 is negative, it is less than 0.

Point A is eliminated.

Because | -1 3/8 | > | 1 |,

Point B is eliminated.

There are 8 tick marks in between (and including) the integers. Each small unbolded tick mark represents 1/8.

Because 3/8 is 3 times 1/8, count 3 down from -1.

You are left with C.

pls guys i need help whats 1 + 1

Answers

Answer:

2

Step-by-step explanation:

Answer: 1 + 1 is two!

Step-by-step explanation:

We know this because, we can count our fingers. Your pointer finger and your index finger put together is a total of two fingers!

There are other ways to do simple addition, but I find counting fingers the easiest!

Hope this helped you! Have a great day :)

the diameter of a circle is 10 yards. find the approximate circumference for the circle, using 3.14 for pie.

Answers

Answer:

31.4 yards

Step-by-step explanation:

Formula for circumference is C = π*d

10*3.14

31.4 yards

Hope this helps!

Answer:

[tex] \sf C = 31.4 \: yards[/tex]

Step-by-step explanation:

The formula to find the circumference of a circle is :

[tex] \sf \: C = \pi \: d[/tex]

Here,

d --> Diameter ---> 10 yards

Let us find it now.

[tex]\sf \: C = \pi \: d \\ \sf \: C = 3.14 \: \times 10 \\ \sf \: C = 31.4 \: yards[/tex]

A contractor purchases 6 dozen pairs of padded work gloves for ​$89.28. incorrectly calculates the unit price as ​$14.88 per pair for the expense report. What is the correct unit​ price?

Answers

Answer:

It is about $0.07 per pair for the expense report.

Step-by-step explanation:

You have to divide 89.28 by 6 to get the unit price. 89.28/6=0.06720430107 or about $0.07. Hope this helps! I am up doing math too -_-. Please don't mark me brainliest, I just love to help.


To get the correct price per pair, divide the total $89.28 by 6*12 = 72 pairs.

please answer fast and a explanation would be nice but doesn’t have to be there

Answers

The inequality in the slope-intercept form is y≥(3x/7)+3 when the graph is in of a linear inequality.

What is meant by slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844)[2] and Todhunter's formulations of the equation for a straight line as y = mx + b and y = mx + c, respectively.

Let the linear equation be

y=m x +c

From the graph the lines are passing through the points (-7,0), (0,3)

Slope m =(3-0)/(0+7)

m=3/7

c=y-intercept

Therefore, c=3

Substitute the values in the above equation.

y=(-3/7)x+3

7y=3x+21

But, here we need to use the inequality which satisfies the shaded region.

Let us consider the point (1,2)

7(2)=3(1)+21

14=24 (But 14≠24)

Therefore, 14≥24

So, we have to use ≥ sign

7y≥3x+21

y≥(3x/7)+3

The inequality in the slope-intercept form is,

y≥(3x/7)+3

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according to a report published by the federal interagency forum on child and family statistics (2015), identify the group of families in which the proportion of children has contracted sharply from 1980 to 2013.

Answers

The group of families in which the proportion of children has contracted sharply from 1980 to 2013 is Middle-Income group.

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Its very annoying and I feel like its impossible

Answers

wouldn’t it be the top middle one ?? they add up to 14
it’s simple, 6+3 is 9 then u add the 2 dots witch makes it 11. The. u add the other number 3 witch makes it 14. Spin conclusion it’s the top middle

1/4 plus (-1/2) equivalent or non

Answers

Solution of 1/4 plus (-1/2) giving the answer in equivalent form of fraction

-1/4 least form of the fraction-2/8 equivalent form of the fraction

How to determine the addition problem

The problem involves addition of fractions

The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.

The fraction required are:

= 1/4 plus (-1/2)

= 1/4 + -1/2

= 1/4 - 1/2

= 1/4 - 2/4

= -1/4

-1/4 is in the least form of the fraction.

The equivalent form is written as

-2/8

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y= mx + b
Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of lemonade they sell.
Write an equation that shows how their total earnings, y, depend on the number of cups sold, x.
Do not include dollar signs in the equation. what does y equal?

Answers

The correct equation that shows their total earnings, y, depend on the number of cups sold, x will be;

⇒ y = 2x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

They earn $2 for each cup of lemonade they sell.

Now,

Let number of cups = x

And, Total earnings = y

Since, They earn $2 for each cup of lemonade they sell.

So, We get;

⇒ y = 2x

Where, x is number of cups and y is total earnings.

Thus, The correct equation that shows their total earnings, y, depend on the number of cups sold, x will be;

⇒ y = 2x

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I have no idea how to do this. Please help.

Answers

Answer:

None

Step-by-step explanation:

In order to solve an inequality you must isolate x on one side, so begin bringing the numbers from one side to another to make x the subject.

(numbers change their sign when brought to the other side)

5 > - 6 - 2x

5 + 6 > - 2x

11 ÷ - 2 > x

-5.5 < x (the sign switches when you divide or multiply by a negative number)

The solution is -5.5, which means none of the values provided are the solution.

Five poitive whole number add up to 47
One of the number i a multiple of 9
The other four number are equal. Work out the reult when the five number are multiplied. Optional working

Answers

The multiplication of 5 whole numbers is 16875

Given that

5 positive whole numbers add up to 47

we solve these by using system of equation  

let 5 whole numbers be p, q, r, s and t

equation is: p + q + r + s + t = 47

one of the number is a multiple of 9 the other four numbers are equal  

let p be the multiple of 9

equation is: p + q + q + q = 47

p + 4q = 47

let's try trial and error method q and p are whole numbers, they cannot be decimal  

let p = 9

9 + 4q = 47

4q = 47-9

4q = 38

q = 9.5 it is not whole number, so this is not the number

let p= 18

18 + 4q = 47

4q = 47-18

4q = 29

q = 7.25 it is not whole number, so this is not the number

let p = 27

27 + 4q = 47

4q = 47 -27

4q = 20

q = 5

then multiplication of these 5 whole numbers is

27 * 5*5*5*5 = 27*625=16875

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Paragraph on cyclone

Answers

Cyclones are cyclic rotating air masses around a low atmospheric pressure center which when viewed from above looks like a circle. It causes heavy rainfall and thunderstorm. The speed of a cyclone often varies between 30 to 50 km which is enough to destroy anything behind its path. It moves clockwise in the southern hemisphere and anticlockwise in the northern hemisphere.

There are two types of cyclones Tropical cyclones and Extratropical cyclones:

Tropical cyclones: Cyclones that develop in the tropics are known as tropical cyclones.Extratropical cyclones: Cyclones that develop behind the tropics are known as extratropical cyclones.

There are different names for cyclones in different countries such as:

Typhoons in the China SeaTropical cyclones in the Indian OceanHurricanes in the Caribbean SeaTornadoes in the USAWilly Willies in Northern Australia

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Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes as nickels. How many of each type of coin does Johnny have?
| BTW this is a system of equations question

Answers

The number of each of the coin in Johnny's possession are

Nickel = $0.75Dimes = $1.5

How to determine the number of each of the coin Johnny has

Information from the question

Johnny has some nickels and dimes in his pocket, and the change is worth $0.75

He has twice as many dimes as nickels

The change worth $0.75

Nickels, N - Dimes, D = 0.75

D - N = 0.75

twice as many dimes as nickels

2N = D

N = D / 2

therefore

D - D/2 = 0.75

D/2 = 0.75 = N

D = 1.5

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In a ale, the cot of a coat i reduced from $85 to $67. 50. Calculate the percentage reduction in the cot of the coat

Answers

The percentage reduction in the cost of the coat is 20.58 %

As given,

Cost of coat =  $ 85  

Price in sale=  $ 67.50

Reduced price =$ 85  - $ 67.50= $ 17.5

Therefore to find the percentage reduction in the cost of the coat

% Reduction = (Reduced price / original price) x 100

= ( 17.5 / 85 ) x 100

= 20.58 %

Hence, the percentage reduction in the cost of the coat is 20.58 %

The percentage reduction formula is a mathematical tool that helps determine how much of a substance can be removed from a sample. This formula can be used to calculate the percentage of a substance that can be removed from a sample if the starting concentration and the ending concentration are known.

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If CP=590 and profit=75, find SP​

Answers

Answer:

Sp=cp+p

sp=590+75

sp=625

An athlete run at a rate of 309 yd. /min. If one lap i 315 yard how many lap doe he run in 19 minute?

Answers

If an athlete runs at a rate of 309 yd. /min. If one lap is 315 yard athlete then athlete covers 18.63 laps in 19 minutes

What is a conversion factor?

A fraction that is equal to "1" is a conversion factor. The numerator and denominator are the same amount, but they are expressed in different units. It is used to change a number's unit of measurement. In order to do that, multiply the initial number by the fraction equal to "1"; this maintains the original number's value but modifies the units.

An athlete run at a rate of 309 yds. /min.

If one lap is 315 yard

Then total number of yards covered by the athlete is 5871.

I.e. 309 x 19 = 5871.

So total laps covered by the athlete in 19 minutes is

     [tex]\frac{5871}{315}=18.63[/tex]

Hence, athlete covers 18.63 laps in 19 minutes

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1 What is the cost to get into a Green Cab?
2 How much does it cost per mile for a Green Cab?
3 What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?

Answers

1. $5

2. $2 for each mile

3.equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Caby=x+5

What is an explanation of the slope-intercept form?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

1. The graph shows that the Green Cab will cost you $5 for a distance of 0 miles.

2. According to the graph, $1 is spent for every mile traveled.

3. Because y increases by the same amount for every 1 increase in x, the slope is 1.

The slope intercept form is y=mx+b.

m=slope

intercept b=y

Since we are aware that the slope is 1, we can enter it.

y=1x+b

=y=x+b

By looking at the graph and calculating what y equals when x is 0, we may get the y intercept.

It is the y intercept (0,5)

So that the equation is in slope intercept form, we may enter that.

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A bag contains 30 red marbles and 15 purple marbles. Mr. Clark wants to add 270 marbles to the bag. He wants the ratio of red to purple marbles to remain the same. How many of each should he add? A. 70 red marbles 200 purple marbles B. 200 red marbles and 70 purple marbles C. 180 purple marbles and 90 red marbles D. 180 red marbles and 90 purple marbles

Answers

Answer: 20 PURPLE marbels

Step-by-step explanation:

no explanation

Answer:

the is 200 purple marbles 70 red marbles

Select the point that is solution to the system of inequalities.
y x^2-6

A. (0,-2) B. (0,6) C.(1,6) D. (-4,-2)

Please help!

Answers

The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

Given that,

The system of inequality

y < x² + 2

y > x² - 6

We have to find the common point of the system of inequality.

We know that,

The graph is shown in the image.

Using the graphing technology,

A will be the first equation's vertex (0,2)

The parabola's outer region will be shaded and its boundary will be a dotted line because y is less than the value required by the quadratic equation.

In a similar way, the second equation's vertex, (0,-6), will be a dotted parabola with shaded inner portions.

The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

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