Construct a quadrilateral RISK in which RI= 4.5 cm, IS=5.6 cm, SK=6 cm, RK=3.5 cm and RS=7.2 cm. Measure the diagonal KI.

Answers

Answer 1

The measure of the diagonal KI is approximately 6.465 centimeters.

The diagonals of the quadrilateral RISK are represented by line segments RS and KI, both measured in centimeters. There are two triangles forming the quadrilateral: [tex]\triangle RIS[/tex], [tex]\triangle RKS[/tex]

By Law of Sine and Law of Cosine we determine the measures of all internal angles:

Triangle RIS

[tex]RS^{2} = RI^{2}+IS^{2}-2\cdot RI\cdot IS \cdot \cos I[/tex] (1)

[tex]\frac{RS}{\sin I} = \frac{RI}{\sin S'} = \frac{IS}{\sin R'}[/tex] (2)

Triangle RKS

[tex]RS^{2} = RK^{2} + KS^{2}-2\cdot RK\cdot KS\cdot \cos K[/tex] (3)

[tex]\frac{RS}{\sin K} = \frac{RK}{\sin S''} = \frac{KS}{\sin R''}[/tex] (4)

[tex]S = S' + S''[/tex] (5)

[tex]R = R' + R''[/tex] (6)

By (1) and (3) we find the values of angles I and K:

[tex]I = \cos^{-1}\left(\frac{RI^{2}+IS^{2}-RS^{2}}{2\cdot RI\cdot IS} \right)[/tex]

[tex]I \approx 90.261^{\circ}[/tex]

[tex]K = \cos^{-1}\left(\frac{RK^{2}+KS^{2}-RS^{2}}{2\cdot RK\cdot KS} \right)[/tex]

[tex]K\approx 94.903^{\circ}[/tex]

By (2) and (4) we find the remaining angles for each triangle:

[tex]S' = \sin^{-1}\left[\left(\frac{RI}{RS} \right)\cdot \sin I\right][/tex]

[tex]S' \approx 38.682^{\circ}[/tex]

[tex]R' = \sin^{-1}\left[\left(\frac{IS}{RS} \right)\cdot \sin I\right][/tex]

[tex]R' \approx 51.057^{\circ}[/tex]

[tex]S'' = \sin^{-1}\left[\left(\frac{RK}{RS} \right)\cdot \sin K\right][/tex]

[tex]S'' \approx 28.969^{\circ}[/tex]

[tex]R'' = \sin^{-1}\left[\left(\frac{KS}{RS} \right)\cdot \sin K\right][/tex]

[tex]R'' \approx 56.128^{\circ}[/tex]

Then, we have the values of angles R and S by (5) and (6):

[tex]S \approx 67.651^{\circ}[/tex], [tex]R \approx 107.185^{\circ}[/tex]

The measure of the diagonal KI is found by the Law of Cosine:

[tex]KI = \sqrt{IS^{2}+SK^{2}-2\cdot IS\cdot SK\cdot \cos S}[/tex]

[tex]KI \approx 6.465\,cm[/tex]

The measure of the diagonal KI is approximately 6.465 centimeters.

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Related Questions

use the mutipler method to increase £88 by 14%

Answers

Answer:

£100.32

Step-by-step explanation:

An increase of 14% on the original amount (100%) is

100 + 14 = 114% = [tex]\frac{114}{100}[/tex] = 1.14 , then

£88 × 1.14 = £100.32

Which expression is equivalent to log Subscript 5 Baseline (StartFraction x Over 4 EndFraction) squared? 2 log Subscript 5 Baseline x log Subscript 5 Baseline 4 2 log Subscript 5 Baseline x log Subscript 5 Baseline 16 2 log Subscript 5 Baseline x 2 log Subscript 5 Baseline 4 2 log Subscript 5 Baseline x log Subscript 5 Baseline 4.

Answers

The required equivalent expression for  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].

Given expression,

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].

We have to find the Equivalent fraction of  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].

We know that from the properties of logarithm, the following identities

[tex]log\ m^{n} =n\ log\ m[/tex] .....(1)

[tex]log\ \frac{m}{n} = log\ m- log\ n\\[/tex].......(2)

Now, [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5} \ \frac{x}{4}[/tex] ( using 1 identity)

Again using 2 identity, we get

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2[ log_{5}\ x-log_{5}\ 4 ][/tex]. (using 2 identity)

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex]

Hence the required equivalent expression for  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].

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Answer:

C on edge

Step-by-step explanation:

The image shows the fossilized remains of Glyptodon, an animal group that became extinct about 10,000 years ago, and a modern armadillo. Both animals are mammals that share similar physical characteristics, such as short legs, a long tail, and a shell composed of bony plates. Which is the best explanation for the similarity between Glyptodon and the armadillo? The armadillo and Glyptodon descended from unrelated animals. The armadillo and Glyptodon descended from unrelated animals. The armadillo and Glyptodon are the same species. The armadillo and Glyptodon are the same species. The armadillo and Glyptodon lived in different environments. The armadillo and Glyptodon lived in different environments. The armadillo and Glyptodon descended from a common ancestor. The armadillo and Glyptodon descended from a common ancestor.

Answers

Answer

The armadillo and Glyptodon descended from a common ancestor.

Step-by-step explanation:

round 0.006772 to 1 significant figure

Answers

Answer:

[tex]0.007[/tex]

Step-by-step explanation:

Round to the required significant figure:

[tex]0.007[/tex]

6- 1/3 = decimal maths

Answers

Answer:

To get 6 1/3 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 6 1/3 mixed number to decimal form: Step 1:Multiply the whole number by the denominator: 6 × 3 = 18

Step-by-step explanation:

The value of the expression 6 - 1/3 will be 17 / 3.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

6 and 1/3

Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 6 - 1/3

⇒ (18 - 1) / 3

⇒ 17 / 3

The value of the expression 6 - 1/3 will be 17 / 3.

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- 3m + 7 - 2n


Can I get the answer

Answers

Answer:

3m + 5

Step-by-step explanation:

uhmm i think 2n is i cant solve here hope it helps

8. What number should come in the box to make the following statement true?
34 + 32 = 9 × ___

Answers

[tex]\huge\boxed{\sf{Hello\:there!}}[/tex]

First of all, we should add 34 and 32:

34+32=66

Now, let's divide both sides by 9:

66÷9=7.3333...

[tex]\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}[/tex]

[tex]\huge\bold{Good\:luck!}\\\huge\mathfrak{LoveLastsAllEternity}[/tex]

Can someone please take the time out of their day and help me with this question

Answers

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

[tex] \red {\mathbb{ \underline { \tt By \: using \: Pythagoras \: theorm}}}[/tex]

[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ x {}^{2} = (7 {}^{2} + 6 {}^{2} )ft {}^{2} \\ x {}^{2} = (49 +3 6)ft {}^{2} \\ x {}^{2} = 85 ft\\ x = \sqrt{85 } ft \\ [/tex]

the length of missing side= √85=9.2 ft

Solve the inequality . Graph solution . 1/5 > d+ 4/5

Answers

Answer:

B

Step-by-step explanation:

Answer:

b. d>-3/5

Step-by-step explanation:

L.C.M=5

5×1/5>5×d+4/5×5

1>5d+4

1-4>5d

-3>5d

-3/5>5d/5

-3/5>d

multiply the expression (1/3 m-n)^2​

Answers

Answer:

{(

Answer : 1/4 m^2 -mn + n^2

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 5 hours of burning, a candle has a height of 26 centimeters. After 24 hours of burning, its height is 14.6 centimeters. What is the height of the candle after 18 hours?

Answers

Answer:Let Y = height

Let X = time

Height is a linear function of time, so Y = mX + b, where m is the slope and b is the y-intercept.  

We can calculate the slope from the given values (8,20.4) and (19,18.2)

Slope = (y2 - y1) / (x2 - x1) = (18.2 - 20.4) / (19 - 8) = -2.2 / 11 = -0.2

This means that the height of the candle is going down by 0.2 cm per hour

Since 16 hours is 8 hours after the first data point of (8,20.4), the height will go down by 8 * (-0.2) = -1.6 cm in the 8 hours between hour 8 and hour 16.  

So the height of the candle after 16 hours = 20.4 - 1.6 = 18.8 centimeters

Step-by-step explanation:

how many steps will it take you to get to 100 if every even number you double and every odd number u take 1 away

Answers

Let’s go with 200 steps. Since 100 are even, 100 odd we can do something like this.

100 * 2 is 200. However since the other 100 is an odd place we will subtract 100 so our final answer is 100.

Logically, you would need 200 steps exactly to reach your goal.

( 100 if this is a trick question (‘: )

What is the sum of ( x - 4) and (4x -1)?

Answers

Answer: 5x-5 or 5(x-1)

Step-by-step explanation:

1. take away parentheses, add because asking for "sum"

=x-4+4x-1

2. add

=5x-5

3. if u need to factor it:

5(x-1)

Isabella made two types of cakes: chocolate and vanilla. She cut all of the

chocolate cakes into 7 slices each and all of the vanilla cakes into 9 slices

each. If Isabella ended up with the same total number of slices of each type

of cake, what is the minimum number of slices of each type?

Answers

Answer:

To get the same total number of slices of each type of cake, the answer must be the LCM (lowest common multiple) of 7 and 9.

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70...

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...

As you can see so far, 63 is the lowest common multiple of both 7 and 9.

Thus, the answer is 63

Answer: 63 ( but give the person above me brainliest because they explained it better )

Step-by-step explanation:

If the cakes have the same amount of slices then we must find the lowest common multiple which is 63

So both cakes have 63 slices

A small van holds 8 students and a large van holds 12 students. There are a total of 48 students who plan to go on the field trip.

Answers

Sorry I don’t really understand the point you are trying to make. What’s the question?

Helppp meeee please

Answers

Answer:

The Equation for lyft is:

4.50x

The Equation for uber is

2.50x+5

Step-by-step explanation:

If you want to determine which one is better then you can just plug in the distance in place of x. For example if it asked you which one was better for 5 miles, uber or lyft you could plug 5 into the equation.

It would look like this

Lyft: 4.50 (5)= 22.5

Uber

2.50 (5) +5= 17.5

If the distance were 5 miles uber would be the better option.

Yes that would be the answer

Item 3 Martin is a chef and a caterer. When catering an event, he plans the amount of food to be prepared based on the number of people he needs to serve. The equation y = 7x represents the number of ounces of chicken required to serve x people. The equation y = 5x represents the number of ounces of fish required to serve x people. What is true of the comparison of the two graphs?

Answers

Answer:

The line representing the number of ounces of chicken required to serve x people is steeper than the line representing the number of ounces of fish required to serve x people.

Step-by-step explanation:

I took the test

Comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x people

Recall:

The linear equation of a proportional graph is represented as y = mx, where m is the slope or gradient.The larger the value of the slope, the steeper the slope of the graph.

Given the following:

Graph representing the number of ounces of chicken required to serve x people: y = 7x

The slope is 7.

Graph representing the number of ounces of fish required to serve x people: y = 5x.

The slope is 5.

Therefore, comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x people

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14. Which transformation from the graph of a function f(x) describes the graph of 10f(x)? 2. ( Responses: horizontal, vertical) 2. ( Responses: shift, stretch) 2. ( Responses: up, down, left, right, by a factor of) 10 units. 2. Answer it and then explain it please​

Answers

Answer: Your mom

Step-by-step explanation:

HEHEHEHA

A music store is having a clearance sale. All items are discounted by 15%. What is the sale price of a radio that regularly costs $20?

Answers

Answer:

17$

Step-by-step explanation:

Answer:

$17

Step-by-step explanation:

Since the discount is 15%, and 100% would be the full price, 100 - 15 = 85. You are paying 85% of the price. 20 * .85 = 17.

The following graph shows a proportional relationship.
What is the constant of proportionality between yyy and xxx in the graph?

Answers

Answer:

The constant of proportionality is thus 1

Step-by-step explanation:

Note that the green line passes through (6, 6) and has a y-intercept of 0.  Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.

The constant of proportionality is thus 1, which is also the slope of this line.

Why are scarcity and choice basic economic questions faced by every society?

Answers

Some areas can not afford the amount of stuff we have, like they can’t afford basic needs while we can afford needs and wants after needs. They have to use the amount they can for food and water.

subtracting 24 is the inverse of

Answers

Answer:

The inverse of subtracting 24 is adding 24.

Step-by-step explanation:

The inverse of subtraction is addition.

Does anyone know how to answer?

Answers

Answer:

  A, D, F

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet evaluate the function for you. Reflection over the y-axis means x is replaced by -x in the original function definition.

The values that show up on the reflected graph are ...

  (-7, -10.206)

  (0.5, -0.221)

  (9, -0.003)

The cafeteria made 19 mushroom pizzas and 57 pepperoni pizzas.What percentage of the pizzas were mushroom?

Answers

Answer:

the answer is 14.04

...............

25 % of pizzas were mushroom pizzas.

What is percentage?

Percentage is a measurement to find value of given number out of hundred.

Given that,

Number of mushroom pizzas = 19,

And number of pepperoni pizzas = 57.

Total number of pizzas = 19 + 57 = 76.

To find the number of percentage of pizzas of mushroom,

Use percentage property,

= (Number of mushroom pizzas / total pizzas) x 100

= (19 / 76) x 100

= 100/ 4

= 25 %

The required percentage of mushroom pizzas = 25 %.

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help please! a is wrong, that was my initial answer.

Answers

Answer:

D -1

Step-by-step explanation:

[tex]-6(3a+4)=3a-3[/tex]

[tex]-18a-24=3a-3[/tex]

[tex]-18a-3a=-3+24[/tex]

[tex]-21a=21[/tex]

a = [tex]\frac{21}{-21} =-1[/tex]

Hope this helps

What is the volume of a rectangular prism with a length of 2x, a width of x−2, and a height of x + 2?

Answers

Answer:2x³ - 8x is the volume of a rectangular prism.Step-by-step explanation:Volume: L x B x H=> (2x) × (x - 2)(x + 2)=> (2x) × (x² - 4)=> 2x(x² - 4)=> 2x³ - 8x units³ [According to DMAS rule]Conclusion:

Therefore, 2x³ - 8x units³ is the volume of a rectangular prism.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

(2x³ - 8x) is the volume of a rectangular prism.

What is volume?

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, a rectangular prism with a length of 2x, a width of (x−2), and a height of (x + 2)

Volume: L x B x H

= (2x) × (x - 2)(x + 2)

= (2x) × (x² - 4)

= 2x(x² - 4)

= 2x³ - 8x units³

Hence, 2x³ - 8x units³ is the volume of a rectangular prism.

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. .. . . . . . .. . .. . so easy

Answers

Answer: 7

Step-by-step explanation: if it's so easy, why do you need brainly? (not judging, just confused why you'd waste points)


Tamara wants to rent a jet-ski. Tamara's deal is to pay $60 to rent the jet-ski, plus $12.50 per hour. If
Tamara has $135 how many hours can Tamara use the jet-ski?

Answers

Answer:

6 hours.

Step-by-step explanation:

deal: 135-(60+12.5h)=y

let h= # of hrs

135-60=75.

75/12.5=6 hours.

What is √101.6064 in to 1 decimal place and in standard form?​
NEED ASAP

Answers

Note that

10² = 100

0.08² = 0.0064

and

101.6064 = 100 + 1.6 + 0.0064

It also happens that

1.6 = 2 • 10 • 0.08

which means

101.6064 = 100 + 1.6 + 0.0064

101.6064 = 10² + 2 • 10 • 0.08 + 0.08²

101.6064 = (10 + 0.08)²

101.6064 = 10.08²

which means

√101.6064 = 10.08

which, to one decimal place, is approximately 10.1.

What is the solution to this inequality?


−15x>75



x<−5


x>−5


x≥−5


x≤−5

Answers

Answer:

x < -5 (the first option)

Step-by-step explanation:

I hope this helps!

The solution of the inequality will be;

⇒ x < - 5

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 15x > 75

Now,

Since, The inequality is,

⇒ - 15x > 75

Hence, The solution of the inequality is,

⇒ - 15x > 75

⇒ - x > 75/15

⇒ - x > 5

⇒ x < - 5

Thus, The solution of the inequality is,

⇒ x < - 5

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