In a rectangle KLMN, the diagonals KM and LN intersect at O. (i) If KO = 4y + 6 and ON = 3y + 11, find the lengths of its diagonals. (ii) If ∠NKM = 32°, find ∠KON and ∠KMN. GUYS, IT'S VERY URGENT. I HAVE TO SUBMIT TOMORRIW. PLS ANS. PLS DON'T GIVE WRONG ANSWERS

Answers

Answer 1

Answer:

Step-by-step explanation:

In a rectangle KLMN, if the diagonals KM and LN intersect at O, then KO = ON

GIVEN

KO = 4y+6

ON = 3y+11

Equate

4y+6 = 3y+11

Collect like terms

4y-3y = 11-6

y = 5

KO = 4(5)+6

KO = 20+6

KO = 26

Note that KO = OM = LO = ON = 26

Hence ON = 26

For diagonal KM,

KO+OM = KM

KM = 26+26

KM = 52

LN = LO+ON

LN = 26+26

LN = 52

From.the digram, ∆KON is isosceles triangle hence <KON = KNO =32°

<KON = 180-(32+32)

<KON = 180-64

<KON = 116°

<ONM = 90-32

<ONM = 58°

∆ONM is also an isosceles triangle,

<ONM = <OMN = 58°

Hence <KMN = 58°


Related Questions

A,C and D are points on a circle of radius 4 cm, centre o. BA and BC are tangents to the circle. OB=10cm work out the length of arc ADC. give your answer correct to 3 significant figures

Answers

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

What is the solution of the equation x2=64

Answers

The answer for the equation is x=32

GEOMETRY/EASY PROBABILITY, urgent!

Answers

Answer:

2/7, 3/7

Step-by-step explanation:

Total outcomes=7

No. 6 outcomes=2

P(E)= Favourable outcomes/total outcomes

    =2/7

Total even no.= 3

∴ P(E)= 3/7

Mark me as brainliest

1.which of the following would save more fuel?
a.Replacing a compact car that gets 34 per gallon(mpg)with a hybrid that gets 54 mpg
b.Replacing a sport utility(SUV)that gets 18 mpg with a sedan that gets 28 mpg
c.Both changes would save the same amount of fuel.
2.Explain your reasoning for your choice.

Answers

9514 1404 393

Answer:

  1. b

  2. For each 1000 miles driven, (a) saves 10.9 gallons, while (b) saves 19.8 gallons

Step-by-step explanation:

The fuel savings will depend on the miles driven. If we use 1000 miles as the reference, the various vehicle fuel usages are ...

  gallons = miles/(miles/gallon)

  18 mpg: 1000/18 = 55.6 gallons

  28 mpg: 1000/28 = 35.7 gallons

  34 mpg: 1000/34 = 29.4 gallons

  54 mpg: 1000/54 = 18.5 gallons

So, ...

  replacing 34 mpg with 54 mpg saves 29.4 -18.5 = 10.9 gallons.

  replacing 18 mpg with 28 mpg saves 55.6 -35.7 ≈ 19.8 gallons.

Replacing the SUV with a sedan saves more fuel, assuming all vehicles are driven the same distance.

__

The fuel use reduction from 18 mpg to 28 mpg is about 36%, whereas from 34 mpg to 54 mpg. the reduction is about 37%. The SUV replacement is a better choice because the smaller fraction of a much larger fuel use is still more savings than obtained by replacing the compact car.

In a sequence of numbers, a3=0, a4=4, a5=8, a6=12, and a7=16. Based on this information, which equation can be used to find the nth term in the sequence, an?

an=4n−12
A sub n is equal to 4 n minus 12

an=−12n+4
A sub n is equal to negative 12 n plus 4

an=−4n+12
A sub n is equal to negative 4 n plus 12,

an=12n−4

Answers

Answer:

an=−4n+12

A sub n is equal to negative 4 n plus 12,

Step-by-step explanation:

4x - 5y = 10 solve for y=mx+b​

Answers

-5y = 10 - 4x

y = - 10 - 4x over 5

y = - 2(5 - 2x) over 5

hopefully this is correct

Plz help :( I don’t understand

Answers

PLEASE MARK AS BRAINLIST

Answer:

1. 2x-20+2x-15=13

4x-35=13

4x=13+35

4x=48

x=12

2. x-4+9=2x-4

2x-x= -4+9+4

x=9

3. IJK=41+130=171

4. KJD=88-50=38

An apple juice company produced 8.3 billion individual-size bottles of apple juice last year. If each bottle contains 355 milliliters of juice, how many milliliters of apple juice did the company produce?

Answers

Answer:

two trillion nine hundred forty-six billion five hundred million

The company produced 2946.5 billion milliliters.

What is multiplication?

Multiplication is a mathematical arithmetic operation.

The process of adding the same number many times is repeated addition.

Multiplication is a repeated addition.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Last year,

a company that makes apple juice produced 8.3 billion bottles of apple juice.

And 355 milliliters of juice occupied by each bottle.

then the company produced,

= 355 x 8.3 billion milliliters,

= 2946.5 billion milliliters.

Therefore, 2946.5 billion milliliters.

To learn more about multiplication;

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Ella purchased a game that was on sale for 12% off. The sales tax in her county is 6%. Let y represent the original price of the game. Write an expression that can be used to determine the final cost of the game.

A y − 0.12y

B 0.06(0.88y)

C 1.06(0.88y)

D y − 0.88y + 0.06y

Answers

Answer:

The expression that can be used to determine the final cost of the game is

1.06(0.88 y) ⇒ (C)

Step-by-step explanation:

If the price of an item is discounted, that mean its new price will be less its initial priceThe taxes on item, makes its new price greater than the initial price because tax is add

Let us solve the problem

∵ Ella purchased a game that was on sale for 12% off

→ That means the new price will (100% - 12%) of the initial price

∵ y represented the initial price of the game

→ Multiply y by (100% - 12%) to get the new price

∴ The new price = y (100% - 12%)

∴ The new price = y (88%)

→ Change 88% to normal number by divide it by 100

∴ The new price = y ([tex]\frac{88}{100}[/tex])

The new price = 0.88 y

∵ The sales tax in her county is 6%

→ That means the final cost will be (100% + 6%) of 0.88 y

∴ The final cost = (100% + 6%) × (0.88 y)

∴ The final cost = 106% × (0.88 y)

→ Change 106% to normal number by divide it by 100

∴ The final cost = [tex]\frac{106}{100}[/tex] × (0.88 y)

The final cost = 1.06(0.88 y)

The expression that can be used to determine the final cost of the game is 1.06(0.88 y)

Answer:

C. 1.06(0.88y)

Step-by-step explanation:

1890s was rounded to the nearest 10 what is the upper bound ​

Answers

Answer:

When rounding to the nearest ten, like we did with 1890 above, we use the following rules:

A) We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.

B) We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.

C) If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.

Step-by-step explanation:

Find the value of x so that line m is parallel to line l.

Answers

Answer:

-17

Step-by-step explanation:

The angles are corresponding angles so when the lines are parallel, the lines are equal

3x-12 = 4x+5

Subtract 3x from each side

3x-12 -3x = 4x+5-3x

-12 = x+5

Subtract 5 from each side

-12 -5 = x+5-5

-17 = x

Answer:

-17

Step-by-step explanation:

The two angles that are shown are *corresponding angles* which means they lie in the same spot, just on two different parallel lines. They are congruent angles. Therefore, you should set up an equation to solve for x. Since the two angles are congruent, you should set the expressions equal to each other. 3x-12=4x+5.

PLZ HELP its a test re rake i really need to get it right or im gonna fail

Answers

Answer:

D

Step-by-step explanation:

if it was written in scientific notation, it would be 5*10^1

There shouldn't be decimals or part of numbers(6.0 is okay because 6.0 =6) in scientific notation

WILL GIVE BRAINLIEST

Which of the following is an equation of the tangent line to y=sin x +cos x at x=3.14/2

Answers

Answer:

y o = 2 sin ( π/6 ) = 2 * 1/2 = 1

x o = π / 6

y ` = 2 cos x = 2 cos (π/6) = 2 * √3 / 2 = √ 3;

m = √3

An equation of the tangent line is:

y - y o = m ( x - x o )

Answer:

y - 1 = √3 ( x - π/6 )

Step-by-step explanation

please give me brainliest     hope it helps

6 inches for every horizontal change of 12 inches

Answers

skjsjskskskkskskskksskksksksksksks

Which of the following situations have a sum of zero? Select all that apply.

1. Shawna spends $20 on materials to make bracelets for her friends. She then earns $20 from selling the bracelets.

2. A diver dove down 20 1/4 feet under water and then descended 20 1/4 feet.

3. A golfer shot 2 over par (+2) on a hole. They then then shot 2 under par (−2) on the next hole.

4. You have $5.50 in your pocket and then you receive $5.50 for doing your chores.

Answers

I’m pretty sure it’s 1. And 2.
The first and the third.

Angela went to the farmers' market to buy some vegetables. She wanted some yellow squash and zucchini which were both on sale for $1.48 per pound. Angela bought 245 pounds of yellow squash and 3110 pounds of zucchini. To the nearest cent, what was the total cost of the vegetables?

Answers

Multiple both the numbers so 1.48*245
And 1.48*3110 and then add the numbers you got together 4,965.40 make sure those are the numbers for pounds

The total cost of 245 pounds of squash and 3110 pounds of zucchini is  $4965.4.

What is Unitary method?

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

The unit rate for squash and zucchini is $1.48 per pound.

In order to calculate the cost for 245 pounds of squash and 3110 pounds of zucchini unitary method can be used as follows,

The cost for 245 pounds of squash is 245 × 1.48 = $362.6

And, the cost for 245 pounds of squash is 3110× 1.48 = $4602.8.

Thus, the total cost is given as 4602.8 + 362.6 = $4965.4.

Hence, the total cost of vegetables at the given rate is $4965.4.

To know more about unitary method click on,

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A local supermarket sells shrimp $9.49/lb and beef for $5.99/lb Todd buys s pounds of shrimp and b pounds of beef. Which of the following inequalities represents that Sandy only has $65 to spend?

Answers

Answer: 9.49s + 5.99b ≤ 65

Plz mark brainliest:)

find the value of x (PLEASE HELP THIS IS a 40 point question)

Answers

Answer:

x=40°

Step-by-step explanation:

We have an isosceles triangle RST where the sides RS and ST are congruent, i.e. they have the same length.

One property of isosceles triangles is that the congruent sides form congruent angles with the other side. In other words, the measures of angles R and T are equal.

The sum of the measures of angles R, S, and T is 180°:

[tex]m\angle R+m\angle S+m\angle T =180^\circ[/tex]

Since [tex]m\angle R=2x-10[/tex] , [tex]m\angle T=m\angle R[/tex] and [tex]m\angle S=x[/tex]:

2x-10+x+2x-10 =180

Simplifying:

5x=180+20

Solving:

x=200/5

x=40°

which of these is correct? will give brainliest C:

Answers

Answer:

$7.50/lb    answer A is correct

Step-by-step explanation:

Find the unit cost:  $ per pound:

 Calculate

      $3.00

--------------------

   (2/5) lb

It's slightly easier to calculate the equivalent

 $3.00

------------- = $7.50/lb    answer A is correct

 0.4 lb

Answer: D. $1.20 per pound

Step-by-step explanation:

Because 2/5= 0.4 in a decimal form.

If you multiply 0.4 times 3= 1.2 just that in D they are adding a zero (0).

1.20= 1.2

2. Find m 21.
(1 point)
339
579
21
O 147°
123°
90°
57°

Answers

Answer:

90°

Step-by-step explanation:

33+57=90

180-90=90

please help me out!!!

Answers

850 because if they are 0.004 gigs and you have 3.4 you just have to divide

If m<5=63°, find the measure of <3.

Answers

Answer:

angle 3's measurement should be 117 degrees

hope this helps :)

The measure of angle 3 is 117 degrees.

Calculation of an angle:

In terms of geometry, an angle refers to the figure i.e. credited by two rays that should be met out at a common endpoint. An angle should be presented by the symbol ∠.

Since the angle 5 is 63 degrees

and, the total of two angles is 180 degrees

So, the angle 3 is

= 180 - 63

= 117 degrees

hence, The measure of angle 3 is 117 degrees.

learn more about an angle here: https://brainly.com/question/11508323

Which graph represents the function f(x) = |x|-4?

Answers

Answer:

Which graph represents the function f(x) = 4|x|?

B is the correct answer

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

Edg2021

Bus A and Bus B leave the bus depot at 9 am. Bus A takes 30 minutes to complete its route once and bus B takes 40 minutes to complete its route once. If both buses continue to repeat their route, at what time will they be back at the bus depot together?

Answers

Answer:

11 am

Step-by-step explanation:

Bus A and Bus B leave the bus depot at 9 am.

Bus A takes 30 minutes to complete its route once

Bus B takes 40 minutes to complete its route once.

We solve this finding the Lowest Common Multiple of the minutes each bus uses to complete it's route

30 = 3 × 10

40 = 4 × 10

= 3 × 4 × 10

= 120 minutes

120 minutes after 9 am is

60 minutes = 1 hour

60 minutes = 1 hour

= 2 hours.

9am + 2 hours

= 11 am.

Therefore, they be back at the bus depot together at 11 am

ASAP HELP ASAP HELPPPP

Answers

Answer:

3 or 2 is the answer to the question

Solve the system of equations below. 3/+4,/9-12 = 17 2v1 +3,11+52 = 18 -V5-VT-12 = -6​

Answers

Answer: -6 You answered your own question-

please help!! i need math help loll

Answers

Answer:

x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3 * 3 * 3 = 27

Hope this helps and pls do mark me brainliest if you can:)

Which point represents (5,-3) on the graph?

Answers

Answer:

Point D

because you go 5 to the right and 3 down.

D

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If mZ3 = 74°, find each measure.

Answers

Answer:

m<1 = 74

m<2 =  74

m<4 = 74

Step-by-step explanation:

If a=2, b=-3 and c=4, evaluate: b(a-c)^2

Answers

the answer is 36
if you substitute the numbers in, the equation would be..

-3(2-4)^2 so
2-4 is -2
-3 x -2 = 6
and 6^ is the same thing as 6 x 6
so 6^2= 36
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