2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, nd in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC.

Answer:The answer is below.Step-by-step explanation:A square is a quadrilateral (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90. The diagonals of a square are equal.In square ABCD:AB = BC = CD = ACGiven that P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.a) In triangle ABP:BC = AB (all sides of a triangle are equal)BP = 1/2 (BC) = 1/2(AB) = 0.5ABUsing Pythagoras theorem:AB + BP = APsubstituting:AB + (0.5AB) = aAB + 0.25AB = a1.25AB = aAB = a / 1.25AB = 0.8aAB = (0.8a)AB = a0.8 b) In triangle ADQ:AD = CD (all sides of a triangle are equal)DQ = 1/2 (CD) = 1/2(AD) = 0.5ADUsing Pythagoras theorem:AD + DQ = AQsubstituting:AD + (0.5AD) = bAD + 0.25AD = b1.25AD = bAD = b / 1.25AD = 0.8bAD = (0.8b)AD = b0.8 c) In triangle ABD, Using Pythagoras theorem:AB + AD = BDSubstituting:0.8a + 0.8b = BDBut AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a = 0.8bBD = (0.8a + 0.8b)BD = (1.6a) 0.8a = 0.8bBD = a1.6D) AC = AD (diagonal are equal)AC = (0.8a + 0.8b)AC = (1.6b) 0.8a = 0.8bAC = b1.6

Mathematics College

2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, ﬁnd in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC.

Answers

Answer 1

Answer:

The answer is below.

Step-by-step explanation:

A square is a quadrilateral (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90°. The diagonals of a square are equal.

In square ABCD:

AB = BC = CD = AC

Given that P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.

a) In triangle ABP:

BC = AB (all sides of a triangle are equal)

BP = 1/2 (BC) = 1/2(AB) = 0.5AB

Using Pythagoras theorem:

AB² + BP² = AP²

substituting:

AB² + (0.5AB)² = a²

AB² + 0.25AB² = a²

1.25AB² = a²

AB² = a² / 1.25

AB² = 0.8a²

AB = √(0.8a²)

AB = a√0.8

b) In triangle ADQ:

AD = CD (all sides of a triangle are equal)

DQ = 1/2 (CD) = 1/2(AD) = 0.5AD

Using Pythagoras theorem:

AD² + DQ² = AQ²

substituting:

AD² + (0.5AD)² = b²

AD² + 0.25AD² = b²

1.25AD² = b²

AD² = b² / 1.25

AD² = 0.8b²

AD = √(0.8b²)

AD = b√0.8

c) In triangle ABD, Using Pythagoras theorem:

AB² + AD² = BD²

Substituting:

0.8a² + 0.8b² = BD²

But AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a² = 0.8b²

BD = √(0.8a² + 0.8b²)

BD = √(1.6a²) 0.8a² = 0.8b²

BD = a√1.6

D) AC = AD (diagonal are equal)

AC = √(0.8a² + 0.8b²)

AC = √(1.6b²) 0.8a² = 0.8b²

AC = b√1.6

2. ABCD Is A Square And P, Q Are The Midpoints Of BC, CD Respectively. If AP = A And AQ = B, Nd In Terms

Related Questions

Which property is used for the following expression (4x2) x 5 = 2 x (5 x 4) ?

Answers

Associative property

Tonya drove 343 miles the first day of her trip. how many days will it take her to drive the remaining 1,200 miles if she continues at the same rate?

Answers

Answer:

3.5 days

Step-by-step explanation:

Given

[tex]Day\ 1 = 343\ miles[/tex]

Required

Number of days to drive 1200 miles

Represent as ratio:

[tex]Day\ 1 = 343\ miles[/tex]

[tex]Ratio = 1 : 343[/tex]

For 1200 miles

[tex]Ratio = x : 1200[/tex]

Equate both ratios

[tex]x : 1200 = 1 : 343[/tex]

Express as fractions

[tex]x/1200 = 1/343[/tex]

Multiply by 120

[tex]x/1200 *1200= 1/343*1200[/tex]

[tex]x= 3.4985[/tex]

[tex]x= 3.5[/tex] --- approximated

Solving linear equations

Answers

Answer:

1. P = [tex]\frac{I}{rt}[/tex]

2. y = [tex]\frac{6 - 3x}{11}[/tex] or [tex]\frac{-3x +6}{11}[/tex] (depending on how you want the equation arranged)

3. c = [tex]\frac{a-bd}{b}[/tex]

4 t = [tex]\frac{A - p }{pr}[/tex]

Step-by-step explanation:

1. I =Prt for P:

I = Prt divide both sides by rt to isolate P

P = [tex]\frac{I}{rt}[/tex]

2. 3x + 11y = 6 for y

3x + 11y = 6 subtract 3x from both sides

11y = 6 - 3x divide both sides by 11

y = [tex]\frac{6 - 3x}{11}[/tex] or [tex]\frac{-3x +6}{11}[/tex] depending on how you want the equation arranged

3. a = b(c + d) for c

a = b(c + d) distribute b to (c+d)

a = bc + bd subtract bd from both sides

a - bd = bc divide both sides by b

c = [tex]\frac{a-bd}{b}[/tex]

4. A = p + prt for t

A = p + prt subtract p from both sides

A - p = prt divide both sides by pr

t = [tex]\frac{A - p }{pr}[/tex]

Find the slope of the line passing through the points (-7, 5) and (2,5).

Answers

There is no slope the y axis is the same in both

Answer:

slope = 0

Step-by-step explanation:

Use formula to find the slope: m = (y2 - y1) / (x2 - x1)

Set (x1, y1) = (-7, 5)

Set (x2, y2) = (2, 5)

m = (5 - 5) / (2 - (-7))

m = (5 - 5) / (2 + 7) FYI, negative * negative = positive

m = 0 / 9

If you plot the coordinates, they'll lie on a horizontal line. Therefore, the slope of the line is 0.

x² + 4 = 55
What is x

Answers

Answer:

7.1414284285

answer...

Which one doesn't belong? 100, 25, 36, 30

Answers

Answer:

Step-by-step explanation:

100 bro

In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued x years since 2016.

Which type of sequence does the situation represent?

A.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.5.
B.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.05.
C.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.5.
D.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Answers

The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

What is geometric series?

A geometric series is a series in which the division of any consecutive two terms will be the same.

here, we have,

to determine the situation:

The given parameters are:

Initial = 5200

Rate = 5%

Because the population by 5% every year, then the situation is a geometric sequence.

The common ratio is then calculated as:

Ratio = 1 + Rate

This gives

Ratio = 1 + 5%

Evaluate

Ratio = 1.05

Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Answers

Answer:

Step-by-step explanation:

68000+6.75b>82000+5.5b. subtract 5.5b from both sides

68000+1.25b>82000. subtract 68000 from both sides

1.25b>14000. divide both sides by 1.25

b>11200

So she must sell more than 11500 books to make more with second publisher.

1.
Write the equation, then find the value of x.

2.
What is the measure of

Answers

Answer:

32+36+2x=180

hope this helps

answer: 1) x=56 :), i can’t see the rest of the second question

Never was given anything to help solve they just assume you know it

Answers

Answer: 0.4575

Step-by-step explanation:

.915/2

Alison rolls two number cubes 90 times. How many times is he going to get a sum of 3?

Answers

Step-by-step explanation:

Answer:

I think 30 im so sure

Step-by-step explanation:

uhm i think its 90 divided by 3 cuz i looked it up and got 30 so yea bye

How do you write 246% as a fraction or mixed number?

Answers

Answer:

246/100 as a fraction, and 2 46/100 as a mixed number..

Step-by-step explanation:

Answer: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

2 and 23/50

or as a simplified fraction 123/50

Step-by-step explanation:

which point on the scatter plot represents the outlier ?

Answers

Answer:

The point that represents the outlier is “B”

Step-by-step explanation:

I know it because I just did it and got it right. Hope it helps!

Answer:

Step-by-step explanation:

I know because i got it correct

three corners of a square are (1, 7), (5, 3), and (9, 7). What are the coordinates of the fourth corner of the square?

Answers

Answer:

i think the answer is 8

Step-by-step explanation:

Answer:(13, 3)

maybe

Hope it helps

a baseball team wins 45% what fraction of the games do they win

Answers

Answer:

= 9/20

Step-by-step explanation:

45% = 45/100

= 0.45

= 0.45/1 × 100/100

= 45/100

= 9/20

Can anyone tell me if this is right? Multiple choice!

Answers

Answer:

yes its correct

Step-by-step explanation:

I don't understand how to do this

Answers

Answer:

x = 86

Step-by-step explanation:

The top right and bottom left angles are part of the reflective property, in turn, the bottom left angle is also 94 degrees; to find the opposite relfective angle set, it would be, in this problem, the top left and bottom right angles; the two top angles make up 180 degrees, so it would be (180-94 = 86) 86 degrees for both the top left and the bottom right angles.

Hope this helps :)

Look at pic plz help

Answers

Answer:

Mochi is growing quicker.

Step-by-step explanation:

At 3 weeks Mochi was 13 pounds but Kappa was only at 11. Hope this helps! I'd really appreciate brainliest.

Answer:

Mochi

Step-by-step explanation:

by 2 weeks Mochi was at weight 9 while Kappa was at 8 in weight the same time.

Mary Chapman had been working at First Savings for 18 years when she
became permanently disabled and could not continue to work. She was 50 years
old and had planned to retire in 12 years. Her final average salary was $34,500.
First Savings' rate of benefits is 2%. What is Chapman's monthly disability
benefit?

Answers

Answer:

17250

Step-by-step explanation:

please help i am really struggling . i really dont get it thanks :)

Answers

Answer:

I=P-A

___________________________

‍♂️‍♂️‍♂️help me plz I dont no 1+1

Answers

Answer:

The answer is 2

Step-by-step explanation:

Since the number 1 plus 1 is 2

11, you do 1+1 n take away the +

What is the slope-intercept form of the equation of the line parallel to the line in the graph that passes through the point (-1, 1)?

Answers

Answer:

undefined

Step-by-step explanation:

can you solve this equation?
-12 2/3 + 2 1/3

Answers

Answer:

-7.333

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

A turtle is crawling up a hill that rises 6 feet for every horizontal change of 36 feet. Write the slope of the hill as a
fraction in simplest form.

Answers

9514 1404 393

Answer:

1/6

Step-by-step explanation:

The slope is the ratio of rise to run.

slope = rise/run = (6 ft)/(36 ft) = 6/36 = 1/6

The slope of the hill is 1/6.

I’m so bad at math Can someone help

Answers

Answer:

B and C

Step-by-step explanation:

It fits the inequality

Step-by-step explanation:

step 1. no one is categorically bad at math; they just haven't practiced.

step 2. this reads: x is less than 30 and x is greater than 15.

step 3. x cannot be 15 but can be 22 and 29.

What is 13x + 21y - 14x - y simplified?

Answers

Answer:

-x + 20y

Step-by-step explanation:

trust me.. its right

Please help me?! I don’t have a lot of time? Please I will give brainiest for the correct answer !

Answers

Answer:

It should be -3

Hope it helped i tried to help you ASAP

Step-by-step explanation:

a square is cut from rectangle the side length of the square is half of the unknown with W the area of the Shaded region is 84 square inches write an equation you can use to find the width in inches

Answers

Answer:

Step-by-step explanation:

Just give me the answer

Campsite fees
(per day)
Tent ...... .. $15.00
Caravan ....... $25.00
The sign shows the fees charged at a campsite.
Today there are 54 tents and 18 caravans on the site.
Calculate the fees charged today.

Answers

Answer:

1260

Step-by-step explanation:

Tents: 15×54=810

Caravans: 25×18=450

450+810=1260

Answer:

$1260

Step-by-step explanation:

Campsite Fees:

Tent - $15 (per day)

Caravan - $25 (per day)

No. of Tents and Caravans today:

Tents - 54

Caravan - 18

Total fees for Tent = 15 x 54

= $810.

Total fees for Caravan = 25 x 18

= $450.

Fees altogether for Today = Total fees for Tent + Total fees for Caravan

= $810 + $450

= $1260

Solve the inequality below:
-3x +5-16
ALGEBRA

please help

Answers

Answer:

The answer is -14x

Step-by-step explanation:

5 - 16 = -11

-3 + -11 = -14

(all we have left is the x)

-14 + x = -14x

Answer:a

Step-by-step explanation:

Other Questions

math algebra HELP!!!! A cylindrical container contains some sand. If the diameter of the container is 10 inches and its height is 3 inches, about how much sand fits inside the container? from The Boy's LifeWhat did he think of the adventure him and his mom was talking HELP ME PLEASEFor this assignment you will write two well-developed paragraphs on the following:What were the reasons the bomb should have been used on Japan?What were the reasons the bomb should not have been used on Japan?Should the atomic bomb have been used on Japan? Why or why not? Support your claim with evidence from the lesson.Information you should consider when writing your two paragraphs:U.S. plans for invading the main Japanese islandsU.S. bombing raids on Japanese cities during early 1945the Japanese code of battlethe number of U.S. dead in the Pacific War by 1945the likelihood of Japan's surrender with the entry of the Soviet Unionthe number of Japanese civilians killed in the bombings of Hiroshima and Nagasakithe level of destruction caused by atomic weaponsthe long-term effects of the use of atomic weapons find the equation of a line that is parallel to the straight line 2x-y=-3 and crosses the x-axis at x=-5 if a cost for a dinner is 459 and the family wants to leave a 20% tip, with the sales tax of 7% also, what is the total cost? Suppose the following sequence of bits arrives over a link: 11010111110101001111111011001111110 Show the resulting frame after any stuffed bits have been removed. Indicate any errors that might have been introduced into the frame. Ifx += 5, find the value of x? 3 less than the product of 4 and n what is the answer A. 3 - 4nB. 4n - 3 C. 3n - 4D. 4n + 3HELP QUICK 16. What information will you not usually find on a printed map or atlasO Alegend that describes map symbolsLocations of hotels and restaurantsO Federal, state, and county roads .Read the rough-draft paragraph.Exercising daily is one of the best ways to help the body fight fatigue, illness, stress, and weight gain. Whether taking a bike ride, enjoying a walk, or going for a swim, the type of activity is not as important as exercising consistently. Often, people begin the new year with the resolution of exercising, but within a few months that commitment is quickly forgotten. The key is to choose something that is accessible, enjoyable, and affordable. Exercising just thirty minutes a day not only strengthens the heart and lungs, but it also helps to boost ones energy. Another way to feel more energized is to eat a balanced diet. Since no single food item can supply the body with everything it needs, it is important to eat a variety of foods. So to maintain a long, happy life, get out there and get moving, and enjoy a wide range of healthy meals.Which statement best describes the mistake the writer makes in this paragraph?The writer makes punctuation and/or grammatical errors.The writer misuses transitions to connect ideas and thoughts.The writer loses focus and shifts to another topic.The writer forgets to include supporting details. The perimeter of the triangle is 9.2 cm. Write an equation and find the missing side. omggggggggg please please help meeeeeeeeee How do humans affect the carbon cycle?Using pencil to write,exhaling carbon dioxide, wearing sunscreen or inhaling oxygen?NEED HELP ASAP please help me answer this math problem Tennis star Rafael Nadal lost at the Australian Open. How many Grand Slams has he won? In which two regions is the population concentrated in coastal communities?Puget Lowlands and Willapa Hills Olympic Mountains and Puget Lowlands Willapa Hills and Olympic Mountains Puget Lowlands and Columbia Basin Which of the following was NOT a piece of evidence supporting continental drift in the early 1900s?a)Fossil recordsb)Glacial depositsc)Continents fit together like a puzzled)DNA evidence What is the variable number in the equation 6=4+2s Can someone explain this to me? I really need help. Thx!