Exercise 21
Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Si.
. CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1 and S2 and S3 in terms of x
Plzzz I need help

Exercise 21Let X Represents A Length In Cm Where X > 1.5.AB = 2x - 3, BC = 4x 6,AD = 2x + 3 And BE

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

area of Δ ABC is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 4x - 6 and h = 2x - 3 , then

A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL

   = [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute

    = 4x² - 12x + 9

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

Area of rectangle CBFG is calculated as

A = lb ( l is length, b is breadth )

Here l = 4x - 6 and b = 3x - 2, then

A = (4x - 6)(3x - 2) ← expand using FOIL

   = 12x² - 26x + 12

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

Area of trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then

A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)

   = [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL

   = [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute

   = 6x² - 5x - 6


Related Questions

How much change from a $50 bill would you receive if you bought
items costing $13.95, $6.08, and $24.35?

Answers

Answer:

$5.62

Step-by-step explanation:

Add all of the cost of the items and then deduct that answer from 50.

Answer:

$5.62

Step-by-step explanation:

50−(13.95+6.08+24.35)

=50−(20.03+24.35)

=50−44.38

=5.62

Are 5 and 0.5 Equal to Each other?

Answers

Answer:

no

Step-by-step explanation:

5 is a whole number 0.5 doesn't equal to 1 it is half of 1

No it is not equal one is in the tenths place

Simplify
2x( x^3-3x^2+5x-8)

Answers

Answer: =2x^4−6x^3+10x^2−16x

Step-by-step explanation:

please help me this is turned in a couoke of minutes!!!!!!!!!!​

Answers

Answer:

mince is the answer

Miguel and three of his friends went to the movies. They originally had a total of $40. Each boy had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying his ticket? Write and solve an equation that represents he situatio.

Answers

Answer:

x = (40/4)-7.50

x= (10)-7.50

x = 2.50

Step-by-step explanation:

each boy had 2.50 left after the movie because miguel went with 3 other boys, which makes four of them all together. If they had forty dollars all together and all had the same amount of money, you can determine that amount by dividing forty(total money) by 4(number of boys). Which gets you to the answer of ten dollars each. Then you subtract the ticket cost(7.50) from 10 dollars, which gets you to 2.50 left over.

Solve for x given the lines are parallel.
(7x - 8)
62°

Answers

Answer:

The answer is 0 ✌

Step-by-step explanation:

70 - 8 =62°

Help me and I’ll give brainliest to u

Answers

Answer:

7p

Step-by-step explanation:

Since it is 7 dollars per person, and p stands for person, the admission fee would be 7p.

Thank you, I hope you learned from this answer! If it did help, please mark this as brainliest! Thank you!

Find the value of x.

Answers

You have to combine your liked terms first

Suppose that a bond has a face value of ₱ 100,000 and its maturity date is 10 years from now. The coupon rate is 5% payable semi-annually. Find the price of the bond, assuming that the required yield is 4%.

Answers

Answer:

Bond Price​= $108,175.71

Step-by-step explanation:

Giving the following information:

Face value= $100,000

Coupon rate= 0.05/2= 0.025

YTM= 0.04/2= 0.02

Time period= 10*2= 20 semesters

To calculate the price of the bond, we need to use the following formula:

Bond Price​= cupon*{[1 - (1+i)^-n] / i} + [face value/(1+i)^n]

Bond Price​= 2,500*{[1 - (1.02^-20)] / 0.02} + [100,000/(1.02^20)]

Bond Price​=  40,878.58 + 67,297.13

Bond Price​= $108,175.71

In this exercise we have to use the knowledge of finance to calculate the stipulated value through the percentages, thus we find that:

Bond Price will be  [tex]\$108,175.71[/tex]

From the information given in the text we found that:

Face value: [tex]\$100,000[/tex] Coupon rate: [tex]0.05/2= 0.025[/tex] YTM: [tex]0.04/2= 0.02[/tex] Time period: [tex]20 \ semesters[/tex]

To calculate the price of the bond, we need to use the following formula:

[tex]Bond\ Price = cupon*{[1 - (1+i)^{-n}] / i} + [face \ value/(1+i)^n][/tex]

So with the formula already informed we will replace the values ​​given in the text find what we want.

[tex]Bond \ Price = 2,500*{[1 - (1.02^{-20})] / 0.02} + [100,000/(1.02^{20})]\\Bond Price= 40,878.58 + 67,297.13\\Bond Price= \$108,175.71[/tex]

See more about finances at: brainly.com/question/10024737

7 × (-5) is equivalent to?
2
-35
35
-12

Answers

Answer:-35

Step-by-step explanation: 7x5 = 35, but since the 5 is a negative it’s -35

Answer:

-35

Step-by-step explanation:

whenever multiplying positive and negative integers, if one of the factors are negative, then the answer will be negative. if both are negative, the answer becomes a positive, and if both are positive, the answers stays positive.

in this case 7 is positive and 5 is negative so  your anwers is -35

hope i helped!

:)

Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups. After the party, 4 cups of juice were left over. At the party, how many cups did people drink? Show your work and complete the explanation of how you found your answer.

Answers

Answer:

60 cups

Step-by-step explanation:

Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups.

From the above question:

1 gallon of juice = 16 cups

Then:

4 gallons of juice = c

Cross Multiply

1 × c = 4 × 16 cups

c = 64 cups of juice

Hence, 4 gallons of juice = 64 cups of juice

We are told that :

After the party, 4 cups of juice were left over.

The cups of juice people drank at the party is calculated as:

Total cups of juice - Number of cups of juice left over.

64 cups of juice - 4 cups of juice

= 60 cups of juice

15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:

Answers

Answer:

Triangle RST is an equilateral triangle.

Step-by-step explanation:

All three sides of the triangle are of equal length, therefore, because an isosceles triangle is when 2 sides of the triangle are the same length, a scalene triangle being when all sides are of different lengths, and a right triangle having a right angle (a 90 degree angle), this only leaves equilateral, all three sides being the same length, like in the triangle shown.

Chase lives 1 and one half blocks west of Ellie. They draw a number line to model this situation. Because Ellie lives 1 and three fifths blocks east of​ school, they give her house the coordinate 1 and three fifths . Chase incorrectly claims that the coordinate of his house is 3 and one tenth . What is the correct coordinate of Chase​'s ​house? What is Chase​'s likely​ error?

Answers

Answer:

1/10

Step-by-step explanation:

A number line is a line which contains numbers marked at intervals (usually regular intervals). Points to the right of the origin are positive numbers while those to the left are negative numbers.

The school is used as the origin. Ellie house is 1 and three fifths blocks east (to the right) of the school. This means that it is + 1 and three fifths (+8/5).

Chase house is 1 and one half blocks (3/2) west of Ellie. Since it is west then it is to the left. Hence the coordinate of chase house = 8/5 - 3/2 = 1/10

Hence the coordinate of chase house is 1/10(one tenths).

The error may be as a result of thinking chase house is to the east of Ellie, hence adding to get  3 and one tenth.

If a relation has more numbers in its range than in its domain, what has to be true?

Answers

Answer:

Both the domain and range are the set of all real numbers. For the absolute value function f(x)=|x| f ( x ) = | x | , there is no restriction on x . ... For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. this is the best i can do if its not helpful i guess u can ask ur teacher.

What is the probability that the selected adult is a smoker?

Answers

Answer:

Alot of adults smoke and very little adults don´t smoke at all

Step-by-step explanation:

14.0% of U.S. adults overall.

like to me 85% of adults smoke

A hybrid car can travel 40 miles per gallon. Approximately how many gallons of fuel will the car need to travel 20 km? (5 points) [1 mile = 1.6 km]

Answers

Answer:

To travel 20 Km, the hybrid car needs 0.3125 gallons of fuel.

Step-by-step explanation:

Proportions

The hybrid car can travel 40 miles per gallon.

Since one mile is equivalent to 1.6 Km, the distance traveled per gallon is 40*1.6 = 64 Km.

Now the distance is expressed in Km, we can find the gallons needed to travel 20 Km, by calculating 20/64 = 0.3125.

To travel 20 Km, the hybrid car needs 0.3125 gallons of fuel.

Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. y =​

Answers

Answer:

Step-by-step explanation:

given: (2,1) & (5-8)

first find the slope,

m= (Y2-Y1) / (X2-X1)    

m=(-8-1)/(5-2)

m=(-9)/(3)

m=-3

we have y=-3x+b

use any point to sub in x and y

1=-3(2)+b

1+6=b

b=7               therefore, y=-3x+7 is the equation

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)

m = [tex]\frac{-8-1}{5-2}[/tex] = [tex]\frac{-9}{3}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 1 ), then

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = - 3x + 7 ← equation of line

helllllllllllllpppppppppppp me plz *waves* hiiiiiiiiiiiii

Answers

Answer:

x=18 and y=72

Step-by-step explanation:

Answer:

d is right

Step-by-step explanation:

Which line has a slope of 1/2 and passed through (2,-4)

Answers

The Answer is: “D” step by step explanation:

lemme get some help plz

Answers

Answer:

6(8x-2)

48x- 12 (this is the answer)

Step-by-step explanation:

to do those, you use the distributive property, which is taking the number outside the parenthesis and multiplying it by everything inside of it

What can you do if your struggling in Volume in Math?

Answers

Answer:

Study Harder

Step-by-step explanation:

please help me. im having one of those days
Write an explicit function to describe the sequence.
-16, -13, -10, -7, ...

Answers

Answer:

Step-by-step explanation:

y = - 3x

A demon possessed woody and turned him into a monster!

He now hunts children aged 7-16 because he likes his meals chewy.

His head turns 360 degrees to spot prey.

If you look at the picture he will rise out of your sheets and put snakes in your shoes.

And he's right behind you.

Answers

Answer:

Ë

Step-by-step explanation:

Im literally going to poop my pants that is SO scawwwy. I deserve compensation for this. My lawyers are coming after you

Answer:

i looked behind me and yes i did see a monster, my brother

Step-by-step explanation:

HELP ME, PLEASE. I REALLY NEED IT
Find x:
[tex]S=\frac{1}{sin2x}+\frac{1}{sin4x}+\frac{1}{sin8x}+...+\frac{1}{sin2^{n}x }[/tex]

Answers

Answer:

cotx - cot2ⁿx

Step-by-step explanation:

Note: finding the sum not x

First rewrite the first term as:

1/sin2x = sinx / (sinxsin2x)  = sin(2x-x) / (sinxsin2x)  =(sin2xcosx - cosxsinx) / (sinxsin2x) = (sin2xcosx)/(sinxsin2x) - (cos2xsinx)/(sinxsin2x) = cosx/sinx - cos2x/sin2x = cotx - cot2x

Now the sum is:

S = cotx - cot2x + cot2x - cot4x +... + cot2ⁿ⁻²x - cot2ⁿx =cotx - cot2ⁿx

Which equation can be used to represent the distance D for the times t given in the table?

Answers

Answer: D

Step-by-step explanation:

If the 3 cans cost 0.78 how much will 2 cans cost

Answers

Answer:

.52

Step-by-step explanation:

math ting

The data in the table are linear. Use the table to find the slope.
2
4
6
8
1
-2.
-5
-8
a.
b.
3
2
3
2
او را
d. 2
3​

Answers

Answer:

[tex]m = -\frac{3}{2}[/tex]

Step-by-step explanation:

Given

x 2 4 6 8

y 1 -2 -5 -8

Required

Determine the slope

First, pick any two corresponding x and y values.

[tex](x_1,y_1) =(2,1)[/tex]

[tex](x_2,y_2) =(8,-8)\\[/tex]

The slope (m) is then calculated using:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

Substitute in, the x and y values

[tex]m = \frac{1 - (-8)}{2- 8}[/tex]

[tex]m = \frac{1 +8}{-6}[/tex]

[tex]m = \frac{9}{-6}[/tex]

[tex]m = -\frac{9}{6}[/tex]

Divide numerator and denominator by 3

[tex]m = -\frac{9/3}{6/3}[/tex]

[tex]m = -\frac{3}{2}[/tex]

Hence, the slope is -3/2

Answer:

Is -3/2.

Step-by-step explanation:

I just took the test!

Help please:):):):):):)

Answers

do eat popcorn in a tub

:)

poopy face

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The shwabble-dabble-wabble-gabble flibba blabba blab
I'm full of shwibbly liber-kind
I am the yeast of thoughts and minds

[Chorus]
Shwabble dabble glibble glabble schribble shwap glab
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I am the Glob-glo-gab-galab
The shwabble-dabble-wabble-gabble flibba blabba blab
I'm full of shwibbly liber-kind
I am the yeast of thoughts and minds

[Chorus]
Shwabble dabble glibble glabble schribble shwap glab
Dibble dabble shribble shrabble glibbi-glap shwap
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What is 1.33 x 10^6 in scientific notation?

Answers

1,330,000
I tried-
Lmk.

helpp meee pleaseeee​

Answers

Answer:

I think its b:/ srry if I'm wrong

identification method
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Hey uh I didnt know where to ask this but does anyone have tips for drawing digitally faster? Im very very slow and often take 10+ hours for something as simple as a headshot and i cant figure out why. Ive looked this up a lot but cant really find an effective solution other then im just downright slow. Tips? Foods labels help consumers make healthy food choices and inform them of allergens,TrueO False A liquid has a ph of 12. It is... A. an acid B. a base C. neutral A rectangular prism has a volume of 1,200 cubic units. The area of the base is 80 square units.What is the height of the prism?(Show work) True or FalseUnsaturated solution contains the maximum amount of solute dissolved by a given amount of solvent Ice floats on water why?give short answer. I need help with the questions when it says what is the topic and rest 1. Which equation does not match the diagram? A. 6 +3x= 30 B. 3(x+6) = 30 C. 3x = 30- 6 D. 30 = 3x + 6 PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ help me!!!!!Classify the following substances as: Pure Substance P Solution S Mechanical Mixture MM Suspension SU Colloid - C SubstanceApple Juice2005 PennyPropaneChicken Noodle SoupMilkSalsa14 Karat Gold RingAirPepsi (in a glass)Chocolate Chip Cookie how can use a BIPHASIC LIQUIDS Current members in the U.S. house of Senate Pleaseeee answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!! Which of these increases as a submarine dives deeper into the ocean?A: The number of plants in the waterB: The freshness of the waterC: The water temperatureD: The water pressure choose a logical word to complete each sentence and conjugate it for the subject Choose the best answer. Quin grit? Esmeralda grita. Esmeralda grit. Esmeralda grit. Esmeralda griti. Mark this and return What is -2(g+5) please help :) (-15)(-4) help meeee write a conversation between two friends asking about what they have done in their lives Which was the main reason for the problems between native Americans and the colonists in North America? 4. If 100.0g of nitrogen gas (N2) is reacted with 100.0g of hydrogen gas (H2) to form NH3. What are the limiting and excess reactants? Hint: Convert grams to moles for each reactant and then convert to moles of NH3. You need your balanced equation from answer 1 to determine the mole relationship between each reactant and the product NH3. Use the periodic table to determine the molar mass of all chemical formulas. Fill in the ? blanks below to show your work. Balanced equation: 1N2 (g) + 3H2(g) 2NH3(g) Molar mass of H2 = g/mol100.0"g " "H" _2(1"mol " "H" _2)/( ? "g " "H" _2 )(" ? mol N" "H" _3)/(" ? mol " "H" _2 )= ? "mol N" "H" _3 Molar Mass of N2 = g/mol100.0"g " "N" _2(1"mol " "N" _2)/(" ? g " "N" _2 )(" ? mole N" "H" _3)/(" ? mol " "N" _2 )= ? "mol N" "H" _3A. What is the excess reactant? Hint: it is the reactant above that makes the most amount of productB. What is the limiting reactant? Hint: it is the reactant above that makes the least amount of productC. What is the theoretical yield of ammonia of the reaction?Molar mass of NH3 = g/mol 100.0"g " "N" _2(1"mol " "N" _2)/( ? "g " "N" _2 )( ? "mol N" "H" _3)/( ? "mol " "N" _2 )(" ? g N" "H" _3)/( 1 "mol N" "H" _3 )= ? "g N" "H" _3