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 Sı.
. CBFG is a rectangle of area S2.
• ADEB is a right trapezoid of area S3.
1) Express S1, S2 and S3 in terms of x.
2) Let S = S1 + S2 -S3.​

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

Answers

Answer 1

Answer:

1) S1 = 4·x² - 12·x + 9

S2 = 12·x² - 26·x + 12

S3 = 6·x² - 5·x - 6

2) S = 10·x² - 33·x + 27

Step-by-step explanation:

The length x in cm > 1.5

Segment AB = 2·x - 3, segment BC = 4·x - 6, segment AD = 2·x + 3 and segment BE = 4·x + 1

1) a) The area of the right triangle ABC = S1 = 1/2 × Base × Height

The base of the triangle ABC = Segment BC = 4·x - 6

The height of the triangle ABC = Segment AB = 2·x - 3

Therefore, The area of the triangle ABC = S1 = 1/2 × (4·x - 6) × (2·x - 3) = 1/2 × (8·x² - 12·x - 12·x + 18) = 4·x² - 12·x + 9

S1 = 4·x² - 12·x + 9

b) The area of the rectangle CBFG = S2 = Base × Height

The base of the rectangle CBFG = BC = 4·x - 6

The height of the rectangle CBFG = BF = 3·x - 2

The area of the rectangle CBFG = S2 =(4·x - 6) × (3·x - 2) = 12·x² - 8·x - 18·x + 12

The area of the rectangle CBFG = S2 = 12·x² - 26·x + 12

S2 = 12·x² - 26·x + 12

c) The area of the trapezoid ADEB = S3 = 1/2 × (Long side + Short side) × The height of the trapezoid ADEB

The long side of the trapezoid ADEB = BE = 4·x + 1

The short side of the trapezoid ADEB = AD = 2·x + 3

The height of the trapezoid ADEB = AB = 2·x - 3

The area of the trapezoid ADEB = S3 = 1/2 × (4·x + 1 + 2·x + 3) × (2·x - 3) = 6·x² - 9·x + 4·x - 6

∴ The area of the trapezoid ADEB = S3 = 6·x² - 5·x - 6

S3 = 6·x² - 5·x - 6

2) S = S1 + S2 - S3 = 4·x² - 12·x + 9 + 12·x² - 26·x + 12 - (6·x² - 5·x - 6) = 10·x² - 33·x + 27


Related Questions

GUYSSS HELPPP MEEE IM SUPPOSED TO SUBMIT IT IN 20 MINS AND I HAVE NO IDEA!!
PLEASE HELP

Answers

1. f(x) = x² + x + 4

f(x) = 0

0 = x² + x + 4

-4 = x² + x

2. linear equation

one solution

252 = 42 x 6
Which statement does the equation represent? Answer options with 4 options
A. 42 is 6 more than 252.
B. 252 is 42 more than 6.
C. 42 is 6 times as many as 252.
D. 252 is 42 times as many as 6.

Answers

Answer:

C. 42 is 6 times as many as 252

Step-by-step explanation:

because 42×6 = 252

Miss Rojas has a container of Jolly Ranchers on her desk. The ratio of Red Jolly Ranchers to Green Jolly Ranchers is 3 to 7. If there are 42 green jolly ranchers in the container, what is the total amount of Jolly Ranchers in the container?

Answers

Answer:

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Step-by-step explanation:

We have a ratio of

Red Jolly Ranchers : Green Jolly Ranchers

3:7

Sum of the proportion = 3 + 7 = 10

Hence:

Let the total number of jolly ranchers = x

7/10 of x = 42 Green Jolly Ranchers

Hence:

7/10 × x = 42

7x /10 = 42

Cross Multiply

7x = 420

x = 420/7

x = 60 Jolly Ranchers

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Identify the following division expressionS that have a quotient of 25. (MORE THAN ONE ANSWER)
(A) 125/5

(B) (100/20) + (100/5)

(C) (100/5) + (25/5)

(B) 125/25

(MULTIPLE CHOICE BRAINLIST IF RIGHT)

Answers

Answer:

a and c are correct

Step-by-step explanation:

i hoped this helped

Drag and drop an answer to each box to correctly complete the proof.

Given: m | n m 1 = 50 m 2 = 48°, and line s bisects ABC

Prove: m/3

49°

It is given that m | n m

1 = 50 m

2

- 48° and fine s bisects

ABC By the

m/DEF = 989 Because

angles formed by two parallel lines and a transversal are congruent

DEF

A BC

SO MZABC 98 By the

angles 4 and 5 are congruent

and m

4 is half m

ABC So the measure of in24_49 Because vertical angles

Answers

Answer:

Step-by-step explanation:

The correct question is shown in the image attached below.

Recall that: the line m is parallel to line n. In addition to that, [tex]m \angle 1 = 50^0[/tex] and [tex]m \angle 2 = 48^0[/tex], and [tex]\angle ABC[/tex] is bisected by line s.

At this moment, by the angle addition postulate, angle DEF i.e.

∠DEF [tex]= m \angle 1 + m \angle 2[/tex]

∠DEF = 50° + 48°

∠DEF = 98°

Similarly, using the rule of the alternate exterior angle ∠DEF = ∠ABC (∵ alternate exterior angles exhibit congruency).

Furthermore, By the definition of a bisector, angles 4 and 5 are congruent due to the fact that the line of a bisector splits the angle into two equal parts.

m∠4 = m∠5

98/2 = 49°

Finally;

from the diagram, angle 3 and 4 are vertical angles

Thus, m∠3 = 49 by substitution property of equality ( because vertical angles are congruent angles).

2. Which expression is equivalent to 1/4 n – 16? ​

Answers

Answer:

1/4n - 16 =

1/4(n - 64)

Step-by-step explanation:

Two expression are said to be equivalent, if after substituting the value of variable by any constant the numerical value of both original expression and equivalent expression are same.

Find X
Coordinates are: 3x, 3x+10, 2x+10

Answers

Answer:

D. 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Geometry

All angles in a triangle add up to 180°

Step-by-step explanation:

Step 1: Set Up Equation

3x + 3x + 10 + 2x + 10 = 180

Step 2: Solve for x

Combine like terms:                    8x + 20 = 180Isolate x term:                              8x = 160Isolate x:                                       x = 20

Find xy when x(-7,10) and y(3,4)

Answers

Answer:

Distance xy = 11.66 unit (Approx)

Step-by-step explanation:

Given:

x(-7,10)

y(3,4)

Find:

Distance xy

Computation:

Distance = √(x2-x1)²+(y2-y1)²

Distance xy = √(3+7)²+(4-10)²

Distance xy = √ 100 + 36

Distance xy = 11.66 unit (Approx)

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I know its not that hard im just doing this for fun lol

Answers

Answers:

0.210.226.50.680.6240.230.10130.200.1916

plus all rounded so i don't cuffuse anyone

answer all questions please.

Answers

Domain: -∞ ≥ x ≥ ∞
Range: y ≥ 0
This graph shows a function

1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.

A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.

B) Who makes more from stuffing the same number of envelopes? Explain how you know using the information above.

C) Anna has savings of $100 at the beginning of the summer and she saves all of her earnings from her job. Graph her savings as an equationof the number of envelopes she’s stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the initial value and slope in each case?

D)You survey 6 other employees and findthe following data on envelopesstuffed (x) and dollars earned(y). Plot a trend lineon the graph. Find the equation of the trend line.

Answers

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. Anna earns $20 for every 400 envelopes. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

Jason has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table of Anna and Jason we can see that Anna makes more stuffing than Jason for the same number of envelopes.

c) Anna has a savings of $100 initially. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

Therefore from the graph there is a y intercept at 100. That is the earnings starts initially is $100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value of y at x = 0)

For the first graph, the slope is 1/20 with an initial value of 0 while for the second graph the slope is 1/15 with an initial value of 100

D) The trend line pass through the points (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

PLEASE HELP!!!!!


A line intersects the points (-8, -1) and
(1, 8). What is the slope-intercept
equation for this line?
y= [?}x+ _

Answers

Answer in the pic
Have a great day
:))

Answer:

m=1

c=7

I hope it will be useful.

What is the final amount if 1102 is increased by 2% followed by a further 1% increase? Give your answer rounded to 2 DP.

Answers

To increase by 2% you multiply to get 1102*0.02=22.04. You then add that to 1102, getting 1124.04. To then decrease it by 1% you multiply to get 1124.04*0.01=11.24. Subtract 11.24 from 1124.04 to get a final answer of 1112.8

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

We have,

Amount = 1102

Percentage increase = 2%

Another percentage increase = 1%

Now,

The final amount.

= 101% of 102% of 1102

This can be written as,

= 101/100 x 102/100 x 1102

= (101 x 102 x 1102) / 10000

= 1135.28

Thus,

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

Learn more about percentages here:

https://brainly.com/question/11403063

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In ΔRST, r = 53 inches, ∠S=6° and ∠T=58°. Find the length of s, to the nearest inch.

Answers

Answer:

s = 6 inches

Step-by-step explanation:

Given:

r = 53 inches,

∠S = 6°

∠T = 58°.

Required:

Length of s

Solution:

Use Sine Rule

Thus:

[tex] \frac{s}{Sin(S)} = \frac{r}{Sin(R)} [/tex]

<R = 180 - (58 + 6)

<R = 116°

r = 53 inches,

∠S = 6°

s = ?

Plug in the values

[tex] \frac{s}{Sin(6)} = \frac{53}{Sin(116)} [/tex]

Multiply both sides by Sin(6)

[tex] \frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6) [/tex]

[tex] s = \frac{53 \times Sin(6)}{Sin(116)} [/tex]

[tex] s = 6 inches [/tex] (nearest inch)

Conceded goals: 0,1,2,3,4 Frequency:2,8,4,10,6 What is the mean number of goals conceded

Answers

Answer:

2.333

Step-by-step explanation:

Given that:

Conceded goals: 0,1,2,3,4

Frequency:2,8,4,10,6

Mean(m) = Σ(fx) / Σf

Σfx = (0*2) + (1*8) + (2*4) + (3*10) + (4*6) = 70

Σf = (2 + 8 + 4 + 10 + 6) = 30

Hence,

Mean = 70 / 30

Mean = 2.333

how many solutions does the nonlinear system of equations graphed below have

a. one
b. four
c. zero
d. two

Answers

Answer:

The nonlinear system of equations has 4 solutions B

Step-by-step explanation:

The number of solutions of a system of equations equal to the number of points of intersection of the graphs of the equations of the system

Let us use this note to solve the question

From the given figure

∵ The nonlinear system of equations represented by two curves and a circle

Each curve intersects the circle into two points

∴ The number of the points of intersection is 4

→ By using the note above

∵ The number of intersection points equal to the number of solutions

∴ The number of solutions is 4

The nonlinear system of equations has 4 solutions

Please help me with part A B and C can you write the answers and show me how you get it in a notebook please

Answers

You can see all answers in the picture

Corrado has 27 books in his room that he has already read. He wants to give them away to his 3 younger siblings. How many books will each of Corrado's siblings receive? If b represents the number of books each sibling receives, which equation could be used to solve the problem?

Answers

Answer:

9 books each

Step-by-step explanation:

27/3=9....

Find the focus, this looks different from the other ones I’ve done which is why I am confused

Answers

Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,0)(0,0)

Focus: (0,32)(0,32)

Axis of Symmetry: x=0x=0

Directrix: y=−32y=-32

xy−223−11600116223xy-223-11600116223

Step-by-step explanation:

please mark me as brainliest thank you

Answer:

A

(0, 3/2)

Step-by-step explanation

In a school of 450 students, 110 of them are in the choir, 240 of them are in the band and 60 students are in the choir and the band.
Please help I've been trying to solve this for an hour (T-T)

Answers

There are 270 in band an 140 in choir and 40 students left

solve: 4y - 6 = 2y + 8

Answers

Answer:

y = 7

Step-by-step explanation:

Given

4y - 6 = 2y + 8 ( subtract 2y from both sides )

2y - 6 = 8 ( add 6 to both sides )

2y = 14 ( divide both sides by 2 )

y = 7

See the Pic for my question.

Answers

Answer:

C. 7

Step-by-step explanation:

4 * Sum (i = 1 to 3) (1/2)^(i - 1) =

= 4 * [(1/2)^0 + (1/2)^1 + (1/2)^2]

= 4 * [1 + 1/2 + 1/4]

= 4 * [7/4]

= 7

Answer:

7

Step-by-step explanation:

because I'm smart like that

 Can someone pleaseeee help if you’re correct I’ll give u brainlist

Answers

Answer:

30

Step-by-step explanation:

I asked the my math tutor lol

Choose the algebraic expression that describes: 13 less than y.

Answers

Y-13 because it’s less than y so it’s subtracting from the y

Can the hypotenuse or a leg be a decimal? Why or why not?

Answers

Answer:

yes

because the of use the Pythagoras theorm

PLEASE ANSWER FAST WILL GIVE YOU BRAINLEST LOL
You are testing two scales for accuracy by weighing two different objects.
Use the drop-down menus to complete the statements about the scales' accuracy.

Answers

Answer:

This is because the object on the 1st scale weighs (more) than the object on second scale, each pound of error results in a (lesser) percent error. The first scale was (10) pounds off the second scale,was (3) pounds off, so 1st scale was (10)% off 2nd scale was (12)% off.

Answer:

Because the object on Scale 1 weighs more than the object on Scale 2, each pound of error results in a lesser percent error. Scale 1 was 10 pounds off and Scale 2 was 3 pounds off, so Scale 1 was 10% off and Scale 2 was 12% off.

Step-by-step explanation:

Got it right on TTM so yeah! :)

A young sumo wrestler goes on a special diet to gain weight.
The variable www models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for ttt months.
w=80+5.4tw=80+5.4tw, equals, 80, plus, 5, point, 4, t
How much weight does the wrestler gain every 222 months?
kilograms

Answers

Answer:

10.8 kg

Step-by-step explanation:

w = 80 + 5.4t

At time 0, when he starts the diet, his initial weight is

w = 80 + 5.4(0)

w = 80

80 kg.

After 2 months, t = 2. His weight is

w = 80 + 5.4t

w = 80 + 5.4(2)

w = 80 + 10.8

w = 90.8

90.8 kg.

His gain in 2 months was 90.8 kg - 80 kg = 10.8 kg

Answer: 10.8 kg

The wrestler gains 10.8 kg every 2 months.

What is an equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation that models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for t months.

w = 80 + 5.4t

We need to find his weight after 2 months.

At time t = 0, when he starts the diet, the wrestler's initial weight would be,

⇒ w = 80 + 5.4(0)

⇒ w = 80 kg

After 2 months, t = 2 the wrestler's weight  weight would be,

⇒ w = 80 + 5.4(2)

⇒ w = 80 + 10.8

⇒ w = 90.8 kg

We need to find the weight gain in 2 months.

90.8 - 80 = 10.8 kg

Therefore, the wrestler gains 10.8 kg every 2 months.

Learn more about an equation here:

https://brainly.com/question/649785

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solve this and explain it to me please

it's weird my brother And I am fighting for this my brother says it's p but I think it's P-Q​

Answers

Answer: U - (P - P∩Q)

Where U represents the universal set.

Step-by-step explanation:

In the image, we can see that the shaded part is all the region minus the part of P that does not share elements with Q.

This part of P can be written as:

P - P∩Q

there we write:

"The elements of P, minus the elements that P share in common with Q"

Then to write the shaded area, we need to write the universal set, U, minus the thing we wrote above, this is:

U - (P - P∩Q)

A circular spinner for a game has a radius of 5 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.

Answers

The total area of a circle is pi * radius^2

The total area of the circle is pi x 5^2 = 25pi sq. cm.

2/5 of this is success, so the answer is 2/5 * 25pi = 10 pi sq. cm.

is 49 greater than or less than 7.1​

Answers

Answer:

Greater

Step-by-step explanation:

just because

Answer:

greater

Step-by-step explanation:

49>7.1

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