Plzzz I need help with this question I tried to solve it many times but I can't
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 Sj.
• 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 = Si + S2 - Sz.
a) Show that S = (2x - 3)(5x - 9).
b) For what values of x, the areas of AFGC and ADEB are equal?
c) Expand and reduce S.
d) What is the value of x, so that the area of AFGC exceed the area of ADEB by 27?
Answers
Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as: [tex]A1=\frac{(base)(height)}{2}[/tex]
Area of a rectangle is calculated as: [tex]A2=(side)(side)[/tex]
Area of a right trapezoid is: [tex]A3=\frac{(a+b)h}{2}[/tex], where:
a is short base
b is long base
h is height
1) Expressing areas in terms of x:
Area of triangle S1:
[tex]S1=\frac{(2x-3)(4x-6)}{2}[/tex]
[tex]S1=4x^{2}-12x+9[/tex]
Area of rectangle S2:
[tex]S2 = (4x-6)(3x-2)[/tex]
[tex]S2=12x^{2}-26x+12[/tex]
Area of trapezoid S3:
[tex]S3=\frac{(2x+3+4x+1)(2x-3)}{2}[/tex]
[tex]S3=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]S3=6x^{2}-5x-6[/tex]
2) a) [tex]S=4x^{2}-12x+9+12x^{2}-26x+12-(6x^{2}-5x-6)[/tex]
[tex]S=4x^{2}-12x+9+12x^{2}-26x+12-6x^{2}+5x+6[/tex]
[tex]S=10x^{2}-33x+37[/tex]
Which is the same as S = (2x-3)(5x-9)
b) For the areas to be the same:
[tex]\frac{(3x-2+3x-2+2x-3)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]\frac{(8x-7)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12[/tex]
[tex]20x^{2}-66x+54=0[/tex]
Using Bhaskara to solve the second degree equation:
[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.54)} }{2(20)}[/tex]
[tex]x_{1}=\frac{66+6}{40}[/tex] = 1.8
[tex]x_{2}=\frac{66-6}{40}[/tex] = 1.5
For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.
c) Expand a polynomial (or equation) is to multiply all the terms, remiving the parenthesis. Reduce a polynomial (or equation) is to combine terms alike,e.g.:
[tex]S=(2x-3)(5x-9)[/tex]
[tex]S=10x^{2}-18x-15x+27[/tex] (expand)
[tex]S=10x^{2}-33x+27[/tex] (reduce)
d) For area of AFCG to be bigger than area of ADEB by 27:
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12+27[/tex]
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x+15[/tex]
[tex]20x^{2}-66x+27=0[/tex]
Solving:
[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.27)} }{2(20)}[/tex]
[tex]\frac{66+46.86}{40}[/tex]
[tex]x_{1}=\frac{66+46.86}{40}=[/tex] 2.82
[tex]x_{2}=\frac{66-46.86}{40}[/tex] = 0.48
According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Given k||w, x||tm, and <5=45 degrees, what is m<7?
Answers
Answer:
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Step-by-step explanation:
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∠ 7 = ∠ 5 = 45°
Y
1
4
3
2-
As
1-
+
-3
-2
-1
1
2
3
-2+
Co
-3
Pro
What is the slope of the line?
Answers
Answer:a
Step-by-step explanation:
"If f(x) = 6x3 + 5x, g(x) = 3x2 + 5, and h(x) = 9x2 – 8, what is the degree of f(g(h(x)))?"
2
3
7
12
Answers
Answer:
the degree of f(g(h(x))) is 12
Step-by-step explanation: I know you want simple and easy answers and thats what im here for, . :D
Answer:
D. 12
Step-by-step explanation:
Edge 2020
write the explicit formula for the geometric sequence 64,32,16,8
Answers
Answer:
[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 64 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{32}{64}[/tex] = [tex]\frac{1}{2}[/tex] , then explicit formula is
[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]
1, 4, 9, 16, 25, ______, ______, ______
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plz help ill mark brailiest
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Answer:A
Step-by-step explanation: plz leave a like
Answer:
The correct graph is A
Step-by-step explanation:
Help me pleaseee !!
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Answer:
the answer is 2
Step-by-step explanation:
because 2x2 is 4 so x=2
1- ? divided by 3 = -7
2- -50 divided by ? =10
3- ? divided by -2 = 10
Answers
2.) 5
3.) -20
bdhdhdhfh
Highest Common Factor of 42
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Answer:
42 is itself it's highest common factor
Please Help! I’m Dum
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Answer:
same im dum 2 :((((
Step-by-step explanation:
Write the equation of the line in SLOPE-INTERCEPT form:
-5
-5
0
5
Slope:
Y-intercept:
Slope Intercept:
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what is the slope???????
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What is a synthetic material made of?
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Synthetic fibers are made from raw materials such as petroleum, based on chemicals or petrochemicals [20]. These materials are polymerized into a long, linear chemical with different chemical compounds and are used to produce various types of fibers.
What are the next three terms in the sequence? 2, -3, -6, 18, … -108, -1,944, -209,952 -108, 1,944, -209,952 -108, -1,944, 209,952 108, 1,944, 209,952
Answers
Answer: -108, -1,944, 209,952
Step-by-step explanation:
The the next term in this sequence is being determined by multiplying the last two numbers of the sequence.
Next three terms are;
= -6 * 18
= -108
= 18 * -108
= -1,944
= -108 * -1,944
= 209,952
What is the value of arccos(sine (StartFraction pi Over 2 EndFraction))?
Answers
Answer:
0 radians or 2π radians
Step-by-step explanation:
arccos(sine (StartFraction pi Over 2 EndFraction)) is expressed as;
cos^(-1) (sin π/2)
Now, (sin π/2) in radians is same as (sin 180/2) = sin 90 in degrees.
Thus;
(sin π/2) = 1
Thus;
cos^(-1) 1 = 0
It could also be 360° in the fourth quadrant since cosine is positive there too.
Thus,
cos^(-1) (sin π/2) = 0° or 360°
In radians, this gives; 0 radians or 2π radians
0 radians or 2π radians is the value of arccos(sine (StartFraction pi Over 2 EndFraction)).
Here, we have,
given that,
The term is: arccos (sine (StartFraction pi Over 2 EndFraction)
so, we get,
arccos(sine (StartFraction pi Over 2 EndFraction)) is expressed as;
cos^(-1) (sin π/2)
Now, (sin π/2) in radians is same as (sin 180/2) = sin 90 in degrees.
Thus;
(sin π/2) = 1
Thus;
cos^(-1) 1 = 0
It could also be 360° in the fourth quadrant since cosine is positive there too.
Thus,
cos^(-1) (sin π/2) = 0° or 360°
In radians, this gives; 0 radians or 2π radians.
To learn more trigonometry click:
brainly.com/question/26719838
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which describes the equation: y=4x-5
1._ the equation has a rate of change of -5 and crosses y intercept at 4
2.- the equation has a rate of change of 4 and crosses y intercept at -5
3._ none of the above
4._ all the above
Answers
Answer:
hello
Step-by-step explanation:
Could someone create Equations & Explanations based on this question, because I need to solve using substitution and later modify it to create a system of inequalities.
Answers
Answer:
3 hours
Step-by-step explanation:
If both the cars are moving in the same direction,
Speed of orange sports car = 60 miles per hour
Since, this car has already moved for 1 hour,
Distance covered by the sports car = speed × time
= 60 × 1
= 60 miles
Speed of the green van = 30 miles per hour
Since, green van has already moved for the duration = 3 hours
Distance covered by the green van = speed × time
= 40 × 3
= 120 miles
Therefore, distance between sports car and green van = 120 - 60
= 60 miles
Relative speed of orange sports car with respect to green van = Speed of sports car - speed of green van
= 60 - 40
= 20 miles per hour
Time taken by the orange sports car to cover 60 miles (Distance between sports car and green van) = [tex]\frac{\text{Distance between the car and van}}{\text{Relative speed of the sports car}}[/tex]
= [tex]\frac{60}{20}[/tex]
= 3 hours
Therefore, orange sports car will take 3 hours to pass the green mini green van.
PLS HELP ME ! ! ! ! !
Answers
Answer:
D (0, 2)
General Formulas and Concepts:
Algebra I
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = 3/4x + 2
Step 2: Break Function
Identify Parts
Slope m = 3/4
y-intercept b = 2
x + y = 8
Let x = 6. What is y?
Enter the correct answer.
DONE
DOO
Answers
Answer:
y=2
Step-by-step explanation:
james ran 25/100 of a mile yesterday and his friend Natasha ran 4/10 of a mile. who ran farther and how do u know
Answers
Answer: Natasha ran further
Step-by-step explanation:
1. Simplify both fractions into a common denominator:
25/100 and 40/100
2. Compare:
40/100 > 25/100
3. Answer:
Natsha ran further
Have a nice day! :D
Answer:
Natasha ran farther
Step-by-step explanation:
This is the answer because:
1) In problems like this, we have to find the common denominator and compare both of the fractions:
[tex]\frac{4}{10} = \frac{4 times10}{10 times 10} = \frac{40}{100}[/tex]
[tex]\frac{40}{100}[/tex] > [tex]\frac{25}{100}[/tex] = 40/100 is greater than 25/100.
Therefore, the answer is Natasha.
Hope this helps! :D
Today, January 4th is the start of a brand new quarter, your starting fresh! What is a math goal that you have for yourself for 3rd quarter?
Answers
Answer: For this 3rd quarter I'm going to start paying attention in class, stop procrastinate, and also do my hw early so I can have a good grade in this class. The # 1 goal is to have a A or B in this class:)
Step-by-step explanation:
What are all possible values of x if x3 + 9 > 27?
Answers
Answer:
x > 6
Step-by-step explanation:
3x + 9 > 27
3x > 27 -9
x > 6
the values of X are greater than 6
Read the excerpt from Heart of a Samurai.
[Manjiro] took one last glance behind them and noticed something strange. Dark streaks ran like ribbons through the water.
Which best states the author’s purpose for using the word “strange”?
A. to develop Manjiro’s character
B. to create a feeling of suspense
C. to describe the story’s setting
D. to quicken the pace of the story
Answers
Answer:
uhm i think its A
Step-by-step explanation:
sorry if i get it wrong
:):
Answer:ITS A
Step-by-step explanation:
HURRY UP PLS
The diameter of a red blood
cell is about 0.0008 cm. The diameter ofa
chicken pox virus is about 1.7 x 10-5 cm. What is the approximate ratio of the
diameter of the red blood cell to the diameter of the chicken pox virus?
OA. 1.9 x 10-2
OB. 4.7 x 101
OC. 1.9 x 10-3
O D. 4.7 x 102
Answers
Answer:
its B my guy I had that question before
Answer:
B.4.7 x 101
Step-by-step explanation:
it's 4.7 x 101
plzzzzzzzzzzzzzzzzzzz
Answers
a) 4p+2p-3p
=> 6p-3p
=> 3p
b) 9s-5s+2s-s
=> 4s+1s
=> 5s
c) 8t+3r-7t-9r
=>8t-7t-9+3
=> t-6r
Hope it helps!
Answer:
3p , 5s , t - 6r
Step-by-step explanation:
(a)
4p + 2p - 3p ← add the first 2 terms
= 6p - 3p
= 3p
(b)
9s - 5s + 2s - s
= 4s + 2s - s
= 6s - s
= 5s
(c)
8t + 3r - 7t - 9r ← collect like terms
= (8t - 7t) + (3r - 9r)
= t - 6r
What has made travel easier in the Alps? 25 points
Answers
Answer:
The Alps are the youngest mountain range in Europe, having formed approximately 65 million years ago. As well as mountains, the Alps are famous for it's clear Alpine lakes, including the stunning Lake Geneva, Lake Constance and Lake Como.
Step-by-step explanation: