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
Related Questions
Is 4/5 greater than 5/6?
Answers
Answer:
5/6 is greater than 4/5
Step-by-step explanation:
4/5 = 0.8
5/6 = 0.833333
Answer:
no
Step-by-step explanation:
5/6 is greater than 4/5
Type the correct answer in each box. Use numerals instead of words.
Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In
the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total
$46.21 on gas.
In the first week, Micah bought
gallons of gas
in the second week, Micah bought
gallons of gas
Answers
Answer:
Micah bought 11 gallons of gas in the first week and 8 gallons of gas in the second week
Step-by-step explanation:
Answer:
Step-by-step explanation:
Micah bought 11 gallons of gas in the first week and 8 gallons of gas in the second week
There are 55 apples in each row. There are 5000 rows. How many apples in all?
Answers
Answer:
you would take the amount of apples per row and multiply it by the amount of rows, so in this case it would be 55x5000 which is 275000
there's 275000 apples in all
Which of the following represents a line parallel to the y-axis
Answers
Answer:
c) x=4
Step-by-step explanation:
Write as a single fraction in its simplest form
(2x-1/3) - (2/x+1)
With steps plz :))
Answers
[tex](2x - \frac{1}{3} ) - ( \frac{2}{x} + 1)[/tex]
[tex]2x - \frac{1}{3} - \frac{2}{x} + 1[/tex]
[tex](2x - \frac{2}{x} ) + ( - \frac{1}{3} + 1)[/tex]
[tex] (\frac{2 {x}^{2} }{x} - \frac{2}{x} ) + ( \frac{ - 1}{3} + \frac{3}{3} )[/tex]
[tex] \frac{2 {x}^{2} - 2 }{x} + \frac{ - 2}{3} [/tex]
We want to write the given expression as a single fraction. We will get the fraction:
[tex]\frac{6*x^2 - 4*x - 6}{3*x}[/tex]
Rewriting the expression.
So we start with the expression:
[tex](2*x - \frac{1}{3}) - (\frac{2}{x} + 1)[/tex]
First, let's rewrite each of these parenthesis as fractions, we need to have the same denominator in all the terms, then in the first one we can multiply and divide by 3 (and in the second one we can do the same but with x) so we get:
[tex](\frac{3}{3} *2*x - \frac{1}{3}) - (\frac{2}{x} + 1*\frac{x}{x} )\\\\(\frac{6*x}{3} - \frac{1}{3}) - (\frac{2}{x} + \frac{x}{x} )\\\\\frac{6*x - 1}{3} - \frac{2 + x}{x}[/tex]
Now we must multiply and divide the left term by x, and the right term by 3, so we get:
[tex]\frac{x}{x} \frac{6*x - 1}{3} - \frac{2 + x}{x}*\frac{3}{3} \\\\\frac{6*x^2 - x}{3*x} - \frac{6 + 3x}{3*x} = \frac{6*x^2 - x - 3x - 6}{3*x}\\\\\frac{6*x^2 - 4*x - 6}{3*x}[/tex]
This is the fraction in its simplest form.
If you want to learn more about fractions you can read:
https://brainly.com/question/11562149
Find the coordinates of the points of intersection of the parabola y=x^2+3x-4 and the line y=2x+2
Answers
x^2+3x-4=2x+2
x^2+x-6=0
(x+3)(x-2)=0
x=-3,2
So, these are the x values of the intersection. To get the y values, you can just plug them back into either formula:
y=2(-3)+2
y=-4
y2(2)+2
y=6
So the coordinates are (-3,-4) and 2,6).
Pleassse HELP WILL GIVE BRAINLIEST
Darrell bought an 80 pound bag of dog food. If ⅝ of a pound are used to
feed the dog each day, how many days will the bag of dog food last?
Answers
Answer:
The 80 p0und bag will last 128 days.
Step-by-step explanation:
In order to find out how much days the 80 pound bag last we have to divide the 80 pounds by the among that the dog eats each day. And so we get.....
80 / [tex]\frac{5}{8}[/tex] = [tex]\frac{80}{1} / \frac{5}{8}[/tex] = [tex](\frac{80}{1})(\frac{8}{5})[/tex] = [tex]\frac{640}{5}[/tex] = 128
Answer:
For some reason my answer got deleted.
The dog food will last 128 days,
Step-by-step explanation:
80 ÷ 5/8 = 128
Since 5/8 is being used each day, you divide.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
The population of new york city in 2013 was about 8,406,000 people which number best appoximates the population as a single digit times a power of ten
Answers
Answer:
8 * 10^6
Step-by-step explanation:
The question is asking us to represent the value 8,406,000 in standard. The standard form of an expression is expressed as;
A * 10^n
A is any integer between 1 and 10
n is any integer.
Given the value 8,406,000
8,406,000.
We are going to move the decimal point at the end to first digit value. This point will be shifted 6 times to have;
8,406,000 = 8.6 * 10^6 (Note that n is positive since the value given is greater than 1)
Since we are to express as a single digit times a power of ten, the required answer will be 8 * 10^6
How would you solve equations with 3 sides or whatever this is
Answers
Answer: B. -4 < y < -1
Step-by-step explanation:
1. Subtract 2 from all three sides to isolate the variable in the center of the inequality
5 < 2 - 3y < 14
3 < -3y < 12
2. Divide each of the three sides by -3 to get y by itself, as each of the answers have y as independent.
3 < -3y < 12
-1, y, -4
3. Rearrange
-4 < y < -1 (b)
Samuel and Joyce both bought CDs. Samuel bought 3x CDs and Joyce bought 2x-1 CDs. If each CD had a Regular price of $18 and a discount of $2. What is the expression for the COST of their CDs, combined?
Answers
Answer:
2(5x – 1)
Step-by-step explanation:
Choose all the factors of 12. (Check all that apply.)
1
5
8
7
6
3
12
11
4
2
10
9
plz help me
Answers
Answer:
1,2,3,4,6,12
Step-by-step explanation:
12•1= 12
2•6= 12
3•4= 12
Simplify. Rewrite the expression in the form 8^n. (8^−8 )(8^3)
Answers
Answer:
Step-by-step explanation:
find the value of angle x
pls answer
Answers
Answer:
110
Step-by-step explanation:
lets assume y is the angle next to x which should complete to form a 360.
50 + 25 + 35 + y = 360
y = 250
x + y = 360
x + 250 = 360
x = 110
Answer:
110
Step-by-step explanation:
lets assume y is the angle next to x which should complete to from a 360.
50 + 25 + 35 + y = 360
y = 250
x + y = 360
x + 250 = 360
x = 110
plzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
4x⁵ z⁸
Step-by-step explanation:
hope it helps!
.......
Answer:
4 x^5 z^8
Step-by-step explanation:
To make it easy I am categorizing this in two groups. One is (xz^3), late us name it A and the other is after the multiplication sign that is (4x^4z^5) which we are naming B. Now 4 from b multiplies 1 from a(as there is no number which means there must be 1). In multiplication of power of bases we have to add the powers which means x from a × x^4 from b= x from a's power 1 + x from b's power 4=x^5 and repeating same process in case of z resulting in z^5.
Hence the above mentioned ans comes...
Hope this helps you
-5x-4y=2a 4x-5y=2 which of the following choices of A will results in a system of linear equations with exactly one solution
Answers
Answer:
Any of them. a ∈ RStep-by-step explanation:
-5x - 4y = 2a 4x - 5y = 2
-4y = 5x + 2a -5y = -4x + 2
y = (5x + 2a):(-4) y = (-4x + 2):(-5)
y = -⁵/₄x - ¹/₂a y = ⁴/₅x - ²/₅
m₁ = -⁵/₄, b₁ = -¹/₂a m₂=⁴/₅, b₂= -²/₅
-⁵/₄ ≠ ⁴/₅
Different slopes means that two lines have one point of intercept (no mater what the b's are). That means that the system of linear equations has exactly one solution for any value of a.
can someone plz help me with this
i give u a brainllest
Answers
Answer:
it is a and b because you have to do step by step
what is –9 – (–13) and how do you solve
Answers
Alex helps his father milk cows on their dairy farm. They are paid $2.25
per gallon of milk, that they get from their cows. Together, Alex and his
father are able to milk 12 gallons over a 2-hour period. How much money
could Alex and his father expect to earn if they worked for 10 hours?
А
$22.50
B
$54.00
C
$135.00
D
$270.50
Answers
Please help!!!!!!!!!!!!!!!
Answers
Answer:
x = 48.59 degrees
Step-by-step explanation:
Do sin-1(12/16) and put it in a calculator. After that, you will get your final answer as 48.59 degrees. This requires sin because the opposite angle is 12 for x. The adjacent angle is something else.
pleasee help me ASAP ITS DUE SOON
I just need to know
1. slope
2. y-intercept
3. slope intercept form
Answers
(-5, 2) ⇒ x₁ = -5, y₁ = 2
(7, -1) ⇒ x₂ = 7, y₂ = -1
Slope:
[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-2}{7+5}=\dfrac{-3}{12}=-\dfrac14}[/tex]
Slope intercept form:
y = mx + b
Plug m and (7, -1) :
-1 = -¹/₄(7) + b
-1 + ⁷/₄ = b
b = ³/₄ ← y-interceptTherefore slope intercept form of h(x):
h(x) = -¹/₄x + ³/₄What are the roots of the polynomial equation: 4k - 144 = 0 Show all of your work!
Answers
Answer:
k = ±6
Step-by-step explanation:
guess your question is 4k²–144 = 0??
4k² = 144
k² = 36
k²–36 = 0
(k+6)(k–6) = 0
k+6 = 0 | k–6 = 0
k = –6, k = 6.
Alternatively; k = ±6.
a group of 6 people equally shares 12 Liters of juice, how many milliliters of juice does each person recive
Answers
Answer: each get 2,000 mil in use
Step-by-step explanation:
A plant is already 8.75 meters tall, and it will grow 25 centimeters every month. the plants height, H (in meters), after x months is given by the following function H(x)=0.25x+8.75 What is the plants height after 40 months?
Answers
Answer:
18.75 meters
Step-by-step explanation:
8.75 + 0.25(40) = 18.75
A circular wire of length 176 cm is rebound to a rectangle whose length is same as the diameter of the circle. Find the difference in both the areas ?
Answers
Answer:
The difference in area is 672 cm^2
Step-by-step explanation:
Firstly, let us get the diameter of the circle
The length of the wire is the measure of the circle’s circumference
mathematically;
C = pi * d
176 = 22/7 * d
22d = 7 * 176
d = (7 * 176)/22
d = 56 cm
So, the area of the circle will be;
pi * d^2/4
= 22/7 * 56 * 56 * 1/4
= 2464 cm^2
Also, the length of the circumference is same as the perimeter of the rectangle
From the perimeter of the rectangle, we can get the width and use that to calculate the area of the rectangle
The formula for the perimeter of the rectangle is;
2(l + b)
2(56 + b) = 176
56 + b = 88
b = 88-56
b = 32 cm
So, the area of the rectangle will be;
32 * 56 = 1792 cm^2
The difference between the two areas will be;
2464-1792 = 672 cm^2
On a test a student got 15 problems correct out of a total of 20 problems. What percent did the student get, begin emphasis, incorrect, end emphasis,?
Answers
Answer:
I think what you got is correct
The percentage of incorrect problems is 25%.
Option D is the correct answer.
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
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of problems = 20
Number of correct problems = 15
The number of incorrect problems.
= 20 - 15
= 5
The percentage of incorrect problems.
= 5/20 x 100
= 25%
Thus,
25% were incorrect problems
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ2
Click here to answer the questions, thanks
Answers
Answer:
a) 3/5=12/20
b) 5/6=25/30
Step-by-step explanation:
a.) To find the answer you would first find how much it took to get to 20. 5 times 4 is 20. Then to find the numerator you would do 3 times 4 and that would be 12.
b) To find the answer you would first find how much it took to get to 30. So 30/6 is 5. Then you would divide 25 by 5 and you would get 5.
Find the length of the missing side. Round to the nearest tenth (one decimal place).
Answers
Answer: pretty sure it is 56.5
Step-by-step explanation:
Which of the points below does not belong?
(0, -3)
(0, 0)
(4, -3)
(4,0)
Answers
Answer:
c
Step-by-step explanation:
A player hits a baseball with an initial velocity of 117 ft/sec at an elevation angle of 50°. When struck, the baseball is 2 feet above the ground. What is the maximum height the baseball reaches?
Answers
Answer:
126
Step-by-step explanation:
uhhhhh straight up guessed, but yeah heres the answer
Answer:
is is 126 got it right on edge
Step-by-step explanation:
The young wizard, Darpinido, got 16 dragons and 12 griffins for his birthday. But his sister, In grid, left the gate open and more a=than 6 dragon and more than 3 griffins flew away. Now the young wizard has more griffins than dragons. What is the greatest number of dragons Darpinido could have now?
Answers
Answer:
7 Dragons.
Step-by-step explanation:
16 dragons 6+ dragons gone
12 griffins 3+ griffins gone
Let's say one more than 3 griffins are gone: 4 griffins are gone.
Then:
Griffins now = 8
Dragons now = <8
One less than 8 dragons is 7 dragons.
In the end, 4 griffins and 9 dragons had left.