Answers
CS = x, and since AB = BC = CD = DA = 1cm -> SD = 1 - x
We see that angle DSP = angle APQ (because they simultaneously equal to 90 when added angle DPS)
So, triangle DSP = triangle APQ (equal hypotenuse - square side and equal angle.)
Similarly, we can prove triangle SCE and QBE in the same way
So, all 4 of the triangles are equal to each other.
-> SD = CE = BQ = AP = 1-x
Calculate the area of 4 triangles : [ x(1-x) : 2 ] x 4 = x(1-x) x 2
Area (PQRS) = 1 - [ x(1-x)] x 2 = 1 - 2x + 2x(squared) = [tex]2x^{2} -2x + 1[/tex]
ii) Half area of PQRS = [tex]x^{2} -x+1[/tex]
= [tex]x^{2} -\frac{1}{2} x-\frac{1}{2} x + \frac{1}{2} = x(x-\frac{1}{2} )- \frac{1}{2}(x-\frac{1}{2} ) + \frac{1}{4} = (x-\frac{1}{2})^{2} + \frac{1}{4}[/tex]
We have : [tex](x-\frac{1}{2}) ^{2}[/tex]
has the smallest value of 0 -> The smallest half value of PQRS = 1/4 -> The smallest value of PQRS = 1/2
Related Questions
4602837593857304985+395283059282352323
Answers
Answer:4998120653139657308
Step-by-step explanation:
Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?
Answers
Answer:
Answer = 0.5 pages per minute.
Step-by-step explanation:
150 ÷ 5 = 30 pages an hour
30 ÷ 60 ( Minutes in an hour ) = 0.5 Pages/ Minute.
Hope this helps.
Passes through 0,2 and has a slope of -5/3
Answers
Answer:
y = - 1 2/3x + 2
Step-by-step explanation:
Step 1:
y = mx + b Slope intercept Form
Step 2:
y = - 5/3x + b Input Slope
Step 3:
2 = - 5/3 ( 0 ) + b Input x and y
Step 4:
2 = b Multiply
Answer:
y = - 1 2/3x + 2 Input b
Hope This Helps :)
A torch and a battery cost £2.50 altogether.
The torch costs £2.00 more than the battery.
What fraction of the total price is the battery's price?
Give your answer in its simplest form.
Answers
Answer:
1/10
Step-by-step explanation:
2.50-2=0.5
0.5/2=0.25
0.25+2=2.25
2.5-2.25=0.25
0.25/2.5= 0.1
0.1 = 1/10
Help pleaseeeeeeeeeee
Answers
Answer:
angle relationship is co-interior
x = 3.94
Step-by-step explanation:
(34x - 1 ) + 45 = 180 [co-interior angles add up to 180 degrees]
34x - 1 = 135
34x = 134
x= 134/34 =3.94
Divide 300 among Ravi and Isha in the ratio 2:3.
Answers
Answer:
Ravi: 120
Isha: 180
Step-by-step explanation:
Think of the ratio as parts. Ravi gets 2 parts while Isha gets 3.
But, we don't know how much each gets. This is written as X.
The ratio of 2:3 can be set up in an equation as 2x and 3x.
We know that the total is 300.
[tex]2x+3x=300\\5x=300\\x=60[/tex]
Ravi has 2 parts:
[tex]2(60)=120[/tex]
Isha has 3 parts:
[tex]3(60)=180[/tex]
Solve the system y = -x + 7 and y = 0.5(x - 3)2s
This is for 25 points.
Answers
(1,6) & (7,0). Step-by-step explanation: y = -x + 7. y = -0.5(x - 3)² + 8. To solve the system, solve these two equations
Step-by-step explanation:
9 = (-6p - (-3)) / -8
Answers
Answer:
p = -0.35
Step-by-step explanation:
-8 ÷ ((-3) - 6 ( -0.35 ) = 8.88( repeating ) Rounding to 9
Hope this helps.
Hi, I can use some help wiTh this thanks!
Answers
Answer:
Square root of 9 = 3 ! ^^
Step-by-step explanation:
[tex]3*3=9 \\3^{2}=9\\\sqrt{9} = 3[/tex]
^^
Mr. Johnson sells and repairs watches at his store. Part A: Mr. Johnson took the price of a watch that was listed at $60 and marked it up by 30%. After the markup, what is the selling price of the watch?
Part B: A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount. Then the customer had to pay a sales tax of 5% on the discounted price. How much did the customer pay for the watch? *
Answers
Part B: 78.54$
x < 1 is the solution to which of the following compound inequalities?
a) x > 3 OR x < 1
b) x < 4 OR x > 1
c) x < 4 AND x < 1
d) x > 3 AND x < 1
Answers
As vrea sa încep sa cant îmi place foarte mult muzica Românească
What is the value of x in the equation −6 + x = −5? (1 point)
1
11
-1
-11
Answers
Answer:
1
Step-by-step explanation:
-6 + 1 = -5
-6 + 1 = -5
This equation is true.
i need help, at midnight, the temperature was -8*f at noon, the temperature was 23*f, which expression represents the increase in temperature? (a) -8 -23
(b) |-8| -23 (c) -8 - |23| (d) |-8 -23|
Answers
Answer:
D. |-8-23|
Step-by-step explanation:
|-8-23| = 31
Which of the following is an example of how self-awareness can affect communication?
a.
Self-awareness can help you choose who to communicate with.
b.
Self-awareness can help you decide how to communicate.
c.
Self-awareness can help you choose when to communicate.
d.
All of the above
Answers
Answer:
d all if these things are a part of self awareness
Answer:
d. All of the above
Step-by-step explanation:
E2020
what are the missing numbers?
Answers
Kenji is playing the video game Dragon Tamer, where players go on adventures finding and training dragons. In the first level of the game, he gets 10 points for finding a Silverthorn Dragon but gets – 6 points when it scorches him with fire. What is Kenji's score at the end of the first level?
Answers
Answer:
[tex]Final\ Score = 4\ points[/tex]
Step-by-step explanation:
Given
[tex]Silverthorn\ Dragon = 10\ points[/tex]
[tex]Fire\ Scorches = -6\ points[/tex]
Required
Determine the final score
Final score is calculated as follows:
[tex]Final\ Score = Silverthorn\ Dragon + Fire\ Scorches[/tex]
[tex]Final\ Score = 10\ points -6\ points[/tex]
[tex]Final\ Score = 4\ points[/tex]
Answer:
4
Step-by-step explanation:
PLZ HELP ASAP! I will mark you brainliest!
Answers
Answer:
c for first page. b for second. d for third page
Step-by-step explanation:
whats 2+2 its so hard
Answers
Answer:
4!
Step-by-step explanation:
Please rate 5 stars and give brainlest.
Is the point (11,5) on the parabola? Show or explain your work.
Answers
Answer:
The point (11, 5) is NOT on the parabola.
Step-by-step explanation:
Let [tex](x_0,y_0)[/tex] be any point on the parabola
Let [tex](a, b)[/tex] be the focus
Let [tex]y=c[/tex] be the the directrix
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-a)^2+(y_0-b)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-c|[/tex]
Given:
focus (6, 4)directrix y = 0Therefore:
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-6)^2+(y_0-4)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-0|[/tex]
Equate the two expressions and solve for [tex]y_0[/tex]:
[tex]\sqrt{(x_0-6)^2+(y_0-4)^2}=|y_0-0|[/tex]
[tex]\implies (x_0-6)^2+(y_0-4)^}=(y_0-0)^2[/tex]
[tex]\implies {x_0}^2-12x_0+36+{y_0}^2-8y_0+16={y_0}^2[/tex]
[tex]\implies {x_0}^2-12x_0-8y_0+52=0[/tex]
[tex]\implies 8y_0={x_0}^2-12x_0+52[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac{12}{8}x_0+\dfrac{52}{8}[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac32x_0+\dfrac{13}{2}[/tex]
Now rewrite with (x, y):
[tex]\implies y=\dfrac18x^2-\dfrac32x+\dfrac{13}{2}[/tex]
Therefore, this is the equation of the parabola
To determine if the point (11, 5) is on the parabola, input x = 11 into the equation:
[tex]\implies y=\dfrac18(11)^2-\dfrac32(11)+\dfrac{13}{2}[/tex]
[tex]\implies y=\dfrac{41}{8}[/tex]
So the point (11, 5) is NOT on the parabola.
The equation of line A is y = 6x + 12. Line B is perpendicular to line A and passes through the point (3, 11 1/2). What would be the solution to the system of equations represented by line A and line B?
Answers
Answer:
use the respective formula and solve
Paper Answer if can (write explanation on paper) - Brainliest given:
Solve for x:
x + 16 = 1068
Answers
Answer:
x = 1052
Step-by-step explanation:
Refer to picture:
Answer:
1052
Step-by-step explanation:
x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052x = 1052
The radius of a circle is 7 kilometers. What is the circle's circumference? Use 3.14 for .
Answers
Answer:
A circle of radius = 7 or diameter = 14 or circumference = 43.98 kilometers has an area of: 153.9 square kilometers (km²) 1.539 × 10 8 square meters (m²)
Step-by-step explanation:
The treasurer counted that there was $200 in the bank account he decided to use 1/2 of the money
Answers
Answer:
That means he will have $100
Step-by-step explanation:
Half of 200 is 100
Can someone help me pleeeease
Answers
Answer:
2 Possible Outcomes
Step-by-step explanation:
This is because you can only get the (x,y) coordinates.
Hello!
Answer:
There are only 2 outcomes
Step-by-step explanation:
This is because when solving a system of equations, your answer will be coordinates (For example>>(x,y)) so you will be getting two numbers, which means two outcomes.
Wish you luck!!
I need helppp pleaseeeeee!!!!!!!!!!!!!!
Answers
Answer:
$5.55
Step-by-step explanation:
The LaSalle High School senior class raised funds for an end of the year cruise getaway. The city gave them a special package for the port fees and taxes - a flat fee of $1,500 for the entire class's port fees and taxes. It costs $367 per student to board the cruise. If your class raised $16,600, how many students can attend?
HELP ME ASAP if ure not sure please dont answer
Answers
Answer:
Depends on what you think your instructor is looking for either it is 45 students, or the answer is 41.
Step-by-step explanation:
41 is the answer if you subtract the port fees from the amount raised then divided the remainder by cost per student .
Austin works as an electrician. If a job requires Austin to work on weekends, the function C(t)=54t+75 represents the customer's cost, C, in dollars of working t hours on the job. What is the interpretation of the y-intercept?
Answers
Answer:
He charges a flat rate of 75, and any extra work will be 54 dollars per hour.
Step-by-step explanation:
Answer:
he charges $75
Step-by-step explanation:
that describes a way to solve the equation x – 23 = 18
Answers
Answer:
One of the ways you could describe the solution is 18+23=x x=41.
Step-by-step explanation:
Answer:
X = 41
▬▬▬▬▬
41 - 23 = 18
23 + 18 = 41x
▬▬▬▬▬
Hope it helps!
Please Mark Brainliest.
Identify the domain and range of the function graphed below
Answers
Answer:
all real numbers
Step-by-step explanation:
there is no end point so domain and range are all real numbers.
What kind of shape is created from the cross section seen here on the square pyramid?
HELP IMAGE INCLUDED
Answers
a triangle.........................................
Answer:
a rectangular pyramid
Step-by-step explanation:
carry out this experiment
get a sheet of paper, create a square from the sheet, after that divide the square in half. Which shape is formed.
Do mark brainliest