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
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 :)
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
what are the missing numbers?
Answers
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.
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 helppp pleaseeeeee!!!!!!!!!!!!!!
Answers
Answer:
$5.55
Step-by-step explanation:
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
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:
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:
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:
4602837593857304985+395283059282352323
Answers
Answer:4998120653139657308
Step-by-step explanation:
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]
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.
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.
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!!
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 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 .
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
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
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 $88 but had a 15% discount. Then the customer had to pay a sales tax of 5% on the discounted price. How much did the customer pay for the watch? *
Answers
Part B: 78.54$
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]
^^
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
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:
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
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
whats 2+2 its so hard
Answers
Answer:
4!
Step-by-step explanation:
Please rate 5 stars and give brainlest.
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
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:
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
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.