Answers
Answer:
A square is defined as a quadrilateral with 4 sides of the same length and 4 right angles. To verify the lengths of the sides, you can use the distance formula. To find the angles, you can use the slopes of the line segments and make sure sides that form an angle have opposite reciprocal slopes.
Step-by-step explanation:
First, find the coordinates of each point. You're provided with the scale and you can just count, but to make it easier, you can label the axes.
A: (0,8)
B: (6,6)
C: (4,0)
D: (-2,2)
The distance formula is used to find the distance between any two points on the coordinate form. Here it is:
d=sqrt((y2-y1)^2 + (x2-x1)^2)
d=distance, and (x1, y1) and (x2, y2) are the points.
Find the length of each side. I'll demonstrate with two sides, AB and BC.
AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)
d=sqrt((6-8)^2 + (6-0)^2)
=sqrt((-2)^2 + 6^2)
=sqrt(4+36)
=sqrt(40)=2sqrt10
BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)
d=sqrt((4-6)^2 + (0-6)^2)
=sqrt((-2)^2 + (-6)^2)
=sqrt(4+36)
=sqrt(40)=2sqrt10
Do the same thing with sides CD and AD, you'll see that they both also have a length of 2sqrt10 inches. (You don't really have to simplify, I just like to.)
To verify if the sides are perpendicular, you need to find the slopes of the sides and make sure that the product of the slopes of each pair of sides that form a vertex is -1. In other words, each pair of sides that form a vertex have to have opposite reciprocal slopes. I'll demonstrate with 2 vertecies, A and B.
To find the slope, you have to use the formula m=(y2-y1)/(x2-x1). m is the slope, and again, (x1, y1) and (x2, y2) are the points you're plugging in.
To find the measure of angle A, you need to find the slopes of sides AD and AB. (These are the sides that meet to form the angle.)
AD: (x1,y1)=(0,8) and (x2,y2)=(-2,2)
m = (2 - 8)/(-2 - 0)
= -6/-2
= 3
AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)
m = (6 - 8)/(6 - 0)
= -2/6
= -1/3
So AD has a slope of 3 and AB has a slope of -1/3. Now you need to make sure they have a product of -1.
-1/3 * 3 = -1
So yes, it works! As I mentioned before, you can also think of them as opposite reciprocals.
The reciprocal of 3 is 1/3. The opposite of 1/3 is -1/3. So yes, the sides are perpendicular.
Let's do it again with angle B. We have to find the slope of BC now, since we already know the slope of AB.
BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)
m = (0 - 6)/(4-6)
= -6/-2
=3
So the slope is exactly the same as the slope of AD. A square is a parallelogram, so it has two pairs of opposite parallel sides. We already verified that 3 and -1/3 are opposite reciprocals, so we now know that angle B has a measure of 90 degrees as well. You can do the same for angles C and D. That way, you'll have proven that all the sides have the same length and all the angles measure 90 degrees-- so the quadrilateral ABCD matches the definition of a square.
Hope this helped!
Related Questions
Adrian and Violetta gat a soccer ball. The soccer ball is size 4.They want it to be size 5.They know the diameter is 9 inches. Find the volume of the soccer ball.
Answers
Answer:
382 inches
Step-by-step explanation:
Given that :
The size of the soccer ball that Adrian and Violetta got is = 4
The diameter of the soccer ball is = 9 inches
Therefore, the radius of the soccer ball is, r = [tex]$\frac{9}{2}$[/tex] inches
So the volume of the soccer ball is :
[tex]V = \frac{4}{3} \pi r^3[/tex]
[tex]V = \frac{4}{3} \times \frac{22}{7} \times \left(\frac{9}{2}\right)^3[/tex]
[tex]V = \frac{4}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times \frac{9}{2}[/tex]
V ≈ 382 inches
if 5 men has 25 eggs, how many eggs will 4 men have
Answers
Answer: 20 eggs
Step-by-step explanation:
The rate is 5. 25/5=5.
4*5=20
Hope this helps!
Answer:
The answer of your question is 20 eggs
A monthly salary is $1622.31. It is given an increase of 3.8%. After the first increase, it receives a second increase of 6.2%. What is the new monthly salary after both increases? Round your answer to two decimal places. Do not put the $ sign in your answer or any units. Only put the number value for your answer.
Answers
Answer:
the new monthly salary after both increase is 1,788.37
Step-by-step explanation:
The monthly salary is 1,622.31
There is an increase of 3.8%
So, the salary after first increase is
= 1,622.31 × (1 + 3.8%)
= 1,683.96
Now there is a second increase of 6.2%, so the salary after second increase is
= 1,683.96 × (1 + 6.2%)
= 1,788.37
Hence, the new monthly salary after both increase is 1,788.37
The goal of the students in the club was to raise $500. They sold 43 flowerpots. By what amount did the students exceed their goal of raising $500?
Answers
Answer:
Exceeded by 145 dollars.
Step-by-step explanation:
First you multiply 15 by 43 because each pot costs 15 dollars and they sold 45.
Then you get the answer of 645 and the goal was 500 so that means you need to subtract to see how much they exceeded by.
Subtract 500 from 645 and you get the answer of 145.
So they exceeded 145 dollars.
What is the domain of the function on the graph?
Answers
Answer:
Option 2
Step-by-step explanation:
Sam rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 97 cents for each mile driven. Sam had to pay $265.21 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
258 miles
Step-by-step explanation:
y = # miles truck driven
m = each mile driven
y = 14.95 + 0.97m
265.21 = 14.95 + 0.97m
250.26 = 0.97m
m = 258
Help I will give you brainliest
Answers
Answer:
b- 3/5
Step-by-step explanation:
divide 6 from both numbers
Answer:
B, 5/3
Step-by-step explanation:
hope this helps have a good day :)
Daniel and Audrey are reading the same book. At the beginning of the month, Daniel was on page 49 and Audrey was on page 22. Daniel will read 17 pages per day and Audrey will read 20 pages per day. Let
D
D represent the page of the book that Daniel is on at the end of
t
t days into the month, and let
A
A represent the page of the book that Audrey is on at the end of
t
t days into the month. Write an equation for each situation, in terms of
t
,
t, and determine what page Daniel and Audrey will be on on the day they are both on the same page.
Can you plz help me because it says that it’s wrong?
Answers
Answer:
202
Step-by-step explanation:
So it has to end in 2 because 20t+22 will always be a 2.
day1:
17x1+49=66
no 2
day2:
17x2+49=83
odd
day3:
D=100
no 2
day4:
odd
day5:
D=134
no 2
etc
keep adding 17 to D until you get one that ends in 2
D=202
A=202
Which known factor affects prices in the financial markets?
A-International stocks
B-Media speculation
C-Government policy
D-Foreign companies
I know it’s not A becuse I failed it on Frist try with that answer
Answers
A large candy bar was 102 calories. The smaller candy bar has 18 percent less
calories. How many calories does the smaller candy bar have?
Answers
Answer:
89 I think
Step-by-step explanation:
my bad if I'm wrong I bearly woke up
The Oates family went out to
dinner. The price of the meal was
$33.95. They left a 15% tip.
What was the total cost?
Answers
Answer:
$39.04
Step-by-step explanation:
1.Approach
To solve this problem, one must first find the amount of tip that was left, then add the value to the cost of the meal. The amount of tip given can be found by dividing the percent value of the tip by (100) and then multiplying the result by the price of the meal.
2.Find the amount of tip
To find the amount of tip that was left, divide the percent value of the tip by (100). This technique converts the percent into a decimal. After doing so, multiply the result by the cost of the meal.
Tip as a percent: 15%
Tip as a decimal: 0.15
Amount of tip left:
33.95 * 0.15 = 5.0925
Round the result
~5.09
3.Find the total bill
Disincluding the tax, one now has to add the tip to the cost of the meal to find the total amount paid.
(tip) + (price)
= (5.09) + (33.95)
= (39.04)
I tried this problem out but I’m not sure if I’m right also this is a test worth 100 points can someone show me if u made any mistake can j explain also ?
Answers
Answer:
Median without outlier should be 40
For the bottom questions, it should go:
Decreases the mean, does not change the median, does not change the mode
It's decreasing the mean because it goes from 44.7 to 39
Median w/ and without outlier is both 40
Mode also stays the same w/ or without the outlier, which is 96
Evaluate 12÷s−∣−2∣ if s=0.6
Answers
Answer:
s=20 divided by 12
Step-by-step explanation:
Find the diameter of a circle with the given dimensions. 1. d = 6 cm
Answers
But the diamerter equals d, so 6.
Answer:
its 6
Step-by-step explanation:
because your finding the diameter.
Which of the following points has coordinates that are 5 horizontal units from point A?
A. left parenthesis 3 comma 2 right parenthesis
B. left parenthesis 3 comma 7 right parenthesis
C. left parenthesis negative 2 comma 7 right parenthesis
D. left parenthesis 5 comma 2 right parenthesis
Answers
Answer:
A. left parenthesis 3 comma 2 right parenthesis
Step-by-step explanation:
It's correct 100%
can someone help me with this
Answers
Answer:
a) 256
b) 24x³z*5 (wouldnt let me make it z to the fifth for some reason lol but)
c)282429536481x∧20
Step-by-step explanation:
GEOMETRY HELP PLEASE!! WILL MARK BRAINLEIST!
1
Answers
Answer:
(5,-1) Hope It Help
Step-by-step explanation:
Brainliest please
How much netherite do i need to make a full beacon again?
Sorry i know this is random i just really wanna know
Answers
Answer:
5,904 scraps
Step-by-step explanation:
36 by 164 blocks
On the first day of school, the cafeteria serves hot dogs and hamburgers together. The cafeteria serves hot dogs every 6th school day and hamburgers every 4th school day for the rest of the year. If there are a total of 180 school days, how many times will the cafeteria serve hot dogs and hamburgers together this year?
Answers
Answer:
The Answer is 12 days or times.
Step-by-step explanation:
The LCM of 6 is 3 and 2, the LCM of 4 is 2 and 1, so we multiply 3 by 2 and 4 by 2 together to get 12, which is the number of days or times.
how to solve x=7y+3 and 9y-x=-1 using the subsituation method
Answers
Answer:
x=10 y=1
Step-by-step explanation:
Which of the following is a good example of inflation? OA. You get a raise and the price of gas goes down. OB. You get a second job and you increase your net income by 15%. O c. The price of gas went from $4.00 last month to $4.25 this month. OD. The price of gas goes down from $4,25 last month to So thir
Answers
Answer:
C. The price of gas went from $4.00 last month to $4.25 this monthStep-by-step explanation:
The inflation is when prices for most of the goods increase with much less income raise.
Closest answer choice is C, provided it was followed up by price increase of most goods.
The diameter of a circle is 19 feet what is the circumference
Answers
Answer:
The circumference of a circle with a diameter of 19 feet is 59.69
Step-by-step explanation:
Not really an explanation to this.
I hope I helped you, and a "Brainliest" is always appreciated! ☺
Answer:
C≈59.69ft
d Diameter
19
ft
Step-by-step explanation:
Using the formulas
C=2πr
d=2r
Solving for C
C=πd=π·19≈59.69026ft
Mia found the volume of a rectangular prism to be 840 mm3. As she was telling her father about it. she remembered that the base had a length of 10 mm and a width of 12 mm, but she could not remember the height maybe there is a way you can find it by going backwards . her father suggested. Can you help Mia find the height of her prism. Explain your solution.
Answers
Answer:
H = 7mm
Step-by-step explanation:
Height of Prism
So to calculate the height, multiply L · H · W. But since there is no height we will multiply what is given and then divide the volume by the product. For this case, the volume of the prism is 840 and its length is 10 and its width is 12. Multiply 10 and 12 then dividing 840 by 120. The height of the prism is 7.
Solve
Volume if the rectangular prism is given by the formula
V = L · H · W
Length, Height, Width of the prism
L = 10mm H = 12mm Volume = 840mm³
10 · 12 · h = 840
∴ 840 ÷ 120 = 7
H = 7mm
Reflect - 25 a positive number or a negative number? Explain how you know.
Find the opposite of -25 and explain how you found your answer.
HURRY ⚠️
Answers
Answer:
-25 is negative
25 is positive
Step-by-step explanation:
-25 is negative because it's 25 spaces to the left of 0
25 is positive because it's 25 spaces to the right of 0
|-25| = 25; The opposite of -25 is 25
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answers
Answer:
The equation is ;
4x - y = 13
Step-by-step explanation:
The general equation of a straight line is;
y = mx + b
where m is the slope and b is the y-intercept
from what we are given, let us write the second equation in the general form
x + 4y = 10
4y = -x + 20
y = -1/4x + 20/4
y = -1/4x + 5
mathematically, when two lines are perpendicular, the product of their slope is -1
So for the second line with slope m2
m2 * -1/4 = -1
m2 = 4
So, using the general form, we have the equation as;
y = 4x + b
To get the value of b, we substitute the coordinates of the given point (3,-1)
-1 = 4(3) + b
-1 = 12 + b
b = -1-12
b = -13
So the equation is;
y = 4x - 13 which can be rewritten as;
4x-y = 13
Can someone please help me with this question?
Answers
Answer:
Answer is D hope this helps :)
Step-by-step explanation:
Which ordered pair is not in the solution set of y > 2x + 1
A. (1, 4)
B.(1, 6)
C.(3, 8)
D.(2, 5)
Answers
Answer:
A. (1, 4)
Step-by-step explanation:
Sana makatulong
The polynomial (x - 2)^2 + x(3x - 1) can be written in the form: ax^2 + bx + c where a, b, and c are constants. What are the values of a, b, and c?
Answers
Find the values of x when y=2
Answers
+2 +2
X^2+2x=4
-2x -2x
X^2=4-2x
/x /x
X=4-2
X=2
4x4+4x3-9x2-x+2 = x-1
Answers
Answer:
x= 13/2
Step-by-step explanation:
multiply 4x4+4x3-9x2-x+2=x-1
calculate 16+12-18-x+2=x-1
move the terms 12-x=x-1
collect like terms calculate -x-x=-1-12
divide both sides -2x=-13
solution x=13/2