Ava wants to draw a parallelogram on the coordinate plane. She
plots these 3 points.
Part A
Find and label the coordinates of the fourth vertex, K, of the
parallelogram. Draw the parallelogram.
Part B
What is the length of side JK? How do you know?
Answers
Answer:
[tex]k =(2,1)[/tex]
[tex]JK = 2[/tex]
Step-by-step explanation:
Given
[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]H = (1,-2)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]I = (3,-2)[/tex] --- [tex](x_3,y_3)[/tex]
See attachment for grid
Solving (a): The coordinates of K
The parallelogram has the following diagonals: IJ and HK
Diagonals bisect one another. So:
Midpoint of IJ = Midpoint of HK
This gives:
[tex]\frac{1}{2}(I + J) = \frac{1}{2}(H+K)[/tex]
[tex]\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)[/tex]
[tex]\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)[/tex]
[tex]\frac{1}{2}(3,-1) = \frac{1}{2}(1+x,-2+y)[/tex]
Multiply through by 2
[tex](3,-1) = (1+x,-2+y)[/tex]
By comparison:
[tex]1 + x = 3[/tex]
[tex]-2 + y = -1[/tex]
Solve for x and y
[tex]x = 3 - 1 =2[/tex]
[tex]y = -1 +2 = 1[/tex]
So, the coordinates of k is:
[tex]k =(2,1)[/tex]
The length of JK is calculated using distance (d) formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]
[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]k =(2,1)[/tex] ---- [tex](x_2,y_2)[/tex]
So:
[tex]d = \sqrt{(0 - 2)^2 + (1 - 1)^2[/tex]
[tex]d = \sqrt{(- 2)^2 + (0)^2[/tex]
[tex]d = \sqrt{4 + 0[/tex]
[tex]d = \sqrt{4[/tex]
[tex]d = 2[/tex]
Hence:
[tex]JK = 2[/tex]
Related Questions
At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only . The sandwiches are made with either turkey or ham. The fruit is either an apple or an orange. The drink is either bottled water or juice. The number of boxes they make for every possible combination is the same. If you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get a turkey sandwich and a bottle of water in your box?
Answers
Answer:
1/8 or 0.125
Step-by-step explanation:
So, I started solving this problem by writing all the possible options, then pairing them each up with a fruit and drink..
...But when I read the question again, I noticed I forgot to leave out the fruit, as this question states that you're trying to retrieve "a turkey sandwich and a bottle of water.."
Well, oof.
Despite that, I'm still giving this answer as if it never left out the fruit. So, let's see what we need to do.
To find all the possible lunch options, I started out by writing down one of our meats, Turkey. As per requested, I made every possible turkey combination that included a fruit and drink, which gave me this:
Turkey, apple and waterTurkey, orange and waterTurkey, orange and juiceTurkey, apple and juiceSame for the ham:
Ham, apple and waterHam, apple and juiceHam, orange and juiceHam, orange and waterPutting these together, this gives up 8 different lunchbox combinations. If we're trying to get one and we randomly select it, then we have a 1/8 chance of grabbing the turkey sandwich and a bottle of water....
..and a fruit.
Hope this helped!
If you need me to show my work, just comment me and I will attach a screenshot!
Source: N/A
Median of 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
Answers
Answer:
10.5
Step-by-step explanation:
Find the two middle numbers, add them together and divide them by two if it is an even number. For odd numbers, your median will be the middle number.
What is x? Please try and show work. ANSWER ASAP! SCAM ANSWERS WILL BE REPORTED. Will award brainliest for correct answer!
Answers
Answer:
x=6
Step-by-step explanation:
Kindly look at the image provided below.
The image shows the relationship between intersecting secants and their corresponding arcs which is important to understand when looking at problems like these.
The relationship states that an angle formed by two intersecting secants is equal to half the sum of its corresponding arc and its vertical angles corresponding arc.
So ∠FHG = 1/2 ( arc FG + arc EB )
* substitute the given expressions for each angle and arc *
we would then have
15x - 2 = 1/2 ( -2 + 12x + 16x + 10 )
We now solve for x
Step 1 multiply each side by 2
1/2 ( -2 + 12x + 16x + 10 ) *2 = ( the 2 and 1/2 cancels out ) -2 + 12x + 16x + 10
(15x - 2 )2 = 30x - 4
we now have -2 + 12x + 16x + 10 = 30x - 4
step 2 combine like terms
-2 + 10 = 8
12x + 16x = 28x
now we have 30x - 4 = 28x + 8
step 3 add 4 to each side
-4 + 4 cancels out
8 + 4 = 12
Now we have 30x = 28x + 12
step 4 subtract 28x from each side
30x - 28x = 2x
28x - 28x cancels out
now we have 2x = 12
step 5 divide each side by 2
2x / 2 = x
12 / 2 = 6
we're left with x = 6
Janette measures the heights in inches of some of the flowers in her garden to see which ones are growing more. The heights are listed below. Which line plot represents the data correctly? 7 1 2 712 7 7 7 1 2 712 6 3 4 634 7 1 4 714 7 1 4 714 7 1 4 714 7 7 6 1 2 612 7 3 4 734 7 3 4 734 6 3 4 634 8 1 4 814 7 7 7 1 2 712 7 7 7 1 4 714 7 7 7 1 2 712 7 1 2 712
Answers
Answer:
Dot plot A
Step-by-step explanation:
In other obtain the solution to the question given, we obtain the frequency distribution of the data values given and compare to the box plots given to identify which boxplot correctly conveys the data.
___ Frequency
6 1/2 - 1
6 3/4 - 2
7 = 5
7 1/4 = 4
7 1/2 = 5
7 3/4 = 2
8 1/4 = 1
What is 0.01857 rounded to the nearest thousandths place?
Answers
....
pls show the process
Answers
Lyla is playing a game in math class where the students describe a number they are thinking of and the class uses clues to determine which type of number it is. Lyla tells her class that she is thinking of a positive number with infinitely many nonrepeating digits after the decimal point. Which type of number is Lyla thinking of?Single choice.
(1 Point)
1. whole
2. integer
3. rational
4. irrational
Answers
Answer:
1 or 3 sorry if wrong
Step-by-step explanation:
4. Find the volume of the figure. The base is a square.
5. Find the volume of the figure. Leave the answer in the terms of pi
Answers
Answer:
A) 283500 ft³
B) 1057.26 π in³
Step-by-step explanation:
A) Volume of square based pyramid
= 1/3 × Area of the base × height
= 1/3 × (90 ft)² × 105 ft
= 283500 ft³
B) This figure is a composite figure
Step 1
Find the volume of the cone
=1/3 πr²h
r = radius = 8.5 in
h = height = 10 in
= 1/3 × π × (8.5 in)² × 10 in
= 240.83333333 π in³
≈ 240.83 π in³
Step 2
Find the volume of the cylinder
= πr²h
= r = radius = 8.5 in
h = height = 11.3 in
= π × (8.5 in)² × 11.3 in
= 816.425 π in³
≈ 816.43π in³
Volume of the figure = (240.83 π + 816.43 π) in³
= 1057.26 π in³
3 − –403,593 positive or negative?
Answers
What is the volume (V) of the cylinder shown below ? Use 3.14 for π .
Answers
The volume (V) of the given cylinder with the height 10 mm and the diameter 14 mm is 1538.6 cubic millimeter.
From the given figure, diameter of a cylinder = 14 mm and height = 10 mm.
Here, radius = [tex]\frac{14}{2}[/tex]
= 7 mm
Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
We know that, the formula to find the volume of a cylinder is [tex]\pi r^2h[/tex].
Here, the volume of a cylinder = 3.14×7²×10
= 3.14×49×10
= 1538.6 cubic millimeter
Therefore, the volume (V) of the given cylinder with the height 10 mm and the diameter 14 mm is 1538.6 cubic millimeter.
To learn more about the volume visit:
https://brainly.com/question/13338592.
#SPJ4
108 identical books have a mass of 30 kg.Find
the mass of 150 such books
the number of such books that have mass of 20 kg
Answers
Answer:
41.67 kg
72 books
Step-by-step explanation:
mass of 150 books = 150/108 × 30 kg
= 41.67 kg
number of books = 20/30 × 108 books
= 72 books
Which statements about the triangles are correct? Select TWO answer choices that apply.
A
Triangle P is similar to triangle Q.
B
Triangle P is a reflection and rotation of triangle Q.
C
Triangle P is congruent to triangle Q.
D
Triangle P is a reflection and a dilation of triangle Q.
E
Triangle P is a dilation and a 180° rotation of triangle Q.
Answers
E-rotation 180 degree ,and dilation
I hope I helped you☺️
NEED IT ASAP
Find the missing side.
3 is A^2
5 is B^2
what is the missing side
Answers
Answer:
5.83
Step-by-step explanation:
Use the Pythagorean theorem:
3^2+5^2 = c^2
34 = c^2
sqrt34 = c
5.83 = c
A^2+B^2=c^2
9+25=34
34=C^2
^2/34
=5.83
PLEASE HELP WITH THIS
Answers
Answer:
a.2b.area of one triangular faces =9m²
2×9m²18m²Solve equation
0=5x+3
Answers
Answer:
the answer is -3/5
Step-by-step explanation:
x=-0.6
Answer:
0 =5x+3
-3 =5x
-3/5=x
x=-3/5
1.
Use synthetic division and the Remainder Theorem to find P(a).
P(x) = x3 + 7x2 + 4x; a = −2
2
12
−2
0
Answers
Answer:
12
Step-by-step explanation:
Please write this function as P(x) = x^3 + 7x^2 + 4x + 0. This third order function has four coefficients. We set up synthetic division with -2 as the divisor:
-2 / 1 7 4 0
-2 -10 12
----------------------
1 5 -6 12
The remainder is 12. Accordng to the Remainder Theorem, the value of P(x) at x = -2 is 12.
is it prependicular or overlapping
Answers
help me pls. not links pls
Answers
y = 1/2x
step-by-step explanation:
first find the y-intercept or b
it is 0
next find the slope, rise/run
it is 5/10 or 1/2x
putting those in the equation it would be
y = 1/2x
because the y-intercept is 0 you wouldn’t add it
In triangle ABC, what is the measure of angle C if A = 120°, a = 25, and b = 24?
Round the answer to the nearest hundredth.
Answers
Answer:
what is the area of the trapezoid
what is the volume of a cylinder in cubic cm with a height of 9cm and a base diameter of 16cm round to the nearest tenths place
Answers
Find the surface area!
Thank you!!
Answers
Answer:
[tex]SA= 720 m^2[/tex]
Step-by-step explanation:
[tex]x=\sqrt{5^2+12^2}=13m[/tex]
[tex]AS=2*1/2*12+12*22+5*22+13*22[/tex]
[tex]= 60+264+110+13*22[/tex]
[tex]AS= 720m^2[/tex]
⋆┈┈｡ﾟ❃ུ۪ ❀ུ۪ ❁ུ۪ ❃ུ۪ ❀ུ۪ ﾟ｡┈┈⋆
hope it helps...
have a great day!!
Answer:
SA=720m^2
Step-by-step explanation:
hope it helps you ..
PLEASE HELP FAST!!!!!!!!!!
Answers
Triangle JKL has vertices J(0, 2), K(–1, 2), and L(0, –3). What are the coordinates of the image of point J after a dilation with a scale factor of 3?
Answers
Given:
The vertices of a triangle JKL are J(0, 2), K(–1, 2), and L(0, –3).
To find:
The coordinates of the image of point J after a dilation with a scale factor of 3.
Solution:
If a figure is dilated by a scale factor of k, then
[tex](x,y)\to (kx,ky)[/tex]
The given triangle JKL dilated by a scale factor of 3. So,
[tex](x,y)\to (3x,3y)[/tex]
The coordinates of point J are J(0,2). By using the above rule, we get
[tex]J(0,2)\to J'(3(0),3(2))[/tex]
[tex]J(0,2)\to J'(0,6)[/tex]
Therefore, the coordinates of the image of point J after a dilation with a scale factor of 3 are J'(0,6).
Borox is loading a freight elevator with 12 boxes: 4 small, 5 medium, and 3 large. A small box and medium box together weigh 20 pounds; a medium box and a large box together weigh 28 pounds, and a large box with a small box weighs 24 pounds. What is the total weight of the 12 boxes?
Answers
Answer:
140 pounds
Step-by-step explanation:
let s == small box
m = medium box
= large box
the following 3 equations can be derived from the question
s + m = 20 equation 1
m + l = 28 equation 2
l + s = 24 equation 3
make m the subject of the formula in equation 1 and 2
m = 20 - s equation 4
m = 28 - l equation 5
equate equation 4 and 5
20 - s = 28 - l
l - s = 8 equation 6
solve equation 3 and 6 using simultaneous equation
l + s = 24 equation 3
l - s = 8 equation 6
subtract equation 6 from 3
2s = 16
s = 8
substitute for s in equation 1
8 + m = 20
m = 12
substitute for m in equation 2
12 + l = 28
l = 16
total weight = (4 x 8) + (5 x 12) + (16 x 3) = 140 pounds
Will name the brainliest !
Answers
Answer:
c = 3477 feet (As rounded to the nearest whole number)
Step-by-step explanation:
We will use the Sin ratio for this problem since the opposite side of the Angle 15 is given and we have to find the triangle's hypotenuse;
Sin(15) = [tex]\frac{900}{c}[/tex]
=> Now isolate the variable c all to itself;
Sin(15) * c = 900
c = [tex]\frac{900}{Sin(15)}[/tex]
c = 3477.33 or 3477 feet
Hope this helps!
If i = V-1, then (3 – i)(3+ i) =
Answers
9-v^+2v-1
-v^2 +2v +8
Can someone help please, this has been stressing me out
Answers
you would get 120+48+jk+li=360 and then you would get jk+il= 192 and divide that by 2
The radius of a cylindrical water tank is 6.5 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
6.5 ft
ft
17 ft
X
Answers
Answer:
pi*36*10 = 1131 cubic feet
Step-by-step explanation:
MARK AS BRAINLEST!!
Step-by-step explanation:
pi*36*10= 1131 cubic feet
What is the measure of the inscribed arc whose inscribed angle measures 36 degrees?
A. 36 degrees
B. 72 degrees
C. 108 degrees
D. 18 degrees
Answers
Answer:
b
Step-by-step explanation:
Answer:
it is A. or B.
Step-by-step explanation:
Which of these expression is equivalent to 10% . 10%?
A. 100'
B. 103
C. 10,000,000
D. 2010
E. 107
what expression is equivalent to