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]
help me out please real answers only (20 points)
Answer:
hope this will help
if correct please give brainliest
Four fifths of the 35 kittens finish their milk how many did not finish their
Answer:
7 kittens did not finish their milk
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Help please!!
and Thank you!!
Find the surface area.
Answer:
2411.52 mm²
Step-by-step explanation:
[tex]40^{2} =32^2+d^2[/tex]
→ [tex]d^2= 1600-1024[/tex]
→[tex]= 576[/tex]
→ [tex]d= 24[/tex] [tex]so, (radius=12[/tex]
[tex]Total~ surface ~ area= (2\pi r)*height[/tex]
→ [tex](2*3.14*12*82)[/tex]
[tex]= 2411.52 mm^2[/tex]
-------------------------------
hope it helps...
have a great day!!
Answer:
2411.52 mm²
Step-by-step explanation:
hope its helpful
You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work.
Answer:
i wrote "13 8/9 because 16 2/3 x 16 2/3= 50/3 x 50/3 = 250/9 then 250/9 ÷ 2 = 125/9 = 13 8/9"
Step-by-step explanation: if u add in some words or something so you teacher isnt sus hope you pass!!
Triangle DEF is shown on the coordinate grid below triangle DEF is reflected across the Y axis which role best describes this transformation
Answer:
I can’t see the picture
Step-by-step explanation:
in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science.
A)How many students were majoring in math only?
B)How many students were not majoring in computer science?
C) how many students were not math or computer science majors?
Answer:
Use n(u) formula of chapter sets
Step-by-step explanation:
Have a good day
11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.
Given that in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science, to determine A) how many students were majoring in math only; B) how many students were not majoring in computer science; and C) how many students were not math or computer science majors; the following calculation must be performed:
Math majors only = 18 - 7 = 11 Not majoring in computer science = 25 - 12 = 13 Not math or computer science majors = 25 - 7 - 11 - (12 - 7) = 18 - 11 - 5 = 2
Therefore, 11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.
Learn more in https://brainly.com/question/20293703
A line passes through the origin and the point (3.5). What is the slope of the line? 0
3/5
-3/5
5/3
Answer:
5/3 is the slope of the line.
What is the mean absolute deviation of the data set?
{5, 7, 12, 11, 3, 10}
Answer:
3
Step-by-step explanation: First, you find the mean of the data set. Then you take that mean and find the difference of that and each value, you add those up and find the mean of that number.
A person is wearing a bracelet with 11 settings around the bracelet. How many different ways can 12 birthstones be
arranged around the bracelet?
O 10!
11!
O 12!
Answer:
10
Step-by-step explanation:
I think I hope this helps
PLEASE HELP ASAP!!!
Answer:
4. x=0 x=5
5. x=-4 x=8
You and three of your friends go parasailing for 128.40 you split the cost
evenly. How much does each person pay?
Answer:
40 each i think maybe 30 if not
Below. What is m∠1?
m∠1 =
Answer:
m∠1 = 70°
Step-by-step explanation:
Step 1
Sum of angles on a straight line = 180°
Hence:
180° - 101°
= 79°
Sum of interior angles in a triangle = 180°
Hence
m∠1 = 180° - (79 ° + 31°)
m∠1 = 70°
Is x=2 a solution to the equation below?
4(x-1)-3(x-2)=-8
Answer:
No
Step-by-step explanation:
To find out if 2 is a solution, replace all the x's with 2.
4(2 - 1) - 3(2 - 2) =8
4(1) - 3(0) = 8
4 - 0 = 8
4 = 8
Nope! False! 2 is not a solution.
4. M is the midpoint of XY. If XM = 8-t and MY = 5t-10, find tand XY.
Answer:
XY = 10
Step-by-step explanation:
By the definition of midpoint, XM would be equal to MY, so we can set both equations equal to each other;
XM = MY
8 - t = 5t - 10
=> Now add "t" to both sides of "="
8 = 6t - 10
=> add 10 from each side;
18 = 6t
=> Finally divide 6 on each side
3 = t
Now that we have the value for t, we can substitute 3 in place of "t" in any of the equation above and solve, when we have the answer, multiply it by 2 to get the value for XY.
=> 8 - 3
=> 5
=> XY = 5 * 2
=> XY = 10
Hope this helps!
A lidless box is constructed by cutting a square with side length x from a rectangular sheet of paper with dimensions a x b. After the cut is removed, the sides are folded up to form the
box.
a) Find the value of x (in terms of a and b) that maximizes the volume of the box.
b) Find the value of x that maximizes the volume of the box when a = 8.5 inches and b= 11 inches.
Answer:
a) [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
b) The volume of the box is maximized when 'x' is approximately 1.585 feet
Step-by-step explanation:
a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;
The length of the side of the square cut from the corners of the rectangular sheet of paper = x
The length of the box formed after cutting the square sides are;
The length of the box, l = a - 2·x
The width of the box, w = b - 2·x
The height of the box, h = x
The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x
The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;
At the extremum, dV/dx = 0
∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0
12·x² - 4·(a + b)·x + a·b = 0
[tex]x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
b), When a = 8.5 inches and b = 11 inches, we have;
x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914
x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585
We get;
When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15
When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65
Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585
(The value of 'x' in terms of 'a' and 'b' is therefore;
[tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex])
The volume of the box is maximized when, x ≈ 1.585 feet
lets find the answer
Answer:
(-3,0)
Step-by-step explanation:
1) find the coordinate of x
x = -3
2) find the coordinate of y
the point lies on x axis so y = 0
The coordinates are (-3, 0)
:)
10 Students were surveyed.
How many hours do you study a week?
8 2 2 6 14 10 3 5 4
Determine the following:
A) Mean
B) Mode
C) Median
Show work please
Will mark brainlisted
Answer:mode
Step-by-step explanation:5+4+9+9+3+75+1=mode
Help me with this please.
2x + 2y = -2
3x - 2y = 12
Answer:
Answer:
(2,-3)
Step-by-step explanation:
2x + 2y = -2
3x - 2y = 12
Add the two equations to eliminate y
2x + 2y = -2
3x - 2y = 12
-----------------------
5x = 10
5x/5 = 10/5
x = 2
Now find y
2x+2y = -2
2(2)+2y = -2
4+2y = -2
Subtract 4 from each side
4-4 +2y = -2-4
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
(2,-3)
U have $77 in your bank account than you write a check for $100 at the store how many do I have now? Please show work
Answer:
$-23
77 - 100 = -23
The cost (c) for g number of gelato ice cream is shown in the table. Complete the table and graph the proportional relationship between the number of gelatos purchased and the total cost.
g c
2 8
5
6
8
a man cycles a distance of 63km in less than 3hours what is the average speed
Answer:
21 km/h
Step-by-step explanation:
Helppppppppppppppppp
Answer:
I just need points sorry love But the answer is A.
Step-by-step explanation:
The graph of a polynomial function may have no x-intercepts.
true or false
true (I don't know if this is the answer but it would be my guess)
what is the product of (3Y^-4) (2Y^-4)
Answer:
the product is 6/Y^8
Step-by-step explanation:
7
Which equation can be used to describe the relationship between x and y shown in the graph
below?
3x + 2
D-3x - 6
D
3-6
D3X2
please help me
i’m so stuck
Answer:
2 cm
Step-by-step explanation:
V=πr2h = 20π
-π -π
r2h = 20
h= 5
r2(5) = 20
/5 /5
r2=4
/2 /2
r=2cm
(my work is complicated, but trust me 2 cm is the answer)
solve the system by substitution
5x+y=-14
5x- 3y=2
Answer:
x=-2 and y=-24
Step-by-step explanation:
plug in the value of y (-5x-14) into the second equationwhat is the measure of each angle
Please answer correctly! I will mark you as Brainliest! Please No links or any joking around or I will call and report you!
Answer:
0, -3
Step-by-step explanation:
So remember, when they say reflect over the x intercept, they do not mean to reflect the x value, they mean to reflect over the hirzontal line of the graph.(x axis)
This is the same with reflection over the y intrecept. This doesnt mean y is flipped, this means that whatever point or line you have is reflected over the vertical line on the graph(y axis)
So our orginal value is (0, 3). We need to reflect over the x axis, which means that y will now be -3, since that is the opposite of what we can see when we flip the x axis.
The 0 x, of course, stays the same since its 0.
So your answer is (0, -3)
Hope this helps! :)