Answer:
The coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].
Step-by-step explanation:
Diagonals are represented by line segments GJ and KH. Since quadrilateral is a parallelogram, then coordinates of the intersection are located at midpoint of each diagonal ([tex]M(x,y)[/tex]). That is:
[tex]M(x,y) = G(x,y) + \frac{1}{2}\cdot \overrightarrow {GJ}[/tex]
[tex]M(x,y) = G(x,y) +\frac{1}{2}\cdot [J(x,y)-G(x,y)][/tex] (1)
If we know that [tex]G(x,y) = (1,3)[/tex] and [tex]J(x,y) = (5,1)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:
[tex]M(x,y) = (1,3) +\frac{1}{2}\cdot [(5,1)-(1,3)][/tex]
[tex]M(x,y) = (1,3) +\frac{1}{2}\cdot (4,-2)[/tex]
[tex]M(x,y) = (1,3) +(2,-1)[/tex]
[tex]M(x,y) = (3,2)[/tex]
There is another form:
[tex]M(x,y) = K(x,y) +\frac{1}{2}\cdot \overrightarrow{KH}[/tex]
[tex]M(x,y) = K(x,y) + \frac{1}{2}\cdot [H(x,y)-K(x,y)][/tex] (2)
If we know that [tex]K(x,y) = (2, 1)[/tex] and [tex]H(x,y) = (4,3)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:
[tex]M(x,y) = (2,1) + \frac{1}{2}\cdot [(4,3)-(2,1)][/tex]
[tex]M(x,y) = (2,1) + \frac{1}{2} \cdot (2,2)[/tex]
[tex]M(x,y) = (2,1) + (1,1)[/tex]
[tex]M(x,y) = (3,2)[/tex]
Therefore, the coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].
Sarah has four friends. Lauren is 1.54m tall, Sophie is 1.50m tall, Kristy is 1.52m tall and Natalie is 1.49m tall. If they all stood on top of eachother how high would theybe?
Answer:
It would be 6.05m tall.
A boy arrived at school at 8:15am if he stayed in the school for 4 hours 20 minutes when did he leave
Answer:
12:35
Step-by-step explanation:
The boy left school at time 12:15 pm.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
To find out when the boy left school, we need to add 4 hours and 20 minutes to the time he arrived at school.
To add minutes, we need to make sure both times are in the same format. Let's convert the arrival time of 8:15 am to minutes:
So,
8:15am = 8 x 60 + 15 = 495 minutes
Now we can add 4 hours and 20 minutes:
495 + 4 x 60 + 20 = 735 minutes
So the boy left school at 735 minutes after midnight.
To convert this back to a time, we can divide by 60 to get the number of hours and minutes:
735 minutes / 60
= 12 hours (with 15 minutes remaining)
Therefore,
The boy left school at time 12:15 pm.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ2
If IJ=16 and JK=9, what is the length of HK⎯⎯⎯⎯⎯⎯?
Answer:
25 or 26
Step-by-step explanation:
add 9 plus 16
so it is 16
Answer:
15
Step-by-step explanation:
A 8-kg load stretches an elastic belt 0.02 m. How much will a 12-kg load stretch the belt?
Answer:
A 12-kg load stretches an elastic the belt 0.03m
Step-by-step explanation:
we know A 8-kg load stretches an elastic belt 0.02 m.
=> 0.02 / 8 = 0.0025
so A 1-kg load can stretch an elastic belt 0.02 m.
=> 12 * 0.0025 = 0.03 m
A 12-kg load stretches an elastic the belt 0.03m
Use your knowledge of functions to complete the table below. Identify whether or not each representation is a function and be sure to justify your answer (pls tell me which one is right)
Answer:
YesUs
Step-by-step explanation:
the vertical LIne test. The lines intercept, so it is not a function.
Can someone please help me out on this one math problem you will get double the points if you help me, I will also give you the brain thing. Please actually help not just takes the points.
•Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer. (2 pts.)
Answer:
answer should be 105 degrees.
Step-by-step explanation:
this is becuase the 75 degree angle given creates a 105 degree angle to its left. and the car turning left onto 3rd street would be a corresponding angle to the 105 degree angle on the top. sorry if its confusing, but the answer is 105 degrees. hope it helps
Answer:The angle formed by turning from traveling southwest on King Avenue to 3rd street is a corresponding angle to the 75° angle. This means its measure is 75°. here is your answer!
Step-by-step explanation:
Please help me with trigonometry and law of sines I’m being timed and really need the help
Step-by-step explanation:
cosA = AC² + BC²- AB² / 2 • AC • BC
cos A = 13.5²+23.9²-12.7²/2• 13.5 • 23.9
25. The heights of three-year-old boys are Normally distributed with a mean of
96 cm. and a standard deviation of 4.5 cm. What is the standard score for a
three-year-old boy who is 99.5 cm tall?
(a)-1.29
(b) -0.67
(c) 0.67
(d) 0.78
(e) 1.29
What is the score?
PLS HELP ME FIND THE MAD, MADIAN, RANGE AND IQR OF THIS DATA SET.
Answer:
The median is 6. The Mean Absolute Deviation is 1.88. The range is 10. I believe the IQR is 5.
Step-by-step explanation:
the median is just the number that falls in the center of a data set. The Mean Absolute Deviation is the distance of the data points from the mean. So, find the sum of the differences of each data point from the mean and divide it by the number of data points. Range is the difference between the smallest and largest values in a data set. The interquartile range is the middle of the data. it is a measure of how widely the middle half of the data is spread around the median.
Answer:
the median is 6, range is 10, the iqr is 6 and the MAD is 1.9378698224852
Step-by-step explanation:
Range
10 - 0 = 10
IQR
median/2
6/2=3
6+3=9 6-3=3
9-3=6
Median
put numbers in ascending order
04445555555566678888899101010
find centre number
6
Mr Thompson, This is my homework! Please help.
Problem 1
ax^2+bx+c is standard form(x+p)(x+q) is factored formThere's not much to say about these. You'll just have to memorize the terms. Note with standard form that the exponents decrease as you move from left to right (2,1,0).
===============================================
Problem 2
Other names for zeros are:
A) x interceptsD) solutionsThe term "root" is also applicable here.
===============================================
Problem 3
We set each piece equal to 0 and solve for x. This is the zero product property
f(x) = (x-2)(x+4)
0 = (x-2)(x+4)
(x-2)(x+4) = 0
x-2 = 0 or x+4 = 0
x = 2 or x = -4
The two x intercepts are located at (2,0) and (-4,0)
Answer: Choice C
===============================================
Problem 4
In the last problem, we found the two roots were x = 2 and x = -4
I'll let p = 2 and q = -4.
Average the roots to get (p+q)/2 = (2+(-4))/2 = -2/2 = -1
This is the x coordinate of the vertex. So h = -1
Plug this into the function to find k, which is the y coordinate of the vertex.
k = f(h)
k = f(-1)
k = (-1-2)(-1+4)
k = (-3)(3)
k = -9
The vertex is located at (h,k) = (-1, -9)
This is another way of saying the vertex is when x = -1 and y = -9
Answer: Choice C
Why might algebra tiles not be a good tool to use to factor x2 + 18x + 80? Explain.
Step-by-step explanation:
Algebra tiles would not be a good tool to use to factor the trinomial because you would need to drag an x-squared tile, 18 x-tiles, and 80 plus tiles. That is a total of 99 tiles. It would take a lot of time to drag that many tiles on the board and there might not be enough space to hold all of them. You would also need to determine how to arrange all those tiles to make a rectangle. Since 80 is a multiple of 10, you might recognize that 10 and 8 are the factors that add to 18, which would give you the values to use in the X method.
There are a lot of tiles to drag onto the board.
You would need to create a rectangle from 99 tiles.
80 is a multiple of 10, so it has factors of 10 and 8, which add to 18.
I'm stuck on this, does anyone know the solution?
The question is:
Calculate (2p - 4q) 2 when p= - 8 and q = - 3.
Answer:
-14 or -28
Step-by-step explanation:
2x-8=-16
4x-3=-12
-16-12=28
-16-(-12)=-14
(i would go with -14)If a = -2 and b = -4 -3i, then find the value of a b in fully simplified form.
Answer:
I'm not so sure but I think it's 6 or 9i
PLEASE HELP ME ASAP! DUE TODAY! (functions) (brainliest)
Answer:
how did you get the graph on here
Complete the function table for y=2.5x−8 .
Answer:
x=3.2
Step-by-step explanation:
The value of the function at x =1 is -5.5.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
Given that the function is y = 2.5x - 8. The value of the function will be calculated as,
At x = 1 the value of y will be,
y = 2.5 x - 8
y = ( 2.5 x 1 ) - 8
y = 2.5 - 8
y = -5.5
To know more about function follow
https://brainly.com/question/10439235
#SPJ2
An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
Find the term of the sequence that has value -93?
Answer:
n = 50
Step-by-step explanation:
Let a be the first term and d be the common difference.
An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
[tex]a_n=a+(n-1)d[/tex]
According to the given condition,
[tex]a_2=3\\\\a_{10}=-13[/tex]
or
[tex]a+(2-1)d=3\\\\a+d=3\ ...(1)\\\\a+(10-1)d=-13\\\\a+9d=-13\ ...(2)[/tex]
Subtract equation (1) from (2).
a+9d-(a+d) = -13-3
8d = -16
d = -2
Put the value of d in equation (1).
a+(-2) = 3
a = 3+2
a = 5
Now,
[tex]a+(n-1)d = -93\\\\5+(n-1)(-2)=-93\\\\5-2n+2=-93\\\\7+93=2n\\\\2n=100\\\\n=50[/tex]
So, 50th term has the value of -93.
A book store sells used
books.
Paperback books cost $1.00.
Hardback books sell for $5.00.
The store sold 100 books and made $260 from the sale.
How many paperback books did the store sell?
Α. 20
В. 40
C. 60
D. 80
Answer:
The correct answer is C
Positive
Monica estimates the recipe makes about 5 cups of fruit salad. Which explanation describes whether Monica's estimate is reasonable?
A Not reasonable. Four fractions cannot equal more than 4 cups.
B) Not reasonable. The whole numbers add up to 3 so the total sum cannot be 5 cups.
C с Reasonable. The grapes and apples is about 2 cups and pears and oranges is exactly 3 cups.
D Reasonable. The pears and apples is about 3 cups and the grapes and oranges is exactly 2 cups.
Answer:
A.
Step-by-step explanation:
Not reasonable, Why did you put that as your answer?
The whole numbers add up to more then 4 cups.
The manufacturer's price for a cooler is $28.50. A camping store that buys the coolers sells them for $40.76. What is the approximate percent of increase in the price of the coolers?
Answer:
43%
Step-by-step explanation:
(40.76 - 28.50) / 28.5 = .43 or 43%
What is the extraneous solution of the given absolute value equation?
-2|-2x-4|=-12
9514 1404 393
Answer:
is no extraneous solution
Step-by-step explanation:
An absolute value equation typically does not have extraneous solutions. The solutions to this one are ...
x ∈ {-5, 1}
__
Unless there is some domain restriction, this equation has no extraneous solutions.
_____
For -2x-4 < 0
-2(2x +4) = -12
x +2 = 3
x = 1 . . . . . . -2(1)-4 = -6 < 0. Not an extraneous solution
__
For -2x-4 > 0
-2(-2x -4) = -12
4x +8 = -12
4x = -20
x = -5 . . . . . . -2(-5) -4 = 6 > 0. Not an extraneous solution
find the volume of cuboid
meausring 19 cm by 15 cm by 10 cm.
WILL MARK BRAINLIEST!! Mr. Brown uses a modern technological machine to till his lands and perform tasks that require high power. This machine has a GDP for navigation purposes and auto-steer systems that minimize Mr. Brown’s work on his field. Which machine is Mr. Brown using?
1. seed drill
2. combine harvester
3. GIS
4. tractor
5. electric motor
FInd the value of x
*giving brainliest*
Answer:
It's 8
Step-by-step explanation:
You can see that the second triangle is three times the size as the first so you divde the same side on the second triangle by 3
Ai Mi went to the store to buy some chicken. The price per pound of the chicken is $3.50 per pound and she has a coupon for $2.50 off the final amount. With the coupon, how much would Ai Mi have to pay to buy 3 pounds of chicken? Also, write an expression for the cost to buy pp pounds of chicken, assuming at least one pound is purchased.
Answer:
$8 for 3 pounds
cost for p pounds: 3.50p - 2.50
Step-by-step explanation:
Cost of 3 pounds:
Original cost = Cost per pound x 3
= 3.50 x 3
= 10.50
Coupon = 2.50
Final cost = Original cost - Coupon
= 10.50 - 2.50
= $8
Cost of p pounds:
Original cost = Cost per pound x p
= 3.50 x p
= 3.50p
Coupon = 2.50
Final Cost = Original Cost - Coupon
= 3.50p - 2.50
A drink is made by mixing 650 ml of water with 150 ml of fruit juice.
What percentage of the drink is fruit juice?
can you please reply quickly?
[tex]\boxed{\color{hotpink}\tt18.75\%} [/tex] of the drink is fruit juice
○=> Steps to derive correct answer :Quantity of water in a drink = 650 ml
Quantity of fruit juice in a drink = 150 ml
Total quantity of both items in the drink :
[tex] =\tt 650 + 150[/tex]
[tex] \color{plum}=\tt 800 \: ml[/tex]
Thus, the total quantity of both items in the drink = 800 ml
Let the percentage of of fruit juice in the drink be x%.
Which means :
[tex] = \tt\frac{x}{100} \times 800 = 150[/tex]
[tex] = \tt \frac{x \times 800}{100} = 150[/tex]
[tex] =\tt \frac{800x}{100} = 150[/tex]
[tex] =\tt 8x = 150[/tex]
[tex] =\tt x = \frac{150}{8} [/tex]
[tex]\hookrightarrow\color{plum} \bold{x = 18.75\%}[/tex]
Then, the percentage of water in the drink :
[tex] = \tt100 - 18.75[/tex]
[tex] \color{plum}= \tt81.25\%[/tex]
Thus, the percentage of water in the drink = 81.25%
○=> Therefore :▪︎Percentage of fruit juice in the drink = 18.75%
▪︎Percentage of water in the drink = 81.75%
Please help! Will mark brainliest if correct! Worth 30 points! Wont give brainliest if you're not correct.
Answer:14.7
Step-by-step explanation:
d = l^2+w^2+h^2 = 10^2+4^2+10^2≈ 14.69694cm
can some help me
out with this problem please ?
Answer:
Step-by-step explanation:
If you are looking for the value of x, use the Pythagorean Theorem.
x² = 58² - 40² = 1764
x = √1764 = 42
Answer: 42cm
Step-by-step explanation:
Using the formula
(Hypotenuse^2)= (Opposite^2) + (Adjacent^2)
Hypotenuse= 58cm
Opposite= 40cm
Adjacent= x
Therefore
(58^2)= (40^2) + (x^2)
3364= 1600 + x^2
3364-1600= x^2
1764= x^2
x= 1764^1/2
x= 42
Adjacent= 42cm
Um número inteiro é expresso por 81:
3^(4 )+3^0. Qual é o oposto ou
simétrico desse número? *
- 2
- 4
-0
-1
- 3
Answer:
the opposite and symmetrical of the given number is 2
Step-by-step explanation:
The computation of an opposite and symmetrical of the given number is shown below:
81:3^4 + 3^0
81:81+1
1 + 1
= 2
Hence, the opposite and symmetrical of the given number is 2
See picture for question
Answer:
b is correct because it is
Step-by-step explanation:
because it is
Answer:
Step-by-step explanation:
well its quite long working out so im not gonna type it
but i didnt get an exact answer but i got to 24.71 closest to the 25 answer
so im not sure but i would take a guess for 25
here it is a second time. Please I just want sleep :)
Answer:
hope this helps you out good luck