Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following proves that PQ=LO?
Answers attached
Answers
The midpoint of a line divides the line into equal segments.
The option that proves PQ = LO is (a)
The given parameters are:
[tex]\mathbf{L = (0,0)}[/tex]
[tex]\mathbf{M = (3,0)}[/tex]
[tex]\mathbf{N = (3,7)}[/tex]
[tex]\mathbf{O = (0,7)}[/tex]
P is the midpoint of LM.
So, we have:
[tex]\mathbf{P = \frac{LM}{2}}[/tex]
[tex]\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}[/tex]
[tex]\mathbf{P = (\frac{3}{2},0)}[/tex]
Q is the midpoint of NO.
So, we have:
[tex]\mathbf{Q = \frac{NO}{2}}[/tex]
[tex]\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}[/tex]
[tex]\mathbf{Q = (\frac{3}{2},7)}[/tex]
Distance PQ is calculated as follows:
[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
This gives:
[tex]\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{PQ = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{PQ = 7}[/tex]
Distance LO is calculated as follows:
[tex]\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{LO = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{LO=7}[/tex]
So, we have:
[tex]\mathbf{PQ = 7}[/tex]
[tex]\mathbf{LO=7}[/tex]
Thus:
[tex]\mathbf{PQ = LO}[/tex]
Hence, the correct option is (a)
Read more about distance and midpoints at:
https://brainly.com/question/11231122
Related Questions
what is the answer of this? 4x²-9y²+36y-36=0
Answers
Answer:
x = + - 3(y-2)
this it ut
Answer:
It will be the oval, yw :)
help its due in 3 mins
Answers
Answer:
Can you please give me the question or link
Step-by-step explanation:
A number is at most -5 or at least 0, but how do you graph it?
Answers
Answer:
Step-by-step explanation:
i am not really fully sure
3. A person jogs 1/7 mile in 1/42 hour. What is the person”s speed in miles perhour?
Answers
Answer:
42/7 = 6 miles per hour
Step-by-step explanation:
Given,
The total distance covered by the person = [tex]1/7[/tex] a miles,
Time taken by him = [tex]1/42\\[/tex]an hour,
We know that, speed = Distance, time
The speed of the person = [tex]1/7 over 1/42[/tex]
42/7
also known as 6 miles per hour
I hope this helps and have a great day!
On a map, 1 inch equals 15 miles. Two cities are 7 inches apart on the map. What is the actual
distance between the cities?
The actual distance between the cities is miles.
Answers
Answer:
105 miles
Step-by-step explanation:
The ratio you have is 1:15
So you must multiply 7 by 15 to find the actual distance in miles.
7*15=105
Determine a series of transformations that would map polygon ABCDE onto polygon A’B’C’D’E’?
Answers
Answer:
1. reflection over y axis
2. dilation over the origin with scale factor of 3
Step-by-step explanation:
1. reflection about y axis
2. dilation over the origin (0,0) with scale factor of 3
(3)
(2)
2 m
5 m
2 m
5 m
Perimeter:
Area:
Answers
Step-by-step explanation:
The area = (5 × 3) + (2 × 3) = 15 + 6 = 21
The perimeter = 2 + 3 + 5 + 5 + 3 + 2 = 20
please give me a brainliest answer
15.35m rounded to the nearest whole number
Answers
Answer:
The answer is 15m
Step-by-step explanation:
The meaning whole number means an actual whole number, decimals are just part's of a whole number, so excluding decimals:
If you look at 5 and compare it to 3 following next, 3 is not higher then 5 and therefore is rounded down.
Hope this helps!
Which statement correctly compares the function shown on this graph with
the function y = 4x + 2?
8
7
6
5
1
543 2
1 2 3 4
5
A. The function shown on the graph has a greater rate of change, but
a lower starting point.
B. The function shown on the graph has a greater rate of change and
a higher starting point.
C. The function shown on the graph has a smaller rate of change, but
a higher starting point.
Answers
The given highest power of x in the given function, y = 4·x + 2, is 1,
therefore, the graph of the function is a straight line.
The statement that correctly compares the function shown on the graph
with the function; y = 4·x + 2 is; C. The function shown on the graph has a
smaller rate of change but a higher starting point.
Reasons:
The given function is; y = 4·x + 2
Comparing with the equation for a straight line; y = m·x + c, we have;
The rate of change or slope, m = 4
The y-intercept, starting point, c = 2
Two points on the function shown on the graph are; (0, 4), and (-2, -2)
The slope of the given graph is therefore;
[tex]m = \dfrac{4 - (-2)}{0 - (-2) } = \dfrac{6}{2} = 3[/tex]
The rate of change of the graph, m = 3
The equation of the graph is therefore;
y - 4 = 3·(x - 0)
Which gives;
y = 3·x + 4
The y-intercept, starting point of the graph, is therefore, c = 4
Which gives;
The function shown on the graph has a higher starting point but a smaller rate of change than the given function.
Learn more here:
https://brainly.com/question/18194679
what is the equivalent value of 1/3×(−15)
Answers
Answer: -5x
(6d+5)−(2−3d) find the difference
Answers
Answer:
10d
Step-by-step explanation:
6d+5 =11d
2-3d = -1d
11d-1d= 10d
What is the slope of the line whose equation is -48 = 2x - 8y?
Enter your answer in the box.
Answers
Answer:
The slope is [tex]\frac{2}{8}[/tex]
Step-by-step explanation:
Take the general equation of a straight line [tex]y = mx+c[/tex]
Here [tex]m[/tex] is the slope of the line.
So let's get the equation of the line in the question in the same form.
[tex]-48 = 2x-8y[/tex]
Add [tex]8y[/tex] to both sides: [tex]8y - 48 = 2x[/tex]
Add [tex]48[/tex] to both sides: [tex]8y = 2x + 48[/tex]
Divide by [tex]8[/tex] to get it into the general equation: [tex]y = \frac{2}{8} x + 6[/tex]
Now compare it to the general equation to find the value of [tex]m[/tex]. The value of [tex]m[/tex] is the coefficient of [tex]x[/tex] which we can see is [tex]\frac{2}{8}[/tex]
PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.
Answers
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]
Do the same for the AROC from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
find the nth term of 11, 20, 35, 56, 83, . . .
Answers
nth number is 83 hope you understand my answer thanks
Answer: 3n^2 + 8
Step-by-step explanation:
an^2 + bn + c
It is a quadratic sequence
11, 20, 35, 56, 83
+8 +15 +21 +27
+6 +6 +6
a + b + c
4a + 2b + c
9a + 3b + c
4a + 2b + c - a + b + c = 20 - 11
4a + 2b + c - a + b + c = 9
3a + b = 9
9a + 3b + c - 4a + 2b + c = 35 - 20
5a + b = 15
-2a = -6
a = -6/-2
a = 3
Substitute to find the values of b & c
For b
5(3) + b = 15
15 + b = 15
b = 15 - 15
b = 0
For c
9(3) + 3(0) + c = 35
27 + c = 35
c = 35 - 27
c = 8
3n^2 + 0n + 8
3n^2 + 8
A 144-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
The shorter piece is inches long.
Answers
Answer:
shorter piece is 28.8 inches
Step-by-step explanation:
Answer28.8
Step-by-step explanation:
28.8 x 5 = 144
If Bryan had 2 apples and one of them is gone what happen to the other apples
Answers
Answer:
other apples should also be taken by another person and Bryan had no apples left.
Step-by-step explanation:
Equivalent (-1)+10+9 please
Answers
Answer:
18
Step-by-step explanation:
1) Simplify the expression
-1 + 10 + 9
9 + 9
18
-11-10-9
show steps for your answer
Answers
Answer:
-11-10=-21
-21-9= -30
Pls help me:
1) 3/5 ÷ 3=
2 )2÷ 2/5=
Answers
1) 0.2
2) 5
Check the image below
What is the sum of 1 + 1?
Answers
1 + 1 = 2
Have a beautiful and joyful day ahead.
Answer:
1+1= 2
have a nice day stay safe <3
(-0.4)^2 sum pls i need this by tonight i have to finish my math corrections pls
Answers
Answer:
(-0.4)²
= -0.4×-0.4
product of two negative numbers is positive
so, 0.4×0.4
=4/10×4/10
=16/100
=0.16
42 points giv away PLZ ANSWER RN (5/8+3/4) divided by (-2/3 - 5/6)
Answers
Answer:
when you divide you get -11/12
if you have a calculator you could add the 5/8 and 3/4
then add the -2/3 and the -5/6
then divide the first answer by the second answer
Answer:
[tex] \frac{( \frac{5}{8} + \frac{3}{4}) }{( - \frac{ 2}{3} - \frac{5}{6} )} \\ \\ \\ \frac{( \frac{5}{8} + \frac{6}{8}) }{( - \frac{4}{6} - \frac{5}{6} ) } \\ \\ \\ \frac{ (\frac{5 + 6}{8}) }{( \frac{ - 4 - 5}{6} )} = \frac{( \frac{11}{8} )}{( - \frac{9}{6} )} \\ \\ \\ \frac{11}{8} \div ( - \frac{9}{6} ) \\ \\ \\ \frac{11}{8} \times ( - \frac{6}{9} ) \\ \\ \\ \frac{11}{8} \times ( - \frac{2}{3} ) \\ \\ \\ \frac{11}{4} \times ( - \frac{1}{3} ) \\ \\ \\ = - \frac{11}{12} \\ \\ \\ = - 0.91666[/tex]
I hope I helped you^_^
The table below shows the number of red, blue, and white ribbons won by 4 girls during last years gymnastic season
Which girl had the largest ratio of red ribbons to her total ribbons?
Answers
Answer: B or D
Step-by-step explanation:
Karens ration is 5:15 whilst chens is 6:19
1/3 of 15 is gonna be 5, while 19 is gonna be around 6.3
I got 1/3 cause there is 3 colors, and red is one of them, since the question is asking about the total. I would be leaning more towards B though.
Answer:
Chen: 6/19
Step-by-step explanation:
Anne: 2/14 = 0.142
Karen: 5/15 = 0.133
Janice: 4/14 = 0.285
Chen: 6/19 = 0.316
Solve for x
9x+7=30
round to the nearest tens digit.
Answers
9x=23
Divide both sides by nine and you get 2.555555555555555
So just say 2.5 recurring
find tge equation of the line
Answers
Answer:
y = -2x + 9 or y = 9 - 2x
Step-by-step explanation:
First find the gradient
Pick two points on the graph, (4, 1) and (1,7)Find the change in y (7 - 1 = 6)Find the change in x (1 - 4 = -3)Divide the change in y by the change in x = 6 ÷ -3 = -2The gradient is -2: y = -2x + cNext, look at where the line intercepts (goes through) the y-axis: 9
The equation of the line is y = -2x + 9
Tip: The gradient is negative because the line is going downwards from left to right; if the line was going upwards, the gradient would be positive.
Hope this helps!
Find h. h - 6 = 5
(A) 5
(B) -1
(C)11 (D)6
Answers
h-6=5
first add 6 to both sides and you’ll get h=11
Answer:
C
Step-by-step explanation:
y=f(x)=x+3÷2,x€{1,5,-3
Answers
Answer:
Yo use gauth mathhhhhhh
pls pls pls help meeee!
Answers
Answer:
x is 90 because it is a right triangle
Another one I'm not very good with algebra.
Answers
Answer:
A mayb
Step-by-step explanation:
175/ 1/3
=58+17
=75
George is looking at stock market charts. He can buy a collection of stocks for 6 shares for $618. How much would it be for 11 shares?