Answer:
Line segment PM = 4.2 length
ML = 6.2
ON = 3
NK = 2
Step-by-step explanation:
Just got it on plato your welcome:)
The segments formed by each transversals and the three parallel lines are
proportional according to the three parallel lines theorem.
The observations are;
The parallel lines divide the transversals in equal proportions, such that the ratio of the lengths of each transversal are equal.[tex]\displaystyle \mathrm{ Ratio \ of \ the \ segments ;\ }\frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}}[/tex]Reasons:
The question is a four part question
Let the equations of the parallel lines be as follows;
Line, x; y = x
Line, y; y = x + 1
Line z; y = x + 2
The points at which transversal 1 intersect the lines x, y, and z, are;
A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)
The length of segment [tex]\overline{AB}[/tex] = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)
The length of segment [tex]\mathbf{\overline{CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)
The ratio of the lengths of the segment formed by transversal 1 is therefore;
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{CB}}{\overline{AB}}} =\frac{2 \cdot \sqrt{37} }{2 \cdot \sqrt{37} } = 1[/tex]
The points at which transversal 2 intersect the lines x, y, and z, are;
D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)
The length of segment [tex]\overline{DE}[/tex] = √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)
The length of segment [tex]\overline{EF}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{EF}}{\overline{DE}}} =\frac{0.2 \cdot \sqrt{17} }{0.2 \cdot \sqrt{17} } = 1[/tex]
Therefore;
[tex]\displaystyle \frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}} = 1[/tex]Which gives;
The proportion with which the parallel lines divide the transversals are equal.The ratio of the lengths for each transversal are equal.The the comparison can also be made with the triangle proportionality theorem.
Learn more about triangle proportionality theorem here:
https://brainly.com/question/8160153
The simple interest on birr 400 invested for 4 months was birr 12, what is the annual (yearly) rate of interest?
Answer:
9%
Step-by-step explanation:
Given :
Principal, P = 400
Time, t = 4 months = 4/12 = 0.33333
Simple interest = 12
Simple interest = (principal * rate * time)
Rate = r
12 = (400 * r * 0.33333)
12 = 133.3333r
r = 12 / 133.3333
r = 0.090000
r = 0.09
rate = 0.09 * 100% = 9%
2. A wooded area is in the shape of a a trapezoid whose bases measure 128 m and $2 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the watkway
Correction in the Question:
A wooded area is in the shape of a a trapezoid whose bases measure 128 m and 92 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the walkway.
Answer:
The wooded area after the addition of the walkway is 4240 [tex]m^2[/tex].
Step-by-step explanation:
we are given
length of the two bases = 128m and 92m
height of the trapezoid = 40m
the approximate figure of the given trapezoid is given as:
__ __ __ 92 __ __ _
/ | | | \
/ | 40 |4| \
/__ _| __ __ | |__ __ __ __ \
128
Area of a trapezoid = [(a + b)/2] * height, where a and b are representing the bases of the given trapezoid.
Area = [(92 + 128)/2] * 40
= [220/2] * 40
= 110 * 40
= 4400 [tex]m^2[/tex]
Now there is a 4m wide walkway is to be constructed in that trapezoid. The pathway will be a rectangle as it has 4m width and 40m height as it is perpendicular to both the bases.
Area of a rectangle = length * width
Area = 40 * 4
= 160
Since the walkway will reduce the area of the trapezoid as it is constructed upon it therefore the wooded area after the addition of the walkway is
4400 + (-160) = 4240 [tex]m^2[/tex].
How many solutions does the system of linear equations have? Use the drop-down menus to explain your answer.
y = 3/4x + 12
y = 4/3x
The system of linear equations will have
Choose...
no solution
exactly one solution
infanite many solutions
because the slopes of the equations are
Choose...
the same
different
, so the lines will
Choose...
not intersect at all
intercect at one point
both be the same line
Answer:
There is one equation, the slopes are different so they will intersect at one point
Step-by-step explanation:
The perimeter of a rectangle is 20m and the length is x m find the
area of the rectangle in terms of x
Answer:
2(x+y)
Step-by-step explanation:
perimeter=20cm
length=x
Take the radius to be y
area of a rectangle=2(length+width)
therefore area of a rectangle=2(x+y)
Find the distance between 2 and -2.
A) -6
B) -4
C) 0
D) 4
Answer:
4
Step-by-step explanation:
We can do this problem by doing the absolute value of the difference between 2 and -2.
2-(-2)=4. Absolute value of 4 is 4.
Hope this helped.
~cloud
Answer:
4
Step-by-step explanation:
Help please :) (asap)
x^2 - x - 6= 0
(x - 3) ( x + 2) = 0
Equating
x - 3 = 0
x = 3
x+ 2= 0
x = -2
Answer: x - 6
Step-by-step explanation:
Jamar to the local snack shop near his school He bought 3 hotdogs and 2 bags of chips for $Kenny went to the same snack shop and bought 5 hotdogs and 6 bags of chips for $9.55 ordered 2 hotdogs and 3 bags of chips, then how much did she pay her order?
Answer:
Marcy paid $4.15
Step-by-step explanation:
Given
Represent hotdogs with x and chips with y.
So, we have:
Jamal
[tex]3x + 2y = 4.85[/tex]
Kenny
[tex]5x + 6y = 9.55[/tex]
See attachment for complete question
Required
Determine the amount for 2x and 3y
From Jamal's and Kenny's orders we have:
[tex]3x + 2y = 4.85[/tex] --- (1)
[tex]5x + 6y = 9.55[/tex] --- (2)
Multiply (1) by 3
[tex]3 * [3x + 2y = 4.85][/tex]
[tex]9x + 6y = 14.55[/tex] --- (3)
Subtract (2) and (3)
[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]
[tex]9x - 5x = 5[/tex]
[tex]4x = 5[/tex]
Solve for x
[tex]x = \frac{5}{4}[/tex]
[tex]x = 1.25[/tex]
Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]
[tex]3 * 1.25 + 2y = 4.85[/tex]
[tex]3.75 + 2y = 4.85[/tex]
Solve for y
[tex]y = \frac{4.85 - 3.75}{2}[/tex]
[tex]y = \frac{1.10}{2}[/tex]
[tex]y = 0.55[/tex]
So, the cost of 2x and 3y is:
[tex]Cost = 2x + 3y[/tex]
[tex]Cost = 2*1.25 + 3*0.55[/tex]
[tex]Cost = \$4.15[/tex]
4. Which ordered pair best represents a point
on Tia's route to the store?
F .(-5, 6)
G. (-2.5, 0)
H. (-2,5)
J. (-3.5, -3)
Answer:
G. (-2.5, 0)
Step-by-step explanation:
Starting from the origin, (0, 0), go 2.5 units to the left (because it's negative) on the x-axis, and then 0 units on the y-axis. You end up on (-2.5,0).
hope this helped :)
PLEASE HELP FOR BRAINLIEST! The sum of two numbers is 4 and the difference of their squares is 64. Find the two numbers.
10 and -6
.....................................................
There are 96 children in a room.
40 of them are girls.
Find the fraction of the children that are boys.
Write your answer in its simplest form.
I will need it by this midnight
Answer:
7/12
Step-by-step explanation:
Basically to find the boys fraction I subtracted 40 from 96 and got 56. Your answer for the number of boys would be 56/96. I divided 4 from each and got 14/24. lastly I divide by 2 and got 7/12.
At 5 am, the temperature was -10°F. By noon the temperature was 7°F, What Integer
represents the change in temperature from 5 am, to noon?
Answer:
The integer that represents the change in temperature is 17.
Step-by-step explanation:
HELP PLEASE
Marcus works at the grocery store. He earns 8.75 per hour. Last week he worked 6.5 hours. How much did Marcus make last week?
Is it 10? Or no pls explain
Answer:
Yes
Step-by-step explanation:
6 + 10 would equal 16
You're right, have a great day!
Answer:
yes, it is 10
Step-by-step explanation:
Subtract 16 and 6 and you get 10.
Or Subtract 6 and 6 and subtract 16 and 6.
It'll still be 10 no matter what.
20 points for this!! thank you
Answer:
not a function becuz 2 repeats its self twice
Step-by-step explanation:
Answer:
You are welcome
Step-by-step explanation:
It cost Erica $9.75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was Erica’s total profit?
Can i please get some help, I NEED A STEP BY STEP TO FULLY UNDERSTAND THE QUESTION AND YOUR ANSWER
Answer: $20.25
Step-by-step explanation:
If each cupcake is sold for $1, then all the cupcakes are sold together for $30. Now subtract 9.75 from 30 and you get 20.25.
Hope this helps :)
Elena notices that when she spends less time on social media the night before a quiz, she gets a higher score. Before one quiz, she spent 107 minutes on social media and eamed 37 points on a
quiz. Before another quiz, she spent 73 minutes on social media and eamed 11 points on a quiz
write a function to model a linear relationship between Elena's social media usage, in minutes, and her quiz scores, assuming that the total number of points on each quiz remains a constant
Respond in the space provided
Answer:
[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
Step-by-step explanation:
Given:
Score of 37 with 107 minutes on social media.
Score of 41 with 73 minutes on social media.
The two pieces of information above can be thought of as two points on a line. Since the quiz score is a function of the number of minutes on social medial, let the number of minutes on social media be x and the score be y. The given information gives us two ordered pairs: (107, 37) and (73, 41).
Now we need to write the equation of a line that passes through these two points.
The two-point form of the equation of a line is:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have [tex] x_1 = 107 [/tex], [tex] y_1 = 37 [/tex], [tex] x_2 = 73 [/tex], and [tex]y_2 = 41[/tex].
[tex] y - 37 = \dfrac{41 - 37}{73 - 107}(x - 107) [/tex]
[tex] y - 37 = \dfrac{4}{-34}(x - 107) [/tex]
[tex] y - 37 = -\dfrac{2}{17}(x - 107) [/tex]
[tex] 17y - 629 = -2x + 214 [/tex]
[tex] 17y = -2x + 843 [/tex]
[tex] y = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]
i need more helppppppppp, i have to find the area of this circle
Answer:
You need to find the radius first,
Half of 23 is = 11.5
Formula you must remember when finding area of circle is:
πr^2
(pie (3.14 or 22/7) x radius squared)
Our pie is 3.14 because they said to use it in this particular question.
3.14 x 11.5^2 (remember we are making our radius squared) <--- Before
Let's evaluate first:
3.14 x 132.25 <--- After evaluating
So, 3.14 x 132.25 = 415.265 <----- your answer
_______
Answer:
U scammer scaming peoiple ans wasting their points!
Step-by-step explanation:
How do you turn 5/2 into 10/4?
Answer:
YOU DO IT X 2
Step-by-step explanation:
Can someone please help me with math
Answer:
A
Step-by-step explanation:
Hello There!
This is the formula for volume of a cylinder
[tex]V=\pi r^2h[/tex]
where r = radius and h = height
we are given the height and diameter height - 10 ft diameter - 22 ft
we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2
22/2=11 so the radius is 11
now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)
[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]
so we can conclude that the answer is A
what is the distance between (3,-5), (-3,0)
Answer: 11 units
Step-by-step explanation:
-3 and 3 are 6 units apart, so that would be 6 units, and when you add the -5 into the problem, the 6 units become 11 units. Hope this helped :)
Answer:
Exact Form:
√ 61
Decimal Form:
7.81024967 …
How would I put this?
Answer:
10.35
Step-by-step explanation:
63,756 x 60 = 3825360
70 x 5,280 = 369600
3825360 ÷ 369600 = 10.35
Help! What does the bracket mean and how do I do the questions?
Answer:
maybe it meane 11/a
Step-by-step explanation:
Answer:
The bracket is the binomial.
The definition is: [tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]
Note that [tex]\binom{n}{k} = \binom{n}{n-k}[/tex]
The meaning is "if we have n elements, how many ways are there to choose k of them?" From this definition it should be obvious that [tex]\binom{n}{k} = \binom{n}{n-k}[/tex] - if you're picking k, it's just as many ways as choosing the (n-k) that you're not picking.
The coefficient can be found by realizing that to get x^9, we need to choose (from the full multiplication):
9 brackets to provide x2 brackets to provide the number 3There's [tex]\binom{11}{9}[/tex] ways to do that, so the component for x^9 will be:
[tex]\binom{11}{9} \cdot 3^2 \cdot x^9 = \frac{11!}{2!\cdot 9!} \cdot 3^2 \cdot x^9 = \frac{10\cdot 11}{2} \cdot 3^2 \cdot x^9 = 55 \cdot 9 \cdot x^9 = 495x^9[/tex]
So:
a = 2
Coefficient is 495
Is 41.77 a integer?
Answer:
nope, an integer must be a whole number, no fractions / decimals
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
An integer is a whole number or a number that is not a fraction or decimal. So, since 41.77 is a decimal it cannot be an integer. Examples of integers are 41 or -2.
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is
a. 22
b. 23
c. 60
d. 61
Answer:
c. 60
Step-by-step explanation:
Given
[tex]n = 61[/tex] --- sample
[tex]\bar x = 23[/tex]
Required
Determine the degrees of freedom (df)
This is calculated as:
[tex]df = n - 1[/tex]
[tex]df = 61 - 1[/tex]
[tex]df = 60[/tex]
Bamboo plants can grow 91 centimeters per day. what is the approximate growth of the plant inches per hour?
Answer:
roughly 1.5
Step-by-step explanation:
Help please I’ll mark brainiest
Answer:
V≈7853.98
Step-by-step explanation:
V=πr2h
r=10
h=25
Solution
V=πr2h=π·102·25≈7853.98163
Help me please!!!!!!!!!!!
Answer:
A reflection over the y-axis.
find the value of two numbers if their sum is 39 and their difference is 1
If an item is on sale for 60% off, that means you actually PAY _____% of the price.
Answer:
40%
Step-by-step explanation:
100-60=40
Mark can make 9 pancakes in 15 minutes, and Charlotte can make 42 pancakes in 45 minutes. Working together, how many minutes would it take to make 138 pancakes?
Answer:
60 mins
Step-by-step explanation:
15+45=60
The time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.
As it is given that Mark can make 9 pancakes in 15 minutes, therefore, the number of pancakes that Mark can make in one minute,
[tex]\text{Number of Pancake in one minute} = \dfrac{9}{15}[/tex]
Now, for Charlotte, it is given that he makes 42 pancakes in 45 minutes, therefore, the number of pancakes that Charlotte can make in one minute,
[tex]\text{Number of Pancake in one minute} = \dfrac{42}{45} = \dfrac{12}{15}[/tex]
Further, the total pancakes that can be made in one minute,
[tex]\text{Total Number of Pancake in one minute} = \dfrac{9}{15} +\dfrac{12}{15} = \dfrac{21}{15}[/tex]
As they both need to make 138 pancakes together, therefore, the time they need is,
[tex]\rm Time\ Needed = \dfrac{\text{Total number of pancakes}}{\text{Total number of pancakes in one minute}}[/tex]
[tex]\rm Time\ Needed = \dfrac{138}{\frac{21}{15}} = \dfrac{138\times 15}{21} = 227.142[/tex]
Hence, the time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.
Learn more about Fraction:
https://brainly.com/question/1301963
