A portion of an amusement park ride is shown. Find EF. Write your answer as a fraction in the simplest form
Answers
The point of intersection of two straight line graphs is the point with coordinates that satisfies both lines equations
The length of segment EF is presented as follows;
[tex]EF =\underline{\mathbf{ 17\dfrac{1}{7} \ ft.}}[/tex]
The reason why the above value is correct is as follows;
The given parameters are;
Height of right triangle ACD = 40 ft.
Height of right triangle BCD = 30 ft.
Required:
To find the length of EF
Solution:
The equation of the lines AC and BD are found and equated to find the height of EF as follows;
The slope of AC = [tex]\dfrac{-40}{CD}[/tex]
The equation of AC is presented as follows;
[tex]y - 40 = \dfrac{-40}{CD} \times (x - 0)[/tex]
[tex]y = \dfrac{-40}{CD} \times x + 40[/tex]
The slope of BD = [tex]\dfrac{30}{CD}[/tex]
The equation of BD is given as follows;
[tex]y - 30 = \dfrac{30}{CD} \times (x - CD)[/tex]
[tex]y = \dfrac{30}{CD} \times (x - CD)+ 30[/tex]
Equating both values of y to find the value of y at the intersecting point E, gives;
[tex]\dfrac{-40}{CD} \times x + 40 = \dfrac{30}{CD} \times (x - CD)+ 30[/tex]
Which gives;
[tex]\dfrac{40 \cdot CD - 40 \cdot x}{CD} = \dfrac{30 \cdot x}{CD}[/tex]
Therefore;
40·CD - 40·x = 30·x
[tex]CD = \dfrac{70\cdot x}{40} = \dfrac{7\cdot x}{4}[/tex]
[tex]CD = \dfrac{7\cdot x}{4}[/tex]
Therefore, at E, we have;
[tex]y = EF= \dfrac{40 \cdot CD - 40 \cdot x}{CD} = \dfrac{30 \cdot x}{CD}[/tex]
[tex]y = EF = \dfrac{40 \times \dfrac{7}{4}\cdot x - 40 \cdot x}{\dfrac{7}{4}\cdot x} = \dfrac{30 \cdot x}{\dfrac{7}{4}\cdot x} = \dfrac{120}{7} = 17\dfrac{1}{7}[/tex]
[tex]\underline {EF = 17\dfrac{1}{7} \ ft.}[/tex]
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Related Questions
;))))
That emoji makes me feel awkward...yeah BYEE
Answers
Answer:
same
Step-by-step explanation:
hello, good afternoon-
An airplane is flying diagonally across the state of Colorado. This state and its
dimensions are represented by the rectangle on the map shown.
Based on the measurements shown in the map, which measurement is closest to the
distance in miles the airplane will fly along the diagonal?
Answers
Answer:
C
Step-by-step explanation:
The measurement is closest to the distance in miles the airplane will fly along the diagonal is given by D = 476.1 miles
What is the diagonal of a rectangle?The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let the dimensions are represented by the rectangle be 280 mi x 385 mi
So , the length of the rectangular path L = 280 miles
The width of the rectangular path W = 385 miles
And , the distance in miles of airplane along the diagonal is given by
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
On simplifying , we get
The distance along the diagonal D = √ ( 280 )² + ( 385 )²
The distance along the diagonal D = √ ( 78400 + 148225 )
The distance along the diagonal D = √ ( 226625 )
The distance along the diagonal D = 476.1 miles
Hence , the distance is D = 476.1 miles
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The complete question is given below :
An airplane is flying diagonally across the state of Colorado. This state and its dimensions are represented by the rectangle on the map shown
280 mi
385 mi
Based on the measurements shown in the map, which measurement is closest to the distance in miles the airplane will fly along the diagonal?
A 665.0 mi
B 25.8 mi
C 36.4 mi
D 476.1 mi
Statements
Sometimes True
Always True
Never True
The sum of a rational number and an irrational number is rational.
O
O
O
The product of a rational number and a rational number is rational.
O
o
о
The sum of an irrational number and a rational number is irrational.
The product of an irrational number and a rational number is irrational.
O
O
о
The sum of a rational number and a rational number is rational.
Answers
Answer:
statement are always true
Sometimes True:
The sum of a rational number and an irrational number is rational.
Always True:
The product of two rational numbers is always rational.
Always True:
The sum of an irrational number and a rational number is irrational.
Sometimes True:
The product of an irrational number and a rational number is irrational.
Always True:
The sum of two rational numbers is rational.
What is a rational number?A rational number is a number that can be written in the form of p/q where q is not equal to zero.
We have,
Sometimes True:
The sum of a rational number and an irrational number can be rational or irrational depending on the numbers chosen.
For example, 1 + √2 is irrational, but 1/2 + √2/2 is rational.
Always True:
The product of two rational numbers is always rational, as can be shown using the definition of rational numbers.
Always True:
The sum of an irrational number and a rational number is always irrational. This can be shown by contradiction.
Assume that the sum of an irrational number a and a rational number b is rational.
Then (a + b) - b is also rational, which implies that a = (a + b) - b is rational, contradicting the assumption that a is irrational.
Sometimes True:
The product of an irrational number and a rational number can be rational or irrational depending on the numbers chosen.
For example, √2 x 2 is irrational, but √2 x (1/√2) = 1 is rational.
Always True:
The sum of two rational numbers is always rational, as can be shown using the definition of rational numbers.
Thus,
Sometimes True:
The sum of a rational number and an irrational number is rational.
Always True:
The product of two rational numbers is always rational.
Always True:
The sum of an irrational number and a rational number is irrational.
Sometimes True:
The product of an irrational number and a rational number is irrational.
Always True:
The sum of two rational numbers is rational.
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28 students 50% increase
Answers
Answer:
=42
Step-by-step explanation:
first find half of 28
=14
now you add that to 28
28+14 =
= 42
In a standard Normal distribution, 1.5% of observations lie above which z-score?
Find the z-table here.
A -2.17
B -1.03
C 1.03
D 2.17
Answers
Answer:
2.17
Step-by-step explanation:
math is so hard but I'm learning
Find the value of x. Show work if you can
Answers
Answer:
Step-by-step explanation:
number of side = n =7
Sum of all the angles of given polygon = (n -2)*180 = 5 *180 = 900
x + 140 +133 +145 + 117 + 119 + 125 = 900
x + 779 = 900
x = 900 - 779
x = 121
(-3,-3) rotated counterclockwise about the origin
Answers
Answer:
4.3
Step-by-step explanation:
Marissa compared coffeepot prices at three different stores. One of the stores advertised a discount, one was an online store that charged shipping,
and one just showed a regular price. The prices are shown below:
Price
Discount
30%
Shipping Cost
NA
$149.49
Name
American
Discounters
The Coffee Hut
The Bean
$91.99
NA
15% of the cost of
the item
NA
$106.49
NA
Part A: Which place is the least expensive place to purchase the coffeepot? Support your answer using words or numbers. (Round to the nearest
cent when calculating.)
Part B: Sales tax for all 3 retailers is 7.5%. What is the cost to purchase the cheapest coffeepot? (Round your answer to the nearest cent.)
Answers
Answer:
American Discounters is the cheapest.
Step-by-step explanation:
American Discounters:
149.49 - 30%
149.49 - (149.49 * 0.3) = 44.847
149.49 - 44.847 = 104.643
The Coffee Hut:
91.99 + 15%
91.99 + 13.8 = 105.79
The Bean:
106.49
Ryan wants to buy a new guitar that costs $325.00. He already has $75 in his account and makes $20 per day. How many days will he have to work before he can buy the guitar?
Answers
I subtracted the total cost for the guitar by the money he already had and got 250
Then I did 250/20 and got 12.5
250 is the money that he still needs for the guitar
Hope it helps
Solve the linear equation for y.
-6y (-) 6 =-14
Answers
Answer:
y=4/3
Step-by-step explanation:
-6y-6=-14
+6 +6
-6y = -8
/-6 /-6
y= 4/3
PLEASE HELP ME I WILL GIVE BRAINLYEST
What is 1,432,000,000,000 equivalent to?
$1.4 trillion
$14.3 trillion
$143.2 trillion
$1 trillion
Answers
Answer:
The answer would be 1.4 trillion hope that helps!
Step-by-step explanation:
What is the slope of the line that passes through the points (0, -4)) and (-2, -1)
Answers
Answer:
Step-by-step explanation:
y = mx + b
m is the slope (what you want)
b is the y-intercept, which is the value of y when x = 0
Oh, right, we already have b, isn't that great!
Given point (0, -4), so b = -4
Point (-2, -1), where x = -2 and y = -1
-1 = -2m -4 (solve for m)
3 = -2m
m = -3/2
Check:
y = -3x/2 -4
y = -3(-2)/2 -4 -> should get y = -1
y = 3 -4 = -1
Yay, we have the answer!
Is x=2 a solution to 3x+5>10? Explain
Answers
To figure out if x = 2 is a solution, plug 2 in for x. If the left side is greater than 10, then x is a valid solution. If the left side is not greater than 10, than x is not a valid solution.
3x+5>10
3(2)+5>10
6+5>10
11>10
11 is actually greater than 10, so x=2 is a solution to this inequality
omg i only need two more need help on this
Answers
Explanation for the slope you need to find rise over run. It goes up 3 and left 4 meaning the slope is 3/4
You start down 5 units from the origin so you get -5
Answer
[tex]y=\frac{3}{4} x+-5[/tex]
Step-by-step explanation:
y= mx+b
mx is the slope (rise over run)
b is the y intercept
Need help due today at 4:00plz help!!
Answers
Answer:i am not quite sure, my advice would be to look up a formula calculator, have a nice day <3
Step-by-step explanation:
Please show work;) goodnight also
Answers
Answer:
k f78iiujyhtgrf
Step-by-step explanation:
Please help me with this!!
Answers
Answer:
C. 72
Step-by-step explanation:
So imagine every straight line you see equals to 180 degrees, so given one side of the angle...180 - 108 = 72
Answer:
72
Step-by-step explanation:
Because as we know the angle of this is 180 and we already have (108°) so we have to add 108° to one of the numbers till we get to (180°)
Good luck
The indoor pool has a temperature of 24°C.
The outdoor pool has a temperature of 23°C.
Which pool has a higher temperature?
Choose 1 answer:
A
Indoor
B
Outdoor
Answers
[tex]y - 4 = 2x \ {7x}^{2} = xy + {y}^{2} [/tex]
solve for x and y simultaneously
Answers
Answer:
2.67
Step-by-step explanation:
n/a because I don't want to be a part of the way u passed out of the way and I will be there
For 1.999 × 2.4, how many decimal hops would you move (right to left) to place in your answer?
Answers
Answer: 4
Step-by-step explanation: it is 4 because there are a total of 4 different decimal places in the equation so if the equation was 1.2 times 1.2 you would decimal hop 2 times because there are to numbers behind the decimal
Answer:
1999 × 24 = 47976
In 1.999 the are 3 digits after the decimal. In 2.4 there is 1 digit after the decimal.
3 + 1 = 4
We move the decimal 4 places to the left or 1 place to the right of 47976.
4.7976
The ratio 132 : 60 as a fraction is....
The ratio 132 : 60 as a decimal is...
The ratio 132 : 60 as a percent is... %
Answers
Answer:
The ratio 132 : 60 as a fraction is 132/60
The ratio 132 : 60 as a decimal is 2.2
The ratio 132 : 60 as a percent is 220%
2 years to 9 months in ratio
Answers
Answer:
Step-by-step explanation:
24/9 would be 8:3
Hope this helps :)
Answer:
8 months: 3 months
When the door was left open, 36 pigeons flew the coop. If this was 40 percent of all the pigeons, how many pigeons were there originally?
Answers
Answer:
100%
Step-by-step explanation:
Cooper is ordering a cheeseburger for lunch. There are 3 cheese and 5 buns to choose from. How many different hamburger can cooper order if he makes exactly one selection for each option?
Answers
Answer: 15
Step-by-step explanation: u multiply
IS IN SPANISH BUT CAN SOMEONE HELP ME?, i need to find the area for the following
Answers
Answer:
10.2 +16.6 = 26.8 x 4.5 = 120.6 divided by 2 = 60.3
Answer:
60.3 cm
Step-by-step explanation:
Be sure to mark me Brainliest!!! I am 10000% this is correct!
I BEGG I'LL GIVE 100 POINTS
Answers
Answer:
Ok what do you need help on
Step-by-step explanation:
Answer:
how do u need help? What one?
Step-by-step explanation:
i need help asap this is urgent
Answers
Answer:
I
Step-by-step explanation:
I don't know love you tho
can someone pls answer this fast? I will mark you BRAINLIST
Answers
Answer:
Transformation
Option D has translation, the other options change the triangles' shape and they won't be congruentScale factor
Option A is correctOption B has wrong ratio, Options C and D shows different angle size which is not the case with similar triangles3x+2y=6 and y=1/3x-11 perpendicular or parallel
Answers
Answer: To determine if two lines are parallel or perpendicular, you have to look at the slopes. For the line y=kx+b, k is the slope.
For two lines y=k1x+b1 and y=k2X+b2 ,When K1=K2, two lines are parallel; when K1=-1/k2, two lines are perpendicular. It doesn't matter whatever b1, b2 are. Hence to save time, you only need to calculate k1 and k2.
To calculate the slope k of any line, you have to change the equation to y=kx+b
For -y=3x-2, k=3/(-1)=-3 (you divide -1 on each side of =, but you don't need to calculate -2/(-1))
For -6X+2y=6, K=6/2=3 (you first move the -6x to right side, it becomes 6x, then divide by 2)
Now you can get the answer: The two lines neither parallel nor perpendicular.
is -2 or 0.9 greater?????? pls answer anyone
Answers
mark brainiest because i had to try xtra hard for that question!
Answer:
0.9
Step-by-step explanation:
We can tell straight away which is greater.
Like I said, fractions are like money
:$
9/10 is 0.9
Which means
0.9 IS a positive number
Remember
THE P-BODY RULE
A POSITIVE NUMBER, NO MATTER HOW LOW IT IS
will always ALWAYS
be greater than a negative number.