Answer:
m∠ABC = 119° and DC = 105 feet
Step-by-step explanation:
For better understanding of the solution see the attached figure of the trapezium ABCD :
m∠BCD = 61°
By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°
⇒ m∠ABC = 180° - 61°
⇒ m∠ABC = 119°
Now, to find length of DC,
Draw a perpendicular BE on CD ⇒ CD = DE + EC
AB = DE
⇒ DE = 80 feet
In ΔBEC, By using Pythagoras theorem
EC² = BC² - BE²
⇒ EC² = 65² - 60²
⇒ EC = 25 feet
Hence, DC = 80 + 25
= 105 feet
Let d represent the distance of the destination from the starting point.
After 45 min, Henry has already driven d-68 miles. After 71 min., he has already driven d-51.5 miles.
So we have 2 points on a straight line:
(45,d-68) and (71,d-51.5). Let's find the slope of the line thru these 2 points:
d-51.5 - (d-68) 16.5 miles
slope of line = m = ----------------------- = ------------------
71 - 45 26 min
Thus, the slope, m, is m = 0.635 miles/min
The distance to his destination would be d - (0.635 miles/min)(79 min), or
d - 50.135 miles. We don't know how far his destination is from his starting point, so represent that by "d."
After 45 minutes: Henry has d - 68 miles to go;
After 71 minutes, he has d - 51.5 miles to go; and
After 79 minutes, he has d - x miles to go. We need to find x.
Actually, much of this is unnecessary. Assuming that Henry's speed is 0.635 miles/ min, and knowing that there are 8 minutes between 71 and 79 minutes, we can figure that the distance traveled during those 8 minutes is
(0.635 miles/min)(8 min) = 5.08 miles. Subtracting thix from 51.5 miles, we conclude that after 79 minutes, Henry has (51.5-5.08), or 46.42, miles left before he reaches his destination.
Hello from MrBillDoesMath!
Answer:
33769/181
Discussion:
Each term contains "x" so factoring it out gives
x( 1/4 + 1/14 + 1/17) = 71 (*)
Use common factor (17*14*4 = 952) as the denominator to combine terms:
1/4 = (17*14)/ 952 = 238/952
1/14 = (17*4)/952 = 68/952
1/17 = (14*4)/952 = 56/952
so 1/4 + 1/14 + 1/17 = (238 + 68 + 56)/ 952 = 362/952 = 181/476
Substituting in (*) gives
x ( 181/476) = 71 => multiply both sides by 476/181
x = (71 * 476)/181 => 71* 476 =33769
x = 33769/181
Thank you,
MrB
Answer:
The input x = 1 has many outputs.
The graph is a vertical line.
Step-by-step explanation:
Hi there!
A function is defined as a relation that only gives one output for every given input. For every x-value, there is only one y-value.
Because the x-value of 1 gives us an infinite number of y-values, this is therefore not a function.
More generally, no vertical line is a function for this reason.
I hope this helps!
Hi there! :)
<u>Answer:</u>
In order to maintain the same ratio, she should sell 18 band posters.
<u>Step-by-step explanation:</u>
<u>Initial ratio:</u>
Ratio is: 105 movie posters for 90 band posters = <u>105 : 90</u>
She sells 21 movie posters, which means that we are left with 105 movies minus the 21 she sold.
105 - 21 = 84 → She now has <u>84</u> movie posters.
In order to answer your question, you'll need to use the cross product method:
105 movie posters → 90 band posters
84 movie posters → X
<u>(90 × 84)</u> ÷ 105 = X
<u>7,560 ÷ 105</u> = X
72 = X ⇒ Number of band posters she should have left to maintain the same ratio.
She has 90 band posters :
90 <u>- X</u> = 72
Add "X" to each side of the equation → 72 + X = 72 + X
90 = <u>72</u> + X
Subtract 72 from each side of the equation → 90 - 72 = 18
<u>18 = X</u>
There you go! I really hope this helped, if there's anything just let me know! :)
