A wall is in the shape of a trapezoid and it can be divided into a rectangle and a triangle. A triangle is with angles 45°- 45° - 90°. The hypotenuse of that triangle is 13√2 ft.Using the 45° - 45° - 90° theorem, sides of that triangle are in the proportion:x : x : x√2, and since that x√2 = 13√2 ( hypotenuse ), x = 13.Therefore h = 13 ft.We can check it: c² = 13² + 13²,c² = 169 + 169c² = 338c = √ 338 = 13√2Answer: h = 13 ft
The <em><u>correct answer</u></em> is:
Ken will have run 3 laps and Hamid will have run 4.
Explanation:
To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM, we multiply the common factors by the uncommon. Between the two numbers, the common factors are 2, 2 and 5. This makes the uncommon 2, 2, and 3, and makes our LCM
2(2)(5)(2)(2)(3) = 240
This means every 240 seconds they will both be at the start line.
Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.
Let the price of 1 shirt be represented by = s
A pair of pants costs twice as much as a shirt, then the cost of pants is = 2s
The total cost of 1 pair of pants and 1 shirt is $18 , means : 
Solving this we get,
So, the price of 1 shirt is $6 and price of 1 pair of pants is = 2s = 2*6 = $12.
Answer:
The slope of the line is -7/8
The point slope-form is y+4=(-7/8)(x-7)
The slope-intercept form is y=(-7/8)x+(17/8)
Step-by-step explanation:
You have to find the slope first using m=y2-y1 divided by x2-x1. After you found the slope of the line, you use one of the points to plug it into the point-slope form which is y-y1=m(x-x1). After you have done that, you would have convert this equation into slope-intercept form which is y=mx + b. In order to convert it, you have to multiply m with x and x1. Then you would have to get rid of y1 by doing the opposite of what y1 is. Finally, you would take the opposite of y1 and add it to the other side of the equation.
Really hope this helps! :)
Answer:
38
Step-by-step explanation:
We can express the 8th term as x and the 12th term as y.
This would mean that 8x=12y
Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y
Now we can use this to substitute y with x in the first equation. This would give us:
8x=12(x-8)
Which we can expand and solve:
8x=12x-96
-4x=-96
Therefore x=24
This means the 8th term is 24 and the 12th term is 16 (24-8).
To test if this is correct we can do:
8x24=12x16
Which indeed are equal, both sides multiply to 192.
Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)
24+14=38.
The first term is 38.
Hope this helped!
