Answer:
m<1 = 130°
m<2 = 50°
Step-by-step explanation:
Since given that line a is parallel to line b, and <1 and 130° are interior angles that alternate each other, therefore:
m<1 = 130° (alternate interior angle theorem)
Also,
130° and <2 lie on same side inside the parallel lines cut across by the transversal, therefore,
m<2 + 130° = 180° (same side interior angles theorem)
m<2 = 180° - 130°
m<2 = 50°
Answer:
The amount of fence needed to surround the mentioned space is:
Step-by-step explanation:
To identify the amount of fence, you must take all the measurements given in the exercise:
- Pool width = 20 ft
- Pool length = 40 ft
- Aditional area in each side = 10 ft
As each side has 10 additional feet, that is the lounge area, you must add 20 feet to each side of the pool, this is because, in the case of the width, you must add 10 feet to the right side and 10 feet to the left side, in the case of the length, you must add to each side 10 feet to the upper part and 10 feet to the lower part, in this form, the measurements of the fence must be:
- Width of fenced area = 40 ft
- Length of fenced area = 60 ft
As you know, the length has two sides and the length has two sides too, by this reason, we must multiply each value by 2 to obtain the amount of fence to all four sides of the lounge area:
- Amount of fence = 2(40 ft) + 2(60 ft)
- Amount of fence = 80 ft + 120 ft
- <u>Amount of fence = 200 ft</u>
As you can see, <u><em>the amount of fence needed to go around the lounge area is 200 feet</em></u>.
Answer:
See the explanation
Step-by-step explanation:
Ball is tossed 24 times
So the total number of outcomes (tosses) = N = 24
The ball lands in Blue section 3 times out of 24 tosses. So it becomes 3/24
The ball lands in Green section 5 times out of 24 tosses. So it becomes 5/24
The ball lands in Red section 12 times out of 24 tosses. So it becomes 12/24
The ball lands in Yellow section 4 times out of 24 tosses. So it becomes 4/24
Now we have to find how many times will the ball most likely land in the yellow section when it’s tossed 200 times. So the total number of outcomes here is N = 200. The favorable outcome here is that the ball lands in Yellow section. So we use the frequency table above for yellow section:
Yellow / Total tosses
4/24 = x/200
4*200 = 24x
800 = 24 x
24 x = 800
x = 800 / 24
x = 33.3
So ball most likely land in the yellow section 33 times when it’s tossed 200 times So it becomes 33/200 = 0.165 or 10.65% probability that ball will land in yellow section.
Answer:
Step-by-step explanation:
Unless we set x^2 + 8x + 15 equal to zero, we don't have an equation to be solved. I will assume that the problem is actually x^2 + 8x + 15 = 0.
The coefficients of this quadratic are {1, 8, 15}, and so the "discriminant" b^2 - 4ac is (8)^2 - 4(1)(15), or 4. Because the discriminant is positive, we know that there are two real, unequal roots.
Continuing with the quadratic formula and knowing that the discriminant is 4, we get:
-8 ± √4 -8 ± 2
x = ---------------- = --------------- , or x = -2 ± 1: x = -3 and x = -5
2 2
