Answer:
acute
Step-by-step explanation:
straight is just a straight line, 180 degrees perhaps
right is exactly 90 degrees
obtuse is over 90 degrees
Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.
4 years ago, the son was:
s-4
So, his father is currently:
3(s-4)
=
3s-12
Therefore:
f = 3s-12
In twelve years, the son will be:
s+12
And the father will be:
f+12
This can also be written as:
3s-12+12 as the fathers younger age would be f = 3s+12
=
3s
So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36
Son’s current age: 36
We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.
2(24)+24 = 72
Father’s current age: 72
Answer:
32 miles
Step-by-step explanation:
Given data
Let the total distance be x miles
Marks speed= 16miles per hour
Trisha's speed= 12 miles per hour
Trisha has covered 8 miles and has (x-8) miles to finish line
We know that
Speed= distance/time
time= distance/speed
Hence the time taken for Mark to finish is
time= x/16---------------1
The time taken for Trisha to finish is
time= (x-8)/12-----------2
equate 1 and 2 above
x/16= (x-8)/12
cross multiply
16(x-8)= 12*x
16x-128= 12x
collect like terms
16x-12x= 128
4x=128
x= 128/4
x= 32 miles
Hence they will meet at exactly 32 miles along the way
The exact measure of the angle is 45°.
<h3>
How to get the angle?</h3>
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
If you want to learn more about angles, you can read:
brainly.com/question/17972372
