Let x be her initial distance from the building, then tan 37 = 130/x
x = 130/tan 37 = 130/0.7536 = 172.5 feet
Let y be her distance from the building after moving forward, then
tan 40 = 130/y
y = 130/tan 40 = 130/0.8391 = 154.9
After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.
Start with the simplest equation of a straight line: y = mx + b.
Subst. 1 for m, 2 for x and 4 for y. Then, 4 = 1(2) + b, or b = 2.
In slope-intercept form, the equation of this line is y = x + 2.
Y=mx+b b is the y intercept which is 4
m is the slope which is rise over run which is -4/2 which is -2
Linear y=-2x+4
Answer:
.
Step-by-step explanation:
We have been given two sets as A: {71,73,79,83,87} B:{57,59,61,67}. We are asked to find the probability that both numbers are prime, if one number is selected at random from set A, and one number is selected at random from set B.
We can see that in set A, there is only one non-prime number that is 87 as it is divisible by 3.
So there are 4 prime number in set A and total numbers are 5.

We can see that in set B, there is only one non-prime number that is 57 as it is divisible by 3.
So there are 3 prime number in set B and total numbers are 4.

Now, we will multiply both probabilities to find the probability that both numbers are prime. We are multiplying probabilities because both events are independent.



Therefore, the probability that both numbers are prime would be
.
Answer:
3 and 2
Step-by-step explanation:
The ratio of the 2 numbers = 3 : 2 = 3x : 2x ( x is a multiple )
When 5 is subtracted from both , that is
3x - 5 : 2x - 5 = 2 : 3
Expressing the ratio in fractional form
=
( cross- multiply )
3(3x - 5) = 2(2x - 5) ← distribute both sides
9x - 15 = 4x - 10 ( subtract 4x from both sides )
5x - 15 = - 10 ( add 15 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
Thus the 2 numbers are
3x = 3(1) = 3 and 2x = 2(1) = 2