hi i know i’m late but to help out any future people, the answer is
Row One: Statement: 3/2=slope Reason: Definition of Slope
Row 2: Statement: 3/2=6/4 Reason: Triangle A is similar to Triangle B
A) We are told that at 2 hours, the velocity is 18 km/h and at 4 hours, the velocity is 4 km/h. Since we are relating two variables - let's give them names.
Let x = time and y = velocity. Since the velocity depends on the time (that is, the time influences velocity), this is a linear function. Any linear function can be written in slope intercept form as y = mx + b. The problem wants the situation in standard from of Ax + By = C, which can be found from slope intercept form.
So now we can make our line. Consider the ordered pairs of (2,18) and (4, 4) with them in (x, y) form. Finding the slope, m, between these points is as such:
m = y₂-y₁ / x₂-x₁
m = 4 - 18 / 4 - 2
m = -14 / 2 = -7.
Our slope is -7.
We take m = -7, x = 4, and y = 4 (it goes 4 km/h in 4 hrs) and use those three things to find the y-intercept.
y = mx + b
4 = -7 * 4 + b
4 = -28 + b
32 = b
So our equation of the line is y = -7x + 32. To put the equation into standard form, we need to place all the variables on one side of the equals sign, all the numbers on the other.
y = -7x + 32
7x + y = 32
In standard form, the equation for this situation is 7x + y = 32
***
To find out the velocity at 8 hours, we evaluate our function at x = 8. Either equation (standard form or slope intercept) works; we use standard form.
7x + y = 32
7*8 + y = 32
56 + y = 32
y = -24
At a time of eight hours, the bicycle is moving at -24 km/h.
Answer:
A kite with a 100 foot-long string is caught in a tree. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 30 feet from the bottom of the tree. Find the measure of the angle between the kite string and the ground.
17°
27°
63°
73°
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
As you go to larger numbers, there are more possibilities of factors for them.
For example, the internal from 20 to 30 contains only two prime numbers (23 and 29) and the interval from 90 to 100 contains only one prime (97).
However, the number of prime numbers in an interval varies. There are four prime numbers between 100 and 110 (101, 103, 107, 109).
