Start by looking at the components of the line, basically the legs if you were to make it a right triangle.
components = < x1 - x2, y1 - y2 >
< 10-5 , 12-4 > = < 5 , 8 >
So the line starts at A and goes right 5 then up 8 to point B.
We need a point 3:1 distance which means that if X is our new point, length AX is 3 times length of XB.
3+1 = 4 parts total
Point X will be 3/4 distance
3/4 the components
< 5(3/4) , 8(3/4) > = < 15/4 , 6 >
Add these to point A to go right and up to the new point X.
(5 + 15/4 , 4 + 6) = (35/4 , 10)
35/4 = 8 3/4
so the first one is correct.
Answer:
Anything after x determines if it goes up since it's a positive 5 it's 5 units up
Answer:
a. About 64
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 70
Standard deviation = 5
Use the empirical rule to determine the number of students who scored less than 65 or more than 75?
65 = 70 - 5
So 65 is one standard deviation below the mean
75 = 70 + 5
So 75 is one standard deviation above the mean.
By the Empirical Rule, 68% of the students scored between 65 and 75. The other 100-68 = 32% scored less than 65 or more than 75.
Out of 200, that is
0.32*200 = 64
So the correct answer is:
a. About 64
Plus means addition and square root means √
3 plus the square root of negative 16: 3 + √-16
Minus means subtraction and square root means √
6 minus the square root of negative 64: 6 - √-64
Its asking you to multiply both quantities.
(3 + √-16) * (6 - √-64)
Best of Luck!
Use the information to write the dimensions of each rectangle in terms of w, the width of the 1st one.
1st rectangle;
l = 2w
w = 2
2nd rectangle:
w = w
l = 2w + 4
If the area of the 2nd rectangle is 70 square meters, you will use the area formula to write an equation that you will solve using the factoring.
A = lw
70 = w(2w + 4)
70 = 2w^2 + 4w
0 = 2w^2 + 4w -70
0 = 2 (w^2 +2w - 35)
0 = 2 (w + 7) (w - 5)
To get zero, the width would need to be -7 or 5. Because it is a distance, it has to be 5 meters.
The width of both rectangles is 5 meters.
