Answer:
(a) 1/6
(b) 1/2
(c) 1/3
Step-by-step explanation:
There are 6 possible outcomes.
(a) The number is 2: only 1 outcome out of 6, hence 1/6
(b) The number is even: {2, 4, 6} - 3 outcomes out of 6, hence 3/6 = 1/2
(c) The number is greater than four: {5, 6} - 2 outcomes out of 6, hence 2/6 = 1/3
Answer:
If two figures are similar, then the correspondent sides are related by a constant factor.
For example, if the base of one side of one of the figures has a length L, then the correspondent side of the other figure has a length k*L where k is the scale factor.
Let's start with the two left triangles.
In the smaller one the base is 5, and the base of the other triangle is 15.
Then we will have:
15 = k*5
15/5 = k = 3
The scale factor is 3.
Then we will have that:
a = scale factor times the correspondent side in the smaller triangle:
a = k*3 = 3*3 = 9
a = 9
For the other two triangles, the base of the smaller triangle is 12, while the base of the larger triangle is 20.
Then we will have the relation:
12*k = 20
k = (20/12) = 10/6 = 5/3
The scale factor is 5/3
This means that the unknown side b is given by:
b*(5/3) = 15
b = (3/5)*15 = 3*3 = 9
b = 9.
The equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
<h3>Equation of a line</h3>
The equation of a line in point slope form is expressed as:
y - y1 = m(x-x1)
Given the equation y = -x + 2, the slope of the line parallel to the line is -1
Substitute the slope and point (-3, -5)
y -(-5) = -1(x - (-3))
y+5 = -(x + 3)
y+5 =-x - 3
y = -x - 3 - 5
y = -x - 8
Hence the equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
Learn more on equation of a line here: brainly.com/question/18831322
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Answer:
y = 1/5x -2
Step-by-step explanation:
When a point and slope are given, sometimes it is easiest to start with the point-slope form of the equation. Then it can be rearranged to the desired form.
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -0 = 1/5(x -10) . . . . . line with slope 1/5 through point (10, 0)
y = 1/5x -2 . . . . . . . eliminate parentheses to get slope-intercept form
_____
Note that the slope in the attached picture is 1/5, but your problem text says it is 5. Very different equations will result from these different slopes.
Let Lin be x years old.
Lin = x
Frank = 4x
<span>The difference in their ages is equal to Lin’s age plus 8
</span>⇒4x - x= x + 8
Solve x:
4x - x= x + 8
Combine like terms:
3x = x + 8
Take away x from both sides:
2x = 8
Divide by 2 on both sides:
x = 4
Lin is 4 years old.
Frank is 4 x 4 = 16 years old.
Answer: Lin is 4 years old and Frank is 16 years old.
