Answer:
v = 25.98
Step-by-step explanation:
You could do this a number of ways. Some are much longer than others. The shortest way is to use the tangent.
Formula
Tan(theta) = opposite / adjacent
Givens
Theta = 30o
Opposite = 15 km
Adjacent = x
Solution
tan(30) = 15 / v Multiply both sides by v
v*tan(30) = 15 Divide by tan(30)
v = 15/tan(30)
tan(30) = 0.5774
v = 15 / 0.5774
v = 25.98
Answer:
First, we need to determine the slope of the line going through the two points. The slope can be found by using the formula:
m
=
y
2
−
y
1
x
2
−
x
1
Where
m
is the slope and (
x
1
,
y
1
) and (
x
2
,
y
2
) are the two points on the line.
Substituting the values from the points in the problem gives:
m
=
5
−
7
3
−
0
=
−
2
3
Now, we can use the point-slope formula to find an equation going through the two points. The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through.
Substituting the slope we calculated and the values from the first point gives:
(
y
−
7
)
=
−
2
3
(
x
−
0
)
We can also substitute the slope we calculated and the values from the second point giving:
(
y
−
5
)
=
−
2
3
(
x
−
3
)
We can also solve the first equation for
y
to transform the equation to slope-intercept form. The slope-intercept form of a linear equation is:
y
=
m
x
+
b
Where
m
is the slope and
b
is the y-intercept value.
y
−
7
=
−
2
3
x
y
−
7
+
7
=
−
2
3
x
+
7
y
−
0
=
−
2
3
x
+
7
y
=
−
2
3
x
+
7
Step 3 is the associative property of addition.
The 12 and -12 are grouped together.
Answer:
$9,000
Step-by-step explanation:
Option A:
In a week he will earn 720 since 18 × 40 = 720
Option B:
(x=the amount of weekly sales)
8x ÷ 100=720
8x=72,000
x= 72,000 ÷ 8
72,000 ÷ 8 = 9,000
The salesperson needs to make a weekly sales of $9,000 to earn the same amount with both options.
