Given the equation
�
=
4
�
y=4x fill in the missing x-value and y-value.
(
3
,
�
)
�
=
(3, y) y=
(
�
,
10
)
�
=
(x, 10) x=
In the equation y = 4x, we need to find the missing x and y values.
1) For the coordinates (3, ?):
Substitute x = 3 in y = 4x:
y = 4(3)
y = 12
So, the missing y-value is 12. Therefore, the coordinates are (3, 12).
2) For the coordinates (?, 10):
Substitute y = 10 in y = 4x:
10 = 4x
Divide both sides by 4:
10/4 = x
x = 2.5
So, the missing x-value is 2.5. Therefore, the coordinates are (2.5, 10).
he distance traveled by the red car is represented by the graph below. Click Here for Help Video.
The distance traveled by the blue car was monitored by a table. Click Here for Help Video.
Number of Hours
Miles Traveled
3
3
162
162
4
4
216
216
5
5
270
270
The speed of the red car is
miles per hour.
The speed of the blue car is
miles per hour.
The
car is faster.
To find the speed of the red car, we need to find the slope of the line representing the distance traveled. Looking at the graph, we can see that the red car traveled a distance of 216 miles in 4 hours.
Slope = Change in distance / Change in time
= (216 - 0) / (4 - 0)
= 216 / 4
= 54 miles per hour
So, the speed of the red car is 54 miles per hour.
To find the speed of the blue car, we can use the table provided. The table shows the number of hours and the miles traveled by the blue car. The blue car traveled a distance of 270 miles in 5 hours.
Slope = Change in distance / Change in time
= (270 - 0) / (5 - 0)
= 270 / 5
= 54 miles per hour
So, the speed of the blue car is also 54 miles per hour.
Since both cars have the same speed, neither car is faster.
Transform
9
�
+
−
4
�
=
−
6
9x+−4y=−6 into slope-intercept form (
�
=
�
�
+
�
y=mx+b ).
To transform the equation 9x + -4y = -6 into slope-intercept form (y = mx + b):
Step 1: Move the term with x to the other side of the equation:
-4y = -9x - 6
Step 2: Divide both sides of the equation by -4 to isolate y:
y = (-9x - 6)/-4
Simplifying the right side:
y = (9/4)x + 3/2
So, the equation 9x + -4y = -6 in slope-intercept form is y = (9/4)x + 3/2.
What is the unit rate if
7
7 bags of chip cost a total of
$
40.37
$40.37? Round your answers to the nearest hundredth.
The unit rate for bags of chips per dollar is
bags per $.
The unit rate of dollars per bag of chips is $
per bag.
To find the unit rate, we need to divide the total cost by the number of bags.
The unit rate for bags of chips per dollar is:
7 bags / $40.37 ≈ 0.173 bags per dollar
The unit rate of dollars per bag of chips is:
$40.37 / 7 bags ≈ $5.77 per bag
The distance traveled by the blue car is represented by
�
=
25
�
y=25x .
The distance traveled by the red car was monitored by a table.
Number of Hours
Miles Traveled
4
4
108
108
5
5
135
135
6
6
162
162
The speed of the blue car is
miles per hour.
The speed of the red car is
miles per hour.
The
car is faster.
To find the speed of the blue car, we can look at the equation y = 25x. Since the equation is in the form y = mx, where m represents the slope, the slope of this equation represents the speed.
In this case, the slope is 25. So, the speed of the blue car is 25 miles per hour.
To find the speed of the red car, we can use the table provided. The table shows the number of hours and the miles traveled by the red car.
For the red car:
- The distance traveled from 4 hours to 5 hours is 135 - 108 = 27 miles.
- The distance traveled from 5 hours to 6 hours is 162 - 135 = 27 miles.
We can see that the red car traveled a consistent distance in each hour, indicating a constant speed. Therefore, the speed of the red car is 27 miles per hour.
Since 27 miles per hour is greater than 25 miles per hour, the red car is faster.
Write the equation of the graph in the form of
�
=
�
�
+
�
y=mx+b that matches.
Line J
�
=
y=
�
+
x +
Line K
�
=
y=
�
+
x+
Line L
�
=
y=
�
+
x+