Write in vertex form: y = x2 - 8x + 19

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Mission Control sends a signal to a Mars robot to travel to a mysterious rock 52.8 meters away. A return signal 59.0 minutes later tells scientists that the robot is at the rock. It took the signal 9.5 minutes to get from Earth to Mars, and the same time to get back. What was the robot’s average speed in meters per minute?

The response time includes the round-trip signal time plus the robot's travel time.
59 min = 2*(9.5 min) +travel time
59 min -2*(9.5 min) = travel time = 40 min

The speed is distance / travel time
speed = (52.8 m)/(40 min) = 1.32 m/min

The robot's average speed was 1.32 meters per minute.

Write the equation of a line that is perpendicular to x = 3 and that passes through the point ( 0 , − 4 )

We have to write the equation of a line that is perpendicular to the line and that passes through the point .

The general equation of a line in the slope-intercept form is given by:

Where, 'm' is the slope and 'b' is the y-intercept.

Now, we need to find the slope first,

The required line is perpendicular to the line . Slope of the line is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.

Therefore, m=0

Now that line is passing through the point .

We can plug in the points to the find the value of y-intercept. After plugging the values, we get:

Hence, the equation of the required line is .

Roger is measuring the length of a hanging spring as various weights are added to it. Using these measurements, he obtained the following regression equation: y = 0.006x + 11.5, where y is the length of the spring in centimeters and x is the mass added to the spring in grams. What is the meaning of the coefficient 0.006 in this equation?
a.)the stretch of the spring by a weight of 1 gram is 0.006 times of that caused by a weight of 11.5 grams
b.) the length of the spring increases by 0.006 cm for every gram added to it
c.) a weight of 6 grams stretches the spring by 1 cm
d.) a weight of 11.5 grams stretches the sprin by 0.006 cm

B.) the length of the spring increases by 0.006 cm for every gram added to it.

y = 0.006x + 11.50

where:
y = length of the spring in centimeters
x = mass added to the spring in grams
11.50 = the first number in the sequence
0.006 = the common difference among numbers in the sequence.

x       y
1      11.5 + 0.006(1) = 11.50 + 0.006 = 11.506
2      11.5 + 0.006(2) = 11.50 + 0.012 = 11.512
3      11.5 + 0.006(3) = 11.50 + 0.018 = 11.518
4      11.5 + 0.006(4) = 11.50 + 0.024 = 11.524
5      11.5 + 0.006(5) = 11.50 + 0.030 = 11.530

For every 1 gram added, the length of the string increases by 0.006cm

What is the sixth term in the addition pattern that begins with 15,29,43,57? A)61
B)71
C)85
D)99