Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
+ = 1 ( multiply through by 2 to clear the fractions )
x + y = 2 ( subtract x from both sides )
y = - x + 2 ← in slope- intercept form
(a) with slope m = - 1
(b) with y- intercept c = 2
(c)
Parallel lines have equal slopes, thus
y = - x + c ← is the partial equation of PQ
To find c substitute (2, - 8) into the partial equation
- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6
y = - x - 6 ← equation of PQ
To show (- 1, - 5) lies on PQ, substitute x = - 1 into the equation and evaluate for y.
y = - (- 1) - 6 = 1 - 6 = - 5 ← the given y- coordinate
Thus PQ passes through (- 1, - 5 )
The value of given expression when m = 3 is 27
<h3><u>Solution:</u></h3>
Given expression is
We have to evaluate the given expression for m = 3
To find for m is equal to 3, substitute m = 3 in given expression
From given expression,
Plug in m = 3 in above expression
------ eqn 1
We know that,
can be expanded as,
Applying this in eqn 1, we get
Simplify the above expression
Therefore, for m = 3 we get,
Thus value of given expression when m = 3 is found
When rates<span> are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called </span>unit rates<span>. To determine the rate, we just divide the distance traveled by the time it takes. Therefore, the rate of the plane would be
rate = 256 / 30(1/60) = 512 miles per hour</span>
Answer:
Rounded to the nearest thousand is better
Step-by-step explanation:
Well if you round to the nearest thousand then it’s 17,000. But if you round to the nearest ten thousand then it would be 20,000. So to find which is more accurate just subtract the original number from the rounded number. So the one rounded to the thousand would be off by 150 whic isn’t bad, but when you subtract the one Rounded to the nearest ten thousand then it would be off by 3150 which is way off. So rounding to the nearest thousandth is the better choice.
Time spent on aerobics is 150 minutes per week and time spent on weight training is 100 minutes per week
Solution:
Given that,
Kay spends 250 min/wk exercising
Therefore,
Exercising = 250 minutes per week
Ratio of time spent on aerobics to time spent on weight training is 3 to 2
Aerobics : weight training = 3 : 2
Let the time spent on aerobics be 3x
Let the time spent on weight training be 2x
Thus,
3x + 2x = 250
5x = 250
x = 50
Thus,
Time spent on aerobics = 3x = 3(50) = 150
Time spent on weight training = 2x = 2(50) = 100
Thus, Time spent on aerobics is 150 minutes per week and time spent on weight training is 100 minutes per week