What line intersects two other complaner lines in different points
2 answers:
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Answer:
Part 1) The rate of change is the amount of money saved by week
Part 2) The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.
Part 3) see the explanation
Step-by-step explanation:
see the attached figure to better understand the problem
<u><em>The complete question is</em></u>
Part 1) What does the rate of change in the example represent?
Part 2) What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?
Part 3) Write ordered pairs for the initial values of each function. Tell what the initial values represent
Part 1) we know that
The rate of change is the slope or unit rate of the linear equation
The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)
In this context the rate of change is the amount of money saved by week
Part 2) we know that
Alyssa’s rate of change is equal to $8 per week
Sarah’s rate of change is equal to $6 per week
That means ----> The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.
Part 3) we know that
The initial value or y-intercept is the value of y when the value of x is equal to zero
In this context , the initial value is the amount of money available at the time of beginning to save
so
<em>Sarah's Savings</em>
Looking at the graph
The initial value is the point (0,8)
That means ----> At the beginning (x=0), Sarah already had $8 saved.
<em>Alyssa's Savings</em>
Looking at the graph
The initial value is the point (0,0)
That means ----> At the begin (x=0), Alyssa had nothing saved.
Distance traveled in clear weather = 50 miles
Distance traveled in thunderstorm = 15 miles
Let speed in clear weather = x
⇒ Speed in thunderstorm = x-20
Total time taken for trip = 1.5 hours
We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).
Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm
⇒ Total time taken for trip = +
⇒ 1.5 = +
⇒ 1.5 =
⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]
⇒ 15x² - 300x = 500x - 10,000 + 150x
⇒ 15x² - 300x = 650x - 10,000
⇒ 15x² - 950x + 10,000 = 0
⇒ 3x² - 190x + 2,000 = 0
The above equation is in the format of ax² + bx + c = 0
To determine the roots of the equation, we will first determine 'D'
D = b² - 4ac
⇒ D = (-190)² - 4*3*2,000
⇒ D = 36,100 - 24,000
⇒ D = 12,100
Now using the D to determine the two roots of the equation
Roots are: x₁ = ; x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = 50 and x₂ = 13.33
So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.
If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.
Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.
Refer to the diagram below.
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°