Graph the following lines and using the graph determine several values of x for which the graph is positive (negative): y=−4x+3
1 answer:
Answer:
Step-by-step explanation:
Given line is,
y=-4x+3
when, x=-1 , y=-4(-1)+3=4+3=7
when, x=0 , y=-4(0)+3=0+3=3
when, x=1 , y=-4(1)+3=-4+3=-1
So, we got the points (-1,7) , (0,3) , (1,-1)
Now, putting the points in the graph and adding them , we will get the graph of given line.
Please check image for the graph.
Now for the second part-
The graph is positive means- it will be above the x-axis, that is y value will be positive.
From the graph we can see that, if x<0 , then y is positive.
So, any value of x which is less than 0 , will give the positive graph here.
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Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P, where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000
→ Divide both sides by 3000
∴ =
→ Insert ㏑ in both sides
∵ ㏑( ) = ㏑(
)
→ Remember ㏑() = n
∴ ㏑( ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%
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Answer:
b ≈ 48.6°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin b = =
, then
b = (
) ≈ 48.6° ( to 1 dec. place )