I need help the time is limited pls what’s the answer
1 answer:
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Answer:
In 2026 car will have a value of $5,000.
Step-by-step explanation:
We have been given that Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year.
Since we know that an exponential function is in form: , where,
a = Initial value,
b = For decay or decrease b is in form (1-r), where r represents decay rate in decimal form.
Let us convert our given decay rate in decimal form.
Upon substituting a =28,000 and r=0.14 in exponential decay function we will get,
, where x represents number of years after 2014.
Therefore, the function represents the value of car x years after 2014.
To find the number of years it will take to car have the value of $5,000, we will substitute y=5,000 in our function.
Let us divide both sides of our equation by 28,000.
Let us take natural log of both sides of our equation.
Using natural log property we will get,
As in the 12th year after 2014 car will have a value of $5,000, so we will add 12 to 2014 to find the year.
Therefore, in 2026 car will have a value of $5,000.
Answer:
1) Reflection in the x-axis
A' = (-2, -3)
2) Rotation of 180° clockwise about the origin
A'' = (2, 3)
3) Translation of 3 units down and 4 units to the right
A''' = (6, 0)
Step-by-step explanation:
The transformations are as follows;
1) Reflection in the x-axis
Here the x-coordinate is the same and the y-coordinate changes sign.
Therefore, we have;
A (-2, 3)
After reflection in the x-axis becomes A' = (-2, -3)
2) Rotation of 180° clockwise about the origin
When, a point (x, y) is rotated 180° clockwise about the origin, it becomes (-x, -y)
Therefore, we have;
A' = (-2, -3) becomes A'' = (2, 3)
3) Translation of 3 units down and 4 units to the right
Translation of 3 units down and 4 units to the right =
Which gives
A''' = (2 + 4, 3 - 3) = (6, 0).
Answer:
7/60
Step-by-step explanation:
Because the question is phrased such that it asks "the ratio of time with father <em>to...."</em>, we know to put the time with father on top, or first. Similarly, since it is asked to put the ratio of time with the father to the time in daycare, we can put the daycare amount second/on the bottom. Therefore, we can write the ratio as
(42 minutes)/(6 hours)
To make both of these in terms of minutes to simplify it, we know that 60 minutes = 1 hour, so 1 hour / 60 minutes =1 . Since multiplying something by 1 keeps it the same, we can multiply our ratio by this amount. We want to multiply with the hour on top so the hours cancel out, as so:
To simplify this even further, we can note that 6 is a factor of both 42 and 360*, so we can multiply this fraction by (1/6) / (1/6) to get
(42/360) * (1/6)/(1/6) = 7/60 as our final answer
If this doesn't come up immediately, you can always find the greatest common factor by listing the factors of each number and finding the highest one that fits both, e.g.
for 42: 42, 21, 14, 7 , 6...
for 360: 360,180, ... 6,5....