A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system.
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Please give brainliest!
Answer:
Step-by-step explanation:
The way I figured this out is to just pick some starting values for the grams of this element and plug them into the formula using t = 1 day and seeing how much is left. I chose 2 different starting amounts and came up with the same percentage each time, so it must be correct! Here's what I did:
First I chose a starting amount, a, of 10 grams. Plugging into the formula:
and got that the amount LEFT was 9.5 grams
Then I chose a starting amount, a, of 20 grams. Plugging into the formula:
and got that the amount LEFT was 19 grams.
I then asked the algebraic question,"What percent of 10 is 9.5?" which translates to
x% * 10 = 9.5 and
x = 95% (that's the amount left as a percentage).
and
x% * 20 = 19 and
x = 95%
Since both of those came out the same, that tells me that after 1 day there is still 95% of the element remaining, so 5% decays each day.
We determine the minimum and maximum scores that Juan needs to get in order to be within the strict average range. We let x be his score.
minimum:
74 = (82 + x) / 2
The value of x from the equation is equal to 66.
maximum:
80 = (82 + x )/2
The value of x from the equation is equal to 78.
Hence, Juan's score should fall between 66 and 78, inclusive.
Answer: <em> 66 ≤ x ≤ 78</em>
Suppose that it will take n years for Dave's investment to be equal to Len's;
thus using the compound interest formula we shall have:
A=p(1+r/100)^n
thus the investment for Len after n year will be:
A=5200(1+3/100)^n
A=5200(1.03)^n
The total amount Dave's amount after n years will be:
A=3600(1+5/100)^n
A=3600(1.05)^n
since after n years the investments will be equal, the value of n will be calculated as follows;
5200(1.03)^n=3600(1.05)^n
5200/3600(1.03)^n=(1.05)^n
13/9(1.03)^n=(1.05)^n
introducing the natural logs we get:
ln(13/9)+n ln1.03=n ln 1.05
ln(13/9)=n ln 1.05-n ln 1.03
ln(13/9)=0.0192n
n=[ln(13/9)]/[0.0192]
n=19.12
thus the amount will be equal after 19 years
Hi there!
Angles of perpendicular lines are always 90 degrees.
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