Step-by-step explanation:
thats is all,just subject of formula
Brainlieat.
1 answer:
So for this, we will be doing a system of equations, with one equation representing the total invested and the other equation representing the total gained from the investments. But first, we have to do calculations:
firstly, to represent a percentage gain (in this case 12% gain) you are to add 0.12 (12% in decimal form) to 1 to get 1.12. <em>Keep 1.12 in mind, as it will be used for the equations.</em>
Next, to represent a percentage loss (in this case 11%), you are to subtract 0.11 (11% in decimal form) from 1 to get 0.89. <em>Keep 0.89 in mind, as it will be used in the equations.</em>
Next, we need to find the total amount of money after the investments. To do this, add 21,000 and 1,715 together to get 22,715. <u>$22,715 is the total amount of money gained in 1 year.</u>
Now that we have all of our information, we can form our equations as such:
- Let x = $ invested into the account with 12% gain and y = $ invested into the account with 11% loss
Now with these system of equations, I will be using the substitution method. So firstly, with the first equation subtract x on both sides of that equation:
Now that we know that y = 21000 - x, replace y for (21000 - x) in the second equation and solve for x as such:
Now that we have the value of x, substitute it into either equation to solve for y:
<u>In short, $17500 was invested into the account that gained 12% and $3500 was invested into the account that had lossed 11%.</u>
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Answer:
Step-by-step explanation:
Let a be the length of the altitude, then from the given triangles, applying the basic proportionality theorem, we get
⇒
⇒
⇒
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Thus, the length of altitude is: 12 cm.
Now,
⇒
⇒
Also,
⇒
⇒
Thus, the lengths of the legs of this triangle are 14.83 and 20 cm.
Problem 5
The function is continuous for the given domain
This is because y = (-5/6)x+5 is itself continuous, and any interval subset of this function is also continuous. We can plug in any real number that is equal to 6 or larger, and get some y output. If we plugged in x = 6, then we'd get
y = (-5/6)x+5
y = (-5/6)*6 + 5
y = -5+5
y = 0
This is the largest y value possible. Why? Because y = (-5/6)x+5 has a negative slope, so the graph is going downhill as you read it from left to right. As x gets bigger, y gets smaller. The smallest x value allowed in the domain produces the largest y value in the range. There is no smallest y value as the y values keep going down forever.
The range is therefore
In interval notation, you can write the range as . The square bracket indicates "include this endpoint as part of the range".
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Problem 6
The function is discrete for this given domain. The domain itself is a discrete list of values. We cannot plug in values between say 0 and 2. We can only substitute one of those values from the list given. Consequently, the y values will also be a list, and not an interval like problem 5 had.
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If you plugged in x = -4, then you should get...
y = (-1/2)*(-4)+2
y = 2+2
y = 4
So the input x = -4 lead the output y = 4
Repeat for x = -2
y = (-1/2)x+2
y = (-1/2)*(-2)+2
y = 1+2
y = 3
and the same for x = 0 as well
y = (-1/2)x+2
y = (-1/2)*0 + 2
y = 0 + 2
y = 2
and x = 2 also
y = (-1/2)x+2
y = (-1/2)*2 + 2
y = -1+2
y = 1
Finally, plug in x = 4
y = (-1/2)x+2
y = (-1/2)*4+2
y = -2+2
y = 0
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If we plugged each of these x values {-4, -2, 0, 2, 4} one at a time into the equation y = (-1/2)x+2, then we get this list of values {4, 3, 2, 1, 0}
Sorting the values from smallest to largest, we have this range {0, 1, 2, 3, 4}