Given:
• AD = 3
,
• DC = 27
,
• BD = x + 3
Let's solve for x.
To solve for x, apply the altitude formula:
Where BD is the altitude.
Cross multiply:
Plug in the values and solve for x:
Take the square root of both sides:
Therefore, the value of x is 6 .
ANSWER:
d. 6
Let x = amount invested in 2% CD and y = amount invested in 3% CD
x + y = 60000
0.02x + 0.03y = 1600
SOLVE THE 1st EQUATION FOR x AND SUBSTITUTE RESULT IN 2nd
0.02(60000 - y) + 0.03y = 1600
1200 - 0.02y + 0.03y = 1600
0.03y = 400
y = 13333.34
x = 46666.66
The factor will result to answer which is D
Okay, so, to find out if an equation has one solution, an infinite number of solutions, or no solutions, we must first solve the equation:
(a) 6x + 4x - 6 = 24 + 9x
First, combine the like-terms on both sides of the equal sign:
10x - 6 = 24 + 9x
Now, we need to get the numbers with the variable 'x,' on the same side, by subtracting, in this case:
10x - 6 = 24 + 9x
-9x. -9x
______________
X - 6 = 24
Now, we do the opposite of subtraction, and add 6 to both sides:
X - 6 = 24
+6 +6
_________
X = 30
So, this particular equation has one solution.
(a). One solution
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(b) 25 - 4x = 15 - 3x + 10 - x
Okay, so again, we combine the like-terms, on the same side of the equal sign:
25 - 4x = 25 - 2x
Now, we get the 2 numbers with the variable 'x,' to the same side of the equal sign:
25 - 4x = 25 - 2x
+ 2x + 2x
________________
25 - 2x = 25
Next, we do the opposite of addition, and, subtract 25 on each side:
25 - 2x = 25
-25 -25
___________
-2x = 0
Finally, because we can't divide 0 by -2, this tells us that this has an infinite number of solutions.
(b) An infinite number of solutions.
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(c) 4x + 8 = 2x + 7 + 2x - 20
Again, we combine the like-terms, on the same side as the equal sign:
4x + 8 = 4x - 13
Now, we get the 'x' variables on the same side, again, and, we do that by doing the opposite of addition, which, is subtraction:
4x + 8 = 4x - 13
-4x -4x
______________
8 = -13
Finally, because there is no longer an 'x' or variable, we know that this equation has no solution.
(c) No Solution
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I hope this helps!
