Answer:
48 kg
Step-by-step explanation:
The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.
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<h3>setup</h3>
Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...
x/y = 8/9
After the changes in weight, they were equal:
x+2 = y-4
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<h3>solution</h3>
Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.
y = x +6 . . . . . . . . . . solve the second equation for y
x/(x+6) = 8/9 . . . . . . substitute for y in the first equation
9x = 8(x +6) . . . . . . . multiply by 9(x+6)
x = 48 . . . . . . . . . . . simplify and subtract 8x
Jane weighed 48 kg at first.
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<em>Alternate solution</em>
The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.
(This mental solution is virtually the same as the solution using equations shown above.)
Well the answer is 12-14=%58=x
Answer:
a = √93
a ≈ 9.64
Step-by-step explanation:
We can use the Pythagorean theorem for this: a² + b² = c²
c is given as the hypotenuse, which is the pole with a length of 17 ft
c² is 17²
b is a leg with a height of 14 ft
b² = 14²
We need to find the base leg, a, distance from the wall to the base of the pole.
Solve:
a² + 14² = 17²
a² + 196 = 289
a² = 93
a = √93
-Chetan K
Answer:
Step-by-step explanation:
x=180-59-41
x=80
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to <em>eliminate</em> a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make <em>one</em> of the 9x's <em>negative</em>. To do this, multiply <em>each term</em> in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
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0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!
