Answer:
Gina is 12 years old
Step-by-step explanation:
First, we will have to write these statements mathematically and then solve.
Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.
The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)
The next statement "Gina's brother is half Gina's age" can be mathematically written as y =
---------------------------------------(2)
Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)
We can now proceed to solve;
Substitute equation (1) and equation(2) into equation (3)
x + y + z = 42
x +
+ 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
= 
x = 12
Therefore, Gina is 12 years old
<h3>
Answer: 6.93</h3>
Work Shown:
Use the pythagorean theorem to find x
a^2 + b^2 = c^2
x^2 + 11^2 = 13^2
x^2 + 121 = 169
x^2 = 169 - 121
x^2 = 48
x = sqrt(48)
x = 6.92820323027551
x = 6.93
The ordered pairs of the solution to the system of equation are [(3, 6), (-3, 18)]
<h3>System of equations</h3>
Given the following system of equations expressed as:
f(x) = x² - 2x + 3 and f(x) = -2x + 12
Since they are both function of x, hence;
x² - 2x + 3 = -2x + 12
x² - 2x + 3 + 2x - 12 = 0
x² - 9 = 0
x² = 9
x = ±√9
x = ±3
If x = 3
f(x) = -2(3) + 12
f(x) = 6
If x = -3
f(x) = -2(-3) + 12
f(x) =18
Hence the ordered pairs of the solution to the system of equation are [(3, 6), (-3, 18)]
Learn more on system of equation here: brainly.com/question/14323743
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Answer:
<em>Solution in the attachment above..</em>
<h3>
<em><u>Hope it helps uh. !!!</u></em></h3><h2 /><h2>
<em><u>Stay</u></em><em><u> </u></em><em><u>Safe</u></em><em><u>!</u></em></h2>