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2 years ago

Evaluate the expression a + c for a = 22 and c = 11.

Mathematics

2 answers:

sineoko [7]2 years ago

8 0

For this case we have the following expression:

$a + c$

We must evaluate the expression when it takes the value of 22 and when c takes a value of 11.

$a = 22\\c = 11$

Substituting the values we have:

$22 + 11$

Equal signs are added and the same sign is placed:

$22 + 11 = 33$

Answer:

bixtya [17]2 years ago

4 0

Answer: 33

Step-by-step explanation: substitute a with 22 and c with 11.

22+11=33

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2 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

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$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

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Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

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$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

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$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

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Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

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