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qwelly [4]
3 years ago
9

5 times the difference of 29 and a number is 215. Which equation below can be used to find the unknown number?

Mathematics
2 answers:
Verdich [7]3 years ago
8 0
Is it multiple choice? If not I would say 215=5(x)-29
Ilia_Sergeevich [38]3 years ago
3 0

Answer:

The required equation is 5(29-n)=215

Step-by-step explanation:

Given : 5 times the difference of 29 and a number is 215.

To find :  Which equation can be used to find the unknown number?

Solution :

Let the number be 'n'.

The difference of 29 and a number i.e. 29-n

5 times the difference of 29 and a number i.e. 5(29-n)

5 times the difference of 29 and a number is 215 i.e. 5(29-n)=215

Therefore, the required equation is 5(29-n)=215

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Step-by-step explanation:

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Parabola equation:

y=ax^2 +bx+c

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x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a

Equation:

y=ax^2 -2ax+c

The y-coordinate of the vertex:

y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10

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

Solve:

c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}

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

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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.

7 0
3 years ago
Read 2 more answers
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