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kykrilka [37]
4 years ago
6

Graph on a coordinate plane each set of (x, y) values. Which set of values describes two quantities that are in a proportional r

elationship?
A) (2, 6)(0, 2)(3, 8)
B) (1, 4)(2, 7)(3, 10)
C) (0, 4)(2, 7)(3, 8.5)
D) (3, 5.1)(0, 0)(5, 8.5)
Mathematics
1 answer:
Ray Of Light [21]4 years ago
8 0

Answer:

(3, 5.1)(0, 0)(5, 8.5)

Step-by-step explanation:

A proportional relationship occurs only with a linear relationship that goes through the origin.

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6. What is the literal coefficient?<br>a. XYZ<br>b. 2xyz<br>C. XYZ<br>d. 2x​
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Solve 5x^2 - 7x + 2 = 0 by completing the square.
Reika [66]

Answer:  The correct option is (c) \dfrac{49}{100}.

Step-by-step explanation:  We are given to solve the following quadratic equation by the method of completing the square:

5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)

Also, we are to find the constant added on both sides to form the perfect square trinomial.

We have from equation (i) that

5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow  \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow  \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.

So,

x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.

Thus, the required solution is x=1,~-\dfrac{2}{5}. and the value of the constant added is \dfrac{49}{100}.

Option (c) is correct.

3 0
3 years ago
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