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3 years ago

8

Kathy's fish tank has many different kinds of fish. In particular 1/6 of the fish are testras, and 2/5 of the fish are guppies.

What fraction of kathy's fish are either testras or guppies?

1 answer:

madam [21]3 years ago

7 0

17/30 of her fish are either testras or guppies :)

(1/6) + (2/5)
(5/30) + (12/30) = 17/30

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3 years ago

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3 years ago

The standard form of the equation of a parabola is y= x2 - 6x + 14.

Bas_tet [7]

<h3><u>Option C</u></h3><h3><u>The vertex form of the equation is:</u></h3>

$y = (x - 3)^2 + 5$

<em><u>Solution:</u></em>

<em><u>The vertex form of equation is given as:</u></em>

$y = a(x- h)^2 + k$

Where, (h, k) is the vertex

Given that,

$y = x^2 - 6x + 14$

We have to find the vertex form of equation

Step 1:

Complete the square for $x^2 - 6x + 14$

$\text{ Use the form } ax^2 + bx + c \text{ to find values of a, b, c }$

a = 1

b = -6

c = 14

Consider the vertex form of a parabola.

$a(x + d)^2 + e ----- eqn 1$

Substitute the values of a and b into following:

$d = \frac{b}{2a}\\\\d = \frac{-6}{2 \times 1}\\\\d = -3$

Find the value of "e" using following formula:

$e = c - \frac{b^2}{4a}\\\\e = 14 - \frac{(-6)^2 }{4 \times 1}\\\\e = 14 - 9\\\\e = 5$

Substitute the values of a, d, e in eqn 1

$y = 1(x -3)^2 + 5\\\\y = (x - 3)^2 + 5$

Thus vertex form form is found. Option C is correct

3 0

3 years ago

Find the slope of the line passing through the points(-6,-5)and (4,4)

sertanlavr [38]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -6 &,& -5~) 
% (c,d)
&&(~ 4 &,& 4~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{4-(-6)}\implies \cfrac{4+5}{4+6}\implies \cfrac{9}{10}$

6 0

4 years ago

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