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3 years ago

Find the missing number of each unit rate. 28/7 = ?/1. and 60/12 = ?/1

Mathematics

2 answers:

Lerok [7]3 years ago

6 0

Answer:

28/7=4 and 60/12=5

Step-by-step explanation:

Zanzabum3 years ago

6 0

Answer:

$\frac{28}{7} = \frac{4}{1} \\\\\frac{60}{12} = \frac{5}{1}$

Explanation: 28 is divisible by 7, when multiplied by 4.

60 is divisible by 12, when multiplied by 5.

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when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3><u>Solution:</u></h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = $a^2$

6 is subtracted from the square of a number = $a^2 - 6$

5 times the number = $5 \times a$

<em><u>So we can frame a equation as:</u></em>

6 is subtracted from the square of a number = 5 times the number

$a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0$

<em><u>Let us solve the above quadratic equation</u></em>

For a quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here in this problem,

$a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6$

Substituting the values in above quadratic formula, we get

$\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}$

We have two solutions for "a"

$\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}$

We have asked negative solution. So a = -1

Thus the negative solution is -1

6 0

3 years ago

13.Simplify the expression below.<br> <img src="https://tex.z-dn.net/?f=%5Csqrt%7B256%7D" id="TexFormula1" title="\sqrt{256}" al

Marina86 [1]

16 because if you multiple 16*16 it would give you 256

7 0

3 years ago

Read 2 more answers

What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.

antiseptic1488 [7]

Check the picture below. So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

$\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5$