160% of 30 what is the number???

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

1/2 +b=1 3/4 <br><br> What does b represent and how to solve it?

LenKa [72]

Answer:

b= 5/4 or 1 1/4

Step-by-step explanation:

First I will make 1 3/4 into an improper fraction

1/2 + b = 7/4

Then I will make the fractions have common denominators

2/4 + b = 7/4

I subtract 2/4 from 7/4

b= 5/4

5 0

3 years ago

Read 2 more answers

An oil tank is leaking into a lake at a rate of 0.1 m3/day. The oil slick forms a semicircular disk whose center is at the leak

gregori [183]

Answer:

17.9 m/s

Step-by-step explanation:

Volume of the slick = 0.5 x π r² h--------------------------------- (1)

Where r = radius of slick

h = thickness of slick, 10⁻⁶m

If 0.5m³ of oil leaked, then the radius of the semicircular slick can be calculated from equation (1)

V = 0.5 x π r² h

0.5= 0.5 x π x r² x 10⁻⁶

r² = 10⁶/ π

r = 10³/√π

dV/dt = πrh dr/dt + 0.5π r² dh/dt----------------------------------- (2)

Asumming the film thickness is constant , equation (2) becomes

dV/dt = πrh dr/dt-------------------------------- (3)

dV/dt = 0.1m³/day

r= 10³/√π

dr/dt= rate of expansion of the slick

Substituting into (3);

0.1 = π x 10³/√π x 10⁻⁶ x dr/dt

dr/dt = 0.1 x 10⁶/ ( π x 10³/√π)

= 17.9479 m/s

≅ 17.9 m/s

8 0

3 years ago

Vu has 2 pizzas that he cuts into sixths how many 1/6-size pizzas does he have?

const2013 [10]

12 slices in total (6 slices per pizza)

8 0

2 years ago

Read 2 more answers

Can someone please help me with all of these problems. They are a ton of them and they are due tomorrow. PLEASE AND THANK YOU

Masteriza [31]

15. $\frac{x}{5} - g = a$

Add "g" on both sides

$\frac{x}{5} = a +g$

Multiply 5 on both sides to get x by itself

x = 5(a + g)

x = 5a + 5g

18. a = 3n + 1

Subtract 1 on both sides

a - 1 = 3n

Divide 3 on both sides to get n by itself

$\frac{a - 1}{3} = \frac{a}{3} -\frac{1}{3}$ = n

21. M = T - R

Add "R" on both sides to get "T" by itself

M + R = T

24. 5p + 9c = p

Subtract "5p" on both sides

9c = p - 5p

9c = -4p

Divide 9 on both sides to get "c" by itself

c = $\frac{-4p}{9}$ or c = $\frac{-4}{9} p$

27. 4y + 3x = 5

Subtract "4y" on both sides

3x = 5 - 4y

Divide 3 on both sides to get "x" by itself

x = $\frac{5-4y}{3}$

x = $\frac{5}{3} -\frac{4y}{3}$

7 0

2 years ago