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3 years ago

Can any kind soul help me ASAP!

Mathematics

1 answer:

Marina86 [1]3 years ago

4 0

Answer:

a) y= ⅔x -4

b) -4

Step-by-step explanation:

Please see the attached pictures for the full solution.

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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

List the integers that satisfy both these inequalities, 2x+9 -12

Flura [38]

Answer:

x < -10.5

Step-by-step explanation:

list the integers that satisfy both these inequalities, 2x+9 <-12

Subtract 9 from both sides;

2x +9 - 9 < -12-9

2x < -21

x < -21/2

x < -10.5

<em>Hence all the integers are values of x less than 10.5</em>

4 0

3 years ago

Kathy has 3/4 a yard of fabroc. She needs 3/10 of a yard for each doll dress she makes. How many doll dresses can she make

marishachu [46]

Kathy can make 2 doll dresses

5 0

3 years ago

Help me please I don’t understand

LuckyWell [14K]

Answer:

14/11

Step-by-step explanation:

A rational number times a rational number is rational

A rational number is written as a/b

14/11 * 1/2 = 7/11

This is rational

8 0

3 years ago

Which conditional has a true converse? Select all that apply

Andrej [43]

The answer is b I hope this helps

3 0

3 years ago

Can any kind soul help me ASAP!​

Can any kind soul help me ASAP!