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3 years ago

To solve the equation 2(x - 1) = 8, you use the_______ to rewrite 2(x - 1) as 2x - 2.

Mathematics

2 answers:

erastova [34]3 years ago

6 0

Answer:

the distributive property

ZanzabumX [31]3 years ago

4 0

Answer:5

Step-by-step explanation:

2(x-1)=8

divide both sides by 2

2(x-1) ➗ 2=8 ➗ 2

x-1=4

Add 1 to both sides

x-1+1=4+1

x=5

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What is the ratio of yellow sections to blue sections, in lowest terms?

ch4aika [34]

Answer:

the answer is B. 5 to 3

Step-by-step explanation:

bevause it is 5 yellows and 3 blues

4 0

3 years ago

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

Rewrite the expression in the form y^n

bazaltina [42]

Answer:

$y^6$

Step-by-step explanation:

$\frac{a^b}{a^c} = a^{b - c}$

Using this rule we have:

$\frac{y^{-7}}{y^{-13}} = y^{-7 -(-13)} = y^6$

6 0

3 years ago

Read 2 more answers

A rectangle sand box has a length of 5 and 1/3 feet and a width of 3 and 3/4 feet. What is the perimeter?

Varvara68 [4.7K]

Answer:

Perimeter of rectangle = ⇒ $18\frac{1}{6}$ feet

Step-by-step explanation:

Given:

Length of a rectangular sand box = $5\frac{1}{3}\ feet$

Width of the box = $3\frac{3}{4}\ feet$

Perimeter of a rectangle = $2(l+w)$

where $l$ represents length of rectangle and $w$ represents width of the rectangle.

Substituting values given for length and width.

Perimeter of sand box = $2(5\frac{1}{3}+3\frac{3}{4})\ feet$

Simplifying by adding fractions:

⇒ $2(5+3+\frac{1}{3}+\frac{3}{4})\ feet$ (Adding whole numbers and fractions separately)

⇒ $2(8+\frac{1}{3}+\frac{3}{4})$ feet

Whole number 8 can be written as $\frac{8}{1}$

⇒ $2(\frac{8}{1}+\frac{1}{3}+\frac{3}{4})$ feet

To add fractions we take LCD for the denominators 3,4,1.

LCD for 3 and 4 = 12 as its the least common multiple of 3,4,1.

Making denominators =12 by multiplying numerator an denominator with the corresponding numbers

⇒ $2(\frac{8\times 12}{1\times 12}+\frac{1\times 4}{3\times 4}+\frac{3\times 3}{4\times 3})$ feet

⇒ $2(\frac{96}{12}+\frac{4}{12}+\frac{9}{12})$ feet

Then we simply add numerators.

⇒ $2(\frac{96+4+9}{12})$ feet

⇒ $2(\frac{109}{12})$ feet

⇒ $2\times \frac{109}{12}$ feet

⇒ $\frac{218}{12}$ feet

Writing fraction as a mixed number by dividing 218 by 12 and writing quotient as whole number and remainder as numerator with divisor as denominator.

⇒ $18\frac{2}{12}$ feet

Simplifying fractions to simplest form.

⇒ $18\frac{1}{6}$ feet

Perimeter =⇒ $18\frac{1}{6}$ feet (Answer)

5 0

3 years ago

Jackie bicycles 9 kilometers west to get from her house to school. After school, she bicycles 12 kilometers north to her friend

klemol [59]

Answer:

21 kilometers!

Explanation: You add the two distances she rode her bicycle and add them together. 9+12 = 21kilometers!

8 0

3 years ago