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3 years ago

What are the solutions of 12 – x2 = 0?

Mathematics

1 answer:

Kruka [31]3 years ago

5 0

Answer:

x = ± 2 $\sqrt{3}$

Step-by-step explanation:

Given

12 - x² = 0 ( add x² to both sides )

12 = x² or

x² = 12 ( take the square root of both sides )

x = ± $\sqrt{12}$

= ± $\sqrt{4(3)}$ = ± 2 $\sqrt{3}$

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Consider three consecutive positive integers, such that the sum of the

Greeley [361]

Answer:

Step-by-step explanation:

Let x represent the smaller integer. Then we have ...

(x +1)² +(x +2)² = 40x +5

2x² +6x +5 = 40x +5

x² -17x = 0 . . . . . subtract (40x+5), divide by 2

x(x -17) = 0 . . . . . factor

The solution of interest is x = 17.

The smaller integer is 17.

4 0

3 years ago

Solve this equation. <br> Leave the answer as an improper fraction. <br> 3x^2 + 2 = 11 - x^2

Nikolay [14]

Answer:

$x = \frac{3}{2}orx=-\frac{3}{2}$

Step-by-step explanation:

The given Equation is

$3x^{2} + 2 = 11-x^{2}$ .................(i)

Adding ( $x^{2} -11$ ) on both sides of (i)

$3x^{2}+2+x^{2}-11 = 11-x^{2}+x^{2}-11$

solving and cancelling out the terms will give

⇒ $4x^{2} -9=0$

⇒ $(2x)^{2} -(3)^{2} = 0$ ...................(ii)

Now we Know that

$(a)^{2} -(b)^{2} = (a-b)(a+b)$

Applying this on equation (ii)

$(2x-3)(2x+3)=0$

This will lead us to

Either 2x-3 =0 .......(iii) or 2x+3=0 ..........(iv)

Solving equation (iii) for value of x

2x - 3 =0

adding 3 on both sides

2x -3 +3 = 0+ 3

2x = 3

Cross multiplying gives

$x=\frac{3}{2}$

Solving equation (iv) for value of x

2x + 3 =0

adding -3 on both sides

2x -3 +3 = 0- 3

2x = -3

Cross multiplying gives

$x=\frac{-3}{2}$

so $x=\frac{3}{2}$ and $x=\frac{-3}{2}$

7 0

3 years ago

What is 1 7/8 times 5/6

hoa [83]

$Solution, 1\frac{7}{8}\cdot \frac{5}{6}=1\frac{9}{16}\quad \left(\mathrm{Decimal:\quad }\:1.5625\right)$

$Steps:$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 1\frac{7}{8}=\frac{15}{8}, =\frac{15}{8}\cdot \frac{5}{6}$

$\mathrm{Cross-cancel\:common\:factor:}\:3, =\frac{5}{8}\cdot \frac{5}{2}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}, =\frac{5\cdot \:5}{8\cdot \:2}$

$\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25, =\frac{25}{8\cdot \:2}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:2=16, =\frac{25}{16}$

$\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{25}{16}=1\frac{9}{16}, =1\frac{9}{16}$

Hope this helps!!!

3 0

3 years ago

How are sets and subsets related

nikklg [1K]

Answer:

Step-by-step explanation:

A set is a well-defined collection of objects. Each object in a set is called an element of the set. Two sets are equal if they have exactly the same elements in them. ... If every element in Set A is also in Set B, then Set A is a subset of Set B

6 0

3 years ago

Please type up your word problem in the box below and then solve it in your notebook so that you have an answer key for your wor

Alik [6]

You have to create your own word problem based off what Uu guys learned in class

6 0

3 years ago