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3 years ago

2x2 - 3x - 2 = x + 4.check all of the solutions to this equation.-137(–1, 3)(3, 7)

Mathematics

2 answers:

g100num [7]3 years ago

6 0

Answer:

The correct option is: (-1, 3)

Step-by-step explanation:

The given equation is: $2x^2-3x-2=x+4$

First we will move all terms to the left side and make the right side as zero. So......

$2x^2-3x-2-x-4=0\\ \\ 2x^2-4x-6=0$

Now, we can divide both sides of this equation by 2. So, we will get......

$\frac{2x^2-4x-6}{2}=\frac{0}{2}\\ \\ x^2-2x-3=0$

Factoring out the left side..........

$x^2-2x-3 =0\\ \\ (x-3)(x+1)=0$

Now, using zero-product property, we will get.........

$x-3=0\\x=3\\ \\and\\ \\ x+1=0\\ x=-1$

So, the solutions to the equation will be: (-1, 3)

Eduardwww [97]3 years ago

6 0

Answer:

-1 and 3

Step-by-step explanation:

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(3x2 + 10x + 3) by (x + 3)

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Explanation: 3 x 2 + 10 x + 3 We can Split the Middle Term of this expression to factorise it. In this technique, if we have to factorise an expression like a x 2 + b x + c , we need to think of 2 numbers such that: N 1 ⋅ N 2 = a ⋅ c = 3 ⋅ 3 = 9 and, N 1 + N 2 = b = 10 After trying out a few numbers we get: N 1 = 9 and N 2 = 1 9 ⋅ 1 = 9 , and 9 + ( 1 ) = 10 3 x 2 + 10 x + 3 = 3 x 2 + 9 x + 1 x + 3 = 3 x ( x + 3 ) + 1 ( x + 3 ) ( 3 x + 1 ) ( x + 3 ) is the factorised form for the expression.

c
, we need to think of 2 numbers such that:
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and,
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After trying out a few numbers we get:
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=
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, and
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is the factorised form for the expression.

6 0

2 years ago

Find the volume of the cone. Round your answer to the nearest tenth if necessary. Use 3.14 for π.

CaHeK987 [17]

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3 years ago

Read 2 more answers

The data given below contain the state cigarette taxâ€‹ (in $) for all 20 regions of a country.

g100num [7]

Answer:

(a) $\bar x= 1.583$ -- Population Mean

(b) $s = 1.032$ --- Population standard deviation

Step-by-step explanation:

Given:

Cigarette tax for 20 regions

Solving (a): The population mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

$\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84$

$\sum x = 31.66$

$n = 20$

So, we have:

$\bar x= \frac{31.66}{20}$

$\bar x= 1.583$

Solving (b): The population standard deviation

This is calculated as:

$s = \sqrt{\frac{\sum( x - \bar x)^2}{n}$

$\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2$