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vlabodo [156]
3 years ago
14

Solve this equation using all three methods 4x^ = 9

Mathematics
1 answer:
Bumek [7]3 years ago
3 0

Answer:

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

Step-by-step explanation:

(1)       To solve by factoring,

Given equation: 4 x^{2}=9

Subtract 9 from both sides of the equation.

\begin{aligned}&4 x^{2}-9=9-9\\&4 x^{2}-9=0\\&(2 x)^{2}-3^{2}=0\\&(2 x-3)(2 x+3)=0\end{aligned}

Using zero factor principle, 2 x-3=0,2 x+3=0

The solutions are x=-\frac{3}{2}, x=\frac{3}{2}.

(2) To solve by complete the square ,

Given 4 x^{2}=9

Divide both sides of the equation by 4.  

\frac{4 x^{2}}{4}=\frac{9}{4}  

\Rightarrow x^{2}=\frac{9}{4}  

Square root on both sides.

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

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

(3) To solve by quadratic formula,  

$4 x^{2}-9=0$

Here, a = 4, b = 0, c = –9

Quadratic formula, $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

x=\frac{-0 \pm \sqrt{0^{2}-4 \times 4 \times(-9)}}{2 \times 4}

\begin{aligned}&\Rightarrow x=\frac{\pm \sqrt{144}}{8}\\&\Rightarrow x=\pm \frac{3}{2}\\&\Rightarrow x=\frac{3}{2}, x=-\frac{3}{2}\end{aligned}

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navik [9.2K]
First things to take note of to have the correct answer: 
1. Adam's sister is obviously a girl. Then when looking at the data we look at the "Women" column. 
2. We are only looking at the fats data. 

We are asked for the percentage given 48 grams of fat and the daily allowance on fat for women is 70 g. To solve we perform the operation: 

% =  \frac{70-48}{70} * 100 = 31.42% ≈ 31%
3 0
3 years ago
The sum of two numbers x and y is 18 and their difference is 14. how is that written as an equation
MrRa [10]

Answer:

16 and 2

Step-by-step explanation:

16+2=18

16-2=14

5 0
2 years ago
Extra points to the person who answer first
vlada-n [284]

In order to know what is the reasonable amount of tile for Mandana to order, you have to divide the choices with the area of the floor and deduct with 1 and multiply by 100. You have to assess if the answer you will get will fall between 15% and 20% which is the goal of Mandana.

<span>a.       </span>131/116.9 = (1.1206 – 1) x 100 = 12.06%, this does not fall between 15% and 20%

<span>b.      </span>138/116.9 = (1.1805 – 1) x 100 = 18.05%, this fall between 15% and 20%

<span>c.       </span>133/116.9 = (1.1377 – 1) x 100 = 13.77%, this does not fall between 15% and 20%

<span>d.      </span>141/116.9 = (1.2062 – 1) x 100 = 20.62%, this does not fall between 15% and 20%

Therefore, the reasonable amount of tile for Madana to order that is between 15% and 20% extra of the materials is 138 square feet.

4 0
3 years ago
In a classic Conan Doyle story, Sherlock Holmes solves a crime mystery by recognizing that a guard dog didn't bark. Therefore, t
ohaa [14]

Answer:

G. Modus tollens

Step-by-step explanation:

This question used the inference called modus tollens.

Modus tollens is a a valid form of argument that is of this form below:

<em>If S, then T</em>

<em>i</em><em>f not S, then not T.</em>

S = dog doesn't know perpetrator

Not S = dog knows who the perpetrator is

T = the dog barked

Not T = the dog did not bark.

So if we put this into the statement in bold letters, we would have:

The dog doesn't know perpetrator, so it barked.

And,

The dog didn't bark, so it knows the perpetrator.

3 0
3 years ago
-77x - 78x = -155x
FromTheMoon [43]

Answer:

I don't understand

Step-by-step explanation:

You answer it.

6 0
3 years ago
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