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HACTEHA [7]
3 years ago
12

Gio weighed 5 boxes before he shipped them, the weights were: 52, 48, 48, 54, and 50 What statement is true

Mathematics
1 answer:
sweet [91]3 years ago
3 0
The mode is equal to the minimum
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Solve the following equation by factoring:9x^2-3x-2=0
olya-2409 [2.1K]

Answer:

The two roots of the quadratic equation are

x_1= - \frac{1}{3} \text{ and } x_2= \frac{2}{3}

Step-by-step explanation:

Original quadratic equation is 9x^{2}-3x-2=0

Divide both sides by 9:

x^{2} - \frac{x}{3} - \frac{2}{9}=0

Add \frac{2}{9} to both sides to get rid of the constant on the LHS

x^{2} - \frac{x}{3} - \frac{2}{9}+\frac{2}{9}=\frac{2}{9}  ==> x^{2} - \frac{x}{3}=\frac{2}{9}

Add \frac{1}{36}  to both sides

x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{2}{9} +\frac{1}{36}

This simplifies to

x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{1}{4}

Noting that (a + b)² = a² + 2ab + b²

If we set a = x and b = \frac{1}{6}\right) we can see that

\left(x - \frac{1}{6}\right)^2 = x^2 - 2.x. (-\frac{1}{6}) + \frac{1}{36} = x^{2} - \frac{x}{3}+\frac{1}{36}

So

\left(x - \frac{1}{6}\right)^2=\frac{1}{4}

Taking square roots on both sides

\left(x - \frac{1}{6}\right)^2= \pm\frac{1}{4}

So the two roots or solutions of the equation are

x - \frac{1}{6}=-\sqrt{\frac{1}{4}}  and x - \frac{1}{6}=\sqrt{\frac{1}{4}}

\sqrt{\frac{1}{4}} = \frac{1}{2}

So the two roots are

x_1=\frac{1}{6} - \frac{1}{2} = -\frac{1}{3}

and

x_2=\frac{1}{6} + \frac{1}{2} = \frac{2}{3}

7 0
2 years ago
4(5a-2b)-2(4a-5b)<br><br><br> Expand the brackets and simplify the question
Nutka1998 [239]

Answer:

12a+2b

Step-by-step explanation:

1. Expand by distributing terms.

20a-8b-2(4a-5b)20a−8b−2(4a−5b)

2. Expand by distributing terms.

20a-8b-(8a-10b)20a−8b−(8a−10b)

 3. Remove parentheses.

20a-8b-8a+10b20a−8b−8a+10b

4.Collect like terms.

(20a-8a)+(-8b+10b)(20a−8a)+(−8b+10b)

5. Simplify.

12a+2b12a+2b

6.Answer

12a+2b

6 0
3 years ago
Read 2 more answers
(4 + 18 ➗3) x 4 - 3 evaluate each expression
erastova [34]

Answer:

Step-by-step explanation:

(4 + 6) x 4 - 3

10 x 4 -3

40 -3

37

7 0
3 years ago
Read 2 more answers
What is the value of (12-5)^2+22-3
charle [14.2K]
Using PEMDAS, 12-5 is 7. 7^2 is 49. 49+22=71. 71-3=68.
8 0
3 years ago
Read 2 more answers
What are the solutions of the equation?
padilas [110]

Answer:

X:-5, 2

Step-by-step explanation:

If you factor the expression, it becomes (x+5)(x-2). In order to make each expression in the paranthesis equal to 0, x must be -5 or 2.

3 0
3 years ago
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