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Ronch [10]
3 years ago
15

Solve the quadratic equation 6x^2-13x-28=0 by factoring.

Mathematics
1 answer:
mixer [17]3 years ago
6 0

First step to factor the trinomial, multiply the constant -28 with the leading coefficient 6.

So, -28 * 6 = - 168.

Next step is to breakdown -168 into two multiples so that their addition will result the coefficient of w= - 13.

So, -168 = -21 * 8.

And addition of - 21 and 8 will give - 13.

So, next step is to replace -13x with -21x + 8. Therefore,

6x² - 21x + 8x - 28 =0

(6x² - 21x) + (8x - 28 )=0 Make the group of two terms.

3x (2x - 7) + 4 (2x - 7) = 0 Take out the common factor from each group.

(2x - 7)(3x + 4) = 0 Again take out the common factor (2x -7).

So, 2x - 7 =0, 3x + 4 = 0 Set both the factor equal to 0.

2x = 7 , 3x = -4

So, x= \frac{7}{2} , -\frac{4}{3}

Hope this helps you !

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What is the nth term of quadratic sequence 4 7 12 19 28
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We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.
Since these are different, this is not linear.
We now find the second differences:
5-3=2; 7-5=2; 9-7=2. Then:

Since these are the same, this sequence is quadratic.
We use (1/2a)n², where a is the second difference:
(1/2*2)n²=1n².

We now use the term number of each term for n:
4 is the 1st term; 1*1²=1.
7 is the 2nd term; 1*2²=4.
12 is the 3rd term; 1*3²=9.
19 is the 4th term; 1*4²=16.
28 is the 5th term: 1*5²=25.

Now we find the difference between the actual terms of the sequence and the numbers we just found:

4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.

Since this is constant, the sequence is in the form (1/2a)n²+d;
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The correct answer is n²+3
7 0
3 years ago
Allen wants to have a mean of 90 on his math quizzes. So far, he has scored 86, 94, 88, 95, and 89. What is the least score that
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Answer:

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Step-by-step explanation:

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The mean would be the sum of all the math quiz grades divided by the number of quizzes taken.

Solve for x:

86 + 94 + 88 + 95 + 89 + x = 540

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x = 88

Thus, Allen needs at least an 88 to obtain a mean of at least 90.

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