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Nataly [62]
3 years ago
9

Factor completely: 3a2 − 14a − 24

Mathematics
2 answers:
GalinKa [24]3 years ago
7 0
I know what it is. it  is (3a+4)(a-6)
Lostsunrise [7]3 years ago
4 0

Answer:

The correct option is (3a+4)(a-6)

Step-by-step explanation:

We have the polynomial 3a^2-14a-24

For the polynomials of the form ax^2+bx+c we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-72 and whose sum is b=(-14)

We have to factorize -14 from -14a:

3a^2-14(a)-24=\\3a^2-(18-4)(a)-24=\\=3a^2-18a+4a-24

Because b=(-18)+4=(-14) and a.c=(-18).4=(-72)

Now we have to factor by grouping:

3a^2-18a+4a-24=\\(3a^2-18a)+(4a-24)=\\3a(a-6)+4(a-6)=\\=(3a+4)(a-6)

Then, the correct option is (3a+4)(a-6)

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4 0
2 years ago
find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive
wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

  • n = number of terms,
  • a = first term and
  • d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

#SPJ1

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2 years ago
What side of the image corresponds to BC ?<br> http://prntscr.com/kvxwsm
coldgirl [10]
I’m pretty sure the answer is xy
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3 years ago
What is the product if 3/5 and 10
STALIN [3.7K]
The product of \frac{3}{5} and 10 is 6. 
5 0
2 years ago
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