I need help on this question please

Explain Step By Step How to Solve the Following Equation by Factoring:<br><br> 3n^2+14n+15

Anuta_ua [19.1K]

The expression 3n^2 can be separated into (3n)(n).

Factored formula is in the form (a+b)(a+b), where b*b is equal to the last term in the expression, 15. The factors of 15 are three and five.

Using these two piece of information, we know it must be either (3n+3)(n+5) or (3n+5)(n+3). To get the middle term, 14n, using FOIL, this is equivalent to ((3n)(3) + (5)(n)) in the latter expression. In the first expression, ((3n)(5) + (3)(n)) = 18n, which is not equivalent to the given equation’s middle term.

Therefore, we know that the factored form of this equation is (3n+5)(n+3).

The solutions, or zeroes, of any equation are where y=0. Therefore, we set the expression 3n^2+14n+15=0, or (3n+5)(n+3)=0. To obtain zero from two products, either of the products must equal zero. Therefore, we can state 3n+5=0 and n+3=0. Solving these equations, we get:

3n+5=0
3n=-5
n=-5/3

and

n+3=0
n=-3.

Finally, the solutions are n=-5/3 and n=-3

3 0

3 years ago

In ΔCAB, point E is the midpoint of segment AC and point D is the midpoint of segment BC. If the measure of segment AB is 8 unit

Jet001 [13]

Answer:

4 units

Step-by-step explanation:

3 0

3 years ago

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If center of dilation is D (-1, -1) and the coordinates for triangle ABC are A(0, -2), B(2, -4), and C(3, -1), then what are the

VashaNatasha [74]

Answer:

A'(1,-3), B'(7,-1) and C'(5,-7).

Step-by-step explanation:

Given,

The coordinates of the triangle ABC are,

A(0, -2), B(2, -4), and C(3, -1)

If a point (x,y) is dilated about a point (p,q) with a scale factor k,

Then the dilation rule is,

$(x,y)\rightarrow (k(x-p)+p, k(y-q)+q)$

Here, the triangle ABC with coordinates A(0, -2), B(2, -4), and C(3, -1) is dilated with scale factor 2 about a point (-1,-1) to form triangle A'B'C'.

That is, k = 2, p = -1, q = -1

Then,

$(0,-2)\rightarrow (2(0+1)-1,2(-2+1)-1)=(1,-3)$

Similarly,

$(2,-4)\rightarrow (5,-7)$

$(3,-1)\rightarrow (7,-1)$

Therefore, the coordinates of triangle A'B'C' are,

A'(1,-3), B'(5,-7) and C'(7,-1)

5 0

3 years ago

CarMax has guaranteed to pay $500 for ANY used car - no matter how old or in what condition. You want to wait as long as possibl

Volgvan

After I looked up some quick information, your car loses 15-25% each year. After 5 years, it goes to only 37%. So, a car that would cost 20000 would be valued at around 7k after 5 years. So, in the first 5 years, it lost 14k. Also, a 1999 Corolla goes for 2.5k, and that's nearly 20 years. So, I'm just going to go with, based off these numbers, probably 25-30 years...if it still works by then.
Also, if you get in a heavy accident the next day, making the car unusable, you rip off your friend. The first scenario only applies if the engine works well and no accidents were on the vehicle either.

8 0

4 years ago

What is 78 million in scientific notation?

mariarad [96]

78000000 in scientific notation is
7.8 x 10 ^ 7

7 0

3 years ago

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I need help on this question please​

I need help on this question please