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2 years ago

Factor 18x^(2)+39x-15

Mathematics

1 answer:

k0ka [10]2 years ago

8 0

Answer:

$3(2x + 5)(3x - 1)$

Step-by-step explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

$f(x) = 18x^2 + 39x - 15$
$f(x) = 3(6x^2 + 13x - 5)$

Now, let's work with what we have inside the brackets.

Standard form of a quadratic: $ax^2 + bx+ c = 0$

Given our equation: $6x^2 + 13x - 5$

a = 6
b = 13
c = -5

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

<h3>Factor by Grouping</h3>

$6x^2 + 13x - 5$
$6x^2 -2x + 15x - 5$
$2x(3x- 1) +5(3x - 1)$
$(2x +5)(3x - 1)$

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution: $3(2x + 5)(3x - 1)$

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Find the measure of angle G

solong [7]

Answer:

135 degrees

Step-by-step explanation:

It is as isosceles trapezoid, so the the base angles are congruent. The sum of the inner angles is 360 degrees

2(4x-7) + 2(11x -8) = 360

8x - 14 + 22x -16 = 360

30x = 390

x = 13

angle F = angle G

angle G = 11 * 13 - 8 = 135 degrees

5 0

3 years ago

How much bigger is 1/2 to 1/3

natka813 [3]

Answer:

16.777% (7 repeating)

Step-by-step explanation:

well 1/2 is 50% and 1/3 is 33.333% so i think its about 16.777%

4 0

4 years ago

What is the value of x?

damaskus [11]

Answer:

x = 19.

Step-by-step explanation:

By the tangent - secant theorem:

BD^2 = AB * EB

so:

8^2 = (x - 7 + 4) * 4

4(x - 3) = 64

4x - 12 = 64

4x = 64 + 12 = 76

x = 76/4

= 19.

7 0

4 years ago

Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a

almond37 [142]

Answer:

5 (for c only)

Step-by-step explanation:

for c:

1st cleaning company: $y=17x+15$

2nd cleaning company: $y=20x$

set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)

it will look like:

$y=17x+15$

$-y=-20x$

make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with

$0=-3x+15$

then you will add 3x to both sides to get $3x=15$ then divide both sides by 3 to get $x=5$

if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5

8 0

3 years ago

Suppose the Tower of Hanoi rules are changed so that stones may only be transferred to an adjacent clearing in one move. Let In

Svet_ta [14]

Answer:

$l_n=3^n-1$

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,

$l_n=3^n-1$

We will prove our base case (when n=1) to be true:

Base case:

As stated in the qustion, $l_1=2=3^1-1$

Inductive hypothesis:

Given a natural n,

$l_n=3^n-1$

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Let´s analyze the problem with n+1 stones. In order to move the n+1 stones from A to C we have to:

Move the first n stones from A to C ( $l_n$ moves).
Move the biggest stone from A to B (1 move).
Move the first n stones from C to A ( $l_n$ moves).
Move the biggest stone from B to C (1 move).
Move the first n stones from A to C ( $l_n$ moves).

Then,

$l_{n+1}=3l_n+2$ .

Therefore, using the inductive hypothesis,

$l_{n+1}=3l_n+2=3(3^n-1)+2=3^{n+1}-3+2=3^{n+1}-1$

With this we have proved our statement to be true for n+1.

In conlusion, for every natural n,

$l_n=3^n-1$

8 0

3 years ago