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2 years ago

Factor this: 18x^2+39x-15

Mathematics

2 answers:

taurus [48]2 years ago

6 0

Steps for Factoring:

1) Find CM (common factor) for the expression: 3

Factor out 3 =>

$3(6x^{2}+13x-5)$

2)Factor the above expression by grouping:

The expression needs to be written as $6x^{2} + ax+ bx -5$

a and b should add up to 13 and multiply up to -30 (6 × -5)

By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)

3) Now we can rewrite $(6x^{2}+13x-5)$ as $(6x^{2} -2x)+(15x-5)\\$

Factor out 2x in the first group and 5 in the second group:

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

As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)

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

The answer is 3(3x-1) (2x+5)

<em>Hope it helps!</em>

frosja888 [35]2 years ago

4 0

Answer is:
3(2x+5)*(3x-1)

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A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night

MatroZZZ [7]

The equation that represents the linear function is y =32x

<h3>What is a linear function?</h3>

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

$y=mx+c$

Where

m represents slope
c represents the y-intercept

The slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{576 - 64}{18-2}$

$m = \frac{512}{16}$

$m = 32$

The linear equation is then calculated as:

$y =m(x -x_1) + y_1$

So, we have:

$y =32(x -2) + 64$

$y =32x -64 + 64$

$y =32x$

Hence, the equation that represents the linear function is y =32x

Read more about linear functions at:

brainly.com/question/14323743

5 0

2 years ago

Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

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3 years ago

Solve using the quadratic formula: 2x2-9x+12=0

marta [7]

Answer:

no solution

Step-by-step explanation:

For getting the nature of solution of the quadratic equation of the form:

ax² + bx + c = 0

We need to find Discriminant which is:

Discriminant (D) = b² - 4ac

If D < 0, there is no solution of equation.
If D = 0, there are two equal and real solution of equation
If D < 0, there are two real and distinct solution of equation

Here we have equation is:

2x² - 9x + 12 = 0

∴ a=2, b = -9, c = 12

⇒ D = 81 - 4 × 2 × 12 = -16 < 0

Hence, there is no solution of given equation.

5 0

3 years ago

4x+5y-5z=196 -11x-7y+12z=-211 -8x-9y-z=-236 Solve for x y z

FrozenT [24]

Have you learned matrices yet? I'm going to use that to solve these, please refer to the photos.

I solved the system by using a matrix calculation. The work always needs to be shown and you do that by setting up the matrix like in the first photo and also writing out all your equations. In a TI calculator, to do this you press 2ND-X^-1,GO TO EDIT - [A] - 3×4- now enter the coefficient of the system of equations variables. NOW 2ND MODE- 2ND-X^-1 -GO TO MATH- ALPHA APPS

Now, if you don't know this you may be confuse so after rref([A]) was enter a matrix came up with [1 0 0 -21] in the top row this means x equal -21. So, the next row is y and it came out as [0 1 0 46] so y equals 46 and I'm going to let you figure out what z is by looking at the matrix.

SO... X=-21 Y=46 and Z=-10

Let's Test it

$4x + 5y - 5z = 196 \\ 4( - 21) + 5(46) - 5( - 10) = 196 \\ - 84 + 230 + 50 = 196 \\ 196 = 196$

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3 years ago

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OverLord2011 [107]

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3 years ago

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