All categories

3 years ago

Express as a trinomial. (3x + 7)(3x + 4)

Mathematics

1 answer:

timama [110]3 years ago

5 0

Answer:

9x² + 33x + 28

Step-by-step explanation:

$(3x + 7)(3x + 4)\\= 3x(3x + 4) + 7(3x + 4)\\= 9x^2 + 12x + 21x + 28\\= 9x^2 + 33x + 28$

You might be interested in

GIVING BRAINLIEST

CaHeK987 [17]

It’s B - 4 your welcome ☺️☺️

5 0

3 years ago

HELP ASAP: Find a hyperbola's equation with vertices at (-7, 0) + (7, 0) and co-vertices (0, -4) + (0, 4).

Harlamova29_29 [7]

Answer:

16x^2 - 49y^2 = 784

Step-by-step explanation:

as we know that this is the standard equation of hyperbola bcz 1 coordinate of vertices is 0.

since in vertices x coordinate is present and y coordinate is 0 so Tranverse axis of hyperbola is along x axis .

vertices in general = (a,0) and (-a,0)

vertices given = ( 7,0) and (-7 , 0)

so a=7

similarly

co vertices in general = ( 0 , b) and ( 0 , -b)

co vertices given = ( 0, 4) and (0 , -4)

so,

b= 4

now equation for x axis is:

(x2/a2) - ( y2/b2) = 1

by putting values we observe the ans is

16x^2 - 49y^2 = 784

6 0

3 years ago

Read 2 more answers

Based on the scatter plot, which equation represents the line best fit for the data about cups of beads?

e-lub [12.9K]

Answer:

Option B. y = 1.81x + 44.36

Step-by-step explanation:

The graph represents a scatter plot with a positive correlations and has a positive y-intercept.

By drawing the best line to fit the data the y-intercept will be approximately at the midpoint of 45 and 50

We will check which option is true:

A. y = 4.25 x

The equation of option A represents a line pass through the point (0,0)

Which mean y-intercept is 0 and this is wrong.

B. y = 1.81x + 44.36

According to the best line to fit the data option B is true.

Also by substitution with x = 2

y = 1.81 * 2 +44.36 = 47.98

which is near to the actual point on the graph (50)

C. y = 1.81 x ⇒ Wrong ⇒ same explanation of option A

D. y = 4.25 x + 50 ⇒ Wrong

Because the y-intercept will be approximately at the midpoint of 45 and 50

<u>So, The answer is option B. y = 1.81x + 44.36</u>

5 0

3 years ago

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

Factorise the following:<br><img src="https://tex.z-dn.net/?f=%7B3x%7D%5E%7B2%7D%20%20%2B%205x%20-%2012" id="TexFormula1" title=

Fed [463]

Answer:

(x + 3)(3x - 4)

Step-by-step explanation:

Given

3x² + 5x - 12

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 12 = - 36 and sum = + 5

The factors are + 9 and - 4

Use these factors to split the x- term

3x² + 9x - 4x - 12 ( factor first/second and third/fourth terms )

= 3x(x + 3) - 4(x + 3) ← factor out (x + 3) from each term

= (x + 3)(3x - 4)

Thus

3x² + 5x - 12 = (x + 3)(3x - 4) ← in factored form

6 0

3 years ago