All categories

2 years ago

Factor this polynomial. -3x^2-5x-2

Mathematics

1 answer:

vovikov84 [41]2 years ago

3 0

Answer:

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

Step-by-step explanation:

Lets factor the trinomial $-3x^2-5x-2$ step-by-step:

Step 1. Since all the terms are negative, we can factor -1 out

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

Step 2. Split the middle term of $3x^2+5x+2$

$5x=3x+2x$ , so $3^2+5x+2=3x^{2} +3x+2x+2$

Step 3. Group common terms

$(3x^2+2x)+(3x+2)$

Step 4. Factor each parentheses

$x(3x+2)+(3x+2)$

Step 5. Factor the common binomial

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

Now, we can put it all together:

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

You might be interested in

Anyone know how to do this??

Ghella [55]

Answer:

csc²(x)

Step-by-step explanation:

csc(x) = 1/sin(x)

sin²(x) + cos²(x) = 1

=> cos²(x) = 1 - sin²(x)

cos(2x) = cos²(x) - sin²(x) = (1 - sin²(x)) - sin²(x) =

= 1 - 2×sin²(x)

=> 2×sin²(x) = 1 - cos(2x)

sin²(x) = 1/2×(1-cos(2x))

=> 1 - cos(2x) = 2×(1/2×(1-cos(2x)) = 2×sin²(x)

=> 2 / (1-cos(2x)) = 2 / (2×sin²(x)) = 1/sin²(x) =

= 1/sin(x) × 1/sin(x) = csc(x)×csc(x) = csc²(x)

6 0

3 years ago

PLEASE HELP I POSTED LIKE 2 HOURS AGO WITH THIS QUESTION AND I NEED HELP:)

garik1379 [7]

A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.

Let's look at the four equations, with each solved as needed, into y = mx + b form.

A: 2x + y = 5

y = 5 - 2x

y = -2x + 5

Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.

B: y = 2x + 5

Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.

C: 2x - 4y = 10

-4y = 10 - 2x

-4y = -2x + 10

y = 2/4x -10/4

Here the slopes are different, so, like A this is not a good choice.

D: 2y - 4x = -10

2y = =10 + 4x

2y = 4x - 10

y = 2x - 5

Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.

Thus, D is the best choice.

7 0

3 years ago

Read 2 more answers

The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).

lesantik [10]

Answer:

(a).

$S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\$

(b).

from general equation:

$S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)$

first term is 4n

common difference:

$16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2}$

8 0

3 years ago

Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1

belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

$F(x) = \int\limits^a_b {f(x)} \, dx$

By using integration formula

$\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c$

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

$\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx$

On integration , we get

= $(\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}$

$F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)$

= $(\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))$

After simplification and cancellation we get

= $\frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6$

on calculation , we get

= $\frac{124,416}{5} + \frac{864}{3} + 180$

On L.C.M 15

= $\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}$

= 25 351.2 units²

Conclusion:-

The area of the region between the graph of the given function and the x-axis = 25,351 units²

6 0

2 years ago

. The estimate regression equation for a model involving two independent variables and 10 observations follows.y = 29.1270 + 0.5

beks73 [17]

Answer:

b) y = 289.815 when $x_1 = 180 \text{ and } x_2 = 310$

Step-by-step explanation:

We are given the following information in the question:

$y = 29.1270 + 0.5906x_1 + 0.4980x_2$

where y is the dependent variable,

$x_1, x_2$ are the independent variable.

The multiple regression equation is of the form:

$y = b_0 + b_1x_1 + b_2x_2$

where,

$b_0$ : is the intercept of the equation and is the value of dependent variable when all the independent variable are zero.

$b_1$ : It is the slope coefficient of the independent variable $x_1$ .

$b_2$ : It is the slope coefficient of the independent variable $x_2$ .

The regression coefficient in multiple regression is the slope of the linear relationship between the dependent and the part of a predictor variable that is independent of all other predictor variables.

Comparing the equations, we get:

$b_1 = 0.5906\\b_2 = 0.4980$

This means holding $x_2$ constant, a change of one in $x_1$ is associated with a change of 0.5906 in the dependent variable.

This means holding $x_1$ constant, a change of 1 in $x_2$ is associated with a change of 0.4980 in the dependent variable.

b) We have to estimate the value of y

$y = 29.1270 + 0.5906(180) + 0.4980(310) = 289.815$

3 0

3 years ago