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2 years ago

Factor completely 2x2 9x 4. (2x 2)(x 2) (2x 1)(x 4) (2x 4)(x 1) (2x 2)(x 4).

Mathematics

1 answer:

lozanna [386]2 years ago

5 0

Factors of the given expression are $(x+4), (2x+1)$

Given expression is

$2x^2 + 9x+4$

<h3>What is a factor?</h3>

A factor is a number that divides another number completely.

Let us split the middle term as:

$2x^2 + 8x + x+4\\\\2x(x+4)+1(x+4)\\\\(x+4) (2x+1)$

Therefore, factors of the given expression are $(x+4), (2x+1)$

To get more about factors visit:

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help finding the perimter of 78.4 inches whats the length of each side and show me how to work the promblem

LuckyWell [14K]

A square has four even sides and the perimeter is equal to the sum of all of the sides.
$P=s+s+s+s=4s$
So we can evaluate the equation for P and then solve for s.
$78.4=4s \\ \frac{78.4}{4} =s \\ s=19.6in$

6 0

3 years ago

The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

$\displaystyle \frac{dl}{dt} = 4 \ m/day$

$\displaystyle w = 23 \ meters$

$\displaystyle \frac{dw}{dt} = 1 \ m/day$

Step 2: Differentiate

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Step 3: Solve

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

8 0

3 years ago

Simplify (6x2 − 3 − 5x3) − (4x3 + 2x2 − 8).

mezya [45]

(6•2 - 3 - 5•3) - (4•3 + 2•2 - 8)
(12 - 3 - 15) - (12 + 4 - 8)
(9 - 15) - (16 - 8)
(-6) - (8)
-14

7 0

3 years ago

Read 2 more answers

Please help with question 22b! Thanks :)

NNADVOKAT [17]

6.5 liters per 100 km travelled. 30% of 5 is 1.5, so adding this to the original amount results in 6.5

8 0

3 years ago

Read 2 more answers

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago