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Evaluate 4(a2 + 2b) - 2b when a = 2 and b = –2

amid [387]

First you simply have to substitute 2 in replace of all the a's, and -2 in replace of all of the b's

4((2)2+2(-2))

Then you want to follow the order of operations, PEMDAS (Parantheses-Exponent-Multiplication-Division-Addition-Subtraction), and multiply within the parantheses.

4(4+(-4))

Next you will add within the parantheses (So add the 4 and -4 together)

4(0)

Lastly multiply

0

Your answer is 0

Hope this helps!

5 0

3 years ago

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A block of ice has a square top and bottom and rectangular sides. At a certain point in

Lilit [14]

Answer:

$\frac{dV}{dt} = 360 \ cm^3/h$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Geometry

Volume of a Rectangular Prism: V = lwh

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h$

Step 2: Differentiate

Rewrite [VRP]: $V = l^2h$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}$

Step 3: Solve for Rate

Substitute: $\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)$
Multiply: $\frac{dV}{dt} = 360 \ cm^3/h$

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

3 0

2 years ago

What is 2 X (6+ 2 + 8) -4

VladimirAG [237]

Answer:

The correct answer is 32x - 4

Step-by-step explanation:

1) Simplify 6 + 2 to 8.

$2x(8 + 8) - 4$

2) Simplify 8 + 8 to 16.

$2x \times 16 - 4$

3) Simplify 2x × 16 to 32x.

$32x - 4$

Therefor, the answer is 32x - 4.

4 0

2 years ago

What is the value of B - A as a fraction?

umka21 [38]

Answer:
A = 1/4
B = 3/4

step-by-step explanation:
the middle should be 1/2 because the middle between 0 and 1 is 1/2
A and B are both in the middle of the sides
therefore A would be closer to 0 so 1/4
and B would be closer to 1 so 3/4

6 0

3 years ago

The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of y

SSSSS [86.1K]

ANSWER:

i) y = 25x + 500

ii) y = 30x + 400

iii) The washing machines would cost the same amount after 20 years of use

iv) Standard machine

Step-by-step explanation:

i)

We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;

The first step step is to determine the slope of the line,

( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25

The equation is slope-intercept form will be;

y = 25x + c

Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;

when x = 1, y = 525

525 = 25(1) + c

c = 500

Therefore;

y = 25x + 500

ii)

The straight line equation that models the cost of Standard washing machine over the years;

Slope = (460 - 430) / (2 - 1) = 30

The equation is slope-intercept form will be;

y = 30x + c

when x = 1, y = 430

430 = 30(1) + c

c = 400

Therefore;

y = 30x + 400

Where y is the cost of the standard washing machine and x the number of years.

iii)

Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;

We have the cost functions;

y = 25x + 500

y = 30x + 400

Equating the two and solving for x;

25x + 500 = 30x + 400

500 - 400 = 30x - 25x

100 = 5x

x = 20

Therefore, the washing machines would cost the same amount after 20 years of use.

iv)

In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)

The cost function of the High-Efficiency washing machine is;

y = 25x + 500

To determine the cost, we solve for y given x = 9

y = 25(9) + 500

y = 725

The cost function of the Standard washing machine is;

y = 30x + 400

We solve for y given x = 9

y = 30(9) + 400

y = 670

Comparing the two values obtained, the cost for the Standard washing machine is more practical.

3 0

2 years ago

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Help me please help help help​

Help me please help help help