Ask question

Ask question

All categories

3 years ago

15

Help me I need the answer ASAP ! Aundrea painted the background of a square mural on the wall using 138ft^2 of paint .which meas

urement is closest to the side length of this mural in feet ?
A.69 ft
B.12 ft
C.139 ft
D.35 ft

1 answer:

Klio2033 [76]3 years ago

8 0

Hey there! I'm happy to help!

Since this mural is a square, all the sides are the same. This means that you square on of the sides to get the area (multiply it by itself). If we have the area and want to find a side, we just go backwards and use something called the square root!

If we plug this into our calculators...

√138≈11.74734

We see that is closest to B. 12 ft.

You could also figure this out without a calculator. 138 is very close to 144, which is 12². All the other answer options are way too big.

Have a wonderful day! :D

You might be interested in

Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of inter

Rudik [331]

Answer:

$y=-6x+10$

Step-by-step explanation:

The point of intersection of

$x+2y=9...eqn1$

and

$4x-2y=-4...eqn2$

is the solution of the two equations.

We add equation (1) and equation(2) to get,

$x+4x+2y-2y=9+-4$

$\Rightarrow 5x=5$

$\Rightarrow x=1$

We put $x=1$ into equation (1) to get,

$1+2y=9$

$\Rightarrow 2y=9-1$

$\Rightarrow 2y=8$

$\Rightarrow y=4$

Therefore the line passes through the point, $(1,4)$ .

The line also passes through the point of intersection of

$3x-4y=14...eqn(3)$

and

$3x+7y=-8...eqn(4)$

We subtract equation (3) from equation (4) to obtain,

$3x-3x+7y--4y=-8-14$

$\Rightarrow 11y=-22$

$\Rightarrow y=-2$

We substitute this value into equation (4) to get,

$3x+7(-2)=-8$

$3x-14=-8$

$3x=-8+14$

$3x=6$

$x=2$

The line also passes through

$(2,-2)$

The slope of the line is

$slope=\frac{4--2}{1-2} =\frac{6}{-1}=-6$

The equation of the line is

$y+2=-6(x-2)$

$y+2=-6x+12$

$y=-6x+10$ is the required equation

4 0

3 years ago

The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars on advertising is

sattari [20]

Answer:

The company should spend $40 to yield a maximum profit.

The point of diminishing returns is (40, 3600).

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

<u>Algebra I</u>

Coordinate Planes

Coordinates (x, y) → (s, P)

Functions

Function Notation

Terms/Coefficients

Factoring/Expanding

Quadratics

<u>Algebra II</u>

Coordinate Planes

Maximums/Minimums

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

1st Derivative Test - tells us where on the function f(x) does it have a relative maximum or minimum

Critical Numbers

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle P = \frac{-1}{10}s^3 + 6s^2 + 400$

<u>Step 2: Differentiate</u>

[Function] Derivative Property [Addition/Subtraction]: $\displaystyle P' = \frac{dP}{ds} \bigg[ \frac{-1}{10}s^3 \bigg] + \frac{dP}{ds} [ 6s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle P' = \frac{-1}{10} \frac{dP}{ds} \bigg[ s^3 \bigg] + 6 \frac{dP}{ds} [ s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Basic Power Rule: $\displaystyle P' = \frac{-1}{10}(3s^2) + 6(2s)$
[Derivative] Simplify: $\displaystyle P' = -\frac{3s^2}{10} + 12s$

<u>Step 3: 1st Derivative Test</u>

[Derivative] Set up: $\displaystyle 0 = -\frac{3s^2}{10} + 12s$
[Derivative] Factor: $\displaystyle 0 = \frac{-3s(s - 40)}{10}$
[Multiplication Property of Equality] Isolate <em>s </em>terms: $\displaystyle 0 = -3s(s - 40)$
[Solve] Find quadratic roots: $\displaystyle s = 0, 40$

∴ <em>s</em> = 0, 40 are our critical numbers.

<u>Step 4: Find Profit</u>

[Function] Substitute in <em>s</em> = 0: $\displaystyle P(0) = \frac{-1}{10}(0)^3 + 6(0)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(0) = 400$
[Function] Substitute in <em>s</em> = 40: $\displaystyle P(40) = \frac{-1}{10}(40)^3 + 6(40)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(40) = 3600$

We see that we will have a bigger profit when we spend <em>s</em> = $40.

∴ The maximum profit is $3600.

∴ The point of diminishing returns is ($40, $3600).

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

Unit: Differentiation (Applications)

5 0

2 years ago

Convert 3 quarts to pints.

Pavlova-9 [17]

It should be 6 pints

8 0

3 years ago

Read 2 more answers

If a coin is thrown with a starting velocity of 0 m/s down a dry well and hits bottom in 1.2 s, what's the depth of the well? Wi

BigorU [14]

Answer:

Depth = 7.06 m

Velocity = 11.77 ms-1

Step-by-step explanation:

We use the equation of motion:-

s = ut + 1/2 g $t^{2}$ where s = distance fallen , t = time , u = initial velocity and g = 9.81 ms^-2 , the acceleration due to gravity.

So s = 0(t) + 1/2 * 9.81 (1.2)^2

= 7.06 m to nearest tenth.

We use another equation of motion to find the final velocity:-

v^2 = u^2 + 2gs where v = final velocity

v^2 = 0 + 2*9.81 * 7.06

= 138.52

v = √138.52 = 11.77 m s-1

5 0

3 years ago

What is the mode of the data set shown below?

viktelen [127]

Answer:

2 (D)

Step-by-step explanation:

it comes up the most (2 times )

4 0

3 years ago

Read 2 more answers