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3 years ago

12

The length of a rectangle deck is 3 times its width. If the deck's perimeter is 16 ft, what is the deck's area?

2 answers:

Ray Of Light [21]3 years ago

5 0

Answer:12

Step-by-step explanation:

3x+3x+x+x=16

8x=16 so x =2

2*3=6 6*2=12

UNO [17]3 years ago

3 0

Answer:

12 sq ft

Step-by-step explanation:

let w = width

let 3w = length

w + w + 3w + 3w = 16

8w = 16

x = 2

Area = 3(2) x 2

A = 6 x 2

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In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?

alexira [117]

We know that
In any quadrilateral where the vertices are on the circumference of a circle, the opposite angles add up to $180$ degrees.

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$x=50degrees$

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3 years ago

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Round 339.4749 to the nearest hundredth

ivanzaharov [21]

The thousandth place is 4, which is less than 5 ⇒ Discard

339.4749 ≈ 339.47

Answer: 339.47

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3 years ago

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Mrs smith bought a.box of 10 cupcake she ate 30% of the cupcake how many did she eat

iogann1982 [59]

Answer:

3 Cupcakes

Step-by-step explanation:

First, multiply the percentage, 30, times the number of cupcakes, 10, ad you get 300. Then, divide that by 100, and oyu get your answer, 3 cupcakes.

*Or since this form of equation is in a simpler form of 10 cupcakes, just get rid of the percentage sign and the 0 in 30%. I hope this helps :)

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3 years ago

I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

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3 years ago

Which value must be added to the expression x2 + x to make it a perfect-square trinomial? One-fourth One-half 1 4

SVEN [57.7K]

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Given

x² + x

To complete the square

add ( half the coefficient of the x- term )² to x² + x

x² + 2( $\frac{1}{2}$ )x + ( $\frac{1}{2}$ )² = x² + x + $\frac{1}{4}$

= (x + $\frac{1}{2}$ )² ← perfect square

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3 years ago

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