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3 years ago

5

Lisa's rectangular living room is 22 feet wide. If the length is 6 feet less than twice the width, what is the area of her livin

g room?

1 answer:

Artemon [7]3 years ago

4 0

Answer: Area = 836 feet²

Step-by-step explanation:

We will call L the length and W the width, then

L = 2W - 6 feet

L = 2 x 22 feet - 6 feet = 44 feet - 6 feet = 38 feet

Area of a rectangle is L x W

Area = 38 feet x 22 feet = 836 feet²

Answer : Area = 836 feet²

$\textit{\textbf{Spymore}}$

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You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

I need help! I would appreciate if you show me the work! Thank you !

iVinArrow [24]

Answer:

-11 for the first one and 0 for the second one

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Given the polynomial 21x 4 + 3y - 6x 2 + 34 What polynomial must be subtracted from it to obtain 29x 2 - 7 ? What polynomial mus

fredd [130]

Answer:

1. 21x⁴+3y-35x² + 41

2. -21x⁴-3y+6x² + x

Step-by-step explanation:

When adding and subtracting polynomials , you can use the distributive property to add or subtract the coefficients of like terms.

1. The polynomial is 21x⁴ + 3y -6x² + 34

To obtain polynomial 29x² -7 , we must subtract some polynomial from it.

Let that polynomial be k.

So, 21x⁴ + 3y -6x² + 34 - k = 29x² -7

k = 21x⁴ + 3y - 6x² +34 - 29x² +7 = 21x⁴ + 3y - 35x² + 41

2. To obtain a first degree polynomial, let that polynomial be x +34

So, 21x⁴ + 3y - 6x² + 34 + K = x + 34

K = x + 34 - 21x⁴ -3y + 6x² - 34

= -21x⁴ - 3y + 6x² + x

6 0

3 years ago

A puppy was born on April 1. The table gives the puppy's weights on three different

Masja [62]

Answer:

it is the middle one

Step-by-step explanation:

i did it

6 0

2 years ago

Which equation describes the line with a slope of -3 that contains the point (2,4)?

Ilia_Sergeevich [38]

Answer: y = 2x - 11

Step-by-step explanation:

A linear equation has the following form.

y = a . x + b

where,

y: independent variable

a: slope

x: independent variable

b: y-intercept

The slope is 2, so a is 2. The ordered pair (4, -3) means that when x takes the value 4, y takes the value -3. We can replace these values in the general equation to find the y-intercept.

y = a . x + b

-3 = 2 . 4 + b

b = -11

The linear equation is

y = 2x - 11

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2 years ago

Read 2 more answers