Complete the inequalities by

The length of a rectangle is five times its width. If the area of the rectangle is 320m, find the perimeter

Roman55 [17]

Answer: The perimeter is 96 m

Step-by-step explanation:

If we tag the length of the rectangle as $l$ and the width as $w$ , and if in addition we are told $l=5 w$ ,the dimensions of the rectangle are as shown in the figure.

Now, the area of a rectangle is given by:

$A=(l)(w)=320 m^{2}$

Since $l=5 w$ :

$A=(5w)(w)=320 m^{2}$

Isolating $w$ :

$5w^{2}=320 m^{2}$

$w=\sqrt{\frac{320 m^{2}}{5}}$

$w=8 m$

On the other hand, the perimeter of a triangle is given by the addition of each of its sides. Then, if the rectangle has two sides that measure $w$ and two sides that measure $5 w$ , the perimeter is:

$P=2(5)(w)+2w$

Substituting the value of $w$ in the last equation:

$P=2(5)(8 m)+2(8 m)$

Finally the perimeter is:

$P=96 m$

7 0

4 years ago

What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?

Gemiola [76]

Answer:

4x + 3y + 9 = 0

Step-by-step explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

$(y - y_1) = m (x - x_1)$

where $m$ is the slope of the line and

$(x_1, y_1)$ is the point passing through it.

Here, $m = \frac{-4}{3}$ and $(x_1 , y_1) = (3 , -7)$ .

Substituting in the formula $y + 7 = \frac{-4}{3} (x - 3)$

$\implies 3y + 21 = -4x + 12$

$4x + 3y + 9 = 0$

3 0

3 years ago

Grace bought 100 yards of ribbon, she needs 2/3 yards of ribbon for each bow she makes How many bows can she need to make?

Zielflug [23.3K]

It is 150, you divide the 100 yards by what I am assuming you meant to be two thirds:)

3 0

4 years ago

What is the equation of the line that passes through (-1, 5) and (3, -7)?

enyata [817]

Answer:

$3x + y = 2$

Step-by-step explanation:

$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

$y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1))$

$y - 5 = \dfrac{-12}{4}(x + 1)$

$y - 5 = -3(x + 1)$

$y - 5 = -3x - 3$

$3x + y = 2$

3 0

3 years ago

In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each poin

Korolek [52]

Step-by-step explanation:

We have cartisean points. We are trying to find polar points.

We can find r by applying the pythagorean theorem to the x value and y values.

$r {}^{2} = {x}^{2} + {y}^{2}$

And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.

$\tan(x) = \frac{y}{x}$