3r + 7 = -8 what does r =

The length of a rectangle envelope is 2 1/2 times its width. A plastic band surrounds the front and back of the envelope to secu

Andreas93 [3]

Answer:

Length of the envelope = 14

Width of the envelope = 5.6

Step-by-step explanation:

Let the width of the rectangle be x

Then the length of the rectangle will be $2\frac{1}{2} \times x$

Also the length of the plastic band to cover the front and back of the envolpe = $39\frac{3}{8}$

To cover one side th band required is

=> $\frac{39\frac{3}{8}}{2}$

=> $\frac{\frac{315}{8}}{2}$

=> ${\frac{315}{16}$

=>39.4

We know that the perimeter of the rectangle is

=> 2( L + B) = ${\frac{39.4}{2}$

=> 2( $2\frac{1}{2} \times x + x$ ) = 19.7

=> 2( $\frac{7}{2}x) = 19.7$

=> $3.5x = 19.7$

=> $x = \frac{19.7}{3.5}$

=> $x = 5.6$

Now length of the envelope =

=> $2\frac{1}{2} \times x$

=> $2.5 \times 5.6$

=> 14

5 0

3 years ago

An equation of the perpendicular bisector of the line segment with end points (3,0) and (-3,0) is

Norma-Jean [14]

Answer:

$x = 0$

Step-by-step explanation:

Given

$(x_1,y_1) = (3,0)$

$(x_2,y_2) = (-3,0)$

Required

The equation of the perpendicular bisector.

First, calculate the midpoint of the given endpoints

$(x,y) = 0.5(x_1 + x_2, y_1 + y_2)$

$(x,y) = 0.5(3-3, 0+ 0)$

$(x,y) = 0.5(0, 0)$

Open bracket

$(x,y) = (0.5*0, 0.5*0)$

$(x,y) = (0, 0)$

Next, determine the slope of the given endpoints.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{0 - 0}{-3- 3}$

$m = \frac{0}{-6}$

$m = 0$

Next, calculate the slope of the perpendicular bisector.

When two lines are perpendicular, the relationship between them is:

$m_2 = -\frac{1}{m_1}$

In this case:

$m = m_1 = 0$

So:

$m_2 = -\frac{1}{0}$

$m_2 = unde\ fined$

Since the slope is $unde\ fined$ , the equation is:

$x = a$

Where:

$(x,y) = (a,b)$

Recall that:

$(x,y) = (0, 0)$

So:

$a = 0$

Hence, the equation is:

$x = 0$

5 0

3 years ago

How much acetic acid is in a 5 liter container that is marked 80% acetic acid. How much is water

Vinvika [58]

Answer:

1 liter of water

Step-by-step explanation:

If 80 % is acid that's means 4 liters of the 5 is acid. (0.8 * 5)

The remaining amount is 1

8 0

3 years ago

Read 2 more answers

Maitri and Aabhas do a work in 12 hours.

tamaranim1 [39]

Answer:

See below ~

Step-by-step explanation:

Given

Maitri and Aabhas do a work in 12 hours
Aabhas and Kavya do the work in 15 hours
Kavya and Maitri do the work in 20 hours

Solving

Take Maitri, Aabhas, and Kavya to be x, y, z respectively
x + y = 12 (1)
y + z = 15 (2)
x + z = 20 (3)

Take Equation 1 and rewrite it so that it is equal to x.

x = 12 - y

Take Equation 2 and rewrite it so that it is equal to z.

z = 15 - y

Now, substitute these values in Equation 3.

x + z = 20
12 - y + 15 - y = 20
-2y + 27 = 20
2y = 7
y = 7/2 = 3.5 hours [Aabhas]

Substitute the value of y in Equation 1.

x + 3.5 = 12
x = 8.5 hours [Maitri]

Substitute the value of y in Equation 2.

3.5 + z = 15
z = 11.5 hours [Kavya]

Add the values of x, y, and z together.

x + y + z
8.5 + 3.5 + 11.5
12 + 11.5
23.5 hours [together]

8 0

2 years ago

A catering company’s recipe for salad uses a ratio of 2 c of dressing to 4 lb of vegetables. Draw a model for the ratio. Write t

s2008m [1.1K]

The ratio of dressing to vegetable in its reduced form is determined by dividing the amount of dressing by the amount of vegetables. This will give us the answer of,
2 c / 4 lb
In its simplest form, we divide both the numerator and denominator by 2 and the final answer would be,
1 c / 2 lb

7 0

3 years ago