All categories

2 years ago

Find the area of the following shape. You must show all work to receive credit. Please help!

Mathematics

1 answer:

lisabon 2012 [21]2 years ago

7 0

This is a compound figure
First, section off a triangle at bcd. The base is 8 units with a height of 2 units so the area is 8 square units.
Form a trapezoid between the areas where x is -3 to 1. Use the formula to find the area (28 square units).
There are two triangles left. Find the area of both of them (4 units and 2 units)
Add all of these values together to get a total of 42 square units

You might be interested in

The Goodsmell perfume producing company has a new line of perfume and is

LenKa [72]

Given:

It is given that surface area must be less than 150 cm².

Solution:

The Maximum Volume With Total Surface Area Less than 150 cm² is shown in the table.

From the table, it can be concluded that for r=3.00 cm and h=4.95 cm the surface area will be less than 150 cm² and the volume will be the maximum.

$S=2\pi rh+2\pi r^2\\S=2\pi (3)(7.95)+2\pi3^2\\S=93.3+56.5\\S=149.8 \text{ cm}^2$

Calculate the volume.

$V=\pi r^2h\\V=\pi(3)^2(4.95)\\V=139.96$

Hence, the required dimensions are r=3.00 cm and h=4.95 cm.

8 0

2 years ago

Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of so

mojhsa [17]

To determine the cost of each item, we need to set up equations. From the problem statement, we have three unknowns so we need three equations. We set up equations as follows:

let x cost of small pizzas
y cost of soda
z cost of salad

two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14

one small pizza, a liter of soda, and three salads cost $15

x + y + 3z = 15

three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22

Solving for x, y and z, we will have:

x = $ 5
y = $ 1
z = $ 3

6 0

2 years ago

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a

STatiana [176]

Answer:

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085

Step-by-step explanation:

The given parameters are;

The coordinates of parallelogram RSTU are;

R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)

The lengths of the sides are (using an online length calculator);

RS = 4.1231

RT = 10

ST = 9.2195

SU = 10.198

TU = 4.1231

UR = 9.2195

Therefore, by definition of a parallelogram, we have;

RS║TU and ST║UR

The slope of RS = (1 - (-3))/(-5 - (-4)) = -4

The slope of ST = (3 - 1)/(4 - (-5)) = 2/9

The equation of the line perpendicular to ST is therefore;

y - 1 = -9/2×(x - (-5))

y = -9x/2 - 43/2

The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1

y = x/4 - 2

The point where the two lines meet is therefore;

-9x/2 - 43/2 = x/4 - 2

x = -78/19

y = -115/38

The length of the side of the rectangle = 4.1245

The excess width of the rectangle = 0.1085

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085.

6 0

1 year ago

A rock climber is planning to climb a mountain cliff over two days. The climb begins at an altitude of 6,400 feet above sea leve

Furkat [3]

Answer:

Step-by-step explanation:

360h+6,400 >8,020, with a solution is h> 4.

3 0

1 year ago

Zane is a dangerous fellow who likes to go rock climbing in active volcanoes. one time while inside a volcano, he heard some rum

defon

From the given scenario is this particular item, the equation that can be derived for the distance traveled after x seconds is,
y = d₀ + (4)x
Substituting the known values x and y in order to solve for d₀ will give us an answer of,
13 = d₀ + 4(3)
d₀ = 1
Thus, the answer is 1 m.

5 0

1 year ago