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3 years ago

The sum of the lengths of the two bases of a trapezoid is 22 cm and its area is 66 cm2.

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

8 0

Answer:

h = 6 cm

Step-by-step explanation:

Given that,

The area of a trapezoid, A = 66 cm²

The sum of the lengths of the two bases of a trapezoid is 22 cm.

We need to find the height of the trapezoid.

The area of a trapezium is given by :

$A=\dfrac{1}{2}\times (\text{sum of parallel sides})\times \text{height}$

Substitute the values,

$h=\dfrac{2A}{\text{sum of parallel sides}}\\\\h=\dfrac{2\times 66}{22}\\\\h=6\ cm$

So, the height of the trapezoid 6 cm.

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What is the perimeter of triangle DEF?

Vikki [24]

Given:

Triangle DEF

To find:

The perimeter of triangle DEF.

Solution:

Coordinate of D = (-1, 1)

Coordinate of E = (2, 1)

Coordinate of F = (-1, 4)

Distance formula:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

<u>Distance of DE:</u>

Here, $x_1=-1, y_1=1, x_2=2, y_2=1$

$d=\sqrt{(1-1)^2+(2-(-1))^2}$

$d=\sqrt{0+9}$

d = 3 units

<u>Distance of EF:</u>

Here, $x_1=2, y_1=1, x_2=-1, y_2=4$

$d=\sqrt{(4-1)^2+(-1-2)^2}$

$d=\sqrt{9+9}$

$d=\sqrt{18}$

d = 4.2 units

<u>Distance of FD:</u>

Here, $x_1=-1, y_1=4, x_2=-1, y_2=1$

$d=\sqrt{(1-4)^2+(-1-(-1))^2}$

$d=\sqrt{9+0}$

d = 3 units

Perimeter of ΔDEF = DE + FE + FD

= 3 + 4.2 + 3

= 10.2 units

The perimeter of triangle DEF is 10.2 units.

5 0

3 years ago

The hose on a power washer is 42-ft. long. If the compressor to which the house is attached is located at the corner of a 28-ft

oee [108]

9514 1404 393

Answer:

a) 14√5 feet

b) about 31.3 feet

Step-by-step explanation:

a) The 42-ft hose is the hypotenuse of a right triangle with one leg 28 ft. We are asked to find the other leg. The Pythagorean theorem is useful.

h² +(28 ft)² = (42 ft)²

h² = (1764 -784) ft² = 980 ft²

h = √(196·5) ft

h = 14√5 ft

b) The approximate height is ...

14√5 ≈ 31.305, about 31.3 feet

4 0

3 years ago

Find the coordinates of each point after the described reflection. Give the distance between each point and its reflection.

AVprozaik [17]

Complete Question:

Find the coordinates of the point after the described reflection. Give the distance between the point and its reflection. R(-5, 8) is reflected across the x-axis _____________.

Answer:

$(a)$ $R' = (-5,-8)$

$(b)$ The distance is 16 units

Step-by-step explanation:

Given

$R = (-5,8)$

Solving (a): Reflection across x-axis

The rule is:

$R(x,y) ==> R(x,-y)$

So, the reflection of $R = (-5,8)$ is:

$R' = (-5,-8)$

Solving (b): The distance between R and R'

Distance (d) is calculated as:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Where:

$R = (-5,8)$ ---- $(x_1,y_1)$

$R' = (-5,-8)$ --- $(x_2,y_2)$

This gives:

$d = \sqrt{(-5- -5)^2 + (-8- 8)^2}$

$d = \sqrt{(0)^2 + (-16)^2}$

$d = \sqrt{256}$

$d = 16$

<em>The distance is 16 units</em>

6 0

3 years ago

Perform the operation indicated, then place the answer in the proper location on the grid. Write your answer in descending power

VikaD [51]

Answer:

<h3>The answer after performing the indicated operation is in descending powers of x is $5x^2-7x+15$ </h3>

Step-by-step explanation:

Given expression is $(6x^2-4x+11)+(4-x^2-3x)$

<h3>To perform the operation indicated, then place the answer in the proper location on the grid and also Write answer in descending powers of x:</h3>

Now solve the given expression as below ( that is perform the operation indicated)

$(6x^2-4x+11)+(4-x^2-3x)$

$=6x^2-4x+11+4-x^2-3x$

Adding the like terms we get

$=5x^2-7x+15$

$(6x^2-4x+11)+(4-x^2-3x)=5x^2-7x+15$

<h3>The answer after performing the indicated operation is in descending powers of x is $5x^2-7x+15$ </h3>

6 0

4 years ago

You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company

tankabanditka [31]

The straight commission offer must be at least as good as the straight commission offer, which requires sales of $12,000 in a week.

<h3>What is Straight Commission?</h3>

Straight Commission: Straight commission can also be referred to as commission-only because it is the only pay an employee receives. There is no base salary or hourly wage included in this pay structure. All compensation is based on an agreed-upon percentage of sales.

Get the complete straight commission offer as the first step.

The straight total commission can be expressed as follows:

A=R x T

A = straight total commission

R=commission rate

T=total sales

In our example,

A=0.06t=0.06 t is replaced by

R=6%=6/100=0.06

T=t in equation 1.

in the 2nd step, the second offer's total value

The total sum of the second offer can be expressed as follows:

A=F+(RT)

A=the amount of income the second company offers

F=weekly fixed wage

R = commission percentage

T = total sales

F in our instance equals $240 weekly.

in the 3rd step

R=4%=4/100=0.04

T=t is replacing A=240+(0.04t)=0.04 t+240 is in equation 2

now equate equations 1 and 2

0.06 t=0.04 t+240

(0.06 t-0.04 t)=240

0.02 t=240

t=240/0.02=12,000

The straight commission offer must be at least as good as the straight commission offer, which requires sales of $12,000 in a week.

To learn more about Straight commission visit:

brainly.com/question/8535450

#SPJ4

6 0

1 year ago