2x+y=70<br> 2y+z=110<br> x+y+z=?

Trapezia ABCD and PQRS are similar.<br> Find the area shaded in green.

avanturin [10]

The area shaded in green is 864 cm²

<h3>Similar figures</h3>

Similar figures, corresponding angles are congruent and the sides are ratio of each other. Therefore,

AB / PQ = CD / RS

30 / 10 = 24 / RS

30RS = 240

RS = 240 / 30

RS = 8 cm

let find the height of trapezium PQRS.

AB / PQ = 36 / h

30 / 10 = 36 / h

30h = 360

h = 360 / 30

h = 12 cm

Therefore,

area of the green portion = area of ABCD - area of PQRS

<h3>Area of a trapezium</h3>

area = 1 / 2(a + b)h

Therefore,

area of ABCD = 1 / 2(24 + 30)36 = 1 / 2 (54)36 = 1944 / 2 = 972 cm²

area of PQRS = 1 / 2(10 + 8)12 = 1 / 2(18)12 = 216 / 2 = 108 cm²

Area of the green portion = 972 - 108 = 864 cm²

learn more on trapezium here: brainly.com/question/11961445

6 0

1 year ago

How tall is a tree which is 15 feet shorter than a pole that is 3 times as tall as the tree?

Citrus2011 [14]

<h2>Height of tree is 7.5 feet</h2>

Step-by-step explanation:

Let t be the height of pole.

Given that the tree is 5 feet shorter than a pole.

Height of pole = t + 15

Also given that the pole is 3 times as tall as the tree.

Height of pole = 3t

So we have

t + 15 = 3t

2t = 15

t = 7.5 feet

Height of tree = 7.5 feet

7 0

2 years ago

Solving systems of Equations Word Problems - CLASSWORK

dem82 [27]

Answer:

Part A) For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's

Part B) For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's

Part C) Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters

Part D) The cost is $90

Step-by-step explanation:

Let

x-------> the number of hours (independent variable)

y-----> the total cost of rent scooters (dependent variable)

we know that

Sam's scooters

$y=8x+30$

Rosie's scooters

$y=10x+20$

using a graphing tool

see the attached figure

A. when does it make more sense to rent a scooter from Rosie's? How do you know?

For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's (see the attached figure) because the cost in less than Sam' scooters

B. when does it make more sense to rent a scooter from Sam's? How do you know?

For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's (see the attached figure) because the cost in less than Rosie' scooters

C. Is there ever a time where it wouldn't matter which store to choose?

Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters. The cost is $70 (see the graph)

D. If you were renting a scooter from Rosie's, how much would you pay if you were planning on renting for 7 hours?

Rosie's scooters

$y=10x+20$

For x=7 hours

substitute

$y=10(7)+20=90$

The cost is $90

4 0

3 years ago

What is the measure of the missing angle?<br> PICTURE BELOW \/

jeka57 [31]

Answer:

The measure of the missing angle is 90°

Step-by-step explanation:

∵ This figure is a quadrilateral

∴ the sum of measures of its angles = 360°

∴ m∠x = 360 - 107 - 72 - 91 = 90°

6 0

3 years ago

Problem 11-93 Waltner Corporation s management... Waltner Corporation's management reports that its average delivery cycle time

Marat540 [252]

Complete question is;

Waltner Corporation's management reports that its average delivery cycle time is 25 days, its average throughput time is 7.7 days, its manufacturing cycle efficiency (MCE) is 0.43, its average move time is 0.3 day, and its average queue time is 3.00 days. Required: a. What is the wait time?

b. What is the process time?

c. What is the inspection time?

Answer:

A) Wait time = 17.3 days

B) Process time = 3.311 days

C) Inspection time = 0.789 days

Step-by-step explanation:

A) we are given;

Delivery cycle time = 25 days

throughput time = 7.7 days

The formula for wait time is calculated from;

Delivery time = wait time + throughput time

So, wait time = Delivery time - throughput time

Wait time = 25 - 7.7 = 17.3 days

B) The process time is calculated from;

MCE = Process time/throughput time

So, process time = MCE x throughput time

We are given MCE = 0.43,thus, and we already know throughput time. Thus;

Process time = 0.43 x 7.7 = 3.311 days

C) The inspection time is gotten from;

throughput time = Process time + Inspection time + Move time + Queue time

Making inspection time the subject;

inspection time = throughput time - Process time - Move time - Queue time

Move time = 0.3 days

Queue time = 3 days.

Thus;

inspection time = 7.7 - 3.311 - 0.3 - 3.3 = 0.789 days

3 0

3 years ago

2x+y=70 2y+z=110 x+y+z=?