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3 years ago

What is the scale factor of triangle ABC to DEF ?

Mathematics

2 answers:

bekas [8.4K]3 years ago

8 0

Answer: The correct option is (A). 3.

Step-by-step explanation: We are given to find the scale factor of dilation from ΔABC to ΔDEF.

As shown in the figure, the lengths of the sides of ΔABC to ΔDEF are

AB = 5 units, BC = 4 units, CA = 3 units,

DE = 15 units, EF = 12 units, FD = 9 units.

We know that the scale factor is given by

$S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.$

Therefore, the scale factor of dilation from from ΔABC to ΔDEF is

$S=\dfrac{DE}{AB}=\dfrac{15}{5}=3.$

Thus, the required scale factor is 3.

Option (A) is correct.

olasank [31]3 years ago

3 0

Answer: the answer is 3.

Step-by-step explanation:

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Jada walks up to a tank of water that can hold up to 10 gallons.When it is active, a drain empties water from the tank at a cons

worty [1.4K]

Answer:

Part A)The amount of water in the tank is changing at -2/3 gallons per minute. 

Part B) it will take 7.5 minutes for the tank to drain completely.

Part C) The water tank was completely full 4.5 minutes before Jada arrived.

Step-by-step explanation:

Information fetching:

Tank of water can hold up-to 10 gallons.

When it is active, a drain empties water from the tank at a constant rate.
7 gallons of water present in the tank when Jade first saw
5 gallons of water left after 3 minutes

Part A) At what rate is the amount of water in the tank changing?

As the gallons were decreased from 7 to 5 in three minutes. It means in three minutes, 2 gallons were decreased.

So, gallons per minute change would be -2/3 gallons per minute. Hence, the amount of water in the tank is changing at -2/3 gallons per minute. 

Note: negative sign indicates the number of gallons of water are decreasing.

Part B) How many more minutes will it take for the tank to drain completely.

Let 'm' be the number of minutes will it take for the tank to drain completely.

As,

(2/3 gallons per minute) (m minutes) = 5 gallons

So,

m = 5 (3/2)

= 15/2

= 7.5 minutes

So, it will take 7.5 minutes for the tank to drain completely.

Part C) How many minutes before Jada arrived was the water tank completely full

As tank of water can hold up to 10 gallons. So, the tank of water is full when there is 10 gallons of water. So, this is 3 gallons of water more than the total 7 number of gallons at the time when Jada arrived.

As Jada arrived when the tank had left 7 gallons.

Let 'm' be the number of minutes before Jada arrived when the water tank was completely full.

So,

(2/3) (m) = 3

m = 3(3/2) = 9/2

= 4.5 minutes

So, the water tank was completely full 4.5 minutes before Jada arrived.

Keywords: time rate of change, time

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3 0

3 years ago

Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and

Leya [2.2K]

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2

= 3cos0 +2

= 3(1) +2

= 3 +2

= 5 !

7 0

3 years ago

Write the expression in factored form s^2-20s-100

KatRina [158]

Answer:

The factors of given expression are 10+10√2 and 10-10√2.

Step-by-step explanation:

We have given a quadratic expression.

s²-20s-100

We have to find factors of given expression.

We use quadratic formula to find factors.

x = (-b±√b²-4ac) / 2a

From given expression, a = 1 , b = -20 and c = -100

Putting values in above formula, we have

x = (-(-20)±√(-20)²-4(1)(-100) ) / 2(1)

x = (20±√400+400 ) / 2

x = (20±√800) / 2

x = (20± √400×2) / 2

x = (20±20√2) / 2

x = 10±10√2

Hence, the factors of given expression are 10+10√2 and 10-10√2.

3 0

2 years ago

10 Adoya deposited sh 4000 for 2 years in a bank which paid 122% p.a. simple interest. What interest did he get after two years?

olga nikolaevna [1]

Answer:

9760

Step-by-step explanation:

Interest=((P.A.)*(Interest Rate)*(Time))/100

Interest=(4000*122*2)/100

Interest=9760

5 0

3 years ago

Read 2 more answers

Seb bought 2 apples and 3 pears.

ryzh [129]

2a + 3p = 1.59

a = 0.24

Plug it in our equation:

2(0.24) + 3p = 1.59

Multiply:

0.48 + 3p = 1.59

Subtract 0.48 to both sides:

3p = 1.11

Divide 3 to both sides:

p = 0.37

So one pair costs £0.37

5 0

3 years ago