If the area of ABC is 20 cm2, what is the area of PQR? Show your work.

Answers

Answer 1

Answer: Since the triangles are similar, the first thing to do is find the scale factor.
We have then:
k = 6/4 = 3/2
Then, the area will be given by:
A '= k ^ 2 * A
Substituting values:
A '= ((3/2) ^ 2) * (20)
A '= 45 cm ^ 2
Answer:
The area of PQR is:
A '= 45 cm ^ 2

Answer 2

Answer:

Answer:

Area of ΔPQR = 45 cm²

Step-by-step explanation:

From the given figure we can see that triangle ABC and triangle PQR are similar triangles.

If two triangles are similar the the ratio of area of two triangle is equal to the square of ratio of corresponding sides

To find the area of triangle PQR

Ar(ABC) = 20, AB = 4 cm and PQ =6 cm

From figure we can write,

Ar(ABC)/ar(PQR) = (AB/PQ)²

20/ar(PQR) = (4/6)²

20/ar(PQR) = 16/36

ar(PQR) = (36 x 20)/16 = 45 cm²

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Two less than two thirds times a number is ten
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What is the area of a circle with a radius of 1 foot?

Answers

Answer:

3.14 ft² or 2,917 cm²

Step-by-step explanation:

To do this, we need to know the expression to calculate the area of a circle.

The area of any circle is:

A = πr²

Where:

π: value of pi, which is 3.14

r: radius of the circle, in this case 1 ft

Calculating the area in units of ft:

A = 3.14 * (1)²

A = 3.14 ft²

Now, if you convert the foot to cm we have:

1 * 30.48 = 30.48 cm

Solvinf for A:

A = 3.14 * (30.48)²

A = 2,917.15 cm²

Answer:

Pi feet squared

Step-by-step explanation:

How many nickles and dimes are $5.20 if there are six times more nickles than dimes?

Answers

In looking for the number of nickel and dimes we need to establish first equations:
n = $0.05
d = $0.1

0.05n + 0.1d = 5.20
0.05n = 6 (0.1d) ; n = 0.083d

Then we will solve it by substitution:
0.05(0.083d) + 0.1d = 5.20
0.42d + 0.1d = 5.20
0.52d = 5.20
d = 10

n = 0.083(10)
n = 0.83

The amount of money in an account with continuously compounded interest is given by the formula A = Pert , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.1%. Round to the nearest tenth.

Answers

A=future amount
P=present amount
r=rate in decimal
t=time in years

when A=2P, then that is double
A=Pe^(rt)
2P=Pe^(rt)
divide by P
2=e^(rt)
r=3.1% or 0.031 solve for t
2=e^(0.031t)
take the ln of both sides
ln(2)=0.031t
divide both sides by 0.031
(ln(2))/0.031=t
use calculator
22.359=t
round to tenth
22.4 years to double

It will take approximately 1.04 years to double the principal amount.

If your company needs to produce 7,800 products by the end of the next 12 weeks, how many products will you need to produce each week to finish on schedule?

Answers

The company will have to produce at least 650 products each week to achieve 7800 products in 12 weeks

(7800 products divided by 12weeks = 650 products per week)

Express v in terms of t

Answers

As per linear equation, 'v' can be expressed in terms of 't' as: v = 4t - 4

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line. "

Given linear equation,

$t = (v)/(4) + 1$

⇒ $(v)/(4) = t - 1$

⇒ v = 4(t - 1)

⇒ v = 4t - 4

Learn more about a linear equation here: brainly.com/question/25170296

#SPJ2

Move the 1 to the other side

t - 1 = v/4

4(t - 1) = v
4t - 4 = v

Four people in a room. Each shakes hands with each of the others once. How many handshakes are there? 6
10
12
16
22

Answers

The correct answer is 6.

The clearest way to determine this is by creating a table of possible hand shaking. If we label the people A-D, the following are the ways they can be combined:
AB
AC
AD
BC
BD
CD

There are no other combinations.

There are 6 handshakes betweenfour people in the room.

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = (n!)/((n - r)!) } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = (n!)/(r! (n - r)!) } }$

Let us tackle the problem.

This problem is about Combination.

If there are 4 people in a room , then the number of handshaking between 2 people is analogy as selecting 2 people from 4 people available. We will use combination formula in this problem.

$^4C_2 = (4!)/(2! (4-2)!)$