Which of the following would be an acceptable first step in simplifying the expression:

If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3

horrorfan [7]

Answer: The correct option is (B) 24 : 25.

Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

$\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Therefore, the ratio of the area of R to the area of S is

$\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.$

Thus, the required ratio of the area of R to the area of S is 24 : 25.

Option (B) is CORRECT.

6 0

3 years ago

Factor 26r3s + 52r5 – 39r2s4.

algol [13]

Answer:

13r²(2rs + 4r³ - 3s⁴)

Step-by-step explanation:

In equation 26r³s + 52r⁵ - 39r²s⁴;

The GCF of 26, 52, and 39 = 13

The GCF of r³, r⁵ and r² = r²

The GCF of s, (no "s"), and s⁴ = no "s" (Since one of the number doesn't have "s")

Now we can factor out 13r² from all three expressions;

26r³s + 52r⁵ - 39r²s⁴

=> 13r²(2rs) + 13r²(4r³) - 13r²(3s⁴)

To factor it all together;

13r²(2rs + 4r³ - 3s⁴)

Hope this helps!

7 0

2 years ago

A large pizza at palanizo pizzeria costs 6.80$ plus 0.90$ for each topping. The cost of a large cheese pizza at guido’s pizza is

r-ruslan [8.4K]

we are going to create a table in excel and we will assign different values of topping to know when the price is equal in both pizzerias

see the attached figure

the answer is

5 toppings from palanzio’s pizzeria

6 toppings from guido’s pizza

cost palanzio’s pizzeria----> 6.80+0.90*5-----> $11.30

cost guido’s pizza------> 7.40+0.65*6----------> $11.30

5 0

2 years ago

the drama club has sold 942 tickets to their play if their theater seats 57 each row how many full rows were there be how many e

Alona [7]

Since 57x17=969 I did 969-942 and got 27 so there is 16 full rows and then 27 left over so that means it won’t be a full row but 27 extra seats will be filled. (If your wondering where the 17 came from that’s how many rows can be made that’s over 942 because if I did 57x16 it would equal 912 and I would not have had a full row of chairs)

3 0

2 years ago

» Which pair of numbers has an LCM of 60? 2 and 12 5 and 12 6 and 12 3 and 12

Mariana [72]

Answer: 5 and 12

Step-by-step explanation:

2 and 12 is not it because 12 can be divided by 2 meaning that the LCM of those two numbers will be 12.

6 and 12 is not it because 12 can also be divided by 6 meaning that the LCM of 6 and 12 is also 12.

3 and 12 is also the same, 12 can be divided by 3 so their LCM will be 12.

With 5 and 12, 12 is not divisible by 5 so you will have to find the multiples of 5 and 12 and it will eventually be 60.

Multiples of 5: 5, 10,15,20,25,30,35,40,45,50,55,60,65

Multiples of 12: 12, 24, 36, 48, 60, 72

As it appears in both multiples, 60 is the least number that appears in both multiples so the LCM of 5 and 12 is 60.

3 0

2 years ago

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