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2 years ago

Given that triangle QRS is similar to triangle DEF, what is x?

Mathematics

2 answers:

marta [7]2 years ago

4 0

So the ratio is 40/26 = 1.54

24 ÷ 1.54 = 15.58

2x-4 = 15.58

2x = 19.58

x = 9.8

klasskru [66]2 years ago

3 0

Answer:

x = 9.8

Step-by-step explanation:

Given that triangle QRS is similar to triangle DEF.

Hence, the ratio of corresponding sides of these triangles are equal.

Thus, we have

$\frac{QR}{DE}=\frac{RT}{EB}$

Substituting the known values from the given figure

$\frac{26}{40}=\frac{2x-4}{24}$

Cross multiplying, we get

$40(2x-4)=26\cdot24\\\\80x-160=624\\\\80x=784\\\\x=\frac{784}{80}\\\\x=9.8$

The value of x is 9.8

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-2(x-5)=6(2- 1/2x) Please show your work. Distributive property, remove variable

schepotkina [342]

The solution of given equation is x=2

Further explanation:

In order to solve the given equation we have to isolate the variable x on one side of the equation. The process will involve distributive property and simplification.

Given:

$-2(x-5)=6(2-\frac{1}{2}x)\\Apply\ distributive\ property\\-2x-2(-5)=(6)(2)-(6)(\frac{1}{2}x)\\-2x+10=12-\frac{6}{2}x\\-2x+10=12-3x\\-2x+3x=12-10\\x=2$

The solution of given equation is x=2

Keywords: Linear Equation, Distributive property

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

What is the simplest form of 3^ √27t^9/729?

Natali [406]

Answer:

$\frac{t^{3} }{3}$

Step-by-step explanation:

$\sqrt[3]{\frac{27t^{9} }{729} }$ 27 is a perfect cube for $3^{3}$ and 729 is a perfect cube for $9^{3}$

$\sqrt[3]{\frac{3^{3} t^{9} }{9^{3} } }$ now you can pull out the numbers from under the root, for t (divide the exponent by 3)

$\frac{3}{9}$ $t^{3}$ now simply to $\frac{t^{3} }{3}$

6 0

2 years ago

Read 2 more answers

At an animal shelter, there are 15 dogs and 12 cats.

Bond [772]

Answer:

Dogs: 44.44 Cats: 55.556

Step-by-step explanation:

*this is only if you are allowed to use a calculator*

1. You have to add the total of the cats and dogs

Why? Here, let me put it this way. You have a test with two sections: math and science. If there are 2 Maths Questions and 2 Science questions, what percent of the test are math questions? You would not say 2/2 and say 100. You would say 2/4 because it is obvious. You do the same in this case but it is not as noticeable because you are dealing with bigger numbers.

15 + 12 = 27.

2. Solve

a. There are 15 dogs and 12 cats that makes up 27 pets total.

So you have to do 12/27 for cats,

15/27 for dogs. The fractions equal one and It shows you how much of one is there compared to the total.

b. Simplify

You can simplify these fractions:

for 12/27, divide the numerator and the denominator by 3.

You get 4/9

Divide 15/27 for dogs by 3 as well to get 5/9.

5+4 is 9, which means that I am doing the math correctly.

According to the calculator, 5/9 is 55.556, and 4/9 is 44.444

They should be accurate because there are more dogs than cats and the percentage for dogs are higher. Hence, this is correct.

Cats = 4/9 = 44.444%

Dogs = 5/9 = 55.556%

Hope this helps :)

-jp524

7 0

1 year ago

If the cost of a 2.5 meter cloth is $30.5. What will be the cost of 22 meters ?

alisha [4.7K]

Answer:

268.40

Step-by-step explanation:

We can write a ratio to solve

2.5 meters 22 meters

----------------- = --------------

30.5 dollars x dollars

Using cross products

2.5 * x = 30.5 * 22

2.5x =671

Divide each side by 2.5

2.5x / 2.5 = 671/2.5

x =268.4

8 0

2 years ago

of 320 consumers polled, some purchase blu-ray movies, some only purchase movies on dvd, and some do both. if 300 people polled

Helga [31]

Answer:

20 people only buy dvds.

Step-by-step explanation:

There are two groups in this problem. One group of people that buys dvds and one that buys blu rays. The total amount of people who buy blu rays is 300, but there's an intersection between the groups and the size of this is 280 people who actually buy both. In order to find out how many people only buy DVDs we first need to figure out how many only buy blu-rays. That is:

people who only buy blu rays = people who buy blu rays - people who buys blu rays and dvds

people who only buy blu rays = 300 - 280 = 20

We can now calculate the amount of people who only buy dvds and that is:

people who only buy dvds =total amount of people - ( people who only buy blu rays + people who buy both)

people who only buy dvds = 320 - (20 + 280) = 320 - 300 = 20 people

3 0

3 years ago