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3 years ago

Evaluate: 13 × 20 – 15 × 9 + 20 × 7 – 6 × 15.

Mathematics

2 answers:

Korolek [52]3 years ago

6 0

Answer:

175

Step-by-step explanation:

Mkey [24]3 years ago

6 0

Answer:

175

Step-by-step explanation:

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Hope this helps. :)

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4 years ago

The ratio of the number of dogs the number of cats is 4:5. There are 270 animals on the rescue Farm. The number of dogs is 4/5.

mafiozo [28]

Answer:

Here is the complete question:

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒ $c+d=270$ ...equation (i)

Arranging the ratio:

⇒ $\frac{4}{5} = \frac{d}{c}$

⇒ $4c=5d$

⇒ $c=(\frac{5}{4})d$ ...equation (ii)

Plugging (ii) in equation (i).

⇒ $c+d=270$

⇒ $\frac{5}{4} d+d=270$

⇒ $\frac{5d+4d}{4} =270$

⇒ $9d=270\times 4$

⇒ $d=\frac{270\times 4}{9}$

⇒ $d=120$

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

The number of dogs is 4/5 the number of cats.

⇒ $\frac{4}{5} \times 150$

⇒ $\frac{4\times 150}{5}$

⇒ $120$

Statement is true.

4/5 of the pets at the farm are dogs.

⇒ $\frac{4}{5} \times 270$

⇒ $216$

Number of dogs = 120

So the above statement is false.

There are exactly 30 more cats than dogs.

⇒ $c-d =30$

⇒ $150-120=30$

Statement is true.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

5/9 of the pets at the farm are cats.

⇒ $\frac{5}{9} \times 270$

⇒ $150$

Statement is true.

So,

Statement a,c and e are true as we could observe in the explanation.

8 0

3 years ago

The midsegment of a trapezoid is always parallel to each base true or false

Deffense [45]

Answer:

True

Step-by-step explanation:

we know that

The Trapezoid Mid-segment Theorem states that : A line connecting the midpoints of the two legs of a trapezoid is parallel to the bases, and its length is equal to half the sum of lengths of the bases

see the attached figure to better understand the problem

EF is the mid-segment of trapezoid

EF is parallel to AB and is parallel to CD

EF=(AB+CD)/2

The mid-segment of a trapezoid is always parallel to each base

therefore

The statement is true