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3 years ago

-18 + 2a = 2(3a + 1)

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

3 0

Answer:

a = -5

Step-by-step explanation:

Given

-18 + 2a = 2(3a + 1)

Expand the bracket on the right

-18 + 2a = 2 x 3a + 2 x 1

-18 + 2a = 6a + 2

Add 18 to both sides

-18 + 18 + 2a = 6a + 2 + 18

2a = 6a + 20

Subtract 6a from both sides

2a - 6a = 6a - 6a + 20

-4a = 20

Divide both sides by -4

-4a/-4 = 20/-4

a = -5

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Parallel to y - 2x = 4 and passes through (0,5)

wolverine [178]

Answer:

y=2x+5

Step-by-step explanation:

y=2x+4 means that the slope is m1=2

A parallel line shall have the same slope so

m2=m1=2

Therefore, the equation of the new line will be

y=2x+q

where q is the y-intercept, that is 5 because the line must pass in (0,5), so

q=5

and

y=2x+5

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

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:

<em>Here is the complete question:</em>

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

2 years ago

How to find height of a triangular prism where length is 9, width is 3.5, and height is unknown. Volume is 50.4, and explain ans

riadik2000 [5.3K]

*The width in your question - I assumed it is refers to the height of the triangle base.

Volume of a triangle prism = base area x height

The base is a triangle:
Volume of a triangle prism = (1/2 x base x height₁) x height₂

Plug in the values and solve for height₂:

50.4 = (1/2 x 9 x 3.5) x height

50.4 = 15.75 x height

height = 50.4 ÷ 15.75

height = 3.2 units

-----------------------------------------
Answer: Height = 3.2 units
-----------------------------------------

5 0

3 years ago

Here is a riddle:

lilavasa [31]

Answer:

The system of inequalities that represents this situation will be:

$f + s < 10$

$f - s > 3$

Step-by-step explanation:

Let 'f' represent the first number

Let 's' represent the second number.

Given that the sum of the two numbers is less than 10. As 'less than' can be represented by '<'.

so the inequality would be: f + s < 10

Given that If we subtract the second number from the first, the difference is greater than 3. As 'greater than' can be represented by '>'.

so the inequality would be: f-s > 3

Thus, the system of inequalities that represents this situation will be:

$f + s < 10$

$f - s > 3$

8 0

3 years ago