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yaroslaw [1]
3 years ago
6

-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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Step-by-step explanation:

3 0
2 years ago
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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:

a.

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.

b.

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.

c.

There are exactly 30 more cats than dogs.

⇒ c-d =30

⇒ 150-120=30

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

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
2 years ago
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