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3 years ago

Solve the inequality y − 6>10

1 answer:

8 0

if y-6 > 10, and 16-6 = 10, then y > 16 since 17-6 = 11, which is greater than 10. Any number greater than 16 can fulfil this inequality.

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A car dealer reported a 7.5% drop in sales from 895 cars. How many cars were sold?

Evgesh-ka [11]

Answer:

its is 38.6

Step-by-step explanation:

4 0

3 years ago

Match each simplified form to it's equivalent radical expression. Tiles: 4√3, 3 3√2, 2 3√3, 3√5

lbvjy [14]

Answer:

Step-by-step explanation:

Given the following simplified expressions:

4√3, 3 3√2, 2 3√3, 3√5

It's radical equivalent is :

4√3 = √4² * √3 = √16 * √3 = √16*3 = √48

3 3√2 = 3 * √3² * √2 = √9 * √2 = √9*2 = 3√18

2 3√3 = 2 * √3² * √3 = √9 * √3 = √9*3 = 2√27

3√5 = √3² * √5 = √9 * √5 = √9*5 = √45

4 0

3 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:

<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

Write the slope-intercept form of the equation of each line.

gregori [183]

Greetings!

Answer:

2y = x - 6

Step-by-step explanation:

First, we must find the slope of the current equation.

This is the number in front of the x.

Seeing as this is -2x, the slope of this line is -2

When finding the slope of a line perpendicular, you need to find the $\frac{-1}{slope}$

So, in this case it is:

$\frac{-1}{-2}$

The negatives cancel out which leave $\frac{1}{2}$

So the gradient is $\frac{1}{2}$

Now, to find the equation of a line, you need to use:

y - y1 = m(x - x1)

Where ya and x1 are the values in the coordinates (2 , -2)

So y1 = -2, x1 = 2, and m is a half. Plug these values in:

y - - 2 = $\frac{1}{2}(x - 2)$

We need to get rid of the half so we multiply the whole equation by 2:

2y - - 4 = (x - 2)

The minus and the negative turn into a positive:

2y + 4 = x - 2

And now simply move the +4 over to the other side, making it a negative:

2y = -2 - 4 + x

Simplify:

2y = x - 6

<h3>So the equation of the line is 2y = x - 6</h3>
<h2>Hope this helps!</h2>

5 0

3 years ago

Decide whether the statement is true or false. If it is false, explain why. The union of the solution sets of 4xplus5equals13,

postnew [5]

The given statement is false because it isn't an empty set!

<u>Step-by-step explanation:</u>

We have following sets of inequalities:

$4x+5=13\\4x+5>13\\4x+5$

From $4x+5=13$ we get ,

$4x = 8 \\x=2$

Therefore solution set is x=2.

Now, for $4x+5>13$ we get ,

$4x+5>13 \\4x>8\\x>2$

Therefore solution set is x>2.

For $4x+5$ we get ,

$4x+5$

Therefore solution set is x<2.

Now, the union of x=2, x<2 & x>2 is -∞<x<∞. i.e. all possible values of x. And so above statement is false because it isn't an empty set!

4 0

2 years ago