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nexus9112 [7]
3 years ago
12

-3x>6 What is the solution set?

Mathematics
1 answer:
evablogger [386]3 years ago
6 0

\boxed{x

<h2>Explanation:</h2>

Here we have the following inequality:

-3x>6

So divide both sides by -3:

\frac{-3x}{-3}

When multiplying or dividing an inequality by a negative number, the direction of the inequality changes. That's the reason why we changed the sign from > to <. Finally, the solution set is:

\boxed{x

<h2>Learn more:</h2>

Inequalities: brainly.com/question/14461691#

#LearnWithBrainly

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A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. How many
Olin [163]

Given:

Total number of marbles in the bag = 150

There are 21 blue marbles for every 4 white marbles.

To find:

The number of blue marbles in the bag.

Solution:

Since, there are 21 blue marbles for every 4 white marbles, therefore the ratio of blue marble to white marbles is 21:4.

Let the number of blue marbles be 21x and white marbles be 4x.

Total number of marbles in the bag = 150

21x+4x=150

25x=150

Divide both sides by 25.

x=\dfrac{150}{25}

x=6

Now,

\text{Blue marbles}=21x

\text{Blue marbles}=21(6)

\text{Blue marbles}=126

Therefore, the number of blue marbles is 126.

8 0
2 years ago
ASAP HELP! Which equation is NOT linear?
Rus_ich [418]

Answer:

y=5x  is not linear

Step-by-step explanation:

option A is not linear

4 0
2 years ago
which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​
coldgirl [10]

9514 1404 393

Answer:

  (a) -(x+7)/y

  (b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

  \dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}

Likewise, the expression of (b) with the minus sign factored out is ...

  \dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}

On the other hand, simplifying expression (c) gives something different.

  \dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

  Given: (-x-7)/y = (-x/y) +(-7/y)

  (a) -(x+7)/y = (-x/y) +(-7/y)

  (b) (x+7)/(-y) = (-x/y) +(-7/y)

  (c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

  a(b+c) = ab +ac

  -a/b = a/(-b) = -(a/b)

  -a/(-b) = a/b

__

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

  \left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

3 0
2 years ago
What is the area of the figure below​
jek_recluse [69]

Answer:

Option A

Step-by-step explanation:

Area of the composite figure = Area of ΔABH + Area of BCGH + Area of ΔDEF

Area of ΔABH = \frac{1}{2}(\text{Base})(\text{Height})

                        = \frac{1}{2}(6)(8-5)

                        = 9 in²

Area of the trapezoid = \frac{1}{2}(CG+BH)(\text{Distance between these lines})

                                    = \frac{1}{2}(6+4)(5)

                                    = 25 in²

Area of ΔDEF = \frac{1}{2}(8)(6)

                       = 24 in²

Therefore, area of the given figure = 9 + 25 + 24

                                                          = 58 in²

Option A will be the correct option.

3 0
2 years ago
54:56
aivan3 [116]

Answer:

String

2.

4

6

Percussion

5

10

15

Step-by-step explanation:

6 0
3 years ago
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