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jasenka [17]
3 years ago
12

Solve the following equation by COMBINING LIKE TERMS FIRST: 3x + 3 - x + 4 = 21

Mathematics
1 answer:
bonufazy [111]3 years ago
8 0
3x + 3 - x + 4 = 21

3x - x = 2x

2x +3 +4 = 21

3 + 4 = 7

2x + 7 = 21
      -7    -7

2x = 14
---    ----
2       2

x = 7
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Tomas bought 80 tickets for rides at an amusement park. Each ride costs 5 tickets, and Tomas has been on x rides so far. Which e
Alex Ar [27]

Answer:

Option A, C and D are correct choices.

Step-by-step explanation:

Let x be the number of rides that Tomas has been on so far. Each ride costs 5 tickets. This means that cost of x rides will be 5x.

We are told that Tomas bought 80 tickets for rides at an amusement park.

To find the number of of tickets that Tomas has left we will subtract cost of x rides from total number of tickets that Thomas bought.

We can represent this information in an expression as: 80-5x

Now let us see which of our given choices in equivalent to our expression.

A. 80-5x

Upon looking at option A we can see that it is same as our expression, therefore, option A is the correct choice.

B. 80+5x

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option B is not a correct choice.

C. 5(16-x)

Upon distributing 5 we will get,

80-5x

Now this expression is same same as our expression, therefore, option C is the correct choice.

D. -5x+80

This expression is also same as our expression as we can rearrange the terms in this expression as: 80-5x, therefore, option D is a correct choice as well.

E. 5(16+x)

Upon distributing 5 we will get,

80+5x

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option E is not a correct choice.

6 0
3 years ago
I’m need this worked out step by step by tonight
Pie

9514 1404 393

Answer:

  -3 ≤ x ≤ 19/3

Step-by-step explanation:

This inequality can be resolved to a compound inequality:

  -7 ≤ (3x -5)/2 ≤ 7

Multiply all parts by 2.

  -14 ≤ 3x -5 ≤ 14

Add 5 to all parts.

  -9 ≤ 3x ≤ 19

Divide all parts by 3.

  -3 ≤ x ≤ 19/3

_____

<em>Additional comment</em>

If you subtract 7 from both sides of the given inequality, it becomes ...

  |(3x -5)/2| -7 ≤ 0

Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.

__

For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...

  |f(x)| < (some number) . . . . or ≤

If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:

  |f(x)| > g(x)   ⇒   f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0

Any solutions to these inequalities must respect their domains.

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1. find the sum of the measures of exterior angles, one at each vertex, of an octagon.
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For #1, C. 1080, For #2, B. 7, For #10, I think its because of the reflexive property (honestly, Google it just to be safe) , And for #11, A Rhombus, Having trouble remembering why but I know its not a rectangle or square.

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