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pshichka [43]
3 years ago
9

4x+2(3x-9)=42 what is x equal

Mathematics
1 answer:
katrin2010 [14]3 years ago
8 0
<span>4x+2(3x-9)=42
first we want to distribute the 2 using the distributive property
4x+6x-18=42
Then we simplify
</span><span>10x-18=42
we add 18 to both sides
10x=60
divide both side by 10
x=6</span>
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Select all of the following that would be an acceptable set builder notation for the set {7, 8, 9, 10, 11, 12, 13, 14}.
ludmilkaskok [199]
<h3>Answer: Choice B</h3>

{x | x is a natural number with 6 < x < 15}

===========================================================

Explanation:

The given set is in roster notation. Think of a baseball or football team (or any sports team) how their roster lists out all of the players. In this case, each number is like a player.

The idea here is to simplify the set so we don't have to write out every single item. Instead we have a rule to make things a bit simpler.

In this case, the set {7, 8, 9, 10, 11, 12, 13, 14} describes all natural numbers from 7 to 14

This means we can say {x | x is a natural number with 6 < x < 15}

Note how the endpoints x = 6 and x = 15 are not included. This is because there isn't a "or equal to" as part of the inequality sign. Sure enough 6 and 15 are not part of the original set.

An equivalent set would be \{ x | \text{ x is a natural number with } \ 7 \le x \le 14\} and here we have "or equal to" involved. For this example, the endpoints x = 7 and x = 14 are included.

--------------

Something like choice A and choice D are not complete answers because we don't know if x is a whole number, natural number, rational number, real number, etc. If x was say a real number, then x = 10.75 would be involved with choice A. But 10.75 is not part of the original set.

5 0
3 years ago
a. In order for ΔABC to be similar to ΔDEF, what must be true about the angles? Be specific. b. If you know that ΔABC is similar
igomit [66]
I) if the triangles are similar then the corresponding angles are congruent. this means that the angles are of the same size.

ii)  If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
thus, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, thus to get m∠C; 
180- (52+65)
=  63 , therefore; m∠C= 63

iii) if two figures are similar they have the same shape and not necessarily the same size while if two figures are congruent then they have the same shape and size
5 0
3 years ago
A hot air balloon rises an initial 525
ludmilkaskok [199]

Answer:

380ft

Step-by-step explanation:

Assuming the balloon rises 525ft from sea level (0ft), all we need to do is subtract both numbers to find the new height.

525 - 145 = 380ft

There could be many different scenarios though because if the question provides the height of land off sea level, you would have to take that into account as well.

Best of Luck!

5 0
2 years ago
Solve the following linear system by graphing <br> 4x+5y=10<br> 3x-3y=21
Inga [223]

Answer:

y = 2

x = 5

Step-by-step explanation:

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×4 |

12x + 15y = 30

12x - 12y = 84

____________--

27y = -54

y = -54/27

y = 2

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×5 |

12x + 15y = 30

15x - 15y = 105

____________+

27x = 135

x = 135/27

x = 5

6 0
3 years ago
I need help with these 2 problems. Please and thank you :)
dsp73

Answer:

2,8

Step-by-step explanation:

the upper arrow goes down just like the other one so which every number you see its on go to that number and look up im at explaining but that is the answer for the 1st page

7 0
2 years ago
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