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kow [346]
3 years ago
5

Solve -7 < 3x + 2 < 14

Mathematics
2 answers:
zepelin [54]3 years ago
5 0

Answer:

- 7 < (3x + 2) < 14 \\  \\ =  \:  \:   - 7 - 2 < 3x < 14 - 2 \\  \\ =  \:  \:   - 9 < 3x < 12 \\  \\  =  \:  \:  \frac{ - 9}{3}  <  \frac{3x}{3}  <  \frac{12}{3}  \\  \\  = { \boxed{ \boxed{ - 3 < x < 4}}}

ratelena [41]3 years ago
4 0

Answer:

-3<x<4

Step-by-step explanation:

Hi there!

We are given the double inequality -7<3x+2<14 and we want to solve it.

If we have a double inequality and we want to do something (like subtract 3), then we must subtract 3 from the left side, middle, and right side.

An example would be with the inequality 1<x+3<5

In order to isolate x, we'll subtract 3 from the center. However, we'll also be needing to subtract 3 from the left (1-3) and the right (5-3)

Hence,

1<x+3<5

-3   -3  -3

___________

-2<x<2

In our problem then, we'll be subtracting 2 from EVERY side.

-7<3x+2<14

-2      -2   -2

________________

-9 < 3x  < 12

Now in order to isolate x, we'll divide by 3, which once again, we divide on EVERY side

-3<x<4

Hope this helps!

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Match these similar triangles proof<br>​
AlekseyPX

Answer:

B

C

F

D

H

A

G

E

Step-by-step explanation:

Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.

The first statement is always the given.

Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.

Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.

Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.

Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.

Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.

The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.

The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.

7 0
3 years ago
Find the opposite of -3
WITCHER [35]
The opposite would be 3

__

4
Just switch out the negatives for positives
8 0
3 years ago
Read 2 more answers
I need this please help ​
Korolek [52]

Answer:

30

Step-by-step explanation:

Add all of them

5 0
3 years ago
If it is equal to (or) greater than 5, add ___ to previous digit.
Lisa [10]

Answer:

<h2>(b) 0 is the right answer.... </h2>
8 0
3 years ago
Question 1 of 10
Darya [45]

Answer:

Log₆ (A⁵C² / D⁶) = –13

Step-by-step explanation:

From the question given above,

Log₆ A = 1

Log₆ C = 3

Log₆ D = 4

Log₆ (A⁵C² / D⁶) =?

Recall:

Log MN / U = Log M + Log N – Log U

Therefore,

Log₆ (A⁵C² / D⁶) = Log₆ A⁵ + Log₆ C² – Log₆ D⁶

Recall:

Log Mⁿ = nLog M

Thus,

Log₆ A⁵ + Log₆ C² – Log₆ D⁶

= 5Log₆ A + 2Log₆ C – 6Log₆ D

Log₆ A = 1

Log₆ C = 3

Log₆ D = 4

= 5(1) + 2(3) – 6(4)

= 5 + 6 – 24

= 11 – 24

= –13

Therefore,

Log₆ (A⁵C² / D⁶) = –13

7 0
2 years ago
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