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3 years ago

Solve the following inequality. 3x + 5 < 6x - 1

Mathematics

2 answers:

Tom [10]3 years ago

7 0

3x-6x<-1-5= -3x<-6=x>2

Sergeeva-Olga [200]3 years ago

4 0

3x-6x<-1-5= -3x<-6=x>2

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Can someone help me with this question?

elena55 [62]

Answer:

238

Step-by-step explanation:

28÷4=7

7x6=42

7x3=21

7x4=28

7x7=49

7x3=21

7x4=28

(28x3)+(21x3)+49+42

84+(21x3)+49+42

84+63+49+42

147+49+42

147+91

238

6 0

2 years ago

Help me find weather or not these sides satisfy the triangle

schepotkina [342]

Answer:

No, the sides do not satisfy the triangle.

Step-by-step explanation:

OK, so you can use either use the Pythagorean Theorem or the 45-45-90 Triangle Theorem to find the answer to the question. I am going to use both in this explanation to help you see how they can be used.

Pythagorean Theorem:

$a^{2}+b^{2}=c^{2}$

45-45-90 Triangle Theorem:

a = b and $c=a\sqrt{2}$ or $b\sqrt{2}$

Use Pythagorean Theorem:

So $a=2\sqrt{3}$ , $b=2\sqrt{3}$ , and $c=6$ .

$(2\sqrt{3})^{2}+(2\sqrt{3})^{2}=6^{2}$ ?

(4×3) + (4×3) = 36 ?

12 + 12 ≠ 36

24 ≠ 36

Sides do not satisfy the triangle.

Use 45-45-90 Triangle Theorem:

$6=2\sqrt{3} \sqrt{2}$ ?

$6=2\sqrt{6}$ ? no

Sides do not satisfy the triangle.

8 0

3 years ago

What is the value of the expression 6n when n=7

zavuch27 [327]

It's 42. Just do 7 X 6.

4 0

3 years ago

Read 2 more answers

The inequality 7-2/3 < x-8 is equivalent to

inn [45]

X>43/3

Or X>29/3

Depending if you mean (7-2)/3 or 7-(2/3)

5 0

4 years ago

indicate whether the measures 8, 14, and 16 can be the side lengths of a triangle. if they can, classify the triangle.

Aleksandr-060686 [28]

Answers:

A triangle is possible.

The triangle is acute and scalene

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

Explanation:

We use the triangle inequality theorem to see if a triangle is possible with these side lengths.

Consider the side lengths a, b, and c. A triangle is possible if and only if the following 3 conditions hold true

a+b > c
a+c > b
b+c > a

Basically pick any two sides. If the sum is larger than the third side, then a triangle is possible.

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

In this case we have: a = 8, b = 14, c = 16. The order of the a,b,c values doesn't really matter.

Then:

a+b = 8+14 = 22 which is larger than c = 16. So a+b > c is true.
a+c = 8+16 = 24 is larger than b = 14. So a+c > b is true.
b+c = 14+16 = 30 is larger than a = 8. So b+c > a is true.

All three inequalities mentioned are true; therefore, a triangle is possible with these side lengths.

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

We'll use those a,b,c values in the converse of the pythagorean theorem to determine what kind of triangle this is. So far we know it's scalene because all three side lengths are different. It would be isosceles if it had exactly two equal sides, and equilateral if all 3 sides were the same length.

$a^2+b^2 = c^2\\\\8^2+14^2 = 16^2\\\\260 = 256\\\\$

The last equation is false, which tells us this triangle is not a right triangle. It's either acute or obtuse.

Since $a^2+b^2 > c^2$ is the case here, we can conclude the triangle is acute

If $a^2+b^2 < c^2$ was the case, then the triangle would be obtuse.

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

Summary:

A triangle is possible with side lengths a = 8, b = 14, c = 16.
This triangle is scalene and acute

4 0

1 year ago