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2 years ago

The inequality 2x+2≤x+4≤3x+4 means that x is in the closed interval [A,B]

Mathematics

2 answers:

Alex_Xolod [135]2 years ago

5 0

Answer:

Step-by-step explanation:

2x+2≤x+4≤3x+4

means : 2x+2≤x+4 ...(1) and x+4≤3x+4

(1) : 2x-x≤4-2 so : x≤2....(*)

(2) :3x+4 ≥x+4 .... 3x-x ≥ 0 so: x≥0 ....(**)

by (*) and (**) : 0≤x≤2 so : A=0 and B = 2

kap26 [50]2 years ago

5 0

Hope you can understand this easily

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Citrus2011 [14]

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6 0

2 years ago

1) Nat's grocery bill was $150, which included a 5% club

a_sh-v [17]

Answer:

$157.89

Step-by-step explanation:

you could say that 150 is 95% of what the original bill was

in equation form: 150 = .95x

150/.95 = 158.89

158.89 = x

3 0

2 years ago

Read 2 more answers

A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute.

bogdanovich [222]

Answer:

the Bision is 10 miles / hour faster if he could keep it up

Step-by-step explanation:

There are 60 minutes in an hour.

Therefore the bison can run [3520 feet / min] * [60 min ] =211288 feet in an hour.

Now you have to convert 212200 to miles. Do this by dividing by 5280

212200/5280 = 40 miles.

Kind of hard to believe isn't it. 40 miles is a long way when you are running it.

The bison is faster by 10 miles / hour.

This can be done all in 1 step if you know how to do dimensional analysis

3520 feet / minute * [ 60 min/ hour ] * [ 1 mile / 5280 feet] = 40 miles

5 0

3 years ago

Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is

aniked [119]

Base case: For $n=1$ , the left side is 2 and the right is $2\cdot1^2=2$ , so the base case holds.

Induction hypothesis: Assume the statement is true for $n=k$ , that is

$2+6+10+\cdots+4k-2=2k^2$

We want to show that this implies truth for $n=k+1$ , that

$2+6+10+\cdots+4k-2+4(k+1)-2=2(k+1)^2$

The first $k$ terms on the left reduce according to the assumption above, and we can simplify the $k+1$ -th term a bit:

$\underbrace{2+6+10+\cdots+4k-2}_{2k^2}+4k+2$

$2k^2+4k+2=2(k^2+2k+1)=2(k+1)^2$

so the statement is true for all $n\in\mathbb N$ .

5 0

3 years ago

Which solid of revolution is produced by rotating the shape below 360° about the given axis?

maxonik [38]

<h3>Answer: Choice A</h3>

Explanation:

When we rotate a rectangle around an axis of symmetry, we end up with a cylinder. Think of a revolving door or a turbine. The flat door moves through 3D space to produce or carve out a 3D cylinder.

This figure is composed of two rectangles, so we'll end up with two cylinders. They will both share the same center, so we'll have a sideways two-layer wedding cake structure when everything is said and done. This points to choice A as the final answer.

5 0

2 years ago