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4 years ago

Use the graph of f(x)=x^2 to find a number δ such that ∣x^2−1∣<0.1 whenever 0<|x−1|<δ.

Mathematics

1 answer:

choli [55]4 years ago

8 0

Answer:

$\delta=0.0333$

Step-by-step explanation:

$|x^2-1}=|x-1||x+1|$

$|x|-|1|$

$|x|$

$|x+1|$

Hence

$|x-1|$

Hopefully you get what I meant!!

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AB is congruent to DE because segment DE was constructed so that DE = AB. BC is congruent to EF because segment EF was construct

Alex Ar [27]

DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

<h3>Congruent shape</h3>

Two shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.

Given that DE = AB and BC = EF.

In right triangle DEF, using Pythagoras:

DF² = DE² + EF²

Also, In right triangle ABC, using Pythagoras:

AC² = AB² + BC²

But DE = AB and EF = BC, hence:

AC² = DE² + EF²

AC² = DF²

Taking square root of both sides, hence:

AC = DF

Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

Find out more on Congruent shape at: brainly.com/question/11329400

6 0

3 years ago

The set of ordered pairs represents a

Murrr4er [49]

Answer:

The rule that represents the function is $y=x^2+1$ therefore the function is $f(x)=x^2+1$

Step-by-step explanation:

We have 5 ordered pairs in the plane xy. This means that every pair has the form (x, y).

Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.

The easy evaluation is that when x=0, the value of y is y=1, and then we can evaluate the rule for x=-1, and x=1, the value of y is the same, y=2. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.

So we propose the rule $y=x^2+1$ which is correct for the first 3 values of x.

Now, we evaluate the proposed rule when x=2, and when x=3. This evaluations can be written as

$f(2)=2^2+1=5$

$f(3)=3^2+1=10$

Therefore, the rule is correct, and the function is

$f(x)=x^2+1$

8 0

4 years ago

<img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%205x%20-%206" id="TexFormula1" title=" {x}^{2} + 5x - 6" alt="

Ymorist [56]

Answer:

(x+6)(x-1)

Step-by-step explanation:

factor using the x-box method

7 0

3 years ago

Read 2 more answers

Simplify the following expression by combining like terms and factoring. 2(x-6)+4(2x+1)+3

Shkiper50 [21]

Answer:

5(2x - 1)

Step-by-step explanation:

Given

2(x - 6) + 4(2x + 1) + 3 ← distribute both parenthesis

= 2x - 12 + 8x + 4 + 3 ← collect like terms

= (2x + 8x) + (- 12 + 4 + 3)

= 10x + (- 5)

= 10x - 5 ← factor out 5 from each term

= 5(2x - 1) ← in factored form

4 0

3 years ago

Easton bought 8 chicken wings for $8.80. How much would it cost for 17 wings?

olga2289 [7]

18.70
Because they are 1.10 each

4 0

4 years ago