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Fudgin [204]
3 years ago
8

Use the definition of continuity and the properties of limits to show that the function

Mathematics
1 answer:
Zepler [3.9K]3 years ago
7 0

Answer:

Applied the definition and the limit.

They had the same result, so the function is continuous.

Step-by-step explanation:

At function f(x) is continuous at x = a if:

\lim_{x \to a} f(x) = f(a)

In this question:

f(x) = x^{2} + 5(x-2)^{7}

At x = 3.

\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14

f(3) = 3^{2} + 5(3-2)^{7} = 14

Since \lim_{x \to 3} f(x) = f(3), f(x) is continuous at x = 3.

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Quadrilateral WXYZ has the coordinates W(b, b), X(4b, b), Y(3b, 0), and Z(0, 0).
AnnZ [28]

The length of side WX in Quadrilateral WXYZ is 3b units.

<h3>Coordinate plane</h3>

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:

AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Given the coordinates W(b, b), X(4b, b), Y(3b, 0), and Z(0, 0). The length of WX is:

WX=\sqrt{(b-b)^2+(4b-b)^2}=3b

The length of side WX in Quadrilateral WXYZ is 3b units.

Find out more on coordinate plane at: brainly.com/question/26100648

7 0
2 years ago
What is 8 groups of0.32?
Lelechka [254]
Okay! In order to find 8 groups of .32 you'd simply divide them. So:

[.32 ÷ 8] = .04

To check you multiply:

[8 x .04] = .32.

The answer is .04
4 0
3 years ago
Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
r-ruslan [8.4K]

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

5 0
3 years ago
Read 2 more answers
Another landscape architect recommends installing a triangular statue
Dima020 [189]

Answer:

A landscape architect recommends installing a triangular statue with

vertices at (10, −10), (10, −8), and (7, −10).

a. Is the triangle congruent to triangle T ? Justify your answer.

b. Propose a series of rigid motions that justifies your answer to part a.

6. Another landscape architect recommends installing a triangular statue

Step-by-step explanation:A landscape architect recommends installing a triangular statue with

vertices at (10, −10), (10, −8), and (7, −10).

a. Is the triangle congruent to triangle T ? Justify your answer.

b. Propose a series of rigid motions that justifies your answer to part a.

6. Another landscape architect recommends installing a triangular statue

5 0
3 years ago
Help
djverab [1.8K]

Answer:

x=7

Step-by-step explanation:

Find slope first

m-\frac{y2-y1}{x2-x1}

m=\frac{6-5}{7-7}

m=\frac{1}{0}\\

m is undefined- so it is a vertical line

x=7

6 0
3 years ago
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