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3 years ago

Determine whether the triangles are congruent by sss sas asa aas hl

Mathematics

1 answer:

Semmy [17]3 years ago

7 0

Answer:

Congruent by SAS

Step-by-step explanation:

The three given sides of one triangle is shown to be equal to the corresponding sides of the other triangle.

This means that all threes sides of one are congruent to all corresponding sides of the other triangle.

By the Side-Side-Side Congruence Theorem, we can conclude that both triangles are congruent.

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3 years ago

1. Ben had 50 baseball cards in each of 25 boxes. How many baseball cards did he have altogether?

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3 years ago

The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ

Nutka1998 [239]

Answer:

equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

(x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

-18-3 = -21
-18-1 = -19
-18+1 = -17
-18+3 = -15

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

(x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

4x +12 = -72 . . . . . collect terms

4x = -84 . . . . . . . . subtract 12

x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

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4 years ago

If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

Step 2: Differentiate

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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