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PIT_PIT [208]
2 years ago
6

18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X

Mathematics
1 answer:
Dmitrij [34]2 years ago
4 0

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

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Samantha measured 40 1/2 inches. Over the next 5 1/2 years, she grew to a height of 57 inches. During the 5 1/2 years, what was
Alexxandr [17]

Answer:3 in. per yr

Step-by-step explanation:

Present height of Samantha is 40\frac{1}{2}=\frac{81}{2}

After next 5\frac{1}{2} years i.e. \frac{11}{2} years

she grew to 57\ inches

Increase in her height=57-\frac{81}{2}=16.5\ inches

Increase in height per year is =\frac{16.5}{5.5}=3\ in.\ per\ year

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3 years ago
Which functions graph has a y-intercept of 2?
jeka57 [31]

Answer:

The y-intercept is the constant [whole number, the one without a variable] in the equation. So you're looking for the equation that has + 2 at the end, not -2.

Step-by-step explanation:

6 0
2 years ago
Help differentiate this
Arte-miy333 [17]

Answer:

\displaystyle y' = 20x^3 + 6x^2 + 70x + 9

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Distributive Property

<u>Algebra I</u>

  • Terms/Coefficients
  • Expand by FOIL
  • Functions
  • Function Notation

<u>Calculus</u>

Derivatives

Derivative Notation

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

Derivative Property [Addition/Subtraction]:                                                            \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. 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:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle y = (x^3 + 7x - 1)(5x + 2)<em />

<em />

<u>Step 2: Differentiate</u>

  1. Product Rule:                                                                                                    \displaystyle y' = \frac{d}{dx}[(x^3 + 7x - 1)](5x + 2) + (x^3 + 7x - 1)\frac{d}{dx}[(5x + 2)]
  2. Basic Power Rule [Derivative Property - Addition/Subtraction]:                   \displaystyle y' = (3x^{3 - 1}+ 7x^{1 - 1} - 0)(5x + 2) + (x^3 + 7x - 1)(5x^{1 - 1} + 0)
  3. Simplify:                                                                                                             \displaystyle y' = (3x^2+ 7)(5x + 2) + 5(x^3 + 7x - 1)
  4. Expand:                                                                                                             \displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5(x^3 + 7x - 1)
  5. [Distributive Property] Distribute 5:                                                                 \displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5x^3 + 35x - 5
  6. Combine like terms:                                                                                         \displaystyle y' = 20x^3 + 6x^2 + 70x + 9

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

Unit: Derivatives

Book: College Calculus 10e

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The output is ten less then the input x
mart [117]

Y=X-10

Step-by-step explanation:

Step 1:

Let X be the input and Y be the output variable

Given:  The output is 10 less than the input

Step 2:

Y=X-10 be the require function

Eg:

for X=1, Y = -9

     X=2, Y=-8, etc

6 0
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