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2 years ago

What is the standard form of the following equation?

Mathematics

1 answer:

scZoUnD [109]2 years ago

7 0

y = 2(x - 1)² + 4

y = 2(x² - 2x + 1) + 4

y = 2x² - 4x + 2 + 4

y = 2x² - 4x + 6

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What are the measurements of the two angles in the figure below?

IgorC [24]

Both angles need to equal 180 degrees .

Add them together:

2x +10 + 3x-5 = 180

5X +5 = 180

Subtract 5 from each side:

5x = 175

Divide both sides by 5:

X = 175 / 5

X = 35

Now replace X with 35 in each equation:

2x +10 = 2(35) +10 = 70 +10 = 80

3x-5 = 3(35) - 5 = 105 -5 = 100

The answer is A. 80 and 100

5 0

3 years ago

A spinner numbered 1 through 12 is spun. Find the probability that

anastassius [24]

Answer:

$\dfrac{1}{6}$

Step-by-step explanation:

Let A be the event of getting an odd number.

P(A) be the probability of getting an odd number.

Total odd numbers here are 6 i.e. $\{1,3,5,7,9,11\}$

Here, total numbers in the game are 12 i.e $\{1,2,3,....,12\}$ .

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}$

Let B be the event of getting 11.

P(B) be the probability of getting 11.

Total number of possible cases is 1.

$P(B) = \dfrac{1}{12}$

$P(A \cap B)$ is the probability that we get 11 and an odd number.

Possible number of cases = 1

$P(A\cap B) = \dfrac{1}{12}$

P(B/A) is the probability that we get an 11 given that it is an odd number.

$P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}$

Hence, P(B/A) = $\dfrac{1}{6}$

4 0

3 years ago

Read 2 more answers

What is the fraction eight twentieths in its simplest form?

Nostrana [21]

Both the numerator and denominator are divisible by 4, meaning that when they are both divided by this number they wll be in their simplest form.

e.g. 8/4=2 and 20/4=5

Therefore the simplest form is 2/5

7 0

3 years ago

You buy tomatoes in 25-pound cases.

julsineya [31]

For a single 25 pound case you can make 133 servings, As a single pound of tomatoes equals 16 ounces; and 16x25 is 400, and when you divide that be 3 it turns into 133.3333333- and goes on, but you round that down to 133 for your answer.

6 0

3 years ago

Determine the value of k

KATRIN_1 [288]

Answer:

$\displaystyle k = 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$

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

Unit: Limits - Continuity

Book: College Calculus 10e

4 0

3 years ago

Read 2 more answers