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nlexa [21]
3 years ago
7

Which ordered pair makes both inequalities true? y > –2x + 3 y < x – 2 (0,0) (0,–1) (1,1) (3,0)

Mathematics
2 answers:
Ivenika [448]3 years ago
8 0

Answer:

Option D is correct.

Step-by-step explanation:

Given inequalities are y > -2x + 3 ..............(1)

and y < x - 2 ...................(2)

Option A).

Inequality (1)

LHS = y = 0

RHS = -2x + 3 = 3

LHS < RHS

So, (0,0) does not satisfy it.

Also there is not to check for other inequality.

Option B).

Inequality (1)

LHS = y = -1

RHS = -2x + 3 = 3

LHS < RHS

So, (0,-1) does not satisfy it.

Also there is not to check for other inequality.

Option C).

Inequality (1)

LHS = y = 1

RHS = -2x + 3 = -2 + 3 = 1

LHS = RHS

So, (1,1) does not satisfy it.

Also there is not to check for other inequality.

Option D).

Inequality (1)

LHS = y = 0

RHS = -2x + 3 = -6 + 3 = -3

LHS > RHS

So, (3,0) satisfy the 1st inequality.

Now, check for other inequality.

Inequality (2)

LHS = y = 0

RHS = x - 2 = 3 - 2 = 1

LHS < RHS

So, (3,0) also satisfy the 2nd inequality.

Therefore, Option D is correct.

dimaraw [331]3 years ago
4 0

We are given inequality y > –2x + 3y < x – 2 .

Given options: (0,0) (0,–1) (1,1) (3,0)

Plugging first coordinate (0,0) in given ineqauality

0 > –2(0) + 3(0) < 0 – 2

0> 0< -2.

First option is not true.

Let us check (0,-1) now.

-1 > –2(0) + 3(-1) < 0 – 2

-1 > -3 < -2.

We can see -1 is greater than -3 and -3 is less than -2.

<h3>Therefore, (0,-1) make the given inequality true.</h3>
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Part a)

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P(junior) = 0.33333 approximately

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Part d)

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P( (Apple or Samsung) | Junior ) = 180/235

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Answer:

\displaystyle 64

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Rule [Variable Direct Substitution Exponential]:                                         \displaystyle \lim_{x \to c} x^n = c^n

Limit Property [Multiplied Constant]:                                                                     \displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle  \lim_{x \to 0} f(x) = 4

<u>Step 2: Solve</u>

  1. Rewrite [Limit Property - Multiplied Constant]:                                           \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4
  2. Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:       \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)
  3. Simplify:                                                                                                         \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64

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

Unit: Limits

Book: College Calculus 10e

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