Evaluating a piecewise defined function

Mathematics

1 answer:

Dafna11 [192]3 years ago

4 0

Given : if x belongs to the interval -2 ≤ x < -1, then f(x) = -2

As x = -2 belongs to the interval -2 ≤ x < -1 ⇒ f(-2) = -2

As x = -1.5 belongs to the interval -2 ≤ x < -1 ⇒ f(-1.5) = -2

Given : if x belongs to the interval 1 ≤ x < 2, then f(x) = 1

As x = 1 belongs to the interval 1 ≤ x < 2 ⇒ f(1) = 1

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WILL GIVE BRAINLIEST! <br>What is the answer for question (iv)? <br>please help!

Leviafan [203]

Step-by-step explanation:

$\triangle ABC \sim \triangle ADE... (given) \\\\\therefore \frac {AC}{AE} = \frac {BC}{DE}.. (csst) \\\\\therefore \frac {5}{5+2x} = \frac {x+3}{4x+1}\\ \\ \therefore \: 5(4x + 1) = (5 + 2x)(x + 3) \\ \therefore \:20x + 5 = 5x + 15 + 2 {x}^{2} + 6x \\ \therefore \:20x + 5 =2 {x}^{2} + 11x + 15 \\ \therefore \:2 {x}^{2} + 11x + 15 -2 0x - 5 = 0\\ \therefore \:2 {x}^{2} - 9x + 10 = 0\\ \therefore \:2 {x}^{2} - 5x - 4x+ 10 = 0\\ \therefore \:x(2x - 5) - 2(2x - 5) = 0 \\ \therefore \:(2x - 5)(x - 2) = 0 \\ 2x - 5 = 0 \: \: or \: \: x - 2 = 0 \\ x = \frac{5}{2} \: \: or \: \: x = 2 \\ x = 2.5 \: \: or \: x = 2 \\ x = 2.5 \: is \: largest \\ \\ \frac{A(\triangle ABC)}{ A(\triangle ADE)} = \frac{AC ^{2} } {AE^{2} } \\ \\ \frac{A(\triangle ABC)}{ A(\triangle ADE)} = \frac{5 ^{2} } {(5 + 2x)^{2} } \\ = \frac{25}{(5 + 2 \times 2.5)^{2} } \\ = \frac{25}{ {10}^{2} } \\ = \frac{25}{100} \\ \\ \frac{A(\triangle ABC)}{ A(\triangle ADE)} = \frac{1}{4} \\$

5 0

4 years ago

The probability of sandy flipping a coin twice and getting heads both times is 0.25 the probability of john's spinner stopping o

Rom4ik [11]

The true statement is (c) Neither. Both events are equally likely.

<h3>Complete question</h3>

The probability of Sandy flipping a coin twice and getting heads both times is 0.25. The probability of John's spinner stopping on the color red is 1/4.

Which of these events is more likely?

-Sandy flips a coin twice and gets heads both times.

-John's spinner stops on the color red.

-Neither. Both events are equally likely.

<h3>How to determine the likely event?</h3>

The given parameters are:

P(Head twice) = 0.25

P(Red) = 1/4

Rewrite P(Red) as:

P(Red) = 0.25

By comparison, we have:

P(Red) = P(Head twice) = 0.25