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4 years ago

Lesson 6: geometry A unit 3: reasoning and proof

Mathematics

2 answers:

Stolb23 [73]4 years ago

7 0

Answer:

1. One way to show that a statement is not a good definition is to find a counterexample. A counterexample refers to an exception to the rule, if we deduct that exception is true, then the proposition is completely false. In this case, we have to find an exception to the definition, if the exception is true, then the definition is not true.

2. The option that show a true conditional is the fourth: If it's raining, then the humidity level is 100%. This shows the correct logical conditional, other options are not logical. In this case, the hypothesis is "if it's raining", and the conclusion is "the humidity is 100%". This is the right order, because humidity derive from raining, not the opposite.

11Alexandr11 [23.1K]4 years ago

6 0

Correct answer: Choice #4

The only valid hypothesis-conclusion matching the statement. Let me know if you need more detail.

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Factor the quadratic expression

Ber [7]

(x - 6)(x - 2) the answer to the question

3 0

4 years ago

Jeans are on sale for 20% off the regular price. Which function would give you the total cost for purchasing a pair of jeans tha

DaniilM [7]

Answer:

0.8X = Final cost

Step-by-step explanation:

Given that jeans are on sale for 20% off the regular price, to determine which function would give you the total cost for purchasing a pair of jeans that costs X dollars, the following calculation must be performed:

1X = Initial cost of the jeans

20% = 0.2

1 - 0.2 = 0.8

0.8X = Final cost

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3 years ago

Which system of equations could be graphed to solve the equation below? log Subscript 0. 5 Baseline x = log Subscript 3 Baseline

Vanyuwa [196]

You can use the fact that two expressions in equality can be considered to be equal to a third variable(not used in given context).

The system of equations that could be graphed to solve the equation given is

$y = \log_{0.5}(x)\\\\$
$y = \log_3(2+x)$

<h3>How can we form a system of equations from an equation?</h3>

Suppose the equation be $a = b\\$

Let there is a symbol $c$ such that we have $a = b = c$

It is because a and b are same measure (that is exactly what a = b means)

and we gave another name c to that measure.

Thus, we have

$a = c\\b = c$

in addition to $a = b\\$

<h3>Using the above method to find the system of equations needed</h3>

Since the given equation is $log_{0.5}(x) = log_2(2+x)$

The 2d graphs are usually expressed as $y = f(x)$ on X-Y plane.

Taking the equation's expressions equal to y, we get

$log_{0.5}(x) = log_2(2+x) = y$

or, we get system of equations as

$y = log_{0.5}(x)\\\\y = log_3{(2 + x)}$

Their graph is plotted below. The intersection point of both curves is the solution to the given equation as it satisfies both the equations of the system of equations formed from the given equation.

Thus,

The system of equations that could be graphed to solve the equation given is