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3 years ago

If 15bx-20>35 where b is a positive constant which of the following best describes all possible values of 4-3bx

2 answers:

8 0

Quora Open This sounds like a multiple-choice test question from a standardized test. But let's take a look at it. If 15bx – 20 > 35 ,where b is a positive constant ... So you are given an equation here. Next you are given something to compare it to. 4 – 3bx. So we want to go from 15bx – 20 to 4 – 3bx. The point is for you to think about the relationship. What is the relationship of -20 to 4? How would you turn -20 into 4? By dividing by -5. Of course, division by a negative means you have to reverse the direction of the inequality. 15bx – 20 > 35 15bx – 20 35 -5 -5 4 – 3bx < -7. Note. You will be given an option with the incorrect inequality! After all, they want to see whether you remember every part of handling an inequality like this. Notice that we didn't have to solve for x. We didn't have to do a lot to the equation. We just had to do enough. That's why it is important to take your time to read the problem carefully and think about what it wants.

kotegsom [21]3 years ago

6 0

Answer: Any values greater than -7

Explanation: answered it

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2 years ago

Factor the expression into an equivalent form 12y^2-75.

elena-14-01-66 [18.8K]

Hello oddworld7836!

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Factor the expression into an equivalent form 12y² - 75.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$12 y ^ { 2 } - 75$

By observing the expression, we can see that, 3 is the only common factor in both the terms of the expression. So, take the common factor 3 out.

$12 y ^ { 2 } - 75 \\ = 3\left(4y^{2}-25\right)$

Now, look at (4y² - 25). They don't have any common factors but they appear in the form of the algebraic identity ⇨ a² - b² = (a + b) (a - b). Here,

a² = 4, a = 2 (√a² = ✓4 = 2)
b² = 25, b = 5 (√b² = ✓25 = 5)

So, the (4y² + 25) becomes...

$(4 {y}^{2} - 25) \\ = \left(2y-5\right)\left(2y+5\right)$

Now, bring the 3 (common factor) & rewrite the complete expression.

$12 y ^ { 2 } - 75 \\ = \boxed{ \boxed{ \bf \: 3\left(2y-5\right)\left(2y+5\right) }}$

We can't further simplify it. Also, remember that the simplified form of an expression is equivalent to the expression. So, 3 (2y - 5) (2y + 5) is equivalent to 12y² - 75.

__________________

Hope it'll help you!

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