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3 years ago

4a² + 8a -100 Factor

1 answer:

8 0

This is not factorable. It can be easily tested using the radicand expression of the quadratic equation. (Perfect square= Factorable, No Perfect= Not Factorable.)

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What happens if the red lines are NOT parallel. Which angle types are still congruent?(please help)

PtichkaEL [24]

Answer:

If they are not parallel they will cross.

The angle types that are still congruent are the angles that are the same size.

Step-by-step explanation:

Parallel lines never cross but non parallel lines cross.

<h2>Could I please have BRAINLIEST?</h2>

5 0

3 years ago

For making a scatter plot of the data set, which would be the best scale and interval for the axis that represents the amount of

Serga [27]

I'd say the answer to the first question is D) 0 to 4 with intervals of 0.2.

Because, you can't just have 1 to 4, as some of the numbers are less than 1. Of course you can't have 2 to 5 either. And intervals of 2 would be too messy.

For the second question:

I believe the answer is A. Because it's obvious that there IS one outlier, and it looks like there are two clusters.

So, the answers are: A) and D).

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3 years ago

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AC=5 and BH=2, find AH and CH.

Yakvenalex [24]

Answer:

AH = 1 or 4

CH = 4 or 1

Step-by-step explanation:

An altitude divides a right triangle into similar triangles. That means the sides are in proportion, so ...

AH/BH = BH/CH

AH·CH = BH²

The problem statement tells us AH + CH = AC = 5, so we can write

AH·(5 -AH) = BH²

AH·(5 -AH) = 2² = 4

This gives us the quadratic ...

AH² -5AH +4 = 0 . . . . in standard form

(AH -4)(AH -1) = 0 . . . . factored

This equation has solutions AH = 1 or 4, the values of AH that make the factors be zero. Then CH = 5-AH = 4 or 1.

3 0

3 years ago

The Flip-Flop-Alot Company makes and sells flip-flops. They have one linear function that represents the cost of producing flip-

Brums [2.3K]

If we let the number of flip-flops be x in the equation and that the cost would be y ( in terms of x) and the income would be z ( in terms of x), these equations will likely intersect each other during breakeven. That is, when the total revenue that the company will gain from sales of the flip-flops just be equal with the total cost.

8 0

3 years ago

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

2 years ago

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