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3 years ago

Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.

Mathematics

1 answer:

lilavasa [31]3 years ago

8 0

Answer:

$=2(2x-5)(x+1)$

Step-by-step explanation:

So we have the trinomial:

$4x^2-6x-10$

First, factor out a 2:

$=2(2x^2-3x-5)$

Now, factor within the parentheses.

To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b

(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.

-5 and 2 works. Therefore:

$=2(2x^2-3x-5)$

Replace -3x with 2x and -5x:

$=2(2x^2+2x-5x-5)$

Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:

$=2(2x(x+1)-5(x+1))$

Grouping:

$=2(2x-5)(x+1)$

And we're done!

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F(x)8x^2 find its inverse

olya-2409 [2.1K]

Answer:

$f^{-1}(x)=\frac{1}{2}\sqrt{\frac{x}{2}}$

Step-by-step explanation:

Given:

The function is given as;

$f(x)=8x^2$

In order to find the inverse, the steps to be followed are:

Step 1: Replace $f(x)$ by $y$ . This gives,

$y=8x^2$

Step 2: Switch 'y' by 'x' and 'x' by 'y'. This gives,

$x=8y^2$

Step 3: Solve for 'y'.

Dividing both sides by 8, we get:

$\frac{x}{8}=\frac{8y^2}{8}$

$\frac{x}{8}=y^2$ or

$y^2=\frac{x}{8}$

Taking square root on both sides, we get:

$\sqrt{y^2}=\sqrt{\frac{x}{8}}$

$y=\frac{1}{2}\sqrt{\frac{x}{2}}$

Now, we replace 'y' by $f^{-1}(x)$ .

Therefore, the inverse of the given function is:

$f^{-1}(x)=\frac{1}{2}\sqrt{\frac{x}{2}}$

3 0

3 years ago

You have at most $10 to spend on notebooks and markers. Markers cost $1 each, and

kherson [118]

Answer is provided in the picture uploaded with steps

5 0

3 years ago

Samantha made 12 necklaces with 240 glass beads. Angelina made 11 necklaces with 231 glass beads. Select all statements that are

Alika [10]

Samantha : 240/12 = 20 glass beads per necklace
angelina : 231/11 = 21 glass beads per necklace

angelina uses 21 glass beads per necklace -- TRUE
samantha uses 1 glass bead for every 20 necklaces -- FALSE
angelina's necklaces have a unit rate of 20 glass beads per necklace -- FALSE
samantha's necklaces have a unit rate of 20 glass beads per necklace -- TRUE
samantha's necklaces have fewer glass beads then angelina's necklaces do -- TRUE

7 0

4 years ago

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pychu [463]

Answer:

waste

Step-by-step explanation:

Try to think of something that doesn't involve energy and you won't get very far. Even thinking—even thinking about energy!—needs some energy to make it happen. In fact, everything that happens in the world uses energy of one kind or another. But what exactly is energy?

Energy is a bit of a mystery. Most of the time we can't see it, yet it is everywhere around us. Revving car engines burn energy, hot cups of coffee hold energy, street lights that shine at night are using energy, sleeping dogs are using energy too—absolutely everything you can think of is using energy in one way or another. Energy is a magical thing that makes other things happen. Everything in the world is either energy or matter ("stuff" around us) and even matter, when you really get down to it, is a kind of energy!

3 0

3 years ago

Find the slope of the line that passes through:<br> (6,7) and (4,2)

snow_lady [41]

Answer:

5/2

Step-by-step explanation:

Slope = Change in y/Change in x

Slope = 2 - 7/4 - 6

Slope = -5/-2

Slope = 5/2

-Chetan K

6 0

3 years ago