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3 years ago

Simplify the expressions below a+2b+5+3a+b 12−a+a+12 4x−12+4x

Mathematics

1 answer:

NeTakaya3 years ago

3 0

Answer:

A. 4a + 3b + 5

B. 24

C. 8x - 12

Step-by-step explanation:

a + 2b + 5 + 3a + b

To simplify this, we'll want to group the similar terms together. In other words, put all of the a's first, then all of the b's, then just the numbers.

a + 2b + 5 + 3a + b

a + 3a + 2b + b + 5

Now, we want to add those similar terms, according to this:

a + a = 2a

So in our expression, we first have

a + 3a = 4a

then

2b + b = 3b

and finally 5, which is just... 5.

Thus, our expression simplified is:

4a + 3b + 5

Now let's do the same for the other expressions.

12 - a + a + 12

First, group them.

12 + 12 - a + a

Then, add them. Let's see, first 12 + 12:

12 + 12 = 24

Then -a + a:

- a + a = 0

24 + 0 = 24

Our 2nd expression, simplified, is just 24.

Finally,

4x - 12 + 4x

First group the x's:

4x + 4x - 12

And then add them, first 4x + 4x:

4x + 4x = 8x

And of course, -12 is just -12.

Thus, our third expression simplified is:

8x - 12

A. 4a + 3b + 5

B. 24

C. 8x - 12

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Find the exact value of cos 120° in simplest form with a rational<br> denominator.

IRINA_888 [86]

Given:

cos 120°

To find:

The exact value of cos 120° in simplest form with a rational denominator.

Solution:

We have,

$\cos 120^\circ$

It can be written as

$\cos 120^\circ=\cos (90^\circ+30^\circ)$

$\cos 120^\circ=-\sin 30^\circ$ $[\because \cos (90^\circ-\theta)=-\sin \theta]$

$\cos 120^\circ=-\left(\dfrac{1}{2}\right)$ $[\because \sin 30^\circ=\dfrac{1}{2}]$

$\cos 120^\circ=-\dfrac{1}{2}$

Therefore, the exact value of cos 120° is $-\dfrac{1}{2}$ .

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2 years ago

What is the discriminant of 3x^2 - 10 = -2?

Tatiana [17]

The formula for the discriminant is b^2-4ac. The formula you wote is in the form of
ax^2+c=0, so first, you need to bring that -2 to the left. When you do that, you get (the original equation would be ax^2+bx+c but you have no bx.)

3x^2-8

So, since there's no b, it would be
b^2-4ac
0^2-4(3)(-8
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96

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3 years ago

There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are the

Shtirlitz [24]

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

We solve the above questions using Combination

Combination = C(n, r) = nCr

= n!/n! ×(n - r)!

(a) How many are there to select 2 pairs of gloves?

We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2

= 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!

= 10 ways.

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

We are told to select 4 gloves out of the 10 gloves = 10C4

We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴

= 80

Hence,

10C4 - 5C4

= [10!/4! × (10 - 4)!] - 80

= 210 - 80

= 130 ways

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3 years ago

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