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Allushta [10]
4 years ago
10

Simplify each expression. Show as much work as possible for each question for full credit. Write all answers in​ standard form

Mathematics
1 answer:
Igoryamba4 years ago
5 0

Answer:

Step-by-step explanation:

3)

a) (- 5 + x)(x + 4)

We would apply the distributive property by expanding the brackets, it becomes

- 5x + 4 × - 5 + x² + 4 × x

- 5x - 20 + x² + 4x

x² - 5x + 4x - 20

x² - x - 20

b) the product of 5 + x and x - 4 is

(5 + x)(x - 4) = 5x - 20 + x² - 4x

= x² + 5x - 4x - 20

= x² + x - 20

Therefore,

(- 5 + x)(x + 4) and (5 + x)(x - 4) are not equal.

c) (2x + 5)(3x² + 4x - 3)

Expanding the brackets, it becomes

6x³ + 8x² - 6x + 15x² + 20x - 15

Collecting like terms, it becomes

6x³ + 8x² + 15x² + 20x - 6x - 15

= 6x³ + 23x² + 14x - 15

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So when does y1 = y2?

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2 (5x + 3) = (x2 -15)

solve and advise answer in comments and will assist further
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3 years ago
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How do you simplify 3:9:15:24
vovikov84 [41]
All of those numbers have a common factor, which is 3. So you divide all of their values by 3.

3:9:15:24
=1:3:5:8

Because the values cannot be divided anymore, this ratio is in it's simplest form.
6 0
4 years ago
The true statement "If x is a rational number and y is a rational number, then the sum of x and y is a rational number" is often
Hitman42 [59]

Answer:

D. if the sum of x and y is a rational number , then x may be a rational number or x may be an irrational number.

Step-by-step explanation:

the statement is false because the sum of a rational number and an irrational number is always equals to irrational number.

therefore, if the sum of x and y is a rational number , then x can only be a rational number.

for example:

if x = 5 ==== rational

if y = 2 ==== rational

x+y = 7 ==== rational

but, if

x = 1.333333......... ======irrational

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8 0
4 years ago
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Find the number of permutations in the word fission <br> 1020<br> 1500<br> 1260<br> 2400
irina [24]
There are 7 letters in fission, which we'll use as a factorial in the numerator. Of those 7 letters, there are two I's and two S's. To account for these repeating letters, we'll use the factorials of how many times the letters repeat and plug them into the denominator.

The factorial of 7 should be your numerator, and two factorials of 2 should be your denominator:

\frac{7!}{2! \times 2!} =  \frac{5040}{2 \times 2} =  \frac{5040}{4} =  1260

There are 1260 different permutations of the word fission.
5 0
3 years ago
how high up a vertical wall will a 30-foot ladder reach if the foot of the ladder is placed 6 feet from the wall
Ksenya-84 [330]

Answer:

The height of wall where 30-foot ladder reaches is 29.39 foot.

Step-by-step explanation:

 Consider a  triangle ABC showing AC be the 30 foot ladder that is resting on a wall AB and foot of ladder is 6 foot  from the wall that is BC = 6

We have to find the height of wall where ladder is reaching.

Since building and foot of   ladder makes a right angle at B.

Let AB be x foot.

PYTHAGORAS THEOREM STATES THAT THE SUM OF SQUARE OF BASE AND PERPENDICULAR IS EQUAL TO THE THE SQUARE OF HYPOTENUSE.

Applying Pythagoras theorem,

(AC)^2=(AB)^2+(BC)^2

\Rightarrow (30)^2=(x)^2+(6)^2

\Rightarrow 900=(x)^2+36

\Rightarrow 900-36=x^2

\Rightarrow 864=x^2

\Rightarrow \sqrt{864}=x

\Rightarrow \sqrt{864}=x

\Rightarrow 29.39=x

Thus, the height of wall where 30-foot ladder reaches is 29.39 foot.

5 0
4 years ago
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