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Elden [556K]
3 years ago
11

When is the equation

Formula1" title="\frac{x-7}{x^2-4x-21} =\frac{1}{x+3}" alt="\frac{x-7}{x^2-4x-21} =\frac{1}{x+3}" align="absmiddle" class="latex-formula"> true?
Mathematics
1 answer:
Vladimir79 [104]3 years ago
8 0

Notice that

x^2 - 4x - 21 = (x - 7) (x + 3)

so on the left side, a factor of <em>x</em> - 7 in the numerator and denominator can cancel

\dfrac{x-7}{x^2-4x-21} = \dfrac{x-7}{(x-7)(x+3)} = \dfrac1{x+3}

But we can only cancel them out as long as <em>x</em> ≠ 7 (because otherwise we'd have the indeterminate form 0/0 on the left side).

So, the equation is true for all <em>x</em> <u>except</u> <em>x</em> = 7. In set notation,

\{x \in \mathbb R \mid x \neq 7\}

In interval notation,

(-\infty,7)\cup(7,\infty)

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Witch expression would be solved first 8+36/6+2-3
Anettt [7]

Answer:

6+2-3

Becuz u immediately can do the problem with lower numbers which makes it easier than adding big numbers like 8+36

7 0
3 years ago
How to find HCF of 16 24 and 36 by long division method​
oee [108]

Answer:

GCF=4

Step-by-step explanation:

16/4=4

24/4=6

36/4=9

7 0
3 years ago
A deep sea diver started at sea level (0 feet) and dove at a rate of 5.6 feet per minute. If the diver dove for ½ hour, what rat
Leona [35]

Given:

A deep sea diver started at sea level (0 feet).

Rate of diving = 5.6 feet per minute.

Time = \dfrac{1}{2} hour

To find:

The rational number that represents his position relative to sea level.

Solution:

We know that,

1 hour = 60 minutes

\dfrac{1}{2} hour = 30 minutes

A deep sea diver, dove at a rate of 5.6 feet per minute.

Distance covered in 1 minute = 5.6 feet

Distance covered in 30 minute = 30 × 5.6 feet

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The diver dove 168 feet in \dfrac{1}{2} hour. Since it is below the sea level, therefore it should be negative.

So, the rational number that represents his position relative to sea level is -168 feet.

Therefore, the correct option is D.

5 0
3 years ago
The sum of two numbers is 63. The larger number is 23 more than the smaller number. What are the numbers?
Sunny_sXe [5.5K]

x+y=63

x=y+23

y+23+y =63

2y +23 = 63

2y =40

y=40/2 =20

y = 20

x = 20+23=43

the numbers are 20 & 43

5 0
3 years ago
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What is 1/3 in decimal form?
lora16 [44]
0.333 repeating is the answer :)
5 0
3 years ago
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