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Otrada [13]
2 years ago
9

What is the least common multiple of x^2-16 and x^2+4x-32?

Mathematics
2 answers:
AlekseyPX2 years ago
7 0

Answer:

  • (x - 4)(x + 4)(x + 8)

Step-by-step explanation:

<u>Factorize the given expressions:</u>

  • x² - 16 = x² - 4² = (x - 4)(x + 4)
  • x² + 4x - 32 = x² + 8x - 4x - 32 = x(x + 8) - 4(x + 8) = (x - 4)(x + 8)

<u>The LCM is the product of all unique  factors of both expressions:</u>

  • (x - 4)(x + 4)(x + 8)
dmitriy555 [2]2 years ago
4 0

The least common multiple is the smallest expression that can be divided by both of the given expressions.

x^2 - 16 = (x - 4)(x + 4)

x^2 + 4x - 32 = (x + 8)(x - 4)

Both of the factored versions of the expressions have an (x - 4) in them. Thus, that will automatically be included in the LCM. Next, we have to include the (x + 4) and the (x + 8) in our LCM.

LCM = (x - 4)(x + 4)(x + 8)

Hope this helps! :)

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Could someone please help me with this thank you very much
elena-s [515]

Answer:

Answer for #10:

y = 2 \: and \: x = 1

Answer for #1:

x = 2 \: and \: y =  - 1

Step-by-step explanation:

In order to solve a simultaneous equation using the substitution method you have to:

Use one of the equation and substitute it into the other equation, in this case equation <em>B</em><em> </em>was substituted into equation <em>A</em><em>.</em>

<em>equ. \: a = (2x - 3y = 7) \\ equ. \: b = (x = 1 - y)</em>

Therefore since x = 1 - y, equation A would be:

2(1 - y) - 3y = 7 \\ (2 - 2y) - 3y = 7 \\  - 2y - 3y = 7 - 2 \\  - 5y = 5 \\ y =  - 1 \: and \: x = 2

8 0
2 years ago
Simplify the given polynomial expressions as much as possible
bazaltina [42]

Answer:

34a^2 + 21a - 20

Step-by-step explanation:

(12a^2 + 6a -8) - (-22a + 12 - 15a)

12a^2 + 6a - 8 + 22a + 12 - 15a

34^2 + 6a - 8 - 12 + 15a

34^2 + 21a - 20

7 0
2 years ago
Charles has read 180 pages of a book this is 3/4 of the total number of pages in the book If P represents the number of pages in
KengaRu [80]
The answer is 240 :3

60+60= 120
120+60 = 180 
and 60 more would be 240 

60 fours would be 240
3  60's  would be 180.  So your answer is 240
4 0
3 years ago
Read 2 more answers
This is my last question it’s due at midnight can I please get help in a hurry
Sophie [7]

N = 9

explanation: If you tilt triangle FGH to where it matches triangle PQR, 9 is matched with N.

more help:

Q = G

10.5 = 7

P = F

H = R

4 = 6

9 = N

5 0
3 years ago
Select the postulate or theorem that you can use to conclude that the triangles are similar.
insens350 [35]

Answer: SAS similarity postulate

Step-by-step explanation:

According to SAS postulate of similarity, two triangles are called similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are congruent.

In triangles, QNR and MNP,

\frac{QN}{MN} = \frac{QM+MN}{MN} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}

\frac{NR}{NP} = \frac{NP+NR}{NP} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}

\implies \frac{QN}{MN} = \frac{NR}{NP}

Also,

\angle QNR\cong \angle MNP  (Reflexive)

Thus, By SAS similarity postulate,

\triangle QNR\sim\triangle MNP

⇒ Option first is correct.

8 0
3 years ago
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