MATHEMATICS HIGH SCHOOL

Factor the following expression, and verify that the factored expression is equivalent to the original: 4x^2-9a^6

Answers

Answer 1
Answer:

Answer:

(2x - 3a³) ,(2x + 3a³)

Step-by-step explanation:

Given that

4x^2-9a^6

As we know that

x² - y² = ( x+y)(x-y)

So

4x^2-9a^6  = (2x)² - (3a³)²

By using the above formula

x² - y² = ( x+y)(x-y)

4x^2-9a^6  = (2x)² - (3a³)²

4x^2-9a^6  = (2x - 3a³) (2x + 3a³)

So the factor is (2x - 3a³) ,(2x + 3a³)

To verify

Multiple both factors

(2x - 3a³) (2x + 3a³)  = 2x .2x -2x . 3a³ + 3a³ . 2x -  3a³. 3a³

                                =4x² - 9 a ⁶

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Which of the following groups of numbers are all prime numbers? A. 2, 5, 15, 19 B. 7, 17, 29, 49 C. 2, 3, 5, 9 D. 3, 11, 23, 31

Answers

So,

The prime numbers from 1 to 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

Group A contains 15, which is a composite number (3 * 5).

Group B contains 49, which is a composite number (7 * 7).

Group C contains 9, which is a composite number (3 * 3).

Group D contains no composite numbers.  They are all prime.

Group D contains only prime numbers.
some prime numbers
2,3,5,7,11,13,17,19,23,29,31
just try to divide by those and if you an, then it isn't prim

A. 15/3=5 so not prime
B. 49/7=7, not prime
C. 9/3=3 not prime
D. all prime


answe ris D

The tangent line to the graph of y = h(x) at the point (-1, 6) passes through the point (4, 2). Find h(-1) and h'(-1).How do I solve this?

Answers

Answer:

h(-1)=7

point slope formula y-y1=m(x-x1), m slope, (x1,y1) point

slope is 2/10=1/5

y-9=(1/5)(x-9)=(1/5)x-(9/5)

y=(1/5)x+(36/5) the equation of the tangent line.

Step-by-step explanation:

The slope of the tangent line is the derivative of h(x). That is the slope of the line which is (1/5). The previous -1/5 was in error.

Two lines, C and D, are represented by the equations given below:Line C: y = x + 12
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why? (5 points)


(4, 14), because one of the lines passes through this point
(4, 14), because the point lies between the two axes
(5, 17), because both lines pass through this point
(5, 17), because the point does not lie on any axis

Answers

Line C: y = x + 12
Line D: y = 3x + 2

(4,14)
C: y = 4 + 12 = 16
D: y = 3(4) + 2 = 12 + 2 = 14

(5,17)
C: y = 5 + 12 = 17
D: y = 3(5) + 2 = 15 + 2 = 17

(5,17) shows the solution to the system of equations, because both lines pass through this point.

Which list shows the order of original appearance on earth, from the earliest to the most recent organism? A. bacteria, lizards, rhinoceros, trilobites   B. bacteria, rhinoceros, lizards, trilobites   C. trilobites, lizards, rhinoceros, bacteria   D. bacteria, trilobites, lizards, rhinoceros

Answers

The order of original appearance on earth, from the earliest to the most recent organism is D. bacteria, trilobites, lizards, rhinoceros. Bacteria appeared in the Proterozoic era (2500-541 million years ago). Trilobites appeared in the Cambrian period (541-485 million years ago). Lizards appeared in the Jurassic period (201-145 million years ago). Rhinoceros appeared in the Neogene period (23-2.6 million years ago). Thus, the choice D is the right choice.

What is 23% of 256?
a. 58.88
b. 5.89
c. 1,113.04
d. 11.13

Answers

A is the correct answer.

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Answers

Answer:

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Step-by-step explanation:
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