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motikmotik
3 years ago
10

SECTION B: LOGARITHMS A Question Three: Solve the equation log₂ (4x² - 9).- log₂ (2x + 3) = 3. Hint: (4x² - 9) is a difference o

f two squares.​
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
5 0

Answer:

x = 11/2

Step-by-step explanation:

Use rules for logarithms to write it as a single log. Then use the hint to simplify further. Change it to exponential form to solve. See image.

Shalnov [3]3 years ago
3 0

Answer: 2x+3

Step-by-step explanation: Simplify   ———————

           2x - 3

Trying to factor as a Difference of Squares:

2.1      Factoring:  4x2 - 9

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  4  is the square of  2

Check : 9 is the square of 3

Check :  x2  is the square of  x1

Factorization is :       (2x + 3)  •  (2x - 3)

Canceling Out :

2.2    Cancel out  (2x - 3)  which appears on both sides of the fraction line.

Final result :

 2x + 3

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All of the middle school mathletes solve math problems at the same pace. Working together, six mathletes complete all of the sum
guapka [62]

Answer:

5 1/2 hours

Step-by-step explanation:

by a factor of 5 means times 4

6*4=24

22/4=5.5 hours

8 0
3 years ago
The tiger at the zoo ate 133 pounds of food in 7 days find the average change in the zoos tiger food supply each day
vfiekz [6]

Which describes the effect of the transformations on the graph of ƒ(x) = x2 when changed to ƒ(x) = 3(x + 2)2 − 4?

A) stretched vertically, shifted left 2 units, and shifted down 4 units  

B) stretched vertically, shifted right 2 units, and shifted up 4 units  

C) compressed vertically, shifted left 2 units, and shifted down 4 units  

Eliminate

D) compressed vertically, shifted right 2 units, and shifted up 4 units

5 0
3 years ago
I need this answer asappppp
Alex Ar [27]
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7 0
3 years ago
Read 2 more answers
Evaluate the following using<br> powers of ten rules.<br> 104)1.042
Alinara [238K]

Answer:

0.0001042

Step-by-step explanation:

Power of tens rule states that if the denominator of a fraction has the positive power of 10, decimal in the numerator will be shifted to the left by the same number of places as exponent.

10⁴) 1.042 = \frac{1.042}{10^4}

In the denominator of the given fraction, exponent of 10 = +4

So the decimal in numerator will be shifted left by 4 places.

\frac{1.042}{10^4}=0.0001042

Therefore, answer is 0.0001042

5 0
3 years ago
Cassandra assigns values to some of the measures of triangle ABC. If angle A measures 30°, a = 6, and b = 18, which is true?
Anna [14]

Answer:

The triangle does not exist because sin(A)/a can not be equal to sin(B)/b

Step-by-step explanation:

we know that

step 1

Find the measure of angle B

Applying the law of sines

\frac{sin(A)}{a}=\frac{sin(B)}{b}

we have

A=30\°

sin(30\°)=1/2

a=6\ units

b=18\ units

substitute

\frac{(1/2)}{6}=\frac{sin(B)}{18}

\frac{1}{12}=\frac{sin(B)}{18}

sin(B)=\frac{18}{12}

sin(B)=\frac{3}{2}=1.5

Remember that the value of sine can not be greater than 1

therefore

The triangle does not exist because sin(A)/a can not be equal to sin(B)/b

8 0
3 years ago
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