Solve log (base 5)(9x-4)=1

What two numbers multiply to 44 and add up to 12?

djverab [1.8K]

This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.    x*y = 44 ..........(a)

Add up to 12. x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a

x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2

x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2

x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2

x = 6 + 2i√2 or    6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2

x = 6 + 2i√2, y = 6 - 2i√2

x = 6 - 2i√2, y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2

8 0

3 years ago

Read 2 more answers

A theater has a discount pass that cost nine dollars with the past admission is $6.50 per movie. mike tyrell and juanita all bou

tia_tia [17]

Answer:

They saw <u>24</u> movies.

Step-by-step explanation:

The question is incomplete so the complete question is below:

A theater has a discount pass that cost nine dollars with the pass, admission is $6.50 per movie. Mike, Tyrell and Juanita all bought a pass and went to see movies together they spent a total of $183. Write and solve an equation to find out how many movies they saw.

Now, to find the number of movies they saw.

Let the number of movies they saw be $x.$

Discount pass = $9.

With the pass admission per movie is $6.50.

Total number of people = 3.

Total money spent = $183.

So, to get the number of movies they saw we write an equation:

$3(9)+6.50(x)=183$

Now, to solve the equation:

$3(9)+6.50(x)=183$

$27+6.50x=183$

<em>Subtracting on both sides by 27 we get:</em>

$6.50x=156$

<em>Dividing both sides by 6.50 we get:</em>

$x=24.$

Therefore, they saw 24 movies.

4 0

3 years ago

Solve the quadratic equation.<br>m^2/15 -3 = 2

Radda [10]

The answer is $5 \sqrt{3}$

<h3>Explanation :</h3>

$\frac{ {m}^{2} }{15} - 3 = 2$

$\frac{ {m}^{2} }{15} = 2 + 3$

$\frac{ {m}^{2} }{15} = 5$

${m}^{2} = 5 \times 15$

${m}^{2} = 75$

$m = \sqrt{75}$

$m = \sqrt{25 \times 3}$

$m = \sqrt{25} \times \sqrt{3}$

$m = 5 \sqrt{3}$

CMIIW

7 0

3 years ago

Is rolling a 3 standard doe and then rolling a sum greater than 4 when counting the next roll an independent event?

zhannawk [14.2K]

Answer:

False

Step-by-step explanation:

In this question, you roll 3 from the standard die and then add it with the next roll to see if the sums are greater than 4.

From this explanation you can see that you use the result from your first roll for the second event, so we can conclude that the event is dependent.

Imagine if we change the result of the first roll into 5, without adding the second roll we can know that the sum will be greater than 4. The first event result will influence the second event, so it is a dependent event.

5 0

3 years ago

ANSWER FAST PLS HAVE 5 MIN FOR THIS

Kobotan [32]

Answer:

Y=375x

Step-by-step explanation:

thats the answer

6 0

3 years ago