log(3+√5) + log(3 - √5) = ?​

Answer:

[tex]y=-3x-8[/tex]

Step-by-step explanation:

slope-intercept form:

[tex]y=mx+b[/tex]

Start with the given equation, and to find the slope, convert it to slope-intercept form by solving for y.

[tex]3x+y=-5[/tex]

In this case, all you need to do is subtract 3x from both sides.

[tex]y=-3x-5[/tex]

Here, the slope is -3. The slope of a parallel line will also be -3.

Now, we have 3 known variables. We have the slope and the x and y of a known point. Use those 3 knowns to solve for the 1 unknown, the y-intercept.

[tex]y=mx+b\\-5=(-3)(-1)+b\\-5=3+b\\-8=b\\b=-8[/tex]

Finally, with the slope and the y-intercept, you can write the equation of the line:

[tex]y=-3x-8[/tex]

The linear equation for this scenario is L = -20t + 140. Layla owes her friend $140 and pays the friend $20 per week.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let L represent the amount Layla owes her friend after t weeks.

Using the point from the graph (0, 140) and (7, 0):

L - 140 = [(0 - 140)/(7 - 0)](t - 0)

L - 140 = -20t

L = -20t + 140

The y intercept is 140

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Answer:

The answer is 6 feet below the surface of the water.

Step-by-step explanation:

So the fish started out as 12m below the surface then went 3m down. If you add 12m and 3m you'll 15m, then minus with a 9m to came up with 6m. But the fish is still below surface, which gives you the answer of " 6 feet below the surface"

Hopes this helped you :)

From the given question we are asked to find the least common multiple of two given numbers. Here for this question, we will use the prime factorisation method and find the factors for the two given numbers and then we find the least common multiple for the numbers given. So, we proceed with our solution as follows.

2 | 5, 8

_______

2 | 5, 4

_______

2 | 5, 2

_______

5 | 5, 1

_________

1, 1

2×2×2×5 = 40

We should remember the concept of least common multiple, which means the smallest number that two numbers both can get to or which is the common multiple between two numbers. We should know that we have different method to find the least common multiple like listing the multiples, prime factorization and division

Your Answer Is : - 31xz + 16xy - 9yz

Answer:

16

Step-by-step explanation:

261 - 256 - 251

-5 by step

to 50th term there is 49 -5's from 261.

261 + 49.(-5) = 261 - 245 = 16

Answer:

16

Step-by-step explanation:

The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.

General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]

where An = nth term, a1 = first term , n = number of terms and d = common difference.

The first term is 261 so a1 = 261

The common difference appears to be -5

( 256 - 261 = -5 ) and ( 251 - 256 = -5 )

so d = -5

We want to find the 50th term so n = 50

We then plug all of this in to get the 50th terms

Formula : [tex]a_n=a_1+(n-1)d[/tex]

a1 = 261 , n = 50 and d = -5

[tex]a_n=261 + (50-1)-5[/tex]

subtract 1 from 50

[tex]a_n=261+(49)(-5)[/tex]

multiply 49 and -5

[tex]a_n=261-245[/tex]

subtract 245 from 261

[tex]a_n=16[/tex]

The 50th term is 16

Minimum value = 12

Maximum value = 37

snumber of observations = 10 (even)

Median = Mean of middle most terms

Middle most terms = 22, 25

Median ={22+25}{2}=23.5222+25=23.5

this makes no sense so maybe  try something better

The third ordered pair that satisfies the equation of the circle is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]

The radius of the circle is calculated as;

[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

[tex]b < r\\\\b < 388.96[/tex]

[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]

Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).

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Answer:

c . f(x)=0,x=????????????

Answer:

9+2i

Step-by-step explanation:

FOIL method, see attached pic

Answer:

Yes, it is a function

Step-by-step explanation:

A function is determined if each input, or x-value has 1 unique output, or y value. No x-value has more than 1 output here, so it is a function

Answer:

I dont quite understand the question could you clarify? What are you trying to ask? how many shirts to break even? Im not quite understanding I'd be more than happy to help if you re worded the question!

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

(4x-20+x-1)/8 = (3x-9+4x-16)/12

(5x-21)/8=(7x-25)/12

(5x-21)/8 x 12/1 = (5x-21)/2 x 3/1 = (15x -63)/2

15x - 63 = 14x - 50

x=13

Answer:

[tex]The \: fraction \: \frac{15}{4} \: is \: equivalent \: to \: 3 \frac{3}{4 } .[/tex]

This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denomintor (4). So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction [tex]3 \frac{3}{4} [/tex]

The fraction [tex] \frac{15}{4} [/tex]

is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.

The fraction 15/4 is equivalent to 3 3/4.

Here, we have,

To simplify the fraction 15/4, you need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (4) and divide both the numerator and denominator by the GCD.

The GCD of 15 and 4 is 1 since there are no common factors other than 1.

Dividing both the numerator and denominator by 1, we get:

(15 ÷ 1) / (4 ÷ 1) = 15/4

This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denominator (4).

So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction 3 3/4.

The fraction 15/4 is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.

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Answer:

640

Step-by-step explanation:

x = total amount of ornaments

480 = 0.75x

(480 is 7 percent of the ornaments after you hang 2 percent of them)

x = 640

Answer:

1.323 pounds I think I'm not too sure thi sorry

Answer:

1.32 pounds

Step-by-step explanation:

convert 1kg to 1000g

[tex]1000g = 2.2pounds[/tex]

Find out how many pounds per 100g

[tex]100g = 0.22 \: pounds[/tex]

multiply by 6 to get 600g and multiply right hand side of the equation as well

[tex]600g = 0.22 \times 6[/tex]

[tex]600g = 1.32 \: pounds[/tex]

Answer:

Quotient: 18; Remainder: 26

Step-by-step explanation:

Please open the PDF file for work.

Hoped this helped.

[tex]GeniusUser[/tex]

========================================================

Explanation:

Start with the f(x) function. Then plug in g(x) like so

[tex]f(x) = 4x+3\\\\f(g(x)) = 4(g(x))+3\\\\f(g(x)) = 4\left(\frac{1}{4}x-\frac{3}{4}\right)+3\\\\f(g(x)) = 4\left(\frac{1}{4}x\right)+4\left(-\frac{3}{4}\right)+3\\\\f(g(x)) = x-3+3\\\\f(g(x)) = x\\\\[/tex]

----------------------------

Now we'll start with the g(x) function and then plug in f(x)

[tex]g(x) = \frac{1}{4}x-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(f(x))-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x+3)-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x)+\frac{1}{4}(3)-\frac{3}{4}\\\\g(f(x)) = x+\frac{3}{4}-\frac{3}{4}\\\\g(f(x)) = x\\\\[/tex]

----------------------------

We've shown that the two equations are true

Therefore, f and g are inverses of each other.

Answer:

{5,6,7}

Step-by-step explanation:

3s>12

divide by 3 on both sides and you get

s>4

so {5,6,7} is the only one that works since it needs to be greater than 4

sorry if I replied too late, but I hope this helps

Answer:

-2 gallons per minute

Step-by-step explanation:

As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.

So, the rate of change is -30 gallons per 15 minutes

However, we can simplify this ratio by dividing both sides by 15, so we get

-2 gallons per minute

Answer:

Step-by-step explanation:

6x + 10 + 2x + 26 = 180

8x + 36 = 180

8x = 144

x = 18

Answer:

cos a cos B-sin a sin B is the right answer

Answer:37

Step-by-step explanation:

[tex]-5x^3y^2 z^4 = 5x^2z^4(-xy^2)\\\\\text{The coefficient of}~ (-xy^2) ~\text{is }~ 5x^2 z^4.[/tex]

Answer:

x= 2y + 20

Step-by-step explanation:

we could say kristian and alejo, Bob and Bill, shelled and Jackie or just about any other two words so let's call them x any y. kristian is x and also is y.

so kristian (x) has twice as much money plus another 20.

this means x has 2 times plus 20 more than y.

so x= 2y + 20

Answer:

y = 4

Step-by-step explanation:

Refer to the two images below

For the graph:

y = 2 - red

x = 2 - blue

y = 4 - green

x = 4 - purple

Horizontal lines are parallel to the x axis. The only two equations parallel to the x axis are y = 2 and y = 4 so x  = 2 and x = 4 cannot be the answer.

The point (2,4) is graphed as well as the equations and the only equation that's horizontal and passes through the point (2,4) is y = 4

Answer:

Step-by-step explanation:

The upper right angle is supplement to 130° and a corresponding angle to (3x + 5)

130 + (3x + 5) = 180

3x + 5 = 50

3x = 45

x = 15