find answer in terms of pi

9514 1404 393

Answer:

  x = 9

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a) -log(b) = log(a/b)

__

Use the rules of logarithms to simplify the left side to a single log, then take the antilogs and solve the resulting equation.

  log(x+1) -log(x-8) = log(10)

  log((x+1)/(x-8)) = log(10)

  (x +1)/(x -8) = 10 . . . . . . . take antilogs

  x +1 = 10(x -8) . . . . multiply by x-8

  81 = 9x . . . . . . . add 81-x, simplify

  9 = x . . . . . . . . . divide by 9

_____

When the equation is rewritten to the form f(x) = 0, the x-intercept is the solution.

[tex] \: \: \: \: \: \: \: \: (5x - 2) + (4x + 6) \\ \\ = > 5x - 2 + 4x + 6 \\ \\ = > 5x + 4x - 2 + 6 \\ \\ = > \green{\boxed { 9x + 4}}[/tex]

Answer:

9x+4

Step-by-step explanation:

First, remove the unnecessary parentheses from (5x-2)+(4x+6) making it 5x-2+4x+6 because when there is a + in front of an expression in parentheses, the expression remains the same.

Next, collect like terms, turning 5x-2+4x+6 into 9x-2+6.

Now, calculate the sum and you should get 9x+4.

Answer:

$1.85

Step-by-step explanation:

Simple Subtraction!

$3.50 - $1.65 = $1.85

$1.85

Answer:

The candle must burn at 2cm per hour in order to be 6cm tall after 4 hours. I know this because the candle has to burn 8cm in 4 hours and that amounts to 2cm per hour.

Step-by-step explanation:

Lets solve!

We have to find out how much of the candle needs to be burned!

14cm - 6cm = 8cm

The candle must burn 8cm in 4 hours!

Lets find out how much the candle burns in 1 hour.

[tex]\frac{8cm}{4hours}[/tex]= 2cm per hour

The candle must burn at 2cm per hour in order to be 6cm tall after 4 hours. I know this because the candle has to burn 8cm in 4 hours and that amounts to 2cm per hour.

Woohoo, We did it! Would you like to mark my answer as brainliest? I would love that!

Answer:

The answer is x = -7

Answer:

2^x = 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given data

total amount = $100

cost of cake=$30

cost of balloon=$20

let the cost of 1 cup be x

so cost of ten cups = 10x

Step two:

The expression for the total amount is given as

100=30+20+10x

100=50+10

100-50=10x

50=10x

divide both sides by 10

x=50/10

x=$5

the cost of one cup is $5

the cost of ten cups is 5*10= $50

Answer: it would be the fourth one with the line going straight across the top

Step-by-step explanation: To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x.

If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.

The fourth graph represents a function as per the vertical line test.

To determine the function:

Simply draw a vertical line through the graph to find the number of times the function's graph is intersected by the vertical line to determine this.

The graph is said to represent a function if the vertical line only crosses it once at any given location on the graph.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output.

There is a range, co-domain, and domain for every function.

As per the given graphs,

the first three graphs do not represent a function.

only the fourth graph represents a function.

To learn more about the function;

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Answer:

y = -1/2x - 11/2

Step-by-step explanation:

Using slope intercept form y = mx + b, to determine the equation, first count the rise(vertical or change in y), and run(horizontal or change in x) of the line.

m is the slope, b is the y-intercept which will remain when x is 0 as this will cancel out the m.

Be careful when determining the slope, and pay attention to the steps(count) of the x, and y axis.

As this graph measures a line with a negative slope passing through the y axis at -5 1/2 → -11/2, with a step of 1, we can count the squares normally to determine the slope.

So since we know that this line has two obvious points (-5,-3) and (1,-6) we can use the equation for slope to measure it's steepness.

m = y2-y1/x2-x1

with (x1,y1) being the first point, and (x2,y2) being the second point.

So: (negative minus a negative makes a positive)

m = -6-(-3)/1-(-5) = -6 + 3/ 1 + 5 = -3/6 = -1/2.

Since m = -1/2, and b = -11/2, the line must be y = -1/2x - 11/2.

Answer:

5,3

Step-by-step explanation:

Took on Ed

Answer:

5,3

Step-by-step explanation  

Vector PQ in component form is 2,4 (5-3),(7-3)

Vector RS in component form is -3,1

After subtracting -3,1 from 2,4 you get 5,3

Answer: 5,3

Answer:

w=1.5 or w=13.5

Step-by-step explanation:

this is one answer:

multiply w on both sides to leave u with

4.5=3w

divide both sides by 3

[tex]\frac{4.5}{3}=\frac{3w}{3}[/tex]

1.5=w

_____________________

this is the second one if the first one is wrong:

multiply 4.5 on both sides so that the 4.5/w would leave u with just only w alone.

then 3*4.5=13.5

w=13.5

hope dis helps if not then im not dat smart enough ;?

Answer:

an image before the image your seeing

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

411

Step-by-step explanation:

Answer: 23 / 24

Step-by-step explanation:

Given that:

Fraction of flowers for sale = 5/8

Fraction of shrubs for sales = 1/3

Amount of flowers that are either flowers or shrubs :

(Fraction of flowers +. Fraction of shrubs)

(5/ 8 + 1 /3)

L.C.M of 8 and 3 = 24

= (15 + 8) / 24

= 23 / 24

Answer: it's $550.57

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The y-intercepts are 0 and -7, so the vertical intercepts are not the same.

The one that is 0 represents a proportional relation; the one that is -7 represents a non-proportional relation. So, one is proportional and the other is not.

The x-coefficient is 2 in both cases, so the equations have the same slope of 2. Since the slopes are the same and the y-intercepts are different, the lines are parallel to each other.

Each is the equation of a line, so both functions are linear.

Step-by-step explanation:

y = 9x - 70 ...1

y = 2x - 32 ...2

...1 - ...2

0 = 7x -38 ...3

7x - 38 = 0

7x = 38

x = 38/7

1. The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;

⇒ x⁻² = 4

2. The value of √e⁷/e⁵ will be;

⇒ e

3. The equivalent expression of 3 will be;

⇒ ln e³

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

1. The expression is the equation [tex]log_{x} 4 = - 2[/tex].

2. The equation is √e⁷/e⁵.

3. The number is 3.

Now,

The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] is calculated as;

[tex]log_{x} 4 = - 2[/tex]

By the definition of logarithmic, we get;

4 = x⁻²

Hence, The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;

⇒ x⁻² = 4

2. The equation is √e⁷/e⁵.

Solve as;

√e⁷/e⁵ = √ e ⁷ ⁻ ⁵

           = √ e²

           = e

Thus,  The value of √e⁷/e⁵ will be;

⇒ e

3. Since, by the definition of logarithmic;

[tex]ln_{e} e = 1[/tex]

So, By option 1;

[tex]ln_{e} e^3[/tex] = [tex]1 * 3[/tex] = [tex]3[/tex]

Thus, The equivalent expression of 3 will be;

⇒ ln e³

Learn more about the expression visit:

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Answer: 1.5ft/seconds

Step-by-step explanation:

From the question, we are informed that a loon is a bird that dives in the ocean for its food and that it can dive to a depth of 12ft in 8 seconds.

The amount of feet it dive per second will be gotten by dividing 12ft by 8 seconds. This will be:

= 12ft / 8sec

= 1.5ft/seconds

Answer:

The answer is 2 songs and the solution is 7.

Step-by-step explanation:

1. Make an equation for each club. The 1st choice music club equation is 5+1x and the Music Club equation is 3.50x.

2. Go down the number line starting with 1 and replace x with that number and solve the equation until you get the same number on each side with the same replacement number.

3. So, 5+1x becomes 5+1(2) and that would equal 7. Then do 3.50x becomes 3.50(2) and that would also equals 7.

Note: When a number has a number next to it in parentheses then that means to have to multiply first. If you don't then you will get the wrong answer.

Answer:

97.35%

Step-by-step explanation:

Empirical rule formula states:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From the question, we have the mean of :

Mean of 56 and a standard deviation of 10.

For 36

36 = μ - xσ

36 = 56 - 10x

56 - 36 = 10x

20 = 10x

x = 20/10

x = 2

Hence, the data falls within 2 standard deviation of the mean

Hence, since it is one side,

= 95%

= 47.5%

For 86

86 = μ - xσ

86 = 56 - 10x

56 - 86 = 10x

-30 = 10x

x = -30/10

x = -3

Hence, the data falls within 3 standard deviation of the mean

Hence, since it is 99.7% one side,

= 99.7%

= 49.85%

Hence, we add up

= 47.5% + 49.85%

= 97.35%

The approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86 is 97.35%

Answer:

where is the rhombus

Step-by-step explanation:

Answer:

sadsadwsd

Step-by-step explanation:

Complete question :

Cheddar Cheese

$3/lb

Swiss Cheese

$5/lb

Keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Answer:

10 lbs of cheddar cheese

6 lbs of Swiss cheese

$3a + $5b = $30

Step-by-step explanation:

Given that :

Cheddar cheese = $3/lb

Swiss cheese = $5/lb

Total amount budgeted for cheese = $30

How many pounds of cheese can Keisha get if she buys only Cheddar cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of cheddar cheese

$30 / 3 = 10 pounds of cheedar cheese

Only Swiss cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of Swiss cheese

$30 / 5 = 6 pounds of Swiss cheese

A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Let amount of cheddar cheese she can get = a

Let amount of Swiss cheese she can get = b

Hence,

(Cost per pound of cheddar cheese * number of pounds of cheddar) + (Cost per pound of Swiss cheese * number of pounds of Swiss cheese) = total budgeted amount

(3 * a) + (5 * b) = $30

$3a + $5b = $30

Answer:

$15.22

Step-by-step explanation:

Given that :

Cost of NFL game = $60

Amount Rico has in bank account = $24.78

Amount earned for mowing lawn = $20

Amount needed more to buy the game :

Total amount Rico has :

Cost of NFL game - (Amount in bank + amount earned for mowing)

$60 - ($24.78 + $20)

$60 - $44.78

= $15.22

Amount needed more to purchase the game = $15.22

Answer:

7 fish

Step-by-step explanation:

1. 4.49x ≤ 35

2. Divide both sides by 4.49 so it cancels out the multiplication. x ≤ 7.79510022272

3. You can't split fish, so you can buy 7 fish.

Not sure how to give Brainliest, though.

Answer:

Do 4.49 times 8 it'll get your answer

Step-by-step explantion

NO it's 8 he can buy 8 Of them fishes

Answer:

1. 24%

2. 30%

3. 30%

Step-by-step explanation:

1. 100%/25= 4%   4%*6=24%

2. 100%/50= 2% 2%*15=30%

3.  100%/40=2.5% 2.5%*12= 30%