3 (6y - 7) > -75

show your work please be quick im in class

Answer: x^2+6x-15

Step-by-step explanation:

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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A(t)=2800x(1/2) t/14

A(40)=2800x(1/2) 40/13

386

Answer:

#1

Step-by-step explanation:

Summer in North America is when the earth is tilted toward the sun, as shown in Number 1 in the diagram.

FYI, #2 is fall, #3 is winter, #4 is spring

Answer:

1:5

Step-by-step explanation:

2:10 = 1:5
Hope it helped !

The variance of X-bar is 12.25.

To find the variance of the sample mean (X-bar) for a normally distributed population, we can use the formula:

Variance of X-bar = (Population Variance) / (Sample Size)

In this case, the population mean (μ) is 138 and the standard deviation (σ) is 14. The population variance (σ^2) can be calculated as the square of the standard deviation, which gives us 14^2 = 196.

Since we are sampling with a batch size of 16, the sample size is also 16.

Now we can substitute these values into the formula:

Variance of X-bar = 196 / 16 = 12.25

Therefore, the variance of X-bar is 12.25.

It's important to note that the sample mean (X-bar) is an unbiased estimator of the population mean (μ). The smaller the sample size, the greater the variability of X-bar around the population mean.

As the sample size increases, the variance of X-bar decreases, indicating a more precise estimate of the population mean.

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The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

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Answer:

the answer to your eqauation is 531,441

Step-by-step explanation:

3^5 x 3^7

243 x 2,187

=531,441

Hope this helped!! :)

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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The value of r*s as required in the task content must be; 15.

The value of r+s as required in the task content is; 8.

It follows from the task content that the equation given is; (x+r)(x+s)=x^2+8x+15

Hence, upon expansion, we have;

x²+rx +sx + r*s = x²+8x+15

x²+(r+s)x + (r*s) = x²+8x+15.

On this note, it follows from comparison of the left and right sides of the equation that;

(r+s) = 8

r*s = 15.

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If  hose fills a hot tub at a rate of 3.49 gallons per minute. Then 1.64 hours will it take to fill a 343​-gallon hot​ tub

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A hose fills a hot tub at a rate of 3.49 gallons per minute.

We need to find how many  hours will it take to fill a 343​-gallon hot​ tub

3.49/1=343/x

Apply cross multiplication

x=343/3.49

x=98.28 minutes

1 hr=60 minutes

So divide 98.28/60

1.64

Hence, it takes 1.64 hours to fill the hot tub.

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:156

Step-by-step explanation:

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).

The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.

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The equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost.

Let s represent the cost of the shoes.

Now, equation is

8% of s=10

8/100 ×s=10

0.08s=10

s=10/0.08

s=$125

Therefore, the equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.

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The number of ways it can be done if order of the choices is taken into consideration is 15,444 ways

Permutation has to do with arrangement and combination has to do with selection.

If we are choosing 5 objects, without replacement, from 15 distinct objects, this has to do with permutation if the order of the choices is taken into consideration

15P5 = 15!/(15-5)!5!
15P5 = 15!/10!5!
15P5 = 15*14*13*12*11/5*4*3*2

15P5 = 15,444 ways

Hence the number of ways it can be done if order of the choices is taken into consideration is 15,444 ways

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Complete question

Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. How many ways can this be done, if the order of the choices is taken into consideration?

Answer:

(a): x = 125 yards.

(c): x = 170 yards.

Step-by-step explanation:

Given

\(f(x) = x(200 - x)\)

\(x = length\\\\\)

\(f(x) = area\)

Required

Determine the possible length

For a length to be possible or usable, the calculated area must be greater than 0.

(a): x = 125 yards.

\(f(x) = x(200 - x)\)

Substitute 125 for x

\(f(125) = 125 * (200 - 125)\)

\(f(125) = 125 * 75\)

\(f(125) = 9375\)

(b): x = 200 yards.

\(f(x) = x(200 - x)\)

Substitute 200 for x

\(f(200) = 200 * (200 - 200)\)

\(f(200) = 200 * 0\)

\(f(200) = 0\)

(c): x = 170 yards.

\(f(x) = x(200 - x)\)

Substitute 170 for x

\(f(170) = 200 * (200 - 170)\)

\(f(170) = 200 * 30\)

\(f(170) = 6000\)

(d): x = 225 yards.

\(f(x) = x(200 - x)\)

Substitute 225 for x

\(f(225) = 200 * (200 - 225)\)

\(f(225) = 200 * (- 25)\)

\(f(225) = -5000\)

(e): x = 210 yards.

\(f(x) = x(200 - x)\)

Substitute 210 for x

\(f(220) = 200 * (200 - 210)\)

\(f(220) = 200 * (- 10)\)

\(f(220) = -2000\)

From the above calculations, only values of x that are 125 and 170 makes the function true

The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

From the question, we have the following parameters that can be used in our computation:

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

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Answer:

Slope = 15/4

Step-by-step explanation:

Use the slope formula and you'll get the same answer.

Hope this helps:)

Answer:

 6%

Step-by-step explanation:

Given data

Principal= $1585

Time = 5 years

Interest =  $475.50

Rate =???

The expression for the interest is given as

SI=PRT/100

substitute

475.50=1585*R*5/100

Cross multiply

475.50*100= 7925R

47550=7925R

R= 47550/7925

R= 6%

Hence the rate is  6%

Answer:

√250 - √490

= 5√10 - 7√10

= -2√10

Answer:

-5/3

Step-by-step explanation:

Note the slope intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Isolate the variable, y. First, Subtract 3x from both sides:

3x (-3x) - 5y = 12 (-3x)

-5y = -3x + 12

Next, divide -5 from both sides. Remember to divide from all terms within the equation:

(-5y)/-5 = (-3x + 12)/-5

y = (-3x/-5) + (-12/5)

Simplify.

y = (3x/5) - 12/5

y = (3/5)x - 12/5

You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:

Original m = 3/5

Flipped m = -5/3

-5/3 is your perpendicular slope.

Answer:

          5                                

m =  - ----    perpendicular slope

          3

Step-by-step explanation:

3x - 5y = 12 -------->> convert to y = mx + b

- 5y = - 3x + 12

- 5y = - (3x + 12) --- eliminate the negative

5y = 3x + 12

     3x + 12

y = -------------

         5

       3           12

y = -----x  +   -----

       5            5  

the above equation is the form of  y = mx + b

where m is the slope and b is the intercept

                            5                                

therefore,  m =  - ----    perpendicular slope

                             3                        

Answer:  12x4= 48 so 48

Step-by-step explanation:

Answer:

a) 2

Step-by-step explanation:

 4:8 and 6:12

4/8 and 6/12

we flip them since we want to find the conversino

8/4 and 12/6

simpilify

2 and 2

scale factor was 2

hope this helps, lmk if it is correct

Answer:

1( first page of volume 1) + 900 (900 book of 100 pages) + 1 (last page of the book)

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

\(Y \sim P( \beta = 2)\)

the probability mass function can be represented as follows:

\(\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}\)

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

\(\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}\)

\(\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}\)

P(y =0) = 0.1353