What is the point-slope form of a line that has a slope of 5 and passes through the point 3/4 )? Y 3 5 x 4 )]?

The price at which the total quantity supplied is 250 is $11.58.

In order to find the price at which the total quantity supplied is 250, we need to equate the total quantity supplied by both producers (Supply 1 and Supply 2) and solve for the price.

Supply 1: P = 6 + 0.7Q

Supply 2: P = 16 + 0.6Q

To find the equilibrium price, we set the total quantity supplied equal to 250:

0.7Q + 0.6Q = 250

1.3Q = 250

Q = 250 / 1.3 ≈ 192.31

Now that we have the quantity, we can substitute it back into either supply function to find the price. Let's use Supply 1:

P = 6 + 0.7Q

P = 6 + 0.7 * 192.31

P ≈ 6 + 134.62

P ≈ 140.62

Therefore, the price at which the total quantity supplied is 250 is approximately $11.58.

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Answer:

See below.

Step-by-step explanation:

For a rational function, the equation is \(\displaystyle \large{f(x)=\frac{a}{b(x-c)}+d}\) where:-

We are given a function \(\displaystyle \large{f(x)=\frac{1}{x}-1}\) . Examine the function, we know that:-

Additional Info

  - Asymptote line is a line that the graph tends to approach but never intersects.

From the information we have, first - draw both vertical asymptote and horizontal asymptote to make it easier to draw a graph.

Then draw a rational function’s graph as it tends to 0 when x = 0 and -1 when x tends to both sides of infinity.

You should receive a graph below that I made, see the attachment. The purple line represents the horizontal asymptote and y-axis is our vertical asymptote.

If you have any questions, do not hesitate to ask in comment!

For all x,

sin²(x) + cos²(x) = 1

so we have

(1 - cos²A) csc²A = sin²A csc²A

and since csc(x) = 1 / sin(x), so the expression reduces to 1.

Answer:

100m

Step-by-step explanation:

Perimeter of square = 4( sides ) = 400m

Let side = a

Therefore,

4a = 400

a = 400 / 4

a = 100m

Hope it helps!

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

g(8) = 45

Step-by-step explanation:

substitute x = 8 into g(x) , that is

g(8) = 7(8) - 11 = 56 - 11 = 45

Answer:

Step-by-step explanation:

Given that \(f(x)=-3x+8\).

The new function,g, whose graph is a transalation of 1 unit up is,

\(g=f+1\)

\(\Rightarrow g(x)=(-3x+8)+1\)

\(\Rightarrow g(x)=-3x+9\)

The value of x is 5 for the given equation 5/3 = x/3.

So, the equation is:

Now, solve for x as follows:

Therefore, the value of x is 5 for the given equation 5/3 = x/3.

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Correct question:

Solve for x. 5/3= x/3

1. Divide 240 by 10 = 24

2. Multiply 24 • 8 = 192

Michele will need 192 oz. of mayonnaise.

Answer:

192 oz

Step-by-step explanation:

Hi there!

1) Create a proportion

\(\frac{8 (oz)}{10(servings)} =\frac{x(mayo)}{240(servings)} \\\frac{8}{10} =\frac{x}{240}\)

2) Solve for x

\(\frac{8}{10} =\frac{x}{240}\)

Multiply both sides by 240

\(\frac{8}{10} *240=x\\192=x\)

Therefore, Michele would need 192 oz of mayonnaise.

I hope this helps!

Most likely invalid.

The dimensions of the tank with minimum  weight  is height= 7 and width and length= 14.

The minimum surface area implies that the tank has minimum weight.

Given that the base is square, its width is equal to its length.

Let x= the base width and length of the tank.

Let h = the height .

We are given the volume of the tank that is 1372 ft^3. The formula is given by

V = hx^2

We're given that V = 1,372 ft^3, so

hx^2 = 1,372

h = 1,372 / x^2  ----------(equation 1)

Surface area can be calculated using the below given formula.

A = x^2 + 4xh

Substituting the value of euation 1, h in A, we get,

A = x^2 + 4x(1,372 / x^2)

= x^2 + 5,488 / x

To get the minimum surface area to get the minimum weight, we need to differentiate  A with respect to x and equate it to zero.

dA/dx = 2x - 5,488 / x^2 = 0

2x^3 - 5,488 = 0

x =\(\sqrt[3]{\frac{5,488}{2} }\)

x= 14

We got the value of x, we substitute the value in equation 1, we get the value of h.

h = 1,372 / 14^2

h= 7

So, the dimensions of the tank with minimum weight are width and length is 14 and height is 7.

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Answer: 44

Step-by-step explanation:

We know that a is a radius so 2a=b because b is the diameter. Then we substitute 7 for a so it is 14=b since the diameter is 14 then the formula for circumference is 2 pi r or pi d so the circumference is 14pi and to simplify that  I will assume pi is 3.14 so 14(3.14)=43.96 and rounding to the nearest tenth would give me 44

Answer: 13 weeks

Step-by-step explanation:

First you have to find 10% of 340.00 which is 28, so each week he saves 28.00 for his bike. To find how many paychecks he has to recieve you divide 340.00 by 28.00, which is 12.1, since there is a decimal place you have to round it up to 13 because it is a little bit more than 12 paychecks. ;)

The amount you will pay back by the end of the term is; 162.18 dollar.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + r)^{t}\)

Given that you borrow $101 at 7% compounded annually for seven years, then we have;

P = 101 dollar

Rate = 7%

Times = 7 yr

Therefore,

\(a = p(1 + r)^{t}\)

\(a = 101(1 + 0.07)^{7}\\\\a = 101 (1.07)^7\\\\a = $162.18\)

Hence, The amount you will pay back by the end of the term is; 162.18 dollar.

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The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Simplified answers, including any radicals.

1. The length of u x v

|u x v| = 8√(17)

2. Direction of u x v

u x v = (2/√(17))i + (8/√(17))j + (9/√(17))k
3. Length of v x u

|v x u| = 8√(17)

4. The direction of v x u

v x u = (2/√(17))i + (9/√(17))j - (8/√(17))k

5. u x v x v times u is equal to 0.

To find u x v, we can use the formula:
u x v = |i j k|
|9 -2 -8|
|8  0 -8|

Expanding the determinant, we get:
u x v = (16)i + (64)j + (72)k

To find the length of u x v, we can use the formula:
|u x v| = √((16)² + (64)² + (72)²) = 8√(17)

To find the direction of u x v, we can normalize the vector by dividing it by its length:
u x v = (2/√(17))i + (8/√(17))j + (9/√(17))k

Now, to find v x u, we can use the formula:
v x u = |i j k|
|8  0 -8|
|9 -2 -8|

Expanding the determinant, we get:
v x u = (16)i + (72)j - (64)k

To find the length of v x u, we can use the formula:
|v x u| = √((16)² + (72)² + (-64)²) = 8√(17)

To find the direction of v x u, we can normalize the vector by dividing it by its length:
v x u = (2/√(17))i + (9/√(17))j - (8/√(17))k

Now, we need to find u x v x v times u. First, we need to find u x v x v:
u x v x v = u x (v x v) = u x 0 = 0

Therefore, u x v x v times u is equal to 0.

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Answer:

(0,0) (3,2) and (-2,-2) (4,2)

Step-by-step explanation:

To find the slope, you do \(\frac{y_{1}-y_{2} }{x_{1}-x_{2}}\), which would work for both.

2-0/3-0=2/3

2-(-2)/4-(-2)=2+2/4+6=2/3

The exact value of sec(3πi) is -1.

The expression sec(3πi) represents the secant function evaluated at 3πi.

The secant function is defined as the reciprocal of the cosine function, so we need to find the value of the cosine function at 3πi.

The cosine function has a period of 2π, which means it repeats every 2π units. Since 3π is already within one period, we can evaluate the cosine function at 3π to find the exact value.

cos(3π) = -1

Therefore, sec(3πi) is equal to the reciprocal of -1, which is:

sec(3πi) = -1/1 = -1

The exact value of sec(3πi) is -1.

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Answer:

The critical value Za /2 that corresponds to 98% confidence level is (d) 2.33

Step-by-step explanation:

To obtain the critical value Za/2 that corresponds to a 98% confidence level, we need to determine the value that leaves 2% (0.02) in the tails of the distribution.

Since the confidence level is two-tailed, we need to divide the significance level by 2 to find the area in each tail. In this case, we have 2% divided by 2, resulting in 1% (0.01) in each tail.

Looking up the critical value in a standard normal distribution table or using statistical software, we obtain that the closest value to 0.01 in the table is approximately 2.33.

Therefore, the correct answer is D. 2.33.

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Answer:

168

Step-by-step explanation:

Area = Length * Width

Area = 14 * 12

Area = 168

Detailed multiplication:

14

* 12

-------

28

+ 140

---------

168

Answer:

53 mph

Step-by-step explanation:

We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.

We can set up a proportion where the unknown variable is the number of miles driven in one hour:

\(\frac{106}{2} =\frac{x}{1}\)

x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph

Answer:

Percent air is calculated as:

Solve for total amount of air:

Substitute the values in hand to get the answer

Answer:

X=10

Step-by-step explanation:

3x=30

3(10)=30

30=30

30+42=72

I hope this helps!

Answer:

D. x=10; angle measure is 30°

Step-by-step explanation:

hope this helps

Answer:

FALSE, (2, 9) is not a solution to the set of inequalities given.

Step-by-step explanation:

Simply replace x by 2 and y by 9 in the inequalities and see if the inequality is true or not:

irst inequality:

\(y\geq 4x\\9\geq 4\,(2)\\9\geq 8\)

so thi inequality is verified as true since 9 is larger or equal than 8

Now the second inequality:

\(y<x+2\\9<(2)+2\\9<4\)

This is FALSE since 9 is larger than 4 (not smaller)

Therefore the answer to the question is FALSE, (2, 9) is not a solution to the set of inequalities given.

Answer:

98.00 - n =

Step-by-step explanation:

The game he found is less than 98.00, which makes it subtraction.

Also, I see you with that Gaara profile picture... (0/-\0)

Answer:

I will try to find the answer right new

Step-by-step explanation:

The integral of f(t,y) = 57 over the region D is 114 - (2 ±√(4 + 4I)).

Let's see the stepwise solution:

1. Determine the equation of the lower boundary curve:

We are given that the lower boundary curve is I = y(2 - y), so we can rewrite this equation as y2 - 2y = I.

2. Use the quadratic formula to solve for y as a function of x:

Using the quadratic formula, we can solve for y as a function of x as

                             y = (2 ±√(4 + 4I))/2.

3. Perform the integration:

We can now integrate f(t,y) = 57 over the region D. We will use the following integral:

                            ∫D 57 dD = ∫D 57dx dy

We can rewrite the limits of integration, from x = 0 to x = 2, as follows:

                           = ∫0 to 2 ∫((2 ±√(4 + 4I))/2) to 2 57dydx

4. Calculate the integral:

Once we have set up the integral, we can evaluate it as follows:

                             = ∫0 to 2 (57(2 - (2 ±√(4 + 4I))/2))dx

                             = 57 ∫0 to 2 (2 - (2 ±√(4 + 4I))/2))dx

                             = 57(2x - (2 ±√(4 + 4I))x/2)|0 to 2

                             = 57(2(2) - (2 ±√(4 + 4I))(2)/2)

                             = 114 - (2 ±√(4 + 4I))

Therefore, 114 - (2 (4 + 4I)) is the integral of the function f(t,y) = 57 over the area D.

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The time taken for investment to reach $ 25000 is t = 0.4581 years

Given data ,

The formula for a certain uninsured certificate of deposit is

A (t) = 10000e^2t

And , 10,000 is the principal amount, and A (t) is the amount the investment is valued in t years

Now , when A = 25,000 ,

A(t) = 10000e^(2t) = 25000

Dividing both sides by 10000, we get:

e^(2t) = 2.5

Taking the natural logarithm of both sides, we get:

ln(e^(2t)) = ln(2.5)

Using the property that ln(e^x) = x, we simplify the left side to:

2t = ln(2.5)

Dividing both sides by 2, we get:

t = ln(2.5) / 2

On simplifying the equation , we get

t ≈ 0.4581 years

Hence , it will take approximately 0.4581 years, or about 5.5 months, for the investment to grow to $25,000

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Answer:

A. y= 1x + 5

Step-by-step explanation:

Answer:

A. y=x+5

Step-by-step explanation:

(0,5):

x=0

y=(0)+5=5

(3,8):

x=3

y=(3)+5=8

I hope this help you

Answer:

There are two roots because of the  

✔ need to identify + and - roots of the radicand.

Step-by-step explanation:

edge

Answer:C

Step-by-step explanation:

There are two roots because of the

✔ need to identify + and - roots of the radicand.