please help...................

Please Help...................

Answers

Answer 1
8(5)-9
40-9

Answer is 31

Related Questions

[tex]x=log125/log25[/tex]

Answers

Answer:

[tex]x = \frac{ log(125) }{ log(25) } = \frac{ log( {5}^{3} ) }{ log( {5}^{2} ) } = \frac{3 log(5) }{2 log(5) } = \frac{3}{2} = 1 \frac{1}{2} [/tex]

if a1=5 and an=an-1 -1 then find the value of a4

Answers

a4 = 2

It is given that,

[tex]a_{1} = 5[/tex], and

[tex]a_{n} = (a_{n-1}) - 1[/tex]

Therefore, it can be said,

[tex]a_{2} = a_{1} - 1\\a_{3} = a_{2} - 1\\a_{4} = a_{3} - 1\\[/tex]

That is,

[tex]a_{2} = 5-1=4\\a_{3} = 4-1=3\\a_{4} = 3-1=2[/tex]

So, a4 = 2

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Question Help


Kimo's Material Company hauls gravel to a construction site, using a small truck and a large truck. The


carrying capacity and operating cost per load are given in the accompanying table. Kimo must deliver a


minimum of 350 cubic yards per day to satisfy her


contract with the builder. The union contract with her drivers


requires that the total number of loads per day is a minimum of 9. How many loads should be made in each


truck per day to minimize the total cost?


Small Truck Large Truck


50


Capacity (yd)


70


Cost per Load


$87


$73


In order to minimize the total cost, the number of loads in a small truck that should be made is


number of loads in a large truck that should be made is


and the

Answers

Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

the total cost will be minimized when the loads are distributed in the following way:

5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)

4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)

This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.

The total cost can be calculated as follows:

Cost of 5 loads in small truck = 5 * $87 = $435

Cost of 4 loads in large truck = 4 * $73 = $292

Total cost per day = $435 + $292 = $727

Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

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Consider the following. u = 71 + 9j, v = 8i+2j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.

Answers

A. proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j

B. u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j

(a) To find the projection of vector u onto vector v, we use the formula:

proj_v(u) = (u·v / ||v||^2) * v

where u = 71 + 9j, v = 8i + 2j, "·" represents the dot product, and ||v|| represents the magnitude of v.

First, let's find the dot product u·v:

u·v = (71)(8) + (9)(2) = 568 + 18 = 586

Next, we find the magnitude of v:

||v|| = √((8)^2 + (2)^2) = √(64 + 4) = √68

Now, we find ||v||^2:

||v||^2 = 68

Finally, we can find the projection of u onto v:

proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j

(b) To find the vector component of u orthogonal to v, we subtract the projection of u onto v from u:

u_orthogonal = u - proj_v(u)

u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j

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Marsha is considering purchasing 3 points on a $350,000 home mortgage for 20 years. If she
purchases the 3 points, at a cost of 1 percent per point, her monthly mortgage would be
approximately $1,878.63. If she decides not to purchase any points, Mercedes' monthly
payment would be approximately $1,987.13. How much money will Mercedes save over the life
of the loan if she purchases the 3 points?

Answers

Marsha would save $26,040 over the life of the loan if she purchases the 3 points.

First, let's calculate the monthly payment if Marsha doesn't purchase any points. We can use a mortgage calculator or the PMT function in Excel to find;

PMT = $1,987.13

Now, let's calculate the monthly payment if Marsha purchases 3 points;

Loan amount = $350,000

Points cost = 3 points × 1% × $350,000 = $10,500

Effective loan amount = $350,000 - $10,500 = $339,500

Interest rate = 4.5% / 12 = 0.375%

Number of payments=20 years × 12 = 240

Using the PMT function, we get;

PMT = $1,878.63

So, by purchasing 3 points, Marsha can save;

$1,987.13 - $1,878.63 = $108.50 per month

Over the life of the loan, which is 20 years or 240 months, the total savings would be;

$108.50 × 240 = $26,040

Therefore, Marsha would save $26,040 amount of money.

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3.
A local town has a population of 3,500 people and has grown by 2.5% each year. Write an exponential function that models the total population p after t years.

Answers

The exponential function that models the total population p after t years is p = 3,500 x 1.025^t.

What is the exponential?

To write an exponential function that models the total population of the town after t years, we need to use the formula:

p = p0 x  (1 + r)^t

where p0 is the initial population, r is the annual growth rate as a decimal (so in this case, 2.5% = 0.025), and t is the number of years.

In this case, we know that the initial population is 3,500, and the annual growth rate is 2.5%, or 0.025. So we can substitute these values into the formula to get:

p = 3,500 x (1 + 0.025)^t

Simplifying this expression gives:

p = 3,500 x 1.025^t

So the exponential function that models the total population p after t years is:

p(t) = 3,500 x 1.025^t

Note that the function is exponential because the population grows at a constant percentage rate each year, which means that the growth itself is increasing over time.

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The line 15 + y = 3x is dilated with a scale factor of 3 about the point (3, -6). Write the equation of the dilated line in slope-intercept form

Answers

The equation of the dilated line in slope-intercept form is:
y' = 3x' - 3

To find the equation of the dilated line in slope-intercept form, we'll follow these steps:

1. Convert the original equation into slope-intercept form (y = mx + b).
2. Find the coordinates of the point after dilation.
3. Use the slope from the original equation and the new point to find the new equation.

Step 1: Convert the original equation into slope-intercept form:
15 + y = 3x
y = 3x - 15

Step 2: Find the coordinates of the point after dilation:
Dilation formula: (x', y') = (a(x - h) + h, a(y - k) + k)
Given point (h, k) = (3, -6) and scale factor a = 3

x' = 3(x - 3) + 3
y' = 3(y + 6) - 6

Step 3: Use the slope from the original equation (m = 3) and the new point (x', y') to find the new equation:
y' = 3x' + b

Substitute the expressions for x' and y' from step 2:
3(y + 6) - 6 = 3(3(x - 3) + 3) + b

Simplify the equation and solve for b:
3y + 18 - 6 = 9x - 27 + 9 + b
3y + 12 = 9x - 18 + b

Now, substitute the original point (3, -6) into the equation to find b:
-6 + 12 = 9(3) - 18 + b
6 = 27 - 18 + b
6 = 9 + b

b = -3

The equation of the dilated line in slope-intercept form is:
y' = 3x' - 3

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FILL IN THE BLANK. Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = x∫4 1/1+4t⁴ dt f'(x)=________

Answers

The derivative of f(x) is: f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

The Fundamental Theorem of Calculus is a pair of theorems that link the concept of differentiation and integration. It states that if a function f(x) is continuous on an interval [a, b] and F(x) is the antiderivative of f(x) on the same interval, then:

Part I: The derivative of the integral of f(x) from a to x is equal to f(x):

d/dx ∫a to x[tex]f(t) dt = f(x)[/tex]

Part II: The integral of the derivative of a function f(x) on an interval [a, b] is equal to the difference between the values of the function at the endpoints of the interval:

∫a to b [tex]f'(x) dx = f(b) - f(a)[/tex]

Using Part I of the Fundamental Theorem of Calculus, we have:

f(x) = x∫4 1/(1+4t⁴) dt

Then, by the Chain Rule, we have:

f'(x) = d/dx [x∫4 1/(1+4t⁴) dt] = ∫4 d/dx [x(1/(1+4t⁴))] dt

= ∫4 (1/(1+4t⁴)) dt

= [tan⁻¹(2t)/2]₄¹

= [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

Therefore, the derivative of f(x) is:

f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

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Please show me the working out
Given the function f (x) 02 +4,2 € (-2,0) + (a) Enter f' (2) 2*x (b) Enter the inverse function, f-1(x) sqrt(x-4) (c) Enter the compound function f' (s 1(x)) (d) Enter the derivative mets-() de 1-12

Answers

The inverse functions:

f'(2) = 4.

[tex]f^{-1}(x)[/tex] = sqrt(x - 4).

f'(s1(x)) = sqrt(x - 4).

(a) To find f'(2), we need to take the derivative of f(x) with respect to x and then substitute x = 2.
[tex]f(x) = x^2 + 4[/tex]
f'(x) = 2x
f'(2) = 2(2) = 4
Therefore, f'(2) = 4.
(b) To find the inverse function [tex]f^{-1}(x)[/tex], we need to first solve for x in terms of f(x) and then switch the roles of x and f(x).
[tex]f(x) = x^2 + 4[/tex]
[tex]x^2[/tex] = f(x) - 4
x = sqrt(f(x) - 4)
Switching x and f(x), we get:
[tex]f^{-1}(x)[/tex] = sqrt(x - 4)
Therefore, the inverse function is [tex]f^{-1}(x)[/tex] = sqrt(x - 4).
(c) To find the compound function f'(s1(x)),

we need to first find s1(x) and then take the derivative of f(x) with respect to s1(x) and then multiply by the derivative of s1(x) with respect to x.
s1(x) = sqrt(x - 4)
f(s1(x)) = (sqrt(x - 4)[tex])^2[/tex] + 4 = x
Taking the derivative of f(x) with respect to s1(x), we get:
f'(s1(x)) = 2s1(x)
Taking the derivative of s1(x) with respect to x, we get:
s1'(x) = 1/(2sqrt(x - 4))
Multiplying these two derivatives, we get:
f'(s1(x))s1'(x) = 2s1(x) * 1/(2sqrt(x - 4))
f'(s1(x))s1'(x) = sqrt(x - 4)
Therefore, the compound function is f'(s1(x)) = sqrt(x - 4).
(d) The given expression "derivative mets-() de 1-12" does not make sense and seems incomplete. Please provide more information or context so that I can help you with this part of the question.

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Liam is standing on a cliff that is 2km tall, he looks out towards the sea from the top of a cliff and notices two cruise liners on is 5km away at a diagonal and the other is 6.8km away at a diagonal. what is the distance between the two cruise liners?

Answers

The distance between the two cruise liners is approximately 3.6 km.

How to find distance between the two cruise liners?

We can use the Pythagorean theorem to find the distances between Liam and the two cruise liners, and then use the distance formula to find the distance between the two cruise liners. Let's call the distance between Liam and the first cruise liner "d1" and the distance between Liam and the second cruise liner "d2". Then:

d1 = sqrt(5² - 2²) = sqrt(21) km

d2 = sqrt(6.8² - 2²) = sqrt(44.44) km

To find the distance between the two cruise liners, we can use the distance formula:

distance = sqrt((d2 - d1)² + (6.8 - 5)²) km

Plugging in the values, we get:

distance = sqrt((sqrt(44.44) - sqrt(21))² + 1.8²) km

Simplifying this expression gives:

distance = sqrt(44.44) - sqrt(21) km

So the distance between the two cruise liners is approximately 3.9 km.

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The table shows nutrients information for three beverages.

a: which has the most calories per fluid ounce?

b: which has the least sodium per fluid ounce?

bevarage/ serving size/ calorie/ sodium
whole milk/ 1 c/ 146/ 98mg
orange juice/ 1 pt/ 210/ 10mg
apple juice/ 24 fl oz./ 351/ 21mg

Answers

Answer:

a) apple juice

b) whole milk

easy pagel

12
Find the lowest common multiple (LCM) of 28, 42 and 63
Show your working clearly.

Answers

Answer:

Least Common Multiple (LCM) of 28,42,63 is 252 ∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 3 = 252

Step-by-step explanation:

Answer:

252 is the answer

Step-by-step explanation:

find the multiples of all of them ( and make sure it is the least. )

28:

28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308

42:

42, 84, 126, 168, 210, 252, 294, 336

63:

63, 126, 189, 252, 315, 378

bolded + undurlined is the answer

you see that 252 is the answer

252 is the answer

What is the arc measure of major arc BDC in degrees?

Answers

The arc measure of major arc BDC in degrees is 240 degrees.


To find the arc measure of major arc BDC in degrees, you'll need to provide more information about the given circle or angles within it. However, I can guide you on how to find the arc measure once you have the necessary information.

1. Determine the measure of the central angle corresponding to the major arc BDC. This can be done by subtracting the measure of the minor arc from 360 degrees.


2. Use the central angle measure to find the arc measure of major arc BDC. Since the arc measure is equal to the measure of the central angle in degrees, the arc measure of major arc BDC will be the same as the central angle measure you found in step 1.

Please provide more information or details about the given circle or angles to help you find the arc measure of major arc BDC.

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17


Type the correct answer in the box. Use numerals instead of words,


Alex is a single taxpayer with $80,000 in taxable income. His investment income consists of $500 of qualified dividends and short-term capital gains


of $2,000


Use the tables to complete the statement.


Single Taxpayers: Income Brackets


Tax Rate Income Bracket


10%


0 to 9,525


1296


9,526 to 38,700


22%


38,701 to 82,500


Single Taxpayers: Qualified


Dividends and Long-Term


Capital Gains


Tax Rate Income Bracket


0%


O to 38,600


15% 38,601 to 425,800


20%


> 425,800


24%


82,501 to 157,500


32%


157,501 to 200,000


35%


200,001 to 500,000


37%


> 500,000


Alex will owe $


in taxes on his investment income.


My

Answers

The exact tax owed cannot be determined without knowing the specific income bracket for Alex's taxable income.

We know that,

Based on the provided information, Alex's investment income consists of

$500 of qualified dividends and $2,000 of short-term capital gains.

Here, we have to calculate the taxes owed on his investment income, we

need to determine the applicable tax rate based on his taxable income.

As the specific income bracket for Alex's taxable income is not mentioned, it is not possible to provide an exact amount of taxes owed.

The tax rate and corresponding income brackets should be referenced to calculate the taxes accurately.

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A path 3 feet wide surrounds a rectangular garden that has a length of 20 feet and a width of 12 feet. Find


the area of the path.

Answers

The area of the path surrounding a rectangular garden is 105 square feet

The area of path will be given by the relation -

Area of path = Outer area - inner area

Inner area = 20 × 12

Multiply the values

Inner area = 240 square feet

Outer area = (20 + 3) × (12 + 3)

Add the values inside parenthesis

Outer area = 23 × 15

Perform multiplication on Right Hand Side of the equation

Outer area = 345 square feet

Area of path = 345 - 240

Subtract the values

Area of path = 105 square feet

Hence, the area of rectangular path is 105 square feet.

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f(x)=-x^(2)-8x+19

1.whats the functions minimum value?

2.where does the minimum value occur?

Answers

The minimum value of the function is -13 and the minimum value of the function occurs at the point (4, -13).

The function F(x) is a quadratic function with a negative coefficient of the squared term.

Therefore, the function has a maximum value.

To find the maximum value, we need to find the vertex of the parabola.

The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x² and x terms respectively.

In this case, a = -1 and b = -8, so x = -(-8)/(2(-1)) = 4.

To find the minimum value, we substitute this x-value into the function to get F(4) = -(4²) - 8(4) + 19 = -13.

Therefore, the minimum value of the function is -13.

We found in part (1) that the x-coordinate of the vertex is x = 4.

To find the y-coordinate, we substitute this x-value into the function to get F(4) = -13.

Therefore, the minimum value of the function occurs at the point (4, -13).

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(01. 04 MC)Simplify the following expression: (-3)(-2) -2) 0-12 0 12 0-18 0 18

Answers

The simplified expression is 4.

How to simplify the expression (-3)(-2) -2)?

To simplify the expression (-3)(-2) -2), we need to follow the order of operations, which are parentheses first, then multiplication and division from left to right, and finally addition and subtraction from left to right.

First, we need to simplify (-3)(-2) to get:

(-3)(-2) = 6

Now we can substitute this value into the expression to get:

6 - 2) = 4

Therefore, the simplified expression is 4.

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Given y = 4x² + 3x, find dy/dt when x= -1 and dx/dt = 3(Simplify your answer.)

Answers

Given the function y = 4x² + 3x, we will find dy/dt by differentiating y with respect to t. Therefore, the value of dy/dt is -15.

Using the chain rule, we have:

dy/dt = (dy/dx)(dx/dt)

Differentiating y with respect to x, we get:

dy/dx = 8x + 3

Now, we are given that x = -1 and dx/dt = 3. We can substitute these values into our equation:

dy/dt = (8(-1) + 3)(3)

dy/dt = (-5)(3)

dy/dt = -15

So, when x = -1 and dx/dt = 3, the value of dy/dt is -15.

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KLM has vertices K 4,-5 L 2,2 and M 7,3 which translation move the triangle so that point K lies on the Y axis

Answers

To move triangle KLM so that point K lies on the Y-axis, you need to apply a translation that shifts the entire triangle horizontally. By translating triangle KLM using the vector (-4, 0), point K now lies on the Y-axis.

To move the triangle so that point K lies on the Y axis, we need to perform a translation. First, we need to determine how far point K is from the Y axis. We can do this by finding the x-coordinate of point K, which is 4. This means that point K is 4 units away from the Y axis.

Next, we need to determine the direction of the translation. Since we want to move point K onto the Y axis, we need to move the triangle in the negative x direction. Therefore, the translation that will move the triangle so that point K lies on the Y axis is a horizontal translation of -4 units. We can express this translation as follows:

T(-4, 0)

This means that we need to move each point of the triangle 4 units to the left (negative x direction) to achieve the desired position of point K on the Y axis.

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A segment with endpoints A (2, 6) and C (5, 9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B.



A. (2. 33, 6. 33)


B. (3. 5, 10. 5)


C. (3. 66, 7. 66)


D. (4. 25, 8. 25)

Answers

To find the coordinates of point B, we can use the section formula which states that the coordinates of the point that divides a segment with endpoints (x1, y1) and (x2, y2) in the ratio of m:n are given by:

((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))

The coordinates of point B are (4.25, 8.25), and the answer is (D).

Here, A (2, 6) and C (5, 9) are the endpoints of the segment, and we want to partition the segment in the ratio of 3:1. So, we have:

m:n = 3:1

m+n = 4

Solving for m and n, we get:

m = 3, n = 1

Now, substituting  values in the section formula, we get:

((35 + 12)/(3+1), (39 + 16)/(3+1)) = (4.25, 8.25)

Therefore, the coordinates of point B are (4.25, 8.25), and the answer is (D).

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Answer:

(4.25, 8.25)

Step-by-step explanation:

i took the quiz

PLEASE HELP Solve for f(x)!!

Answers

Answer:

8.81

Step-by-step explanation:

Substitute x for 7 and then solve normally

{2(7)^2+7-8}/(7)+4

{(2x49)+7-8}/11

98+7-8/11

97/11

8.81

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the
cost of each.

Answers

Answer:

Let's solve this problem using algebra. Let x be the cost of one orange and y be the cost of one apple. Then we have the system of equations:

12x + 7y = 5.36

8x + 5y = 3.68

To solve for x and y, we can use elimination. Multiplying the second equation by 3 and subtracting it from the first equation multiplied by 5, we get:

(5*12 - 7*8)x + (5*7 - 3*5)y = 26.8 - 11.04

20x = 15.76

x = 0.788

Substituting x back into one of the equations, we can solve for y:

12(0.788) + 7y = 5.36

y = 0.308

Therefore, one orange costs $0.788 and one apple costs $0.308.

Do not answer 7 and 9

Answers

Answer:

[tex]32 \div 4 = 8[/tex]

Answer: 32 divided by 4 =8

Step-by-step explanation:

Draw a triangle with side lengths that are 3 inches, 5 inches, and 6 inches long. Is this the only triangle that you can draw using these side lengths? Explain

Answers

The combination of these side lengths uniquely determines the shape of the triangle.

Hi! To draw a triangle with side lengths 3 inches, 5 inches, and 6 inches, make sure that the sum of any two sides is greater than the third side. In this case, 3 + 5 > 6, 3 + 6 > 5, and 5 + 6 > 3, so a triangle can be formed.

Yes, this is the only triangle you can draw using these side lengths.

The reason is that the side lengths are fixed, and according to the triangle inequality theorem, the combination of these side lengths uniquely determines the shape of the triangle.

The combination of these side lengths uniquely determines the shape of the triangle.

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A toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 19 ft. Its width is 7 ft. The width of the


die-cast replica is 1. 4 in. Find the length of the model.


Let x be the length of the model. Translate the problem to a proportion. Do not include units of measure.


Length - x = Length


Width -


Width


(Do not simplify. )


H-1

Answers

Answer:

Step-by-step explanation:

Since the length of the actual racecar is 19 feet, and the length of the model is represented by x, we can set up the following proportion:

Length (model) / Length (actual) = Width (model) / Width (actual)

This can be written as:

x / 19 ft = 1.4 in / 7 ft

To solve for x, we can cross-multiply and simplify:

x * 7 ft = 19 ft * 1.4 in

x = (19 ft * 1.4 in) / 7 ft

x = 3.8 in

Therefore, the length of the model is 3.8 inches.

To explain this solution in more detail, we can use proportionality concepts and unit conversions. The proportion relates the length and width of the actual racecar to the length and width of the model.

We set up the proportion with the length of the model as the unknown (x) and solve for it by cross-multiplying and simplifying. Since the width of the model and actual racecar are given in different units, we convert the width of the model from inches to feet before using the proportion.

The final answer is expressed in inches, which is the same unit as the width of the model.

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1) Using the definition of the​ derivative, find f'(x). Then find f'(-3), f'(0), and f'(6) when the derivative exists.
f(x)=36/x
2) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=2x^2-5x+7. Find the average rate of change of profit as x changes from 4-6.

Answers

f'(x) = -36/x²,  f'(-3) = -4,  f'(0) = Undefined , f'(6) = -1/6

The average rate of change of profit as x changes from 4-6 is 17.

Using the definition of the​ derivative, find f'(x). Then find f'(-3), f'(0), and f'(6) when the derivative exists. Given f(x) = 36/x. We need to find the derivative of f(x) to solve the problem.

To find the derivative of f(x), we use the quotient rule of differentiation.

(d/dx) (u/v) = [(v × du/dx) - (u × dv/dx)] / v²

The derivative of f(x) using the quotient rule is:

(d/dx)(36/x) = [(x × d/dx (36)) - (36 × d/dx(x))]/(x²)= [-36/x²]

So, f'(x) = -36/x²

Then we can find f'(-3), f'(0), and f'(6) when the derivative exists.

We know f'(x) exists if x ≠ 0.So, f'(-3) = -36/(-3)²= -4 f'(0) = Undefined (since x = 0) f'(6) = -36/6²= -1/6

Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x² - 5x + 7. We need to find the average rate of change of profit as x changes from 4-6. We know that the average rate of change of a function f(x) over the interval [a, b] is: (f(b) - f(a)) / (b - a)Here, P(x) = 2x² - 5x + 7, a = 4, and b = 6.

So, the average rate of change of profit as x changes from 4-6 is:(P(6) - P(4)) / (6 - 4)=(2(6)² - 5(6) + 7 - 2(4)² + 5(4) - 7) / (6 - 4)= (72 - 30 - 8) / 2= 17

The average rate of change of profit as x changes from 4-6 is 17.

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Taylor has 7 pounds of navel oranges and
6 1/2 pounds of temple oranges. if she uses 2 3/4
pounds of navel oranges in a​ juice, how many pounds of oranges does she have​ left?

Answers

The total of oranges left by the taylor is about 10 3/4 pounds

To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:

total weight = 7 pounds + 6 1/2 poundstotal weight = 13 1/2 pounds

Next, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:

Navel oranges left = 7 pounds - 2 3/4 poundsNavel oranges left = 4 1/4 pounds

In the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:

total oranges left = Navel oranges left + Temple orangestotal oranges left = 4 1/4 pounds + 6 1/2 poundstotal oranges left = 10 3/4 pounds

Therefore, the total of oranges left by the taylor is about 10 3/4 pounds

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Simplify this equation

Answers

Answer:

(d)

Step-by-step explanation:

Jack starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2. 1% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jack is ready to purchase the vacation home?



$11,000



$11,231



$44,000



$44,924

Answers

The future value of the investment when Jack is ready to purchase the vacation home is $44,924.

To solve this problem, we can use the formula for future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

Where:

Pmt = $1000 (quarterly contribution)
r = 0.021 (annual interest rate)
n = 40 (number of quarters until Jack turns 50)

Plugging in the numbers, we get:

FV = $1000 x [(1 + 0.021)^40 - 1] / 0.021
FV = $44,924.38

Therefore, the future value of Jack's investment, rounded to the nearest dollar, is $44,924. So the correct answer is $44,924.

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A triangle has vertices at (–4, 0), (2, 8), and (8, 0). What are the coordinates of the centroid, circumcenter, and orthocenter? If needed, write mixed numbers with a single space between the whole number and the fractional parts.

Answers

The centroid of the given triangle (2, 8/3), the circumcenter of the triangle is (0,2), the orthocenter of the triangle is (2,8).

What is centroid?

In geometry, the centroid of a triangle is the point where the three medians of the triangle intersect.

To find the centroid of a triangle with vertices at (x1,y1), (x2,y2), and (x3,y3), we can use the formula:

(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3

Using this formula, we get the centroid of the given triangle as:

((-4 + 2 + 8)/3 , (0 + 8 + 0)/3) = (2, 8/3)

To find the circumcenter, we first need to find the equations of the perpendicular bisectors of any two sides of the triangle. Let's choose the sides formed by the points (-4,0) and (2,8), and (2,8) and (8,0).

The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1,4), and the slope of the line passing through (-4,0) and (2,8) is (8-0)/(2-(-4)) = 8/6 = 4/3. So the equation of the perpendicular bisector of this side is y-4 = -(3/4)(x+1), or 3x + 4y = 8.

Similarly, the midpoint of the second side is ((2+8)/2, (8+0)/2) = (5,4), and the slope of the line passing through (2,8) and (8,0) is (0-8)/(8-2) = -8/6 = -4/3. So the equation of the perpendicular bisector of this side is y-4 = (3/4)(x-5), or 3x - 4y = -8.

The intersection of these two lines gives us the circumcenter of the triangle. Solving the system of equations:

3x + 4y = 8

3x - 4y = -8

We get x = 0, y = 2. So the circumcenter of the triangle is (0,2).

To find the orthocenter, we first need to find the equations of the altitudes from any two vertices of the triangle. Let's choose the vertices (2,8) and (8,0).

The altitude from (2,8) is perpendicular to the side formed by the points (-4,0) and (8,0), so its slope is 0. Therefore, its equation is y = 8.

The altitude from (8,0) is perpendicular to the side formed by the points (-4,0) and (2,8), so its slope is the negative reciprocal of the slope of that side, which is -4/3. Using the point-slope form, we get the equation:

y - 0 = (-4/3)(x - 8)

y = -4x/3 + 32/3

To find the intersection of these two lines, we can substitute y = 8 into the second equation:

8 = -4x/3 + 32/3

-8/3 = -4x/3

x = 2

Substituting x = 2 into either equation gives us y = 8, so the orthocenter of the triangle is (2,8).

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