Work out the value of x and the value of y in the simultaneous equations below. 4x + 7y = 40 - 4x + 4y = 4​

a)  When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

Using implicit differentiation, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dy/dt, we get:

dy/dt = -(x/y)(dx/dt)

Substituting x = 6, y = 8, and dx/dt = 4, we get:

dy/dt = -(6/8)(4) = -3

Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

b) Using implicit differentiation again, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dx/dt, we get:

dx/dt = -(y/x)(dy/dt)

Substituting x = 8, y = 6, and dy/dt = -2, we get:

dx/dt = -(6/8)(-2) = 1.5

Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.

To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).

In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.

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The  [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex]  are orthogonal.So, the value of k is 8/3.

A quantity or phenomenon with separate characteristics for both magnitude and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, energy, electromagnetic fields, and weight are a few examples of vectors in nature.

Two vectors are orthogonal if and only if their dot product is zero. Therefore, we need to find the value of k such that the dot product of [tex]$\vec{a}$[/tex] and[tex]$\vec{b}$[/tex] [tex]$\vec{b}$[/tex][tex]\vec{b}[/tex] is zero.

The dot product of [tex]$\vec{a}$[/tex] and [tex]$\vec{b}$[/tex] is given by:

[tex]$$\vec{a} \cdot \vec{b} = (2)(-4) + (3)(k) = -8 + 3k$$[/tex]

For the vectors to be orthogonal, their dot product must be zero, so we set -8 + 3k = 0 and solve for k:

-8 + 3k = 0

3k = 8

[tex]$k = \frac{8}{3}$$[/tex]

Therefore, [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex]  are orthogonal.So, the value of k is 8/3.

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The angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.

The angle of depression from the top of the center support to the end of the support cable can be found using trigonometry. Let's call this angle "x". Using the given information, we can form a right triangle with the center support, the end of the support cable, and a point directly below the center support on the ground.

The height of the center support, 297 meters, is the opposite side of the right triangle, while the distance from the center of the bridge to the connection of the suspension cable, 995 meters, is the adjacent side. Using the tangent function, we can calculate the angle of depression as follows:

tan(x) = opposite/adjacent

tan(x) = 297/995

x = tan^-1(297/995)

Using a calculator, we can find that x is approximately 16.59 degrees. Therefore, the angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.

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Cracking the code: 8 2One number is correct and well placed One number is correct but in the wrong placeTwo numbers are correct but in the wrong place38Nothing is correctCODE8One number is correct but in the wrong placeCracking the code of this sequence of numbers can be a bit tricky, but let's do it step by step. We are given the following clues about the sequence of numbers:

One number is correct and well placed: Since the sequence of numbers is 8 2, we know that the number 8 is in the first position. So the code is either 8 _ _ _ or _ _ _ 8.One number is correct but in the wrong place: This clue tells us that the number 2 is not in the second position of the code, but it is somewhere else.

Therefore, we know that the code is not 8 2 _ _ or _ _ 2 8.Two numbers are correct but in the wrong places: This clue tells us that the code contains the numbers 3 and 8, but they are in the wrong position. Since the code cannot be 8 2 _ _ or _ _ 2 8, we know that the two correct numbers are not in the last two positions. Therefore, the code must be _ 3 8 _ or _ 8 3 _.Nothing is correct: This clue tells us that the code cannot be 3 8 _, 8 3 _, or _ 3 8 because they all contain at least one correct number. Therefore, the code must be _ _ 3 8 or 3 8 _ _.One number is correct but in the wrong place: This clue tells us that the code cannot be 3 8 _, so it must be 8 3 _. Therefore, the code is 8 3 _ _.I hope this helps you crack the code!

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Answer:

If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:

(x + 3)(x + 4) = 0

To convert this to standard form, we can multiply out the factors:

x^2 + 7x + 12 = 0

Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:

x^2 + 7x + 12 = 0

The number of students that are in the sixth grade is given as follows:

250 students.

The number of students is obtained applying the proportions in the context of the problem.

We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.

190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:

0.76n = 190

n = 190/0.76

n = 250 students.

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Answer:

x=1.9

Step-by-step explanation:

[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]

[tex]11x=21.16[/tex]

[tex]X=1.9[/tex]

Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

6x + 21  =  5x + 25

Then, subtract 5x from both sides:

x + 21  = 25

Then, subtract 21 from both sides.

x = 4

Therefore, x is equal to 4 degrees

Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12

Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.

In the given experiment of rolling two dice, the following probabilities are to be determined:

P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:

1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.

Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15

Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.

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The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours when the average speed is 90 km/h.  the distance between the two towns is  60 km.

Considering the distance between the Winston and carver be "d", since here we got that during off-peak hours, the average speed is 90 km/h. so  by using the formula of  distance which is  distance =speed x time=> d = 90t.

Whereas in rush hour, the average speed is 75 km/h, we also know that the trip takes 8 minutes longer during rush hour.  calling the time it takes to travel during rush hour "t+8/60"( since 8 minutes is 8/60 of an hour). Now using the same formula as before:

d = 75(t + 8/60), since here we have  two equations for d we can equal  them to each other  then we get :

90t = 75(t + 8/60)

=>90t = 75t + 10

=>90t-75t=10

=>t = 2/3

Since during the off-peak hours, it takes 2/3 hours or 40 minutes to travel the distance between Winston and carver. now  using either equation to find the distance we get  

d = 90t = 90(2/3) = 60 km or d = 75(t + 8/60) = 75(2/3 + 8/60) = 60 km

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2.75  is the decimal of fraction .

In math, what is a fraction? 

The amount is represented mathematically as a quotient, where the numerator and denominator are split. In a simple fraction, both are integers. A complicated fraction includes a fraction, either in the denominator or the numerator.

                                    The numerator and denominator must be smaller in a proper fraction. A fraction is a number that is a component of a whole. A whole is appraised by dissecting it into many sections. Half of a whole number or item, for instance, is represented by the number 12.

= [tex]2\frac{75}{100}[/tex]

 = [tex]2\frac{3}{4}[/tex]

  = 11/4

  =  2.75

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Answer:

$109.99

Step-by-step explanation:

The original price of each tire is [tex]\[/tex][tex]109.99[/tex]

Take the amount saved and divide by 4 to find the amount saved on each tire

[tex]96.16\div4 =24.04[/tex]

Add that to the sale price of each tire to find the original price

[tex]85.95+24.04 =109.99[/tex]

Therefore, The original price is $109.99.

the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

Why it is and how to form a graph?

To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.

Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:

y' = -0.08176x + 0.4485

0 = -0.08176x + 0.4485

x = 5.484

This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).

To verify this, we can plug in x = 2 into the quadratic equation:

y = –0.04088(2)²2 + 0.4485(2) + 1.862

y = 2.31752

Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:

Month (x) Precipitation

January 1 2.27 inches

February 2 2.32 inches

March 3 2.57 inches

April 4 2.94 inches

May 5 3.43 inches

June 6 3.94 inches

July 7 2.72 inches

August 8 2.86 inches

September 9 2.59 inches

October 10 2.03 inches

November 11 1.46 inches

December 12 1.03 inches

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Answer:

D: December

The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:

| Month (x) | Precipitation |

|-----------|---------------|

| January   | 2.27 inches   |

| February  | 2.27 inches   |

| March     | 2.24 inches   |

| April     | 2.18 inches   |

| May       | 2.09 inches   |

| June      | 1.98 inches   |

| July      | 1.84 inches   |

| August    | 1.68 inches   |

| September | 2.59 inches   |

| October   | 1.50 inches   |

| November  | 1.30 inches   |

| December  | 1.08 inches   |

According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.

91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.

The elimination method is a technique for solving a system of linear equations, which involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable.

Let x be the number of student tickets sold, and y be the number of adult tickets sold. Then we can set up a system of two equations to represent the information given:

x + y = 128 (1) (the total number of tickets sold is 128)

5x + 8y = 751 (2) (the total revenue from ticket sales is $751)

We can solve for one of the variables in terms of the other in the first equation:

x = 128 - y

Substituting this expression into the second equation to eliminate x, we get:

5(128 - y) + 8y = 751

Expanding and simplifying:

640 - 5y + 8y = 751

3y = 111

y = 37

Therefore, 37 adult tickets were sold. Substituting this value back into equation (1) to solve for x, we get:

x + 37 = 128

x = 91

Therefore, 91 student tickets were sold.

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Answer:

Step-by-step explanation:

see diagram

From the given list of vegetables, the number of different ways in which these vegetables can be selected from a list of vegetables such that no vegetable is selected more than once given here by the formula of Combination, which is: [tex]^nC_k[/tex] = n!/[k!(n-k)!].

The city café is known for its vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. If the four vegetables can be selected from a list of ten vegetables, the formula to determine how many different vegetable plates there are would be a combination of 10 vegetables taken 4 at a time.

The number of different ways that four vegetables can be selected from a list of ten vegetables is given by the formula of Combination, which is:

[tex]^nC_k[/tex] = n!/[k!(n-k)!]

where, n = number of elements in the set = 10 vegetables

k = number of elements chosen = 4 vegetables

n - k = number of elements not chosen = 10 - 4 = 6 vegetables

Therefore, the number of different vegetable plates is:

[tex]^nC_k[/tex] = 10!/ [4!(10-4)!]

[tex]^nC_k[/tex] = (10×9×8×7)/ (4×3×2×1) = 210

Hence, there are 210 different vegetable plates.

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Answer:

Let's use the formula for the volume of a right circular cone to solve this problem:

V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.

Using the chain rule of differentiation, we can express the rate of change of the volume as follows:

dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)

To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:

dV/dr = (2/3)πrh

dV/dh = (1/3)πr^2

Substituting the given values and their rates of change, we have:

dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)

dV/dt = 55,742.4 - 1,994,598.4

dV/dt = -1,938,856 in^3/s

Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.

Step-by-step explanation:

Answer:

y=-3x -8

Step-by-step explanation:

4= -3(-4) = b

b=4-12 = -8

y=-3x -8

Answer:

Anita is 11 years old and sarun 55 years old( not so sure about this answer... what do you think)

Step-by-step explanation:

let Anita's age be x

and sarun's age be 3x

if, x-5 = 3x+7

3x+7 = 5(x-5)

3x+7=5x-25

32=2x

x=16

their ages 3 years ago,

Anita= 16-5=11yrs

sarun= 3*16+7 = 55yrs

The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.

The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.

I found one that shows the following:

Z value Table entry

0.67   0.7486

0.68   0.7517

As a result, the Z value for 0.75 is between 0.67 and 0.68.

Interpolation yields the z value of 0.6745.

If you have a TI-84 calculator, you may calculate the z value as follows:

VARS - 2nd (this will show the DISTR menu)

To select invNorm, press 3.

Enter the value for the area/table (0.75)

If you press enter, it will return the z value.

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Complete question:

what is the z-score for the 75th percentile of the standard normal distribution is:

Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.

To calculate his earnings, we subtract his price from his revenue.

profit = revenue - cost

In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.

Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.

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The equation of Line 1 in the form y=-12x+28

A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.

Coordinates of Line 2 M(4,5) and N(6,-19)

Slope of Line 2 is =(-19-5)/(6-4)

=-24/2=-12

Slope of line 1 and line 2 are same

Cordinate of Line 1 is D(2,4)

D(2,4) must pass through line 1, so it must satisfy the equation

y=mx+b

4=2(-12)+b

4+24=b

b=28

the equation of Line 1 in the form y=-12x+28

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The population increase according to the given years will be 27500, 23750 and 20833.

Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the number.

In this question,

p = 200,000 3/4t

When t=0

p=0

When t=1

p= 20000 3/4= 27500

when t=2

p= 20000 3/8 = 23750

When t=3

p= 20000 3/12 = 20833

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The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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The amount that would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the present value is $37,537.19.

The investment can be treated as a continuous stream with the interest paid at a rate of 4.2% compounded continuously.The present value of the investment can be calculated using the formula:P = C/e^(rt)Where,P = Present ValueC = Cash Flowsr = Interest Rate Per Periodt = Number of Periodse = Euler’s numberThe given values are as follows:C = $8,000 per yearr = 4.2% compounded continuously for 15 years.

C = $8,000e = 2.71828t = 15 yearsNow, we need to calculate the present value using the above formula.P = 8000/e^(0.042 x 15) = $82,273.24.The formula to calculate the amount that would have been invested 15 years ago is:A = P x e^(rt)Where,A = Future Value of the investmentP = Present Value of the investmentr = Rate of Interest Per Periodt = Number of Periodse = Euler’s numberThe present value of the investment is $82,273.24.

The rate of interest is 4.2% compounded continuously.t = 15 yearsNow, we need to calculate the amount that would have been invested 15 years ago.A = 82,273.24 x e^(0.042 x 15) = $37,537.19

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Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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