What is the solution to this system of linear equations? x + y = 4 x - y = 6 a. (4, 6)b. (6, 4) c. (5, −1) d. (−1, 5)

Answer:

y<-3/2x+1

Step-by-step explanation:

Answer:

Step-by-step explanation: Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(8, 5)=1. In the next intermediate step the fraction result cannot be further simplified by cancelling. In words - four multiplied by two fifths=eight fifths.

Answer:

9y+18

Step-by-step explanation:

Distribute the 9 to the terms in the parentheses.

9(y)+9(2)

9y+18

Answer:

For High School A, let  denote the number of students after  years. Define  analogously.

Then  and .

After 6 years the number of students in both high schools would be the same.

Step-by-step explanation:

For High School A, let  denote the number of students after  years. Define  analogously.

Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that .

Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that .

Setting the two equations equal to each other, we see that

So after 6 years the number of students in both high schools would be the same.

Solution:

Concept:

To solve the length of the hypotenuse, we will use the Pythagoras theorem below

By substituting the values, we will have

Hence,

The length of hypotenuse C , is

The circumferences of the three tracks at Driver's Delight are approximately 376.99 feet (Track 1), 534.07 feet (Track 2), and 691.15 feet (Track 3).

Driver's Delight features three circular go-cart tracks, each with a different radius. To calculate the circumference of each track, we can use the formula C = 2 * π * r, where C is the circumference, π is a constant (approximately 3.14159), and r is the radius.

For Track 1, with a radius of 60 feet, the circumference can be calculated as follows: C = 2 * 3.14159 * 60 ≈ 376.99 feet.

For Track 2, with a radius of 85 feet, the circumference can be calculated as follows: C = 2 * 3.14159 * 85 ≈ 534.07 feet.

For Track 3, with a radius of 110 feet, the circumference can be calculated as follows: C = 2 * 3.14159 * 110 ≈ 691.15 feet.

By rounding the circumferences to the nearest hundredth, we find that the three tracks at Driver's Delight have circumferences of approximately 376.99 feet, 534.07 feet, and 691.15 feet, respectively.

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The derivative of f(x) is \(f'(x) = -9 sec(x) tan(x) - sec(x).\)

To find the equation of the tangent line to the curve y = 6 sec(x) - 12 cos(x) at the point (7/3, 6),

we need to find the slope of the tangent line at that point, which is equal to the derivative of the function at that point.

We can find the derivative of y with respect to x using the product rule of differentiation:

y' = 6 sec(x) tan(x) + 12 sin(x)

Now we can substitute the x-coordinate of the point of tangency into this expression to find the slope of the tangent line:

y'(7/3) = 6 sec(7/3) tan(7/3) + 12 sin(7/3)≈ 6.098

So the slope of the tangent line is approximately 6.098.

To find the y-intercept of the tangent line, we can use the point-slope form of the equation of a line:

y - 6 = 6.098(x - 7/3)

Simplifying this equation, we get:

y = 6.098 x - 11.89

So the equation of the tangent line to the curve y = 6 sec(x) - 12 cos(x) at the point (7/3, 6) is y = 6.098x - 11.89.

To find f'(x) if f(x) = 9 sec(x) - cot(x), we need to use the chain rule and the quotient rule of differentiation.

Using the chain rule, we can find the derivative of the first term:

\(d/dx [9 sec(x)] = 9 sec(x) tan(x)\)

Using the quotient rule, we can find the derivative of the second term:

\(d/dx [cot(x)] = -csc^2(x)\)

Now we can use the quotient rule to find the derivative of f(x):

\(f'(x) = [9 sec(x) tan(x) (-1) - (-cot^2(x))] / [cos^2(x)]\)

Simplifying this expression, we get:

\(f'(x) = [-9 sin(x) - cos(x) / cos^2(x)]\)

\(= -9 sin(x)/cos^2(x) - 1/cos(x)\)

\(= -9 sec(x) tan(x) - sec(x)\)

So the derivative of f(x) is \(f'(x) = -9 sec(x) tan(x) - sec(x).\)

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Answer:

220

Step-by-step explanation:

55 percentage of x = 121

so X = 220

as simple as that

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Answer:

Total amount = R41 337.50

Step-by-step explanation:

The value of the deposit is 15% of the total purchase price:

Deposit = 15/100 x R35 000

Deposit = R5 250

To calculate the balance that Claire will have to pay off, we need to subtract the deposit from the total purchase price:

Balance = Total purchase price - Deposit

Balance = R35 000 - R5 250

Balance = R29 750

To calculate the interest that Claire will have to pay on the balance, we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the balance

Rate is the annual interest rate (13%)

Time is the duration of the loan in years (3)

So, the interest that Claire will have to pay is:

Interest = R29 750 x 0.13 x 3

Interest = R11 587.50

Therefore, the total amount that Claire will have to pay back over the 3-year period is:

Total amount = Balance + Interest

Total amount = R29 750 + R11 587.50

Total amount = R41 337.50

Note that this assumes that the interest is calculated annually and added to the balance at the end of each year. In reality, the interest may be calculated differently depending on the terms of the hire purchase agreement.

Answer:

56%

Step-by-step explanation:

divide 14/25 = 0.56

9514 1404 393

Answer:

  (x +2)^2 +(y -5)^2 = 9

Step-by-step explanation:

The circle shown has a radius of r = 3 and a center at (h, k) = (-2, 5).

The equation of a circle is ...

  (x -h)^2 +(y -k)^2 = r^2

For the given center and radius, the equation is ...

  (x +2)^2 +(y -5)^2 = 9

Answer:

Step-by-step explanation:

Remember PEMDAS

2 - 8 : (2^4 : 2) =

2 - 8 : (16 : 2) =

2 - 8 : 8 =

2 - 1 =

Answer:

n = 4

Step-by-step explanation:

Combine like terms and solve.

n + n + 2 = 10

2n + 2 = 10

2n = 8

n = 4

The probability that at most three grafts fail is 0.98 and the probability that at least two grafts fail is 0.1.

To find the probability that at most three grafts fail, we need to find the sum of the probabilities for x = 0, 1, 2, and 3.

Using the given values of f(x), we get:

P(X <= 3) = f(0) + f(1) + f(2) + f(3)

= 0.7 + 0.2 + 0.05 + 0.03

= 0.98

So the probability that at most three grafts fail is 0.98.

To find the probability that at least two grafts fail, we need to find the sum of the probabilities for x = 2, 3, and 4 and subtract it from 1.

Using the given values of f(x), we get:

P(X >= 2) = 1 - (f(0) + f(1)) = 1 - (0.7 + 0.2) = 0.1

So the probability that at least two grafts fail is 0.1

--The question is incomplete, answering to the question below--

"Grafting the uniting of the stem of one plant with the stem or root of another; is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with hardy root system: Most Florida sweet oranges grow on trees grafted to the root of sour orange variety. The density for X, the number of 'grafts that fail in series of five trials.

For the values of x = 0, 1, 2, 3, and 4 value of f(x) is 0.7, 0.2, 0.05, 0.03, and 0.01 respectively.

Use f(x) to find the probability that at most three grafts fail; that at least two grafts fail."

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The answer is

\( {x}^{2} {y}^{3} \)

I hope this helps, have a great day!

The area of the figure is 289 square unit

The area of a rectangle can be calculated by multiplying the length and the width of the shape.

Given that

But the length and the width have two equal opposite sides. The shape is a square

20 - x = 3x + 8

20 - 8 = 3x + x

12 = 4x

x = 12/4

x = 3

L = 20 - 3 = 17

B = 3(3) + 8

B = 9 + 8

B = 17

A = 17 x 17

A = 289 square unit

Therefore, the area of the figure is 289 square unit

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In computer programming, variables are used to store and manipulate data. In this case, an int variable named strawsoncamel has been declared and assigned a value.

To increase the value of strawsoncamel by 1, you can use the increment operator (++). This operator adds 1 to the current value of the variable and assigns the result back to the variable.

For example, if strawsoncamel has a value of 5, the statement strawsoncamel++; would increase its value to 6. This can be useful in many scenarios, such as counting or iterating through a loop. It's important to note that the increment operator can also be used in other ways, such as ++strawsoncamel, which increments the value of the variable before it is used in an expression.

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To increase the value of the variable strawsoncamel by 1, you can use the increment operator "++". So the statement would be:
strawsoncamel++;

This will increment the value of strawsoncamel by 1. The increment operator is an example of an operator in programming, which performs a specific operation on a variable. In this case, it increases the value of the variable by 1, which is also known as an increment.
To increase the value of the integer variable `strawsoncamel` by 1 using the increment operator, follow this step:
Write the statement: `strawsoncamel++;`
This line of code will use the increment operator (`++`) to increase the value of the variable `strawsoncamel` by 1.

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Answer:

v = 105°

Step-by-step explanation:

According to Angle Sum Property of a triangle ,

Sum of measure of all the 3 interior angles of the triangle 180°.

Now , lets use this property in this question . So,

\(36 + (v - 27) + (v - 39) = 180\)

\( = > 2v - 66 + 36= 180\)

\( = > 2v - 30 = 180\)

\( = > 2v = 180 + 30 = 210\)

\( = > v = \frac{210}{2} = 105\)

It takes approximately 0.0533 seconds for the sound of the coin hitting the bottom of the well to reach Sara's ears.

If Sara hears the coin hit the bottom of the well, that means she is able to hear the sound produced by the coin reaching the bottom. The time it takes for sound to travel from the top of the well to the bottom is what we need to find.
To calculate the time it takes for sound to travel, we can use the formula:
Time = Distance / Speed
In this case, the distance is the depth of the well, which is 60 feet. The speed of sound is approximately 1,125 feet per second.
Plugging these values into the formula, we get:
Time = 60 feet / 1,125 feet per second
Simplifying this expression, we find:
Time ≈ 0.0533 seconds
Therefore, it takes approximately 0.0533 seconds for the sound of the coin hitting the bottom of the well to reach Sara's ears.

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So the answer is 1.3 after rounding to 10.

Answer:

60 degrees

Step-by-step explanation:

Since the two lines are intersecting, the angles formed by them are vertical angles. Therefore:

2x+24=144

2x=144-24=120

x=120/2=60

Hope this helps!

Step-by-step explanation:

Therefore,

2x+24= 144° [ Vertically positive angles]

Or, 2x= 144-24

Or, 2x= 120

Or, x= 120/2

Therefore, x= 60°

Yes, Since there are no free variables, the system has a unique solution for every b, b is in the range of the linear transformation x↦ax.

Since the range of the linear transformation x↦ax is the column space of the matrix A, and b can be written as a linear combination of the columns of A, then b is in the range of the linear transformation x↦ax. Specifically, we can write b as the linear combination of the columns of A as follows:

b = (−7, 1, −2, 5) = (−7, 1, −2, 5)⋅

         1     0     0     0     0

         3     1     3     4    −2

        13     0     4    −5     1

         6    −5    −4    −1    −5

Therefore, b is in the range of the linear transformation x↦ax.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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The correct answer is option a) "0.9429" because P(Z > -1.58) represents the probability of the standard normal random variable Z being greater than -1.58.

To calculate P(Z > -1.58), we need to find the probability of the standard normal random variable Z being greater than -1.58. Since Z follows a standard normal distribution, we can use the standard normal distribution table or a statistical calculator to find this probability.

In the standard normal distribution table, we look for the value closest to -1.58, which is -1.6. The corresponding probability for Z > -1.6 is 0.9452. However, since -1.6 is slightly smaller than -1.58, the actual probability P(Z > -1.58) would be slightly greater.

Therefore, the correct answer is option a) 0.9429, which is the closest approximation to the actual probability.

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Answer:

ka=2.8×10>4

Step-by-step explanation:

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