(05.03 MC)
A system of equations is given.
-5y = 10 - 5x
-2y = 8 - 4x
Solve for (x, y) using the elimination method. Show all work.

To graph the parametric path x = t^2, y = (t - 1)(t^2 - 4) on a Slope-Direction diagram, we need to plot points by evaluating the expressions for different values of t within the given interval [-3, 3].

First, let's calculate the coordinates for several values of t:

For [tex]t = -3: x = 9, y = 0[/tex]

For[tex]t = -2: x = 4, y = 6[/tex]

For [tex]t = -1: x = 1, y = 0[/tex]

For [tex]t = 0: x = 0, y = -4[/tex]

For[tex]t = 1: x = 1, y = 0[/tex]

For[tex]t = 2: x = 4, y = 6[/tex]

For [tex]t = 3: x = 9, y = 0[/tex]

Plotting these points on the Slope-Direction diagram, we can observe the shape of the curve. The path starts at (9, 0), moves downward to (4, 6), reaches the lowest point at (0, -4), and then goes back up to (4, 6) and (9, 0).

To find the length of the curve given by (2cost - cost2t, 2sint - sin2t) over the interval 0 ≤ t ≤ π/2, we can use the arc length formula:

L = ∫√(dx/dt)² + (dy/dt)² dt

First, calculate the derivatives of x and y with respect to t:

dx/dt = -2cost - 2costsin2t

dy/dt = 2cost - 2sintcos2t

Next, square and add these derivatives:

(dx/dt)² + (dy/dt)² = 4cost² + 4costsin2t + 4cost² + 4sint²cos²2t

Simplify the expression:

(dx/dt)² + (dy/dt)² = 8cost² + 4costsin2t + 4sint²cos²2t

Now, integrate the square root of this expression over the given interval 0 ≤ t ≤ π/2 to find the length of the curve:

L = ∫√(8cost² + 4costsin2t + 4sint²cos²2t) dt, from 0 to π/2

Evaluating this integral will provide the final answer for the length of the curve.

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Your question isn’t worded correctly. I will answer it two ways because I’m not sure which is right -

If a student weights 45 lbs how much does the water weigh? 33.75 lbs

And if a student has 45 lbs of water, how much does the student way? 60 lbs

Answer:

$6.00

Step-by-step explanation:

In order y find the cost of one muffin, we divide the price of 6 muffins by 6.

$3.00 / 6 = $0.50

Therefore, the cost of one muffin is $0.50.

To find the price per dozen, we multiply the cost of one muffin by 12.

$0.50 * 12 = $6.00

Therefore, the price per dozen muffins is $6.00.

Answer:

The terms of "2/10, n/30 R.O.G." mean that the buyer (Air Yukon) can take a cash discount of 2% if they pay the invoice within 10 days. Otherwise, the full amount is due within 30 days of the invoice date. "R.O.G." means "receipt of goods," indicating that the 30-day period begins on September 2, the date Air Yukon received the shipment.

To determine the last day for taking the cash discount, we start with the date of the invoice, August 15, and add 10 days for the discount period. This gives us August 25, which is the last day Air Yukon can pay the invoice and still receive the 2% discount.

If Air Yukon takes the cash discount, they will pay 98% of the invoice amount. We don't know the exact amount of the invoice from the information given, but if we assume it was $1,000, Air Yukon would pay $980 if they take the cash discount ($1,000 x 0.98).

Answer:

∠x

Step-by-step explanation:

Vertical angles are defined as angles opposite each other where two lines cross. In this case, it is given that you are trying to find the opposite angle of y. By the definition of vertical angles, it will mean that it is ∠x.

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Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

1)

When the points (1, 150) and (6, 900) are used:

a)

Slope of line is 150.

Given points,

(1, 150) and (6, 900)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 900 - 150 / 6 - 1

Slope = 150

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =150

Hence the equation of line is:

y = 150x

c)

For every TV ad, CD sales increased by about 150 as the slope of line is + 150 which indicates the increase in  sales of CD .

2)

When the points (1, 100) and (8, 800) ae used:

a)

Slope of line is 100.

Given points,

(1, 100) and (8, 800)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 800 - 100 / 8 - 1

Slope = 100

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =100

Hence the equation of line is:

y = 100x

c)

For  every magazine ad, CD sales increased by about 100, as the slope of line is + 100 which indicates the increase in  sales of CD .

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The range in battery life for each data set are Brand X: 11 and Brand Y: 17

The brand Y batteries last longer

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

The box plots

Where, we have

Brand X: 10 to 21

Brand Y: 6 to 23

The range is the difference between the boundaries

So, we have

Brand X: 21 - 10 = 11

Brand Y: 23 - 6 = 17

In (a), we have the range to be

Brand X: 11

Brand Y: 17

The above means that the brand Y batteries last longer than the brand X battery

This is because it has more spread i.e. bigger range

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Answer:

C. Subtract the coefficients (5 – 3)

Step-by-step explanation:

[tex]5y^2-3y^2=(5-3)y^2=2y^2[/tex]

Answer:

To calculate the time it will take to pay off the account, we can use the formula for the future value of an annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where:

PV = Present value (current balance)

PMT = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

PV = $14,790

PMT = $570

r = 0.0097 (0.97% expressed as a decimal)

n = ?

Plugging in the values, we can solve for n:

14,790 = 570 * ((1 - (1 + 0.0097)^(-n)) / 0.0097)

Let's solve this equation to find the value of n:

((1 + 0.0097)^(-n)) = 1 - (14,790 * 0.0097) / 570

((1 + 0.0097)^(-n)) = 0.9742105

Taking the logarithm of both sides:

-n * log(1.0097) = log(0.9742105)

n = log(0.9742105) / log(1.0097)

Using a calculator, we find that n is approximately 28.56.

Therefore, it will take approximately 28.56 months (or 28 months and 17 days) to pay off the account.

Step-by-step explanation:

The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6)  after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).

We know that,

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates

The following translation is being used: (x, y) ⇒ (x + 2, y - 3)

First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.

You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)

Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.

You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)

Finally, you would take each one and put it together, or piece it together.

Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).

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The probability that spinner one will land on four, and spinner two will land on blue is (1/24) x (2/24) = 1/288, or approximately 0.3%.

Megan has two spinners with one spinner divided into six equal parts, while the second spinner is divided into four equal parts. The probability that spinner one will land on four, and spinner two will land on blue is required.

The fundamental principle of probability states that the probability of an event happening is the number of favorable outcomes to the total number of outcomes.

To find the probability, it is essential to determine the total number of outcomes by multiplying the number of sections on each spinner.

The total number of outcomes = (Number of sections in spinner one) x (Number of sections in spinner two)

Number of sections in spinner one = 6Number of sections in spinner two = 4Total number of outcomes

= 6 x 4 = 24

The number of outcomes that will result in spinner one landing on four is one, and the number of outcomes that will result in spinner two landing on blue is two.

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The number of cars Captain's Autos sold in total that week is 160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that:

Now,

Let's call the total number of cars sold during the week "x".

We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:

[tex]\sf 22 + 18 = 0.25x[/tex]

Simplifying, we get:

[tex]\sf 40 = 0.25x[/tex]

Dividing both sides by 0.25, we get:

[tex]\bold{x = 160}[/tex]

Hence, by the unitary method the answer will be 160.

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Answer:

  A.  82 cm

Step-by-step explanation:

You want the perimeter of the L-shaped figure that is 12.5 cm high and 28.5 cm wide.

The top two horizontal line segments have the same total length as the bottom horizontal line segment. We don't need to figure what the missing length is, because we only need their total for the perimeter.

The right side two vertical line segments have the same total length as the left vertical line segment. As with the horizontal segments, we don't need to figure out the missing length, because we only need their total for the perimeter.

The perimeter is the sum of horizontal line segments plus the sum of vertical line segments:

  2(28.5 cm) + 2(12.5 cm) = 57 cm + 25 cm = 82 cm

The perimeter of the figure is 82 cm.

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The total cost T of the floor algebraically is T = c x (3√3/2) x s²

We have,

To express the total cost T of the floor of the hexagonal gazebo algebraically, we need to consider the area of the hexagonal floor and the cost per square unit of flooring.

The area of a regular hexagon can be calculated using the formula:

Area = (3√3/2) x s²

Where s is the side length of the hexagon.

To find the total cost, we multiply the area by the cost per square unit of flooring (c):

T = c x Area

Substituting the area formula into the equation:

T = c x (3√3/2) x s²

Now, we have expressed the total cost T algebraically in terms of the side length s and the cost per square unit of flooring c.

Thus,

The total cost T of the floor algebraically is T = c x (3√3/2) x s²

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Answer:

[tex]( { \frac{ {r}^{2} }{s} })^{3} = \frac{ {r}^{2 \times 3} }{ {s}^{1 \times 3} } = \frac{ {r}^{6} }{ {s}^{3} } [/tex]

The area to the right of z = 1.16 in the standard normal distribution is approximately 0.1357, or 13.57% as per the given details.

To discover the location to the right of z = 1.16 in the general everyday distribution, we are able to use the same old regular table or a statistical software.

Using the usual normal desk, the values provided are typically for the place to the left of a given z-rating.

However, seeing that the entire region below the same old normal distribution curve is 1, we can discover the place to the right of z = 1.16 by way of subtracting the region to the left of z = 1.Sixteen from 1.

Area to the right = 1 - Area to the left

= 1 - 0.8643

= 0.1357

Thus, the answer is 0.1357.

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To find an expression representing the width of the rectangular garden, we need to use the given information about the area and length of the garden.

The formula for the area of a rectangle is:

Area = Length × Width

We are given that the area of the garden is x^2 - 36, and the length is x^2 - 2x - 24.

Let's substitute these values into the formula:

x^2 - 36 = (x^2 - 2x - 24) × Width

To isolate the width, we divide both sides of the equation by (x^2 - 2x - 24):

Width = (x^2 - 36) / (x^2 - 2x - 24)

Therefore, an expression representing the width of the garden is:

Width = (x^2 - 36) / (x^2 - 2x - 24)

Account equations are mathematical relationships used in accounting to record various financial transactions and help ensure that the accounting records remain accurate and balanced.

Account equations serve as the foundation of double-entry bookkeeping, which is the system used in accounting to maintain accurate financial records.

The fundamental equation in double-entry bookkeeping is known as the accounting equation or the balance sheet equation which states that Assets = Liabilities + Owner's Equity.

This equation reflects the principle that every financial transaction affects at least two accounts and that the total value of assets must always be equal to the total value of liabilities and owner's equity.

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Answer:

64 inches.

Step-by-step explanation:

To find the amount of inches in 5 1/4 feet, you must first multiply 12 by 5 because there are 12 inches in one foot.
12x5=60.

The next step in order to complete the equation would be to find how many inches are in 1/4 of a foot.
To find how many inches are in 1/4 of a foot you must divide 12 by 4.
12 divided by 4= 4.

Now, you must as the two numbers together to get the total number of inches.
60+4=64.

This, 64 is your final answer.

Hope this helps! :)

a. The equation of the line of best fit is y = 1.2x + 375.

b. The correlation coefficient for the line of best fit is 0.97.

c. The correlation coefficient of 0.97 is very close to 1, which indicates that there is a strong positive correlation between the number of calories and the amount of sodium in beef hot dogs.

Mean of x-values: (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139) / 8 = 169

Mean of y-values: (495 + 477 + 425 + 322 + 482 + 587 + 370 + 322) / 8 = 437.5

Calculate the slope of the line of best fit.

Slope = (y2 - y1)/(x2 - x1) = (587 - 495)/(190 - 186) = 1.2

Calculate the y-intercept of the line of best fit.

y-intercept = mean of y-values - slope * mean of x-values

= 437.5 - 1.2 * 169

= 375

The equation of the line of best fit is y = 1.2x + 375.

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The given statement is false because A deviation score is computed as the difference between an individual data point and the mean of a distribution, not the population size (n) minus the population mean (μ).

The correct formula for computing a deviation score is:

Deviation Score = Data Point - Mean

In this formula, the data point represents an individual observation from the population or sample, and the mean represents the average value of the data set.

The deviation score measures how far each data point is from the mean. A positive deviation score indicates that the data point is above the mean, while a negative deviation score indicates that the data point is below the mean. The magnitude of the deviation score represents the distance between the data point and the mean.

The formula n - μ is used to calculate the sum of deviations from the population mean, which is used in certain statistical calculations such as the sum of squares. However, it does not represent a deviation score for an individual data point.

Therefore, the statement "A deviation score is computed as n - μ" is false. The correct formula for a deviation score is Data Point - Mean.

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Answer:

The explicit arithmetic formula can be used to find the 39th term of this sequence.

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

In order to use this formula, we must know a_1, the first term, and , the common difference.

In this case, the first term is given as -15.

The difference can be found by looking at the difference between each following term. In this case, d = +5.

(Notice to get from -15 to -10, we add 5, to get from -10 to -5, we add 5, etc.)

Now that we have everything we need, we can plug everything in to find the 39th term:

[tex]a_{39} = -15 + 5(39-1)\\a_{39} = -15 + 190\\a_{39} = 175[/tex]

The 39th term of this sequence is 175.

*Note n represents the term number we are trying to find. That's why we substituted 39 for n when plugging everything into the formula. [tex]a_{39}[/tex] denotes the 39th term

If x = -2 is a zero with a multiplicity of one, x = 3 is a zero with a multiplicity of two, and x = 1 is a zero with a multiplicity of one, then the polynomial can be written in factored form as:

[tex]f(x) = (x + 2)(x - 3)^2(x - 1)[/tex]

To find the polynomial in expanded form, we can use the distributive property and the rules of exponents:

[tex]f(x) = (x + 2)(x - 3)(x - 3)(x - 1)\\= (x^2 - x - 6)(x - 3)(x - 1)\\= (x^3 - 4x^2 + 3x + 18)(x - 1)\\= x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

Therefore, the polynomial that has a lead coefficient of one and exactly three distinct zeros, with x = -2 as a zero with multiplicity of one, x = 3 as a zero with multiplicity of two, and x = 1 as a zero with multiplicity of one, is:

[tex]f(x) = x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

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The value of the given expression is [tex]6\frac{11}{24}[/tex].

The given fractional expression is [tex]4\frac{1}{8}+2\frac{1}{3}[/tex].

Here, [tex]4\frac{1}{8}[/tex] can be written as 33/8 and [tex]2\frac{1}{3}[/tex] can be written as 7/3

Now, 33/8 + 7/3

= 99/24 + 56/24

= (99+56)/24

= 155/24

= [tex]6\frac{11}{24}[/tex]

Therefore, the value of the given expression is [tex]6\frac{11}{24}[/tex].

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About 95% of the housing Prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

Given that housing prices in a small town are normally distributed with a mean of µ. We are to use the empirical rule to complete the following statement.

The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean,

and approximately 99.7% of the data falls within three standard deviations of the mean.Since we do not have information about the standard deviation of the housing prices,

we cannot provide exact values for the empirical rule. However, we can make some general statements:

About 68% of the housing prices are between (µ - σ) and (µ + σ).

About 95% of the housing prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

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Hello!

abc * cd

= a * b * c * c * d

= abc²d

[tex] \bold{abc \: \: by \: \: cd}[/tex]

[tex] \bold{(abc) \cdot(cd)}[/tex]

[tex] \sf{abc {}^{1 + 1} d}[/tex]

[tex] \sf{abc {}^{2} d}[/tex]

The general rule for multiplication of monomials says that: multiply the coefficients and then write the letters of the factors in alphabetical order. Each letter is given an exponent equal to the sum of the exponents it has in the factors. The sign of the product result will be given by the Law of Signs.

Answer:

16

Step-by-step explanation:

To solve this problem, you need to follow the order of operations (PEMDAS):

First, you need to solve the parentheses: 2+2 = 4

Next, you need to solve the multiplication: 2 x 4 = 8

Finally, you need to solve the division: 8 ÷ 2 = 16

Answer:

[tex]\Huge \boxed{\boxed{x = 10}}[/tex]

Step-by-step explanation:

To solve the equation [tex]5x = 50[/tex] and find the value of [tex]x[/tex], we need to isolate [tex]x[/tex] on one side of the equation.

Step 1: Divide both sides of the equation by 5.

[tex]\frac{5x}{5} = \frac{50}{5}[/tex]

Step 2: Simplify this expression

[tex]x = 10[/tex]

Therefore, the solution to the equation [tex]\boldsf{5x = 50}[/tex] is [tex]x = 10[/tex].

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Answer:

[tex]11\frac{7}{10}[/tex]

Step-by-step explanation:

[tex]\displaystyle 3\frac{1}{4}+\biggr(3\frac{1}{4}+5\frac{1}{5}\biggr)\\\\3\frac{5}{20}+3\frac{5}{20}+5\frac{4}{20}\\\\(3+3+5)+\biggr(\frac{5}{20}+\frac{5}{20}+\frac{4}{20}\biggr)\\\\11+\frac{14}{20}\\\\11\frac{7}{10}[/tex]

Again, make sure all denominators are the same by using the least common denominator (in this case it's 20 since 5*4=20).