Solve the system of two linear equations below graphically y= -x + 1 y= -1/3x + 3​

The Cartesian equation 2xy = 1 has the following polar equation r²·sen2θ = 1.

To convert the Cartesian equation 2xy = 1 into polar equation form, we need to use the relationships between Cartesian coordinates and polar coordinates. The relationships are as follows:

Substituting these relations in the Cartesian equation, we proceed to solve:

2 (r·cosθ)(r·sinθ) = 1

2r²·cosθ·sinθ = 1

r²·(2cosθ·sinθ) = 1

r²·sen2θ = 1

In conclusion, the polar equation has the following form: r²·sen2θ = 1.

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Answer:

The answer is C.

106.0 in^3

Answer:

106.0 in^3

Step-by-step explanation:

The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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Answer:

[tex]x=\pm\,9i[/tex]

Step-by-step explanation:

[tex]x^2=-81\\x=\pm\,9i[/tex]

The requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describe the relationships between x and y for each table. Option C is correct.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

In Table A, y is 2.5 more than x, and in Table B, y is 3 more than x. Both tables represent additive relationships. the requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describing the relationships between x and y for each table. Option C is correct.

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The statement that correctly compares the two anthills is "the second anthill is one and one-third times as many ants as the first anthill."

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

Using the above as a guide, we have the following:

First = 982

Second = 1 1/3 * First

This means that "the second anthill is one and one-third times as many ants as the first anthill."

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Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.

4 = 2y - 10

14 = 2y

7 = y

The measure of angle DEF is 50 degrees

The question that would be more appropriate for Enrique's survey of high school teachers is Among high school teachers, what is the most popular restaurant to eat dinner at in town?

Enrique's conclusion about adults liking to eat dinner at The Bistro more than other restaurants in town may not be accurate since his survey was only limited to high school teachers.

To make his conclusion more reliable, Enrique could have asked a more specific question that is relevant to high school teachers. Here are a few examples of more appropriate questions for Enrique's survey of high school teachers:

Among high school teachers, what is the most popular restaurant to eat dinner at in town?

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The total volume in the 6 cups is  638.30 in^2

Remember that the volume of a cylinder of height H and radius R is:

V = pi*R^2*H

Here the diameter is 4.4 inches, then the radius is half of that:

R = 4.4in/2 = 2.2in

The height is 7 inches, then the volume of each cup is:

V = 3.14*(2.2in)^2*7in = 106.38 in^2

And in 6 cups the total volume will be:

volume = 6*106.38 in^2 = 638.30 in^2

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The average speed with the given distance and time is 119/40 miles per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, number of miles jogged = [tex]3\frac{2}{5}[/tex] = 17/5 miles and the time taken = 7/8 hours

Here, average speed = 17/5 ÷ 7/8

= 119/40 miles per hour

Therefore, the average speed is 119/40 miles per hour.

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Answer:

the answer you are looking for here is 3/7

Answer:

3/7

Step-by-step explanation:

6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7

The amount the the home buyer saves in total by choosing Loan A is  most closest to $11,427. The Option B is correct.

In order to compare the total cost of each loan, we need to consider both the monthly payment and the discount points.

For Loan A, we have Loan amount: $390,000, Loan term: 15 years, Discount points: 4 and Monthly payment: $3,509.71. For Loan B, we have Loan amount: $390,000, Loan term: 15 years Discount points: 0 and  Monthly payment: $3,659.86.

The total cost of Loan A is the sum of the discounted upfront cost (discount points) and the total of all monthly payments over the life of the loan:

= (4% of $390,000) + ($3,509.71 x 180)

= $15,600 + $631,948.80

= $647,548.80

The total cost of Loan B is the total of all monthly payments over the life of the loan:

= ($3,659.86 x 180)

= $658,574.80

Now, the amount saved by choosing Loan A over Loan B is the difference between their total costs which equals:

= Total cost of Loan B - Total cost of Loan A

= $658,574.80 - $647,548.80

= $11,026

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The ratio of trombones to all the brass section members is 3:7.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of Trumpets = 4

Number of Trombones= 3

Total = 4 + 3= 7

So, the ratio of trombones to all the brass section members

= Number of Trombones/ Total

= 3 /7

= 3:7

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The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.

This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.

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The values of the variable are:

x is 45.

y is 18.

z is 18.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 45 = z / (18√2)

Sin 45 = 1 /√2

So,

1/√2 =z / 18√2

z = 18

Cos 45 = y / (18√2)

1/√2 = y/18√2

y = 18

Tan x = y / z

Tan x = 18/18

Tan x = 1

x = [tex]tan^{-1}[/tex]1
x = [tex]tan^{-1}[/tex] tan 45

x = 45

Thus,

x is 45.

y is 18.

z is 18.

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The line plot which can be used to represent the teachers record of how many miles each student ran during gym class is attached.

A Line plot can be defined as a graphical representation of data as points or check marks above a number line, showing the frequency of each value along a line. It is used to analyze data

Given Data:

3/4, 1/4, 1/2, 3/4, 1/2, 1/2, 1/4, 3/4, 1/4, 1/2, 1/4, 3/4

From the given Data, the frequency of

1/4 = 5

1/2 = 4

3/4 = 3

Therefore, the line plot is attached as a diagram.

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Answer: 1,422

Step-by-step explanation:

2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.

2/10 Net 30:

The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).

For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.

This example 2/10 net 30 step by step.

Day Start counting days from the invoice date.

Quick Formula: 100% Discount % x Invoice Amount.

100% - 2% = 98% x $500 = $490.

Formula:

(immediate discount) x (invoice amount) = less payment

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Step-by-step explanation:

[tex]y = a(x - h) {}^{2} + k[/tex]

If the triangles are similar but no congruent, then the triangles have different size, thus the only correct option is the dilation (first option).

We know that two figures are congruent if the figures have the same shape and size, while two figures are similar only if have the same shape (but the figures can have different size).

Here we know that the triangles are similar but no congruent, so the triangles must have different size. From the given transformations, the only one that changes the size is the first option, a dilation.

And for example, if we apply a dilation AND the other transformations, then we still will get a similar figure, but if we apply a reflection/rotation/translation alones, we will get a congruent triangle.

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Answer:

C

Step-by-step explanation:

-4 is greater than -7

We can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

One who has retired is known as a retiree.

Many seniors underestimate their retirement income by not accounting for inflation.

Wages, a gauge of the income that retirees must replace, will be the basis for benefits.

One who has retired is known as a retiree.

According to the U.S. Bureau of Labor Statistics most recent Consumer Expenditure Survey, the typical retiree household—one that is headed by a person 65 or older—spends $50,220 annually.

Comparatively, the average yearly household expenditure is $63,036.

So, from the above description, we can state that the average cost of living for a retiree per year is (A) around $50,000.

Therefore, we can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

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Complete question:

What is the average cost of living for a retiree per year?

A. around $50,000

B. around $60,000

C. around $70,000

D. around $80,000

Interval of increase and decrease refers to a period of time in which a quantity rises or falls. For example, a stock market index may have an interval of increase and decrease over a certain period, such as a month or a year.

Interval of increase and decrease is a term used to describe a period during which a certain quantity either increases or decreases. This phenomenon is commonly seen in financial markets, such as the stock market, where indices may go up and down over a certain period of time. This interval of increase and decrease can be measured using different measures such as time, percentage growth, and movement. This interval helps investors and analysts to determine how the stock market is performing and if there are any changes in the market. It also helps them to predict future trends and make better investment decisions. During this interval, it is important to monitor the stock market and any changes that may occur. This helps to ensure that investments are made with the best possible outcome.

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Coordinates of the circumcenter are (7.7, -6.6)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

we first need to find the midpoint of each side, and then find the intersection of the perpendicular bisectors of each side.

Midpoint of AB is (7, -3)

Midpoint of BC is (2.5, -1.5)

Midpoint of AC is (4.5, -2.5)

The slope of the line passing through A and B is:

m= (-4 - (-2))/(9 - 5) = -1/2

the slope of the perpendicular bisector is 2

By point slope form

y - (-3) = 2(x - 7)

y = 2x - 17

And the equation of the perpendicular bisector of AC is:

y - (-2.5) = -1/2(x - 4.5)

y = -1/2x + 5

Now 2x - 17 = -1/2x + 2.25

2.5x = 19.25

x = 7.7

Substituting x = 7.7 into the equation for the perpendicular bisector of AB, we get:

y = 2(7.7) - 17

y = -6.6

Hence, coordinates of the circumcenter are (7.7, -6.6)

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Answer:

The decimal 6.25 would be 6 25/100 as a mixed number. In lowest terms, it would be 6 1/4.

Answer: 1/4

Step-by-step explanation:

To find the product of two fractions, you simply multiply the numerators together and multiply the denominators together. That is:

(5/8) x (6/15) = (5 x 6) / (8 x 15)

Simplifying the numerator and denominator by dividing both by their greatest common factor, which is 2, we get:

(5 x 6) / (8 x 15) = 30 / 120

Further simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 30, we get:

30 / 120 = 1 / 4

Therefore, the product of 5/8 and 6/15 is 1/4.

Answer:

To multiply two fractions, you simply multiply their numerators (top numbers) and denominators (bottom numbers), respectively.

So, 5/8 x 6/15 = (5 x 6) / (8 x 15) = 30 / 120

To reduce this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common factor, which is 30.

30 / 120 = (30 ÷ 30) / (120 ÷ 30) = 1/4

Therefore, the product of 5/8 x 6/15 is 1/4

A congruent triangles worksheet is a type of educational resource that provides practice problems and exercises for students to work on to help them understand and apply the concept of congruent triangles.

The worksheet typically includes a variety of problems, such as identifying pairs of congruent triangles, determining congruent sides and angles, and applying congruence postulates or theorems to solve problems. The problems may involve using the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or hypotenuse-leg (HL) congruence criteria.

Congruent triangles are triangles that have the same size and shape. In other words, they are identical in every way except for their position and orientation in space. Understanding congruent triangles is important in geometry, as it can help students to solve problems involving triangles, as well as more complex geometric figures.

Worksheets are a useful tool for students to practice and reinforce their understanding of congruent triangles, and can be used in the classroom or as homework assignments.

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The estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is 0.45 which is denoted as option C.

This is referred to as a number that indicates how likely the event is to occur.

Probability for drawing at least 5 beads before she picks a grey bead from her collection

= 1-Probability for drawing at least one grey bead in the first 5 draws.

No of grey beads drawn in first 5 trials = (5, 80/80+160+240)

                                                                 = (5, 1/6)

Probability for drawing at least one grey bead in the first 5 draws.

=1 - Prob of no grey

Required probability = P(X=0 in first 5 draws) = (1/6)⁵ = 0.4018 and th nearest value is therefore 0.45.

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The work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

First we need to calculate the total amount of water that needs to be lifted and the height it needs to be lifted to.

The volume of water in the aquarium is given by:

V = 7 m * 1 m * 1 m = 7 m^3

Since we need to pump out the top half of the water, the volume of water that needs to be lifted is:

V = (1/2) * 7 m^3 = 3.5 m^3

The mass of the water can be calculated as:

m = V * density of water = 3.5 m^3 * 1000 kg/m^3 = 3500 kg

The height that the water needs to be lifted to is equal to the height of the aquarium, which is 1 m.

The work needed to lift the water can be calculated using the formula:

W = m * g * h

where

So, the work needed is:

W = 3500 kg * 9.8 m/s^2 * 1 m = 34,300 J (joules)

Therefore, the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

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As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given a scatter plot  in terms of the time the player spent practicing and the number of points he scored in the game.

A scatter plot uses dots to represent values for two different numeric variables.

The position of each dot on the horizontal and vertical axis indicates values for an individual data point.

As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.

Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

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