Find the slope of the line.

The width of the rectangle is 9 meter.

Now, According to the question:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Now, Solving the problem:

Perimeter of rectangle is 50 meter sq.

Length of the rectangle(L) is 16 meter.

We have to find the width (W) of the rectangle.

We know that,

Perimeter of rectangle is = 2 (L + W)

50 = 2(16 + W)

50 = 32 + 2W

2W = 50 - 32

2W = 18

W = 18/2

W = 9

Hence, The width of the rectangle is 9 meter.

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x = 9.21° or x = 22.5°

cot²2x – 4cot2x + 3 = 0

Let cot2x = y

y² - 4y + 3 = 0

Factorizing, we have

y² - y - 3y + 3 = 0

y(y - 1) -3(y - 1) = 0

(y - 1)(y - 3) = 0

y - 1 = 0 or y - 3 = 0

y = 1 or y = 3

Since cot2x = y

cot2x = 1 or cot2x = 3

1/tan2x = 1 or 1/tan2x = 3

tan2x = 1 or tan2x = 1/3

2x = tan⁻¹(1) or 2x = tan⁻¹(1/3)

2x = 45° or 2x = 18.43°

x = 45°/2 or x = 18.43°/2

x = 22.5° or x = 9.21°

So, x = 9.21° or x = 22.5°

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Answer:

In the explanation

Step-by-step explanation:

AB = line segment

ABC = angle

AB = line segment

CD = intersecting line

AC = line segment

AB = line segment

EBC = angle

BC = line segment

Answer:

See below.

Step-by-step explanation:

Part A

"The graph passes through (0,2), (2,6), (3,12).

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points.

Using (0,2) and (2,6), the slope would be 2.

Using (2,6) and (3,12), the slope would be 3 1/3.

Since the slope is not constant everywhere, the function is non-linear."

Part B

An example of a linear function is y=2x+6.

An example of a nonlinear function is xy=3.

-hope it helps

Answer:

x=3, y=0

Step-by-step explanation:

3x+2y=9--(i)

Multiplying by 3,

3(3x+2y)=3*9

9x+6y=27---(ii)

2x+6y=6---(iii),

Subtracting (ii) from (iii),

2x+6y=6

-9x+6y=27

=-7x+0=-21

x=-21/-7

x=3

In (i),

3x+2y=9

3*3+2y=9

y=0/2

y=0

Answer:

25.43

Step-by-step explanation:

Correct trust me!

Answer:

persepctive

Step-by-step explanation:

have a great day<3

Answer: 11

Step-by-step explanation: Calculators answer

total expenses= 1/4 + 1/8

the denominators should be equal to add the values.

1/4×2(divide both the numerator and denominator by two)

=2/8

=2/8+1/8

3/8//

3/8(fraction of the salary he spent)

3/8 of the salary

3/8×50,000

R.s 6250

balance = 50,000-6,250

= R.s 43,750//

Answer:

x = ± √ 22 − 3

Step-by-step explanation:

The reasoning that may be used for finding the measure of m∠12, is the

same side interior angles theorem.

The correct options using the drop-down menu are;

The sum of ∠1, ∠7, and ∠8 is 180°

∠8 and ∠12 are the same side interior angles

The measure of ∠12 must be = 120°

Stuart is not correct

The complete question is given below:-

In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.​

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given parameters;

Line x ║ line y

m∠1 = 65°, m∠7 = 55°

m∠12 = 60°

Stuart states ∠12 = 60°

The reasoning is presented as follows;

Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°

Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles

Step 3: So, m∠12 = 60°

Using the drop-down menu, we have;

The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)

∠8 and ∠12 are same side interior angles (by definition)

Same side interior angles are supplementary, therefore;

∠8 +∠12 = 180°

∠12 = 180°  - ∠8

Which gives;

The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°

The measure of ∠12 must be = 120°

Stuart is not correct

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Given QRS = 115°

Since, PQR + QRS = 180°

Angles on the same side of the transversal are supplementary.

Now,

PQR + 115° = 180°

PQR = 180° - 115°

PQR = 65°

Hence, the measure of PQR = 65°

Answer:

The area of the trapezium is 216 cm²

Step-by-step explanation:

The parameters of the trapezium are;

The point of intersection of the diagonals ac and bd = point o

The area of ΔCOD = 24 cm²

The area of ΔAOB = 96 cm²

Let h represent the height of the trapezium and let x represent the height of triangle ΔCOD, we have;

The height of ΔAOB = h - x

Therefore;

The area of ΔCOD = (1/2) × The length of CD × x = 24

∴ The length of CD = 24/((1/2) × x) = 48/x

The area of ΔAOB = (1/2) × The length of AB × (h - x) = 96

The length of AB = 96/((1/2) × (h - x)) = 192/(h - x)

The area of the trapezium, A = ((48/x + 192/(h - x))/2) × h

We note that ΔCOD ~ ΔAOB, therefore;

(AB)²/(CD)² = (h - x)²/x² = (arΔAOB)/(arΔCOD) = 96/24 = 4

∴ √((h - x)²/x²) = (h - x)/x = √4 = 2

∴ h - x = 2·x

h = 2·x + x = 3·x

A = ((48/x + 192/(h - x))/2) × h

∴ A = ((48/x + 192/(2·x))/2) × 3·x = ((48 + 192/(2))/2) × 3 = 216

The area of the trapezium, A = 216 cm².

Answer:

here's your answer

hope it helps

(look at attachment)

Given:

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

To find:

The percent of increase in the number of members.

Solution:

We have,

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

Now, the percent of increase in the number of members.

\(\%\text{ of increase}=\dfrac{{Members in this month - Members in last month}}{\text{Members in last month}}\times 100\)

\(\%\text{ of increase}=\dfrac{686-490}{490}\times 100\)

\(\%\text{ of increase}=\dfrac{196}{490}\times 100\)

\(\%\text{ of increase}=\dfrac{2}{5}\times 100\)

\(\%\text{ of increase}=2\times 20\)

\(\%\text{ of increase}=40\)

Therefore, the gym members increased by 40%.

The value of the line integral ∫c (11y dx + 7x dy) is -4π. To evaluate the line integral ∫c (11y dx + 7x dy) using Green's theorem, we need to follow these steps:

1. Recognize that the given circle is x² + y² = 1, with a positive (counter-clockwise) orientation.

2. Green's theorem states that for a positively oriented, simple, closed curve C, ∫c (P dx + Q dy) = ∬D (Qx - Py) dA, where D is the region bounded by C, and P and Q are functions of x and y.

3. In our case, P = 11y and Q = 7x. So, we need to compute Py and Qx.
Py = ∂(11y)/∂y = 11, and Qx = ∂(7x)/∂x = 7.

4. Apply Green's theorem: ∫c (11y dx + 7x dy) = ∬D (7 - 11) dA = -4∬D dA.

5. Now, we need to find the area of the circle. The area of a circle is given by A = πr². Since the circle is x² + y² = 1, the radius r is 1. Thus, A = π(1)² = π.

6. The final step is to multiply the area by the constant factor from step 4: -4∬D dA = -4A = -4π.

So, the value of the line integral ∫c (11y dx + 7x dy) is -4π.

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The required fill-in-the-blanks are "same" and "line segments".

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

Sometimes, the relationship between the variables doesn't stay the "same". This type of relation is called a piecewise linear relationship.

The graph of a piecewise linear relationship is made of non-overlapping "line segments", like this one.

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The percentage error in measuring the line segment is 4%. The correct option is (4)4%.

The actual length of the line segment is 5 cm, but it was measured as 5.2 cm, which is 0.2 cm more than the actual length.

The percentage error in measuring the line segment can be calculated as follows:

Percentage error = (Error / Actual value) x 100%

where Error = Measured value - Actual value

Substituting the given values, we get:

Error = 5.2 cm - 5 cm = 0.2 cm

Actual value = 5 cm

Percentage error = (0.2 cm / 5 cm) x 100% = 4%

Therefore, the percentage error in measuring the line segment is 4%.

Hence, the correct option is (4)4%.

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Ricardo's gross pay.: $460

What is Multiplication?

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the result of multiplying 6 and 5 is 30, and the result of multiplying x and (2+x) is (2+x) (indicating that the two factors should be multiplied together).

Separating the straight time with over time

44 - 40 = 4hours

Convert 4 hours to time and a half .

To do so multiply 4 hours with 1.5

4 x 1.5 = 6 hours

Adding straight time to time and a half

40 + 6 = 46

46 hours of time to compute gross pay

Multiply the total time by the rate per hour

46 x 10 = $460

Hence, Ricardo's gross pay is $460

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Answer:

? 40.50

Step-by-step explanation:

90 ÷ 20 × 9 = 40.5

Answer:

cost of 9article is 40.50

hope it helps.

NOTES: The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

THE ANSWER IS A

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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Answer:

Step-by-step explanation: IONK BUT I LIKE YOUR PFP

Answer:

Era

Step-by-step explanation:

Century, Decade and Millennium have something in common and that which they have in common is that they are all measurement of time.

The keyword measurement implies that they are units of time just like seconds, minutes, hours, etc.

Century -> 100 years

Decade -> 10 years

Millennium -> 1000 years

However, era is used to describe events in history;

Take for instance; the era of the first generation of computer;

So, from the list of given options; Era best answers the question

An era describes a time period marked by a change that begins a new period.

An era :

Examples of eras include:

All the eras mentioned above were distinct in how people behaved so in conclusion we can say that an era is a time period that begins a new period of development.

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1. \(\(x^2 + y^2 - 4x - 12y - 20 = 0\)  -- > \((x - 2)^2 + (y - 6)\) = 60,

3. \(\(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)  -- > \((x + 2)^2 + (y + 3)^2 = 18\)\),

4. \(\(5x^2 + 5y^2 - 10x - 20y - 30 = 0\)  -- > \((x - 1)^2 + (y - 2)^2 = 11\)\)

To match the circle equations in general form with their corresponding equations in standard form, we can use the following steps:

General Form: \(\(Ax^2 + By^2 + Cx + Dy + E = 0\)\)

Standard Form: \(\((x - h)^2 + (y - k)^2 = r^2\)\)

1. \(\(x^2 + y^2 - 4x - 12y - 20 = 0\)\)

  Completing the square for \(x\) and \(y\):

 \(\((x^2 - 4x) + (y^2 - 12y) = 20\)\)

 \(\((x^2 - 4x + 4) + (y^2 - 12y + 36) = 20 + 4 + 36\)\)

\(\((x - 2)^2 + (y - 6)^2 = 60\)\)

2. \(\(6x - 8y - 10 = 0\)\)

  This is a linear equation, not a circle equation.

3. \(\(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)\)

  Dividing by 3:

\(\(x^2 + y^2 + 4x + 6y - 5 = 0\)\)

  Completing the square for \(x\) and \(y\):

\(\((x^2 + 4x) + (y^2 + 6y) = 5\)\)

\(\((x^2 + 4x + 4) + (y^2 + 6y + 9) = 5 + 4 + 9\)\)

\(\((x + 2)^2 + (y + 3)^2 = 18\)\)

4. \(\(5x^2 + 5y^2 - 10x - 20y - 30 = 0\)\)

  Dividing by 5:

\(\(x^2 + y^2 - 2x - 4y - 6 = 0\)\)

  Completing the square for \(x\) and \(y\):

 \(\((x^2 - 2x) + (y^2 - 4y) = 6\)\)

 \(\((x^2 - 2x + 1) + (y^2 - 4y + 4) = 6 + 1 + 4\)\)

\(\((x - 1)^2 + (y - 2)^2 = 11\)\)

The matched pairs are:

1. \(\(x^2 + y^2 - 4x - 12y - 20 = 0\)  -- > \((x - 2)^2 + (y - 6)^2 = 60\)\)

3. \(\(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)  -- > \((x + 2)^2 + (y + 3)^2 = 18\)\)

4. \(\(5x^2 + 5y^2 - 10x - 20y - 30 = 0\)  -- > \((x - 1)^2 + (y - 2)^2 = 11\)\)

The other equations are not in circle form and are not matched.

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Since the p-value (0.034) is less than the significance level of 0.05, we reject the null hypothesis. This suggests evidence against the claim that the median percent of impurities in the brand of jam is 2.5%.

To perform the sign test, we compare the observed values to the hypothesized median value and count the number of times the observed values are greater or less than the hypothesized median. Here's how we can proceed:

State the null and alternative hypotheses:

Null hypothesis (H0): The median percent of impurities in the brand of jam is 2.5%.

Alternative hypothesis (Ha): The median percent of impurities in the brand of jam is not 2.5%.

Determine the number of observations that are greater or less than the hypothesized median:

From the given data, we can observe that 5 jars have impurity percentages less than 2.5% and 11 jars have impurity percentages greater than 2.5%.

Calculate the p-value:

Since we are performing a two-tailed test, we need to consider both the number of observations greater and less than the hypothesized median. We use the binomial distribution to calculate the probability of observing the given number of successes (jars with impurity percentages greater or less than 2.5%) under the null hypothesis.

Using the binomial distribution with n = 16 and p = 0.5 (under the null hypothesis), we can calculate the probability of observing 11 or more successes (jars with impurity percentages greater than 2.5%) as well as 5 or fewer successes (jars with impurity percentages less than 2.5%). Summing up these probabilities will give us the p-value.

Compare the p-value to the significance level:

Since the significance level is 0.05, if the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

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