1. What information can be seen most easily in the dot plot?

Both angles 1 and 2 are supplementary and linear angles.

So, options (1) and (3) are the correct options.

If consider, ∠1 and ∠2 are supplementary. If two angles form a linear pair, the angles are supplementary. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.  

If consider complementary angles. They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 2 are corresponding. The 1 is external and the 2 is internal. Angles that are on opposite sides of the transversal of two other lines.

If consider linear pair angles. The sum of angles of a linear pair is always 180 degrees. Consider the image as shown. Here angle 2 and angle 1 are said to be a linear pair because they are formed on the same line with a standard arm S and common vertex point Q. Also, the sum of angles 1 and 2 is equal to 180 degrees.

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.

We can see all images.

So, that

When two lines intersect each other at a point, angles formed on the point are called as linear pair.

Since pair of linear angles is supplementary, sum of linear angles will be 180°.

m∠1 + m∠2 = 180°

Therefore, both angles 1 and 2 are supplementary and linear angles.

Options (1) and (3) are the correct options.

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Solution to the system by using elementary row operations of equations is \(x1 = 3\) and \(x2 = 1\).

This can be understand by:

Step 1: Subtract 3 times the first equation from the second equation:

\(4x1 + 5x2 = 30\\-3(3x1 + 6x2) = 18\\ -x1 + -x2 = -12\)

Step 2: Add the equations to eliminate x2:

\(3x1 + 6x2 = 18\\-x1 + -x2 = -12\\2x1 = 6\)

Step 3: Divide both sides by 2 to solve for x1:

\(2x1 = 6\\x1=6/2\\x1 = 3\)

Step 4: Substitute x1 = 3 into either equation to solve for x2:

\(3(3) + 6x2 = 18\\6x2 = 6\\x2 = 1\)

Therefore, the solution to the system of equations is x1 = 3 and x2 = 1.

To reduce a matrix into row-echelon form, a series of procedures known as elementary row operations is used. These operations include multiplying one row by a nonzero value and adding it to another row, adding two rows together, switching two rows, and adding two rows together. They can be used to determine a matrix's inverse and to resolve linear equations.

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Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

The area of a rectangle is given by the formula A = lw, where l is the length of the rectangle and w is the width. Therefore, to find the dimensions of the rectangle, we can set up the equation 4p² + 12p = lw.

To solve this equation, we can first distribute the 4p² on the left side of the equation to get 4p² + 12p = 4p²l + 12pw. Then, we can rearrange the terms to get 12pw - 4p²l = 0.

To solve this equation for w, we can divide both sides by 4p(p - l), which gives us w = 3l/4p.

Therefore, the dimensions of the rectangle are l and 3l/4p. You can choose any value for l and then use the equation above to find the corresponding value for w. For example, if you choose l = 4, then w = 3(4)/4p = 3/p.

To draw, first, decide on a value for the length of the rectangle, l. Then, use the equation w = 3l/4p to calculate the corresponding value for the width of the rectangle, w.

Next, use the ruler or straight edge to draw two straight lines that are perpendicular to each other, forming the sides of the rectangle. The length of the rectangle should be equal to l, and the width of the rectangle should be equal to w. Make sure to label the length and width on your drawing.

Hello.

Let's solve the absolute value inequality.

In order to do that, let's imagine that |3x-4| is positive.

Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:

\(\mathrm{3x-4\geq 8}\)

Now, move -4 to the right, using the opposite operation:

\(\mathrm{3x\geq 8+4}\)

Add:

\(\mathrm{3x\geq 12}\)

Divide both sides by 3:

\(\mathrm{x\geq 4}\)

However, this is only 1 solution.

Let's imagine that |3x-4| is a negative number.

So, the inequality looks like so:

\(\mathrm{-3x+4\geq 8}\)

Move 4 to the right:

\(\mathrm{-3x\geq 8-4}\)

\(\mathrm{-3x\geq 4}\)

Divide both sides by -3:

\(\mathrm{x\leq \displaystyle-\frac{4}{3} }\)

Therefore, the solutions are

\(\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }\)

\(\bigstar\) Note:

If we divide both sides of an inequality by a negative number, we flip the inequality sign.

I hope this helps you.

Have a nice day.

\(\boxed{imperturbability}\)

answer:

1

1/3

all real numbers.

Answer:

Analyze the graph of the exponential decay function.

The initial value is (1)

The base, or rate of change, is (1/3)

The domain is (all real numbers)

Step-by-step explanation:

hope this helps :)

The total amount payable at the end of 4 years is 406

In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.

here we have to apply the formulla of simmple interest :

(principal × rate of interest × no. of years )/ 100

In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4

Simple interest = pnr/100

= (350 × 4 × 4)/100  = 56

Matured Amount = Principal + Interest

= 350 + 56 = 406

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To solve the inequality:

we need to remeber the property:

Then:

Therefore the solution of the inequality in interval form is:

and the graph is:

Answer:

I think it's C and E and A

Answer:

~4.75 inches or 4 3/4 inches

The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by the cost decreases for each additional shirt.

The cost of n t-shirts is given by the equation:

c = 15 + 9(n + 1)

c is the cost in dollars and n is the number of t-shirts.

The cost for 2 t-shirts, we substitute n = 1 into the equation:

c = 15 + 9(1 + 1) = 33

So it will cost \($33\) for 2 t-shirts.

The cost for 5 t-shirts, we substitute n = 4 into the equation:

c = 15 + 9(4 + 1) = 51

So it will cost \($51\) for 5 t-shirts.

The cost of additional shirts after the first one is \($9\) per shirt.

The equation for the cost of n t-shirts is c = 15 + 9(n + 1), the term 9(n + 1) represents the cost of additional shirts beyond the first shirt, and the coefficient 9 represents the amount by which the cost decreases for each additional shirt.

The following formula calculates the price of n t-shirts: c = 15 + 9(n + 1).

n is the quantity of t-shirts, and c represents the price in dollars.

We change n = 1 to represent the price of 2 t-shirts:

c = 15 + 9(1 + 1) = 33

the price will be.

t-shirts for two.

We enter n = 4 to get the price for 5 t-shirts: c = 15 + 9(4 + 1) = 51

the price will be.

Five t-shirts worth.

After the first shirt, additional shirts cost each shirt.

The cost of n t-shirts is given by the equation c = 15 + 9(n + 1), where the phrase 9(n + 1) denotes the price of subsequent shirts after the first shirt and the coefficient 9 denotes the amount by which the cost increases.

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Answer:

Step-by-step explanation:

Confidence interval formula is expressed as;

CI = xbar ±(z*s/√n)

xbar is the mean = 36

z is the z score at 95% CI = 1.96

s is the standard deviation = 6.9

n is the sample size = 22

Substitute

CI = 36  ±(1.96*6.9/√22)

CI = 36  ±(1.96*6.9/4.6904)

CI = 36  ±(1.96*1.4711)

CI = 36  ± 2.8833

CI = (36 - 2.8833, 36 + 2.8833)

CI = (33.1167, 38.8833)

Hence the 95% CI for the true population mean is 33.12<x<38.88

Answer:

12 * 3 * 5 * 5 = 900

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

Given that two lines are

y = 3.5x + 15

and y = 4x + 10

The condition for two lines to intersect is

So, for the given lines the condition will be

Since it had satisfied the condition then the given lines will intersect.

Now to find the intersecting point we will put both the equation equal.

3.5x + 15 = 4x + 10

4x - 3.5x = 15 - 10

0.5x = 5

x = 5/0.5 = 50/5

x = 10

So from the equation (i)

y = 3.5x + 15

y = 3.5 (10) + 15 = 35 + 15 = 50

y = 50

Hence the intersecting point is (x,y) = (10,50)

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

6 2/3 minutes

Step-by-step explanation:

6 2/3 minutes

Step-by-step explanation:

Amare runs 1/10 mile in 2/3 minutes

Therefore his speed in miles per minutes clean be calculated as follows

= 1/10, the denominator here is 10

= 10 × 2/3

= 20/3

= 6 2/3 minutes

Consider that the rate of bagels per hour is obtained by calculating the quotient between 300 and 2:

300/2 = 150

Hence, the bakers make 150 bagels per hour. To determine how many bagels the bakers make in 21 hours, just multiply the previous result by 21:

150 x 21 =

Answer:

The width of the rectangle is 20 inches, and the length is 36 inches.

Step-by-step explanation:

2(2x-4) + 2x = 112

4x - 8 + 2x = 112

6x - 8 = 112

6x = 120

x = 20

I hope this helps️️

Answer:

12/2652

Step-by-step explanation:

First, the probability of drawing a king for the first time is 4/52. The chance of drawing another is 3/51. Multiplying, we get the 3rd answer choice, 12/2652

Answer:

d = 4 and a₁ = 12

Step-by-step explanation:

the nth term of an AP is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₆ = 32 and a₁₀ = 48 , then

a₁ + 5d = 32 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 4d = 16

4d = 16 ( divide both sides by 4 )

d = 4

substitute d = 4 into (1) and solve for a₁

a₁ + 5(4) = 32

a₁ + 20 = 32 ( subtract 20 from both sides )

a₁ = 12

Answer:

x = ±2

Step-by-step explanation:

log 7 (x^2 + 11) = log 7 15

We know that log a ( b) = log a(c)   means b =c

x^2 + 11 = 15

Subtract 11 from each side

x^2 = 15-11

x^2 =4

Take the square root of each side

sqrt(x^2) =±sqrt(4)

x = ±2

◈ Area of square room :

\(:\implies\sf\:A_s=(side)^2\)

\(:\implies\sf\:A_s=(12)^2\)

\(:\implies\bf\:A_s=144\:m^2\)

◈ Area of triangular carpet :

\(:\implies\sf\:A_t=\dfrac{1}{2}\times base\times perpendicular\)

\(:\implies\sf\:A_t=\dfrac{1}{2}\times 10\times 8\)

\(\:\implies\sf\:A_t=\dfrac{1}{2}\times 80\)

\(:\implies\bf\:A_t=40\:m^2\)

◈ Uncovered area of room :

\(:\implies\sf\:\Delta A=A_s-A_t\)

\(:\implies\sf\:\Delta A=144-40\)

\(:\implies\:\boxed{\bf{\blue{\Delta A=104\:m^2}}}\)

Answer:

360

Step-by-step explanation:

To solve to volume you need to times the width, length, height. so 3 times 6 is 18 and 18 times 20 is 360.

Answer:

One of these

Step-by-step explanation:

Here we have the following system of equations:

We could solve it by the substitution method.

We're going to solve any of both equations given for a variable. I'll pick the variable "y" and the equation 1.

We're going to replace the previous expression in the equation 2. This is:

As you can see, the system is inconsistent. So it doesn't have a solution.

Answer:

8<n+1/5<98

Step-by-step explanation:

The value of x for the second triangle if it is the reduction of the first drawing is 6.3 feet.

Given two triangles.

Also given that, the scale drawings given are the reduction of the figure.

Most probably, the second triangle must be formed after a reduction with a scale factor of k.

Let k be the required scale factor.

The value of k can be found by taking the ratio of the corresponding sides.

k = 5.2 / 10.4

  = 0.5

So all the corresponding sides will be half of the first triangle.

x = 0.5 × 12.6

  = 6.3 feet

Hence the value of x is 6.3 feet.

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Answer:

It is b and a

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

y>−7/3+2x/3

Answer: b and a is ur answer

Step-by-step explanation:

Answer:

150 kilometres

Step-by-step explanation:

Imagine it as a ratio 6 : 100

If they have given you the first side which is 9 you need to figure out the other side (9 : ?)

To do this you simply need to figure out how you get from 6 to 9 which is times by 1.5

Then to find the other side you do the same as they are proportional to each other

So 100 times by 1.5 which is 150

This gives you the answer that you can travel 150 kilometres with 9 litres of fuel

1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)

2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)

3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)

4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)

5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)

6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)

7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)

8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)

9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)

10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)

11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)

12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)

13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)

14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)

Here are the journal entries for the given transactions:

1. Bricks and timber purchased for construction:

Debit: Bricks (Asset) - Rs 60,000

Debit: Timber (Asset) - Rs 35,000

Credit: Bank (Liability) - Rs 95,000

2. Transfer to fixed deposit account:

Debit: Fixed Deposit (Asset) - Rs 13,000

Credit: Current Account (Asset) - Rs 13,000

3. Appointment of Mr. S.N. Rao as Accountant:

Debit: Salary Expense (Expense) - Rs 300

Debit: Security Deposit (Asset) - Rs 1,000

Credit: Accountant (Liability) - Rs 300

4. Goods sold to Shruti:

Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000

Credit: Sales (Income) - Rs 80,000

5. Goods purchased from Richa:

Debit: Purchases (Expense) - Rs 60,000

Credit: Accounts Payable - Richa (Liability) - Rs 60,000

6. Goods sold to Shilpa:

Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000

Credit: Sales (Income) - Rs 50,000

7. Goods sold to Garima:

Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000

Credit: Sales (Income) - Rs 1,00,000

8.Purchase of land:

Debit: Land (Asset) - Rs 2,00,000

Debit: Brokerage Expense (Expense) - Rs 2,000

Debit: Registration Charges (Expense) - Rs 15,000

Credit: Bank (Liability) - Rs 2,17,000

9. Goods and cash taken away by proprietor:

Debit: Proprietor's Drawings (Equity) - Rs 65,000

Credit: Goods (Asset) - Rs 25,000

Credit: Cash (Asset) - Rs 40,000

10. Goods sold to Charu:

Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000

Credit: Sales (Income) - Rs 1,20,000

Credit: Cost of Goods Sold (Expense) - Rs 80,000

Credit: Profit on Sales (Income) - Rs 40,000

11. Rent paid for the building:

Debit: Rent Expense (Expense) - Rs 60,000

Credit: Bank (Liability) - Rs 60,000

12. Goods sold to Sunil:

Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000

Credit: Sales (Income) - Rs 24,000

Credit: Cost of Goods Sold (Expense) - Rs 20,000

Credit: Profit on Sales (Income) - Rs 4,000

13. Goods purchased from Nanda and supplied to Helen:

Debit: Purchases (Expense) - Rs 1,000

Debit: Accounts Payable - Nanda (Liability) - Rs 1,000

Credit: Accounts Receivable - Helen (Asset) - Rs 1,300

Credit: Sales (Income) - Rs 1,300

14. Goods received from Rohit and Sons and supplied to Madan:

Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)

Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700

Debit: Accounts Receivable - Madan (Asset) - Rs 3,000

Credit: Sales (Income) - Rs 3,000

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Step-by-step explanation:

AC=base(b)=5cm

BC=hypotenuse(h)

For Area of right angle triangle,

we have,

Area(a)=1/2(b×h)

=1/2(5h)

=(5h)/2cm²