Juan is hiking a trail that is 2 miles long. He hikes 14 miles before resting.
How much farther does he have to hike?

Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:

Coefficient matrix:

[1  4]

[2 -3]

Augmented matrix:

[1  4 | 9]

[2 -3 | 7]

To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.

Performing row operations:

Multiply the first row by 2 and subtract the result from the second row:

[1  4 | 9]

[0 -11| -11]

Divide the second row by -11:

[1  4 | 9]

[0  1 | 1]

Subtract 4 times the second row from the first row:

[1  0 | 5]

[0  1 | 1]

The row echelon form of the augmented matrix is:

[1  0 | 5]

[0  1 | 1]

Therefore, the solution is x = 5 and y = 1.

So the solution of the system of equations is x = 5 and y = 1.

Step-by-step explanation:

Answer:1,200,000

Step-by-step explanation:

The length οf side x can be any value, as lοng as it is nοt 0.

We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.

In a 30°-60°-90° triangle, the sides are in the ratiο:

1 : √3 : 2

In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.

Sο we can set up the fοllοwing equatiοn:

x√3 = 2x sin 60°

Simplifying the right side:

sin 60° = √3/2

2x sin 60° = 2x(√3/2) = x√3

Substituting back intο the equatiοn:

x√3 = x√3

This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.

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On solving the provided question we cans ay that As a result, x + 4 function denotes the number of years the principal is older than the instructor, where x is the student's age in years.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

Let's start by writing down the phrases from the problem:

• The teacher's age is six years older than the student's age: T = 2x + 6, where T is the age of the instructor.

• The principal's age is ten years older than the student's age: P = 3x + 10, where P is the age of the principal.

To determine how many years the principal is older than the instructor, subtract the teacher's age from the principal's age:

P - T = (3x + 10) - (2x + 6)

When we simplify the equation, we get:

P - T = x + 4

As a result, x + 4 denotes the number of years the principal is older than the instructor, where x is the student's age in years.

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The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically

Given the following expression

23 - √81

The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.

We know that the square root of 81 is 9, so we can simplify the expression to:

23 - √81 = 23 - 9

Evaluate the difference

23 - √81 = 14

Therefore, the value of the expression is 14.

In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.

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[tex]f(-11) = 3(-11)^{2} - 5 = 3(11)^{2} - 5 = 3(121) - 5 = 363-5= \bf 358[/tex]

Answer:D

Step-by-step explanation:

if x==-11

then,

f(-11) means you should write -11 in every x you see.

[tex]f(-11)=3*(-11)^{2} -5=3*121-5=363-5=358[/tex]

Net accounts receivable is calculated by subtracting allowance for uncollectible from gross accounts receivable.

1- The journal entries are used to record the business transactions.

2- Ledger accounts are used to summarize thee recorded transactions.

3- Net accounts receivable (2024) = 8,640

Net accounts receivable (2025) = 4,280

1. The Turner Corporation's transactions are recorded as follows:

Date Account Title Debit Credit Journal Entries

Accounts Receivable $35,000 on June 12, 2024

$35,000 in revenue from services

Cash $20,000, September 17, 2024

$20,000 in accounts receivable

Bad Debt Cost $5,760 as of December 31, 2024

Uncollectible Allowance: $5,760

Accounts Receivable $46,400 on March 4, 2025

$46,400 in revenue from services

Cash $10,000, May 20, 2025

$10,000 in Accounts Receivable

Allowance for Uncollectible $4,400 on July 2, 2025

$4,400 in Accounts Receivable

On October 19, 2025, the cash value is $40,000.

$40,000 in accounts receivable

Bad Debts Cost $2,400 on December 31, 2025

Uncollectible Allowance: $2,400

2. The following is the procedure for posting transactions to the chosen accounts:

Account Titles Debit Credit Cash Account Date Account Titles Debit Credit

Accounts Receivable $17,000 on September 17, 2024

Accounts Receivable $10,000 on May 20, 2025

The date is October 19, 2025 $37,000 in accounts receivable

Date Account Titles Debit Credit Accounts Receivable

Service Revenue of $31,400 on June 12, 2024

17th of September, 2024, $17,000 cash

$46,400 in service revenue on March 4, 2025

$10,000 cash, May 20, 2025

Allowance for Uncollectible Accounts $4,400 on July 2, 2025

On October 19, 2025, a cash payment of $37,000 is made.

Balance $9,400 on December 31, 202 $77,800

Provision for Uncollectible Accounts

Debit Credit Date Account Titles

Bad debt expense of $5,760 as of December 31, 2024

Accounts Receivable $4,400 on July 2, 2025

Bad Debts Cost $2,400 as of December 31, 2025

Balance of $3,760 at the end of December 2025

3. The balance sheet net accounts receivable at the end of 2024 and 2025 include:

Net accounts receivable = $8,640 in 2024

Net accounts receivable = $5,640 in 2025.

Transaction Analysis: Accounts Receivable $31,400 on June 12, 2024 $31,400 in service revenue September 17, 2024, $17,000 Cash Accounts Receivable $17,000

Bad Debt Cost $5,760 as of December 31, 2024 Provision for Uncollectible Accounts $5,760 ($31,400 minus $17,000 multiplied by 40%)

Accounts Receivable $50,000 on March 4, 2025 $50,000 in service revenue

May 20, 2025, $10,000 Cash Accounts $10,000 is available for receipt.

Allowance for Uncollectible Accounts $4,400 Accounts Receivable $4,400 July 2, 2025

The date is October 19, 2025. $37,000 in cash and accounts Receivable: $37,000

Bad Debts Cost $2,400 on December 31, 2025 Uncollectible Accounts Allowance $2,400

Net Accounts Receivable: $8,640 in 2024 ($14,400 - $5,760)

2025: $5,640 ($9,400 - $3,760).

Answer:

see the attachment

Step-by-step explanation:

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the shipment does not meet requirements.

The measure of angle ZUB is 32.8°.

A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.

Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighborhood, b is the triangle's base, and h is the triangle's height.

Since the angles given are 90 degrees and 57.2 yοu can add thοse tοgether then subtract them  frοm 180 tο find the answer.

180 - 90 + 57.2 = 32.8

Thus,

32.8° is the answer.

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Complete question:

Point Z is the circumcenter of ΔTUV.

Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. Angle Z T B is 32.8 degrees and angle B Z U is 57.2 degrees.

What is m Angle ZUB?

23.7°

32.8°

33.5°

57.2°

Answer:

a) p(-6) = 30

b) c = -2 ,1

Step-by-step explanation:

[tex]p(c)=c^2+c[/tex]

a) Evaluate p(-6)

This mean input -6 into the equation to solve for p(-6) =

[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]

(b) Solve for p(c) = 2.

[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]

After answering the presented question, we can conclude that triangle Therefore, the answer is A. 29 inches, since it falls within this range.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.  

So, for triangle ABC with sides AB, BC, and AC, we have:

[tex]AB + BC > AC\\16 + 25 > AC\\41 > AC\\BC + AC > AB\\25 + AC > 16\\AC > -9 \\AB + AC > BC\\16 + AC > 25\\AC > 9\\[/tex]

So, the possible lengths of side AC are between 9 and 41 inches.

Therefore, the answer is A. 29 inches, since it falls within this range.

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Step-by-step explanation:

3x squared -9 = 12

3x squared = 12 + 9

3x squared = 21

am i doing the wrong maths?

is it find what 3x squared is or....

After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.

We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.

In the prior auction, the following amount of muffins were sold in total:

25 + 12 + 3 + 10 = 50

The percentage of muffins that were wheat muffins is as follows:

25/50 = 0.5

This indicates that wheat muffins accounted for 50% of all sales.

This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:

0.5 x 16 = 8

Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

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Answer:

Step-by-step explanation:

Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.

Mathematically, we can express this as:

Exterior angle = Sum of remote interior angles

Or, in symbols:

∠ABC = ∠A + ∠C

where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.

Here are two more examples that illustrate the Exterior Angle Theorem:

Example 1:

Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.

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Copy code

      C

     / \

    /   \

   /     \

  /       \

 /         \

/______\

A             B

      D

According to the Exterior Angle Theorem, we have:

∠DCE = ∠B + ∠A

Answer:

80

Step-by-step explanation:

The inequality to replace the symbol is > and the expression is -4/9 > -5/9​.

We can utilize the following parameters in our calculation based on the question:

-4/9* -5/9​

Represent the symbol * as a blank

This gives

-4/9 [  ] -5/9​

Evaluate the quotients

-0.44444444444 [  ] -0.55555555555

By comparison, 0.44444444444 is greater than -0.55555555555

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

-0.44444444444 [ > ] -0.55555555555

So, we have

-4/9 > -5/9​

Hence, the inequality is >

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Step-by-step explanation:

The Victoria (Old Traffic) Bridge in Saskatoon, Canada, has a length of approximately 230 meters (755 feet). To estimate the length of the bridge in both SI and imperial units, you can use the following referents:

SI Units:

To estimate the length of the bridge in SI units, you can use meters as the referent. The length of the Victoria Bridge can be measured using a distance measuring device such as a surveyor's wheel, a laser distance meter, or a tape measure. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in meters.

Imperial Units:

To estimate the length of the bridge in imperial units, you can use feet as the referent. You can use a tape measure or a distance measuring wheel that measures in feet. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in feet.

To convert the length from meters to feet or vice versa, you can use the following conversion factors:

1 meter = 3.28 feet

1 foot = 0.3048 meters

Therefore, to convert the length of the Victoria Bridge from meters to feet, you can multiply the length in meters by 3.28. For example, 230 meters x 3.28 = 754.4 feet (rounded to the nearest tenth).

To convert the length of the Victoria Bridge from feet to meters, you can multiply the length in feet by 0.3048. For example, 755 feet x 0.3048 = 230.1 meters (rounded to the nearest tenth).

The value of x, considering the similar triangles, is given as follows:

B) 6.

Similar triangles are triangles that share these two features listed as follows:

Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:

9/3 = 12/4 = x/2.

Since the constant is of 3, the value of x is obtained with cross multiplication as follows:

x/2 = 3

x = 6.

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Answer:

x < -3

Step-by-step explanation:

x + 5 < 2

x < -3

So, the answer is x < -3

Answer:

1000-39=961

so 961 apples are left.

Step-by-step explanation:

The height of the cable above the bridge is given by the function:

h(x) = 0.25x^2 - 0.8x + 30

To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.

The x-coordinate of the vertex is given by:

x = -b / 2a

where a = 0.25 and b = -0.8. Substituting these values, we get:

x = -(-0.8) / 2(0.25) = 1.6

So the vertex is at x = 1.6.

To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):

h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48

Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).

Answer:

Step-by-step explanation:

C.

Answer:

Step-by-step explanation:

We can use the identity for the cosine of the sum of two angles:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

In this case, we can write:

cos(60°) = cos(55° + 5°) = cos(55°)cos(5°) - sin(55°)sin(5°)

We know that cos(60°) = 1/2, and we also know that cos(55°) = p. We can solve for cos(5°):

1/2 = p cos(5°) - sin(55°)sin(5°)

sin(55°)sin(5°) = p cos(5°) - 1/2

We also know that sin²(55°) + cos²(55°) = 1, so:

sin²(55°) = 1 - cos²(55°) = 1 - p²

Substituting this into the previous equation:

(1 - p²)sin(5°)² = p cos(5°) - 1/2

Rearranging and factoring:

p cos(5°) = 1/2 - (1 - p²)sin(5°)²

Using the fact that sin²(5°) + cos²(5°) = 1, we can substitute cos²(5°) = 1 - sin²(5°):

p cos(5°) = 1/2 - (1 - p²)(1 - cos²(5°))

Simplifying:

p cos(5°) = 1/2 - (1 - p²) + (1 - p²)cos²(5°)

p cos(5°) = 1 - 2p² + (2p² - 1)cos²(5°)

Solving for cos²(5°):

cos²(5°) = (1 - p cos(5°) + 2p²) / (2p² - 1)

Substituting the value we found for p, cos²(55°) = p²:

cos²(5°) = (1 - p cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)

Finally, substituting p = cos(55°):

cos²(5°) = (1 - cos²(55°) cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)

cos²(5°) = (2cos²(55°) - cos²(55°) cos(5°) + 1) / (2cos²(55°) - 1)

cos²(5°) = (cos²(55°) + 1) / (2cos²(55°) - 1)

Therefore, the value of cos 5° in terms of p = cos 55° is:

cos 5° = ±sqrt[(cos²(55°) + 1) / (2cos²(55°) - 1)]

Note that the sign of the square root is determined by the quadrant in which 5° lies. Since 5° is in the first quadrant, cos 5° is positive.

A loan for $3,400 at 16% should be paid first as it has the highest interest rate.

A loan is a financial agreement in which one party (the lender) agrees to give money, property, or other assets to another party (the borrower) in exchange for the promise of repayment with interest or other charges. Loans are typically used by individuals, businesses, or governments to finance specific projects, make purchases, or cover expenses.

Assuming that all other factors such as minimum payments and penalties are the same, the loan that you should try to pay off first is the one with the highest interest rate, as it will be accruing interest at a faster rate than the others.

Based on this reasoning, the loan that you should try to pay off first is option A, which has a higher interest rate of 16%.

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To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:

5 + 3 + 4 = 12

Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:

240g ÷ 12 = 20g

So, one part of the ratio is equal to 20g.

To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:

5 parts x 20g = 100g (for the first part)

3 parts x 20g = 60g (for the second part)

4 parts x 20g = 80g (for the third part)

Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.

Answer:

5) A = 70°

6) X = 55°

7) Y = 8°

8) A = 51°

Step-by-step explanation:

There really no way to explain. All you ahve to do is inverse function to solve for the angle. Use a calculator.

5) sin(A) = 0.9397

[tex]A=sin^-1(0.9397)\\\\A=69.701...\\\\A = 70\\[/tex]

6) cos(X) = 0.5763

[tex]X=cos^-1(0.5763)\\\\X=54.998...\\\\X=55\\[/tex]

7) tan(Y) = 0.1405

[tex]Y=tan^-1(0.1405)\\\\Y=7.997...\\\\Y = 8\\[/tex]

8) sin(A) = 0.7771

[tex]A=sin^-1(0.7771)\\\\A=50.995...\\\\A = 51\\[/tex]