Solve the system of inequalities by graphing.
y < 6
y > x + 3

1. The loan term of the truck is 5 years.

2. The contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. In in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

1. The loan term of the truck in years is calculated as follows:

Number of years = Loan term in months / 12

Number of years = 60 months / 12

Number of years = 5 years

Therefore, the loan term of the truck is 5 years.

2. Monthly repayments = Monthly instalment of the truck + Insurance premium

Monthly repayments = R22,301.67 + R8,500

Monthly repayments = R30,801.67

Therefore, the contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. Number of instalments paid = Loan term in months / 2

Number of instalments paid = 60 months / 2

Number of instalments paid = 30 months

The total amount of money owed to the financer excluding the insurance in June 2022 would be:

Total amount owed = Remaining instalments x Monthly instalment of the truck

Total amount owed = (Loan term in months - Number of instalments paid) x Monthly instalment of the truck

Total amount owed = (60 months - 30 months) x R22,301.67

Total amount owed = 30 months x R22,301.67

Total amount owed = R669,050.10

Therefore, in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

The significance of including an insurance cover when a contractor purchases a water tanker is to protect the asset from unforeseen circumstances such as accidents, theft, or damage. If the contractor did not have insurance, they would have to pay for any repairs or replacements out of pocket, which could be expensive and financially devastating. Insurance also provides peace of mind and allows the contractor to focus on their business operations without worrying about potential risks to their asset.

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Answer:

The limit of f(x) as x approaches -6 from the positive side is 6.

When x gets closer to 2 on the positive side, we can see that the function seems to be heading towards a value of -8. As a result, f(x) has a limit of -8 as x approaches 2 from the positive side.

The function seems to be heading towards a value of 6 when x approaches 2 from the negative side. Hence, when x gets closer to 2 from the negative side, the limit of f(x) is 6.

The function seems to be getting closer to a value of 6 when x approaches -6 from the positive side. Hence, as x gets closer to -6 on the positive side, the limit of f(x) is equal to 6.

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The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.

Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.

To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.

Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.

Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The vector V in linear form will be v = –11i + 6j i.e. A.

In mathematics, a vector is a mathematical object that has both magnitude and direction. It is typically represented as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Now,

Vector RS can be represented as the difference between the coordinates of R and S:

RS = S - R

RS = (-36, 11) - (-25, 5)

RS = (-36 + 25, 11 - 5)

RS = (-11, 6)

To represent RS in linear form, we can use the components of the vector as coefficients of the basis vectors i and j:

RS = -11i + 6j

Therefore,

               the correct option is v = -11i + 6j.

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Answer:

A is right

Step-by-step explanation:

The value of x in the diagram is 12.5

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

The ratio of the corresponding sides of similar shapes are equal.

Therefore;

3x/60 = 5x/8x

3x/60 = 5/8

300 = 24x

divide both sides by 24

x = 300/24

x = 12.5

therefore the value of x is 12.5

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Answer:

The mathematical symbols used to indicate that the endpoints of an interval are not included in the graph of an inequality are "<" and ">" signs with a small circle or parenthesis next to them.

The symbol "<" with a circle or parenthesis on the right side indicates that the endpoint is not included, while the symbol ">" with a circle or parenthesis on the left side indicates that the endpoint is not included.

For example, the inequality x > 3 indicates that the variable x is greater than 3, but does not include 3 in its solution set. Similarly, the inequality y < -2 with a circle or parenthesis on the left side indicates that the variable y is less than -2, but does not include -2 in its solution set.

Step-by-step explanation:

The oven will heat up by 18 degrees in 1 minute at this rate.

What is the rate of change?

The term "rate of change" refers to how fast a quantity is changing with respect to time, or some other independent variable.

If the oven's temperature rose 3 degrees in 1/6 of a minute, we can find the rate of temperature increase by multiplying both sides by 6 to get:

3 degrees / (1/6 minute) = 18 degrees/minute

Hence, the oven will heat up by 18 degrees in 1 minute at this rate.

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The equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is option (B) [tex]6x^3z[/tex] . The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2.

What is square root ?

Square root is a mathematical operation that, when applied to a non-negative number, returns another non-negative number that, when multiplied by itself, gives the original number as a result.

The expression [tex]\sqrt{36x^6z^2[/tex]  represents the square root of the product of 36, x raised to the power of 6, and z raised to the power of 2. To simplify this expression, we can use the following rules of exponents and radicals:

[tex]\sqrt{(a * b)} = \sqrt{a} *\sqrt{b[/tex]

[tex]\sqrt{(a^2)} = a[/tex]  for all non-negative values of a

Using these rules, we can write:

[tex]\sqrt{36x^6z^2 }= \sqrt{(36 * x^6 * z^2)[/tex]

[tex]= \sqrt{(6^2 * (x^3)^2 * z^2)[/tex] (grouping factors with perfect square roots)

[tex]= 6 * x^3 * z[/tex]  (simplifying the square root of the perfect square 6^2)

Therefore, the equivalent expression of [tex]\sqrt{36x^6z^2[/tex] is [tex]6x^3z[/tex]. This means that the square root of [tex]36x^6z^2[/tex] is equal to 6 times the product of x raised to the power of 3 and z.

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Answer:

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

In this case, we have two similar regular hexagons. Let x be the side length of the smaller hexagon, and y be the side length of the larger hexagon. Then, we have:

Area of smaller hexagon / Area of larger hexagon = (x^2 * 6 * sqrt(3)) / (y^2 * 6 * sqrt(3)) = x^2 / y^2

We are given the areas of the two hexagons:

x^2 * 6 * sqrt(3) = 16 * sqrt(3)

y^2 * 6 * sqrt(3) = 25 * sqrt(3)

Dividing the second equation by the first equation, we get:

(y^2 * 6 * sqrt(3)) / (x^2 * 6 * sqrt(3)) = 25 * sqrt(3) / (16 * sqrt(3))

Simplifying this expression gives:

y^2 / x^2 = 25 / 16

Taking the square root of both sides, we get:

y / x = 5 / 4

Therefore, the scale factor from the smaller hexagon to the larger hexagon is 5/4.

Answer: Three equivalent ratios of 8 : 5 are 16 : 10, 24 : 15 and 32 : 20.

Step-by-step explanation:

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.

The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.

In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.

Here we have

Problem 1:

10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.  

The down payment was 10% of the purchase price of the home

=> Down payment = 10% of $110,000

= [10/100] × $110,000 = $11,000

∴ You will be paid $11,000 as your down payment.

Amount borrowed = the purchase price of the home - Down payment

=> Amount borrowed = $110,000 - $11,000 = $99,000

∴ Your mortgage (loan) was for $99,000.    

To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:

P = (A / D) x (r / 12)

Where:

A = amount borrowed

D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)  

r = monthly interest rate,      

n = total number of payments,  

=> P = ($99,000 /124.4) x 0.0075 = $471.15  

∴ The current monthly payment is $471.15.  

The formula for total interest = (P x n) - A  

=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00              

∴ You will pay a total of $169,334.00 in interest over the life of the loan.    

Therefore,

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.      

Problem 2

This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.

i. Amount paid off = Original loan amount - Current loan balance

Original loan amount = $99,000

Current loan balance = $88,536

Amount paid off = $99,000 - $88,536

Amount paid off = $10,464

∴ you have paid off $10,464 of the loan.

ii. Total paid = Monthly payment x Number of payments

P = ($99,000 / 207.483) x 0.0075

P ≈ $471.15

The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.

Total paid = $471.15 x 120

Total paid = $56,538

∴ you have paid $56,538 to the loan company so far.

iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:

Interest paid = Total paid - Amount paid off

Interest paid = $56,538 - $10,464

Interest paid = $46,074

∴ you have paid $46,074 in interest so far.

iv. Equity = Current value of the home - Current loan balance

Equity = $150,000 - $88,536

Equity = $61,464

∴ you have $61,464 of equity in your home.

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Answer:

When a marble is taken out from the bag and replaced, the probability of getting a red or blue marble on the first draw remains the same for the second draw. Therefore, we can use the multiplication rule of probability to calculate the probability of getting two marbles of the same color.

Let's denote the event of getting a red marble as R and the event of getting a blue marble as B. Then, the probability of getting two marbles of the same color can be calculated as follows:

Probability of getting two red marbles: P(R and R) = P(R) * P(R) = (3/7) * (3/7) = 9/49

Probability of getting two blue marbles: P(B and B) = P(B) * P(B) = (4/7) * (4/7) = 16/49

Therefore, the probability of getting two marbles of the same color is the sum of the probabilities of getting two red marbles and two blue marbles, which is:

P(same color) = P(R and R) + P(B and B) = 9/49 + 16/49 = 25/49

So the probability of getting two marbles of the same color is 25/49.

Step-by-step explanation:

It satisfies the vertical line test and represents a function.

What is function ?

Function can be defined in which it relates an input to output.

Based on the image you provided, it seems to represent a function since each input value (x-value) corresponds to a unique output value (y-value) and there is only one output value for each input value.

To verify if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. However, in this graph, for any vertical line drawn, it only intersects the graph at one point.

Hence, it satisfies the vertical line test and represents a function.

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Answer:

c

Step-by-step explanation:

60>30 since pi is 180 ........

Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

The expression that represents the area of the given door is (3w+8)w.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

So, we know that:
width = w

And we also know that:

length = 3w + 8

Now, the area formula is:
l*w

Insert values as follows:

l*w

(3w + 8)w

Therefore, the expression that represents the area of the given door is (3w+8)w.

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Answer:

See below

Step-by-step explanation:

[tex]7(6+ x)[/tex] = [tex](7)(6) + (7)(x)[/tex]
            = [tex]42 + 6x[/tex]

The triangles include:

4) To determine if a triangle is right, obtuse, or acute, we need to use the Pythagorean Theorem to determine if the square of the longest side equals the sum of the squares of the other two sides.

Here, the longest side is 9, and the other two sides are 6 and 7.

9² = 6² + 7²

81 = 36 + 49

81 = 85

Since 81 is not equal to 85, the triangle is not a right triangle. To determine if it's obtuse or acute, we need to check the cosine of the largest angle using the Law of Cosines.

cos A = (b² + c² - a²) / 2bc

Let's choose 9 as side a, since it's the largest side:

cos A = (6² + 7² - 9²) / (84)

cos A = 0.048

Since cos A is positive, angle A is acute. Therefore, the triangle is acute.

5) Using the same process as above:

16² = 10² + 12²

256 = 100 + 144

256 = 244 + 12

Since 256 is greater than 244, the triangle is obtuse.

6) Again, using the same process as above:

(8√6)² = 8² + 16²

192 = 64 + 256

192 = 320

Since 192 is less than 320, the triangle is obtuse.

7) 29² = 20² + 21²

841 = 400 + 441

841 = 841

Since 841 is equal to 841, the triangle is a right triangle.

8) √73 is greater than 8 and 3, so it must be the largest side.

(√73)² = 8² + 3²

73 = 64 + 9

73 = 73

Since 73 is equal to 73, the triangle is a right triangle.

9) 12² = 8² + 10²

144 = 64 + 100

144 = 164 - 20

Since 144 is less than 164, the triangle is obtuse.

10) 15² = 9² + (3√34)²

225 = 81 + 306

225 = 387 - 162

Since 225 is less than 387, the triangle is obtuse.

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Answer:

Step-by-step explanation:

To relate the angular motion of the hour hand (h) and the angular motion of the second hand (s), we can use the following formula:

h = (s/360) * 30

The second hand makes a full rotation of 360 degrees in one minute, so in 60 minutes (or one hour), it rotates 21,600 degrees. We know that during this time, the hour hand moves 30 degrees.

Therefore, the equation relating h and s is h = (s/360) * 30.

9% percent of Team B’s mean absolute deviation is the difference in the mean of the individual times of members.

The result of dividing the sum of a set of values by the total number of values in the set is mean.

The average distance between each observation and the mean is shown via a measure of variability known as the mean absolute deviation (MAD).

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

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Answer:

Step-by-step explanation 0.4 0.8 5 7 10, 10

The man's daily wage is given as follows:

$42.

The man's daily wage is obtained applying the proportions in the context of the problem.

The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:

24/8 = $3 per hour.

Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:

7/5 x 3 = 21/5 = $4.2 per hour.

The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:

10 x 4.2 = $42.

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The man's daily wage is $42.

We know that the woman works 8 hours per day and gets $24 per day, then her hourly pay is the quotient between these two values.

$24/8 = $3 per hour.

And we also know that their wages per hour are in the ratio 7: 5.

Then the man's hourly pay 7/5 times the hourly pay of the woman, then we just need to solve the product below:

(7/5)*$3 = x

(7/5)*$3 = $4.2

And the man works for 10 hours, then the daily wage is 10*$4.2 = $42.

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Answer:

"B"

Add all the sides together
Step-by-step explanation:

48

The line of best fit has the following equation

y = 3.2x + 25

Since the x-values are 20 and 35, we must enter these values into the equation and subtract them to determine the difference in the y-values:

y(20) - y(35) = (3.220 + 25) - (3.235 + 25)

y(20) - y(35) = (64 + 25) - (112 + 25)

y(20) - y(35) = 89 - 137

y(20) - y(35) = -48

For x-values of 20 and 35, 48 is the most logical prediction for the difference in y-values.

Thus, Option (A) 48 is the correct answer.

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