A shoes delear net birr 8000 worth of shoes from a shoe company.Then,find the amount it is to pay including VAT

Answers

Answer 1

The total amount to pay would be 8800 Ethiopian Birr.

To find the amount to pay including VAT, we need to know the applicable VAT rate. VAT, or Value Added Tax, is a consumption tax added to the value of goods and services. The VAT rate can vary from country to country or even within different regions.

Assuming a VAT rate of 10%, we can calculate the VAT amount by multiplying the net value of the shoes by the VAT rate. In this case, the net value of the shoes is 8000 Ethiopian Birr. Therefore, the VAT amount would be 8000 * 0.10 = 800 Ethiopian Birr.

To find the total amount to pay including VAT, we add the VAT amount to the net value of the shoes. Thus, the total amount to pay would be 8000 + 800 = 8800 Ethiopian Birr.

It's important to note that the VAT rate and regulations can vary, so it's always advisable to check the specific VAT rate applicable in a given country or region. Additionally, different goods and services may have different VAT rates or exemptions, so it's crucial to consider the specific rules governing the shoe industry in the relevant jurisdiction.

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Related Questions

Write an inequality and solve.

Negative one hundred eighty three is at least nine more than 24 times a number.

Answers

Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x

15. A landscaper uses a wheelbarrow to move soil to a certain region of the garden. A
wheelbarrow can hold approximately 6 cubic feet of soil. The soil is damped out into a pile
that makes the shape of a cone. The landscaper calculates that once the pille has a diameter
of 13 foet and a height of 3 feet, there will be sufficient soil for the project How maty
wheelbarrow loads of soil are needed for this project?

Answers

The number of wheelbarrow loads of soil required for this project is 71.

The landscaper uses a wheelbarrow to transport soil to a particular region of the garden. A wheelbarrow can accommodate roughly 6 cubic feet of soil. Once the pile has a diameter of 13 feet and a height of 3 feet, the landscaper determines that there will be enough soil for the project.

Area of a cone =1/3πr²hwhere r = 13/2 feet and h = 3 feet.

Substituting the given values to find the area of the cone.1/3 x 3.14 x (6.5)² x 3 = 422.55 cubic feet.Then, divide the total amount of soil required by the volume of soil that a wheelbarrow can hold to determine the number of wheelbarrow loads required.

Number of wheelbarrow loads = (Volume of soil needed) / (Volume of one wheelbarrow)Volume of one wheelbarrow = 6 cubic feet.The total volume of soil required is 422.55 cubic feet.

Therefore, the number of wheelbarrow loads required is:Number of wheelbarrow loads = (422.55) / (6) = 70.42 ≈ 71 wheelbarrow loads, which is the final answer.

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Please i give 25 points

Answers

1. A and C
2. B and E
3. D and F

5. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30°. Another person at point B, notes that the angle of elevation to the top of the
cliff is 45°. If the height of the cliff is 80.0 m, find the distance between A and B. Show the steps of your solution.

Answers

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.

In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.

AB = AC - BC = (80√3 - 80) meters

= 80(√3 - 1) meters

= about 58.56 meters

The distance between points A and B is approximately 138.6 meters.

To find the distance between points A and B, we can use the concept of trigonometry and the given information.

Let's denote the distance between points A and B as x.

From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:

tan(30°) = opposite/adjacent

tan(30°) = 80.0/x

Simplifying the equation, we have:

x = 80.0 / tan(30°)

Using a calculator, we can find the value of tan(30°) ≈ 0.5774.

Substituting the value, we get:

x = 80.0 / 0.5774

Calculating the value, we find:

x ≈ 138.6 meters

In light of this, the separation between positions A and B is roughly 138.6 metres.

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A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

Answers

Answer:

2 Litres

Step-by-step explanation:

A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

find Volume ( Volume = L x W x h)

20 * 10 * 10 = 2000cm^3

Convert cubic centimeters to litres

1000 cm^3 = 1 Litres

​2000 cm^3 = 2 Litres

Find the midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b).

(0, h/2)
(h/2, b/2)
(0, b/2)
(h/2, 0)

Answers

Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

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pls helpppppppppppppppppp

Answers

Answer:

Step-by-step explanation:

Bisector means breaking the segment in half.

answer is A. to have a length exactly half the segment

What is the prime factorization of 625?

Answers

Answer:

5⁴

Step-by-step explanation:

625= 5×5×5×5

Jana entered the following group of values into the TVM Solver of her
graphing calculator. N=48; 1% = 0.6; PV = ; PMT=-290; FV = 0; P/Y = 12; C/Y
= 12; PMT:END. Which of these problems could she be trying to solve?
OA. A person can afford a $290-per-month loan payment. If he is being
offered a 48-year loan with an APR of 7.2%, compounded monthly,
what is the mosioney that he can borrow?
B. A person can afford a $290-per-month loan payment. If he is being
offered a 4-year loan with an APR of 0.6%, compounded monthly,
what is the most money that he can borrow?
C. A person can afford a $290-per-month loan payment. If he is being
offered a 48-year loan with an APR of 0.6%, compounded monthly,
what is the most money that he can borrow?
D. A person can afford a $290-per-month loan payment. If he is being
offered a 4-year loan with an APR of 7.2%, compounded monthly,
what is the most money that he can borrow?

Answers

Answer:

Jana is likely trying to solve option B:

"A person can afford a $290-per-month loan payment. If he is being offered a 4-year loan with an APR of 0.6%, compounded monthly, what is the most money that he can borrow?"

Step-by-step explanation:

Option B is the correct choice because it aligns with the values entered by Jana into the TVM Solver. Jana set the loan term (N) to 48, which represents 48 months (4 years). The APR value of 0.6% also matches what Jana inputted.

By selecting option B, Jana is attempting to find out the maximum amount of money she can borrow given that she can afford a $290-per-month loan payment and is offered a 4-year loan with an APR of 0.6%, compounded monthly.

This calculation will help Jana determine the loan amount that corresponds to her desired monthly payment and the given loan terms.

125
(a) What is the measure of ange L?
(b) What is x?
(22-10)
I
(c) What is the measure of angle M?
65 N

Answers

The values of L and M in the triangle displayed are 55 and 60 respectively.

The value of angle L can be obtained thus :

125 + L = 180 (sum of angles in a triangle)

L = 180 - 125 = 55°

B.

The value of L can be calculated thus:

55 + (2x - 10) + 65 = 180 (sum of internal angles of a triangle)

120 + 2x - 10 = 180

110+2x = 180

2x = 180-110

x = 35

M = 2(35) -10 = 60°

Therefore, L = 55 and M = 60.

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Use the LinReg(ax+b) function in the calculator to determine the regression line for the following data:
X 14.56 13.58 12.69 14.87 15.68 14.28
Y 0.25 0.84 0.71 0.65 0.35 0.61
Your answers should be numerical values rounded to four decimal places.
The regression line is y =
Check
x+

Answers

The regression line is y = -0.1471x + 2.2386.

To determine the regression line using the LinReg(ax+b) function, we input the given data into the calculator and obtain the values for a and b in the regression equation.

Using the LinReg(ax+b) function with the given data, we have:

X: {14.56, 13.58, 12.69, 14.87, 15.68, 14.28}

Y: {0.25, 0.84, 0.71, 0.65, 0.35, 0.61}

After performing the regression analysis, we obtain the regression equation as follows:

y = -0.2012x + 3.4986

Therefore, the regression line is y = -0.2012x + 3.4986.

Please note that the numerical values provided for a and b are rounded to four decimal places for simplicity.

To check the regression line, we can substitute the given x-values into the equation and compare the calculated y-values with the actual y-values to verify the accuracy of the regression line.

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Which of these situations can be represented by the opposite of −​5? Use pencil and paper. Describe two more situations that can be represented by the opposite of −5.

Answers

The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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WHOEVER CAN ANSWER 50 POINTS IF U CAN SOLVE IT PLEASE IM DESPERATE

Answers

Answer:

First, the graph is overall decreasing with two local maximums and two local minimums.

Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.

Considering the above observations we can state that:

The degree of f(x) is odd;The leading coefficient is negative;There are 5 distinct zeros;There are 2 relative maximum values.

Find the tangent line and the normal line to the curve at the given point.

Answers

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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How much is 700000 in Penny’s

Answers

Answer:

$7000

Step-by-step explanation:

700,000 dollars is equal to 70,000,000 pennies.

To convert 700,000 to pennies.

We need to multiply the number by 100, since there are 100 pennies in a dollar.

1 dollar = 100 pennies.

So,  700,000 × 100

= 70,000,000

Therefore, 700,000 is equal to 70,000,000 pennies.

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Chad created a table that shows the ratio of his sports game cards.Next, Chad created the graph below showing possible ratios for Pitchers cards to Infield cards in his deck. Which of the following statements are true?

Answers

Answer:

The 3rd answer is correct.

Step-by-step explanation:

Final answer:

The question involves a mathematical understanding of graphs and data interpretation, specifically ratios. To answer a question like this, typically, you would need to analyze both the graph and table for consistent ratio values. Though the question specifics are unclear, the broader concept involves understanding how ratios can be graphically represented.

Explanation:

Given that the question involves ratios and cards, it appears to fall under a mathematical scope, specifically the interpretation of graphs and data. However, the information provided doesn't give specific details about Chad's data, the ratios of his sports game cards, or the graph he created that shows the possible ratios for Pitchers cards to Infield cards.

Typically, to validate any findings, you would need to look at the graph and the table. Comparing the values of the ratios in the table to the characteristics of the graph would help substantiate any claims. For instance, if Chad's graph shows that there's a 1:2 ratio of pitcher cards to Infield cards, this should be reflected in the table of his sports game cards.

Despite the ambiguous details in the question, you can still grasp the concept of ratios and how they can be represented graphically. For example, if you have a 3:5 ratio of oranges to apples, this can be depicted on a graph where one unit on the Y-axis represents 3 oranges and the corresponding unit on the X-axis signifies 5 apples.

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Given that g(x)=2x^2 - 2x + 9 , find each of the following.

a) g(0)
b) g(- 1)
c) g(2)
d) g( - x)
e) g(1 - t)

Answers

Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

Write the inequality and solve.

Negative nine times one more than a number is not as much as twelve times that number plus nine.

Answers

Answer:

-9(x+1) < 12x+9

if you need me to solve it here it is:

-9x - 9 < 12x + 9

     + 9           +9

-9x      < 12x + 18

-12x       -12x

-18x     <          18

(divide by -18 on both sides)

x < - 1

Therefore, any number is that is greater than -1 will work for this inequality.

Hope this helps!

find the value of x. 142 3x+22

Answers

Answer:

x = 40

you can guess and check.

it’s 40 i did it last night on the test

The conditional statement below is true. If possible, write the biconditional statement.

If 2x = 18, then x = 9.

Answers

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.

Answers

From the Table display of scores and students on a recent exam, The mean of the scores to the nearest 10th is  83.7.

To find the mean of the scores, we need to calculate the sum of the products of each score and its corresponding number of students, and then divide it by the total number of students.

Here's the calculation:

(70 * 6) + (75 * 3) + (80 * 9) + (85 * 5) + (90 * 7) + (95 * 8) = 420 + 225 + 720 + 425 + 630 + 760 = 3180

Total number of students = 6 + 3 + 9 + 5 + 7 + 8 = 38

Mean = Sum of products / Total number of students = 3180 / 38 ≈ 83.7 (rounded to the nearest tenth)

Therefore, the mean of the scores is approximately 83.7.

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Two sets that contain exactly the same elements are called ___ sets.

Answers

Two sets that contain exactly the same elements are called "equal sets" or "identical sets."

In set theory, the concept of equality between sets is defined by the axiom of extensionality, which states that two sets are equal if and only if they have the same elements.

To illustrate this concept, let's consider two sets: Set A and Set B. If every element of Set A is also an element of Set B, and vice versa, then we say that Set A and Set B are equal sets. In other words, the sets have the exact same elements, regardless of their order or repetition.

For example, if Set A = {1, 2, 3} and Set B = {3, 2, 1}, we can observe that both sets contain the same elements, even though the order of the elements is different. Therefore, Set A is equal to Set B.

In summary, equal sets refer to two sets that possess exactly the same elements, without considering the order or repetition of the elements. The concept of equality is fundamental in set theory and forms the basis for various operations and theorems in mathematics.

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A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this
equation?
-5
1
6
Save and Exit

Answers

The discriminant value associated with this equation include the following: A. -5.

What is a quadratic equation?

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

In this scenario, we would determine the number of zeros by using the discriminant formula as follows;

Discriminant, D = b² - 4ac

This ultimately implies that, the discriminant value must be a negative numerical value and two complex roots such as -5;

-5 = b² - 4ac

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Complete Question:

A quadratic equation has zero real number solutions. which could be the discriminant value associated with this equation?

a. –5 b. 0 c. 1 d. 6

the sum of five consecutive even numbers is 220. find the smallest of these numbers.​

Answers

Let's denote the smallest even number as "x". The next four consecutive even numbers would be "x + 2", "x + 4", "x + 6", and "x + 8".

According to the given information, the sum of these five consecutive even numbers is 220:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 220

Now, let's solve this equation:

5x + 20 = 220
5x = 220 - 20
5x = 200
x = 200 / 5
x = 40

Therefore, the smallest even number among these five consecutive even numbers is 40.

Answer:

The smallest number is 40.

Step-by-step explanation:

Let the number be x. Then the next 4 number will be x+2, x+4, x+6, x+8

.°. x+x+2+x+4+x+6+x+8 = 220

5x + 20 = 220

5x = 200

x = 40

Therefore the smallest of the five consecutive numbers is 40

Mark me as brainliest if you find my answer''Mark-worthy'' :)

If sin 0=8/17, and tan0<0, what is cos(0)
Use exact values. No decimals.
(0 means theta)

Answers

Answer:

Given that sin(θ) = 8/17 and tan(θ) < 0, we can use the trigonometric identity to find cos(θ).

Since sin(θ) = opposite/hypotenuse, we can assign a value of 8 to the opposite side and a value of 17 to the hypotenuse.

Let's assume that θ is an angle in the second quadrant, where sin(θ) is positive and tan(θ) is negative.

In the second quadrant, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is positive.

Using the Pythagorean theorem, we can find the length of the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2

adjacent^2 = 17^2 - 8^2

adjacent^2 = 289 - 64

adjacent^2 = 225

adjacent = √225

adjacent = 15

Therefore, the length of the adjacent side is 15.

Now we can calculate cos(θ) using the ratio of adjacent/hypotenuse:

cos(θ) = adjacent/hypotenuse

cos(θ) = 15/17

So, cos(θ) = 15/17.

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

B. Lenghts of the diagonals

Step-by-step explanation:

Please help me with this question

Answers

Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

A gravel company charges a fee for a load of gravel Plus a charge for each mile from
the gravel pit to the final destination of the load. Let x represent the number of
miles to the destination and y
represent the total cost of the load. The charge to deliver a load 40 miles is $280
and the charge to deliver a load 56 miles is $292.
Find the slope.
1) 16
2) 7
3) 0.75
4) 21.3
5) 5.21

Answers

The slope of 0.75 corresponds to option 3. So, the correct answer is 3) 0.75.

To find the slope, we can use the formula for the slope of a line:

slope (m) = (change in y) / (change in x)

In this case, x represents the number of miles to the destination and y represents the total cost of the load.

Given that the charge to deliver a load 40 miles is $280 and the charge to deliver a load 56 miles is $292, we can set up two points on the line: (40, 280) and (56, 292).

Now let's calculate the change in y and change in x:

Change in y = 292 - 280 = 12

Change in x = 56 - 40 = 16

Plugging these values into the slope formula:

slope (m) = (change in y) / (change in x) = 12 / 16 = 0.75

Therefore, the slope of the line representing the relationship between the number of miles (x) and the total cost of the load (y) is 0.75.

Option 3 is correct.

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Pregunta 1
Resuelve el siguiente problema aplicando las estrategias de solución de problemas.
• El área de un triángulo es de 30 pies cuadrados y la base mide 5 pies. ¿Cuál es la
altura del triángulo en pulgadas?

Answers

Answer:

I can't understand the language but try people who can

Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4

Answers

Answer:

[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

[tex]\cos(105\°)[/tex]

Using the angle sum identity for cosine.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]

Now applying the identity.

[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]

Now utilizing the unit circle.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]

[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]

Now simplifying...

[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]

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