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Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.

The value of sin M is [tex]\frac{15}{17}[/tex], tan M is [tex]\frac{15}{8}[/tex] and cos M is [tex]\frac{8}{17}[/tex]. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is a discipline of mathematics that deals with the study of right-angle triangle's and their sides, angles, and connections.

We are given perpendicular as 15, base as 8 and hypotenuse as 17.

We know that sin θ is ratio of perpendicular to hypotenuse.

So,

⇒ Sin M = [tex]\frac{15}{17}[/tex]

Similarly, cos θ is ratio of base to hypotenuse.

So,

⇒ Cos M = [tex]\frac{8}{17}[/tex]

Similarly, tan θ is ratio of perpendicular to base.

So,

⇒ Tan M = [tex]\frac{15}{8}[/tex]

Hence, the value of sin M is [tex]\frac{15}{17}[/tex], tan M is [tex]\frac{15}{8}[/tex] and cos M is [tex]\frac{8}{17}[/tex].

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The tensions in the string are approximately 37.5 lb and 57.39 lb for T1 and T2, respectively.

Tension is the force that is transmitted through a string, rope, cable, or any other object that is pulled taut by a force. It is a pulling force that is exerted on an object by the string or cable that is attached to it. Tension is a scalar quantity, meaning that it has a magnitude but no direction.

The tension in a string or cable depends on several factors, including the strength and stiffness of the material, the angle at which the string is attached to the object, and the amount of force applied to the string. In general, the tension in a string is equal to the force applied to the string, divided by the cross-sectional area of the string.

To find the tensions T1 and T2 in the string, we can use trigonometry and the fact that the weight is in equilibrium (i.e., not moving).

First, we can use the fact that the weight is in the middle of the string to split the weight into two equal components, one pulling on each end of the string.

The weight component pulling on T1 can be found by multiplying the weight by the sine of the angle between T1 and the horizontal:

W1 = (75 lb) * sin(50°)

W1 ≈ 57.39 lb

Similarly, the weight component pulling on T2 can be found by multiplying the weight by the sine of the angle between T2 and the horizontal:

W2 = (75 lb) * sin(30°)

W2 ≈ 37.5 lb

Since the weight is in equilibrium, the tensions in the string must be equal and opposite to these weight components:

T1 = W2 ≈ 37.5 lb

T2 = W1 ≈ 57.39 lb

Therefore, the tensions in the string are approximately 37.5 lb and 57.39 lb for T1 and T2, respectively.

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For the given triangles,  EF/EI=DF/HI and also ED/EH=DF/HI.

What is a triangle's definition?

A triangle is a closed two-dimensional shape with three straight sides, three angles, and three vertices (or corners). It is formed by connecting three non-collinear points in a plane with straight lines. The sum of the interior angles of a triangle is always 180 degrees, and each exterior angle is equal to the sum of its two adjacent interior angles. Triangles can be classified based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

Now,

As given triangle are similar by SSS.

that means ratio of respective sides will be equal.

Then,  ED/EH=EF/EI=DF/HI

Hence,

            we can see that EF/EI=DF/HI and also ED/EH=DF/HI.

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The equation of an exponential function given the points on the curve is  y= 35

A mathematical functiοn called an expοnential functiοn is emplοyed frequently in everyday life. It is mοstly used tο cοmpute investments, mοdel pοpulatiοns, determine expοnential decline οr expοnential grοwth, and sο fοrth.

Here An exponential function is in the general form is

=> y = [tex]a(b)^x[/tex]

We know the points are  ( 3 , 71.88 ) and ( 10 , 1.79 ) , so the followings are true,

=> 71.88 = [tex]a(b)^3[/tex] and 1.79 = [tex]a(b)^{10}[/tex]

Now divide second equation by first equation then,

=> [tex]\frac{a(b)^{10}}{a(b)^3}=\frac{1.79}{71.88}[/tex]

=> [tex]b^7[/tex] = 0.0249

=> b = 0.59

Now put b=0.59 int0 1.79 = [tex]a(b)^{10}[/tex] then,

=> 1.79 = a[tex](0.59)^{10}[/tex]

=> a = [tex]\frac{1.79}{0.59^{10}}[/tex] = 350.2

Now the exponential function is y= 350.2[tex](0.59)^x[/tex].

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Answer:

David has 25 percent of green pencils and 75percent of purple ones

Answer: The surface area of the rectangular prism is 1356 square meters.

Step-by-step explanation:

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Substituting the given values, we get:

SA = 2(16m)(19m) + 2(16m)(2m) + 2(19m)(2m)

SA = 1216m^2 + 64m^2 + 76m^2

SA = 1356m^2

Therefore, the surface area of the rectangular prism is 1356 square meters.

By using the problem page method, we can determine that there are six possible outcomes: AB, AC, AD, BC, BD, and CD. This is because each letter can only be chosen once, so the total number of possible outcomes is the number of combinations of two letters out of four.

The Problem Page Method is a method used to help students explore and reflect on their problems. It is used as a tool to guide students in understanding the issues that they are facing and to help them come up with solutions. It is based on the idea that it is important for students to be able to identify their problems and to reflect on them in order to come up with solutions that are meaningful and effective.

The problem page method can be used to answer this question. This method consists of drawing a grid and listing all the possible outcomes in the grid. The grid has four columns, with each column representing a letter. The first row of the grid is used to list the letters, while the remaining rows are used to list the possible combinations of two letters.

The problem page method is a useful tool for solving problems that involve choosing items from a set without replacement. It allows us to quickly and easily calculate the number of possible outcomes and list all the possible combinations. This method can also be used to solve more complex problems, such as choosing three or more items from a set.

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On solving the question we have that As a result, the total amount paid equation by the lease's end is $63,475.

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

To compute the total cash paid at the end of the lease, we must take into account all of the lease's charges. Here's how it works:

$3,900 as a down payment

Monthly payments: $775 divided by 24 months equals $18,600.

The security deposit is $975.

The acquisition charge is $500.

After-lease automobile purchase price: $39,500

To compute the total amount paid, add all of these costs together:

$3,900 + $18,600 + $975 + $500 + $39,500 = $63,475

As a result, the total amount paid by the lease's end is $63,475.

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According to the figure having m parallel to n and p parallel to q the value of z and x is

The value of z is solved using the concept of supplementary angles since and z and angle 65 degrees are supplementary angles hence we have that

z + 65 = 180

z = 180 - 65

z = 115 degrees

Also angle 6x - 23 degrees and angle z are equal according to the alternate internal angle theorem

hence we have that

6x - 23 = 115

solving for x

6x = 115 + 23

6x = 133

x = 23 degrees

hence angles z and x are solved to be 115 degrees and 23 degrees respectively

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Answer:

22.5 Divided by 5 equals 4.5

Step-by-step explanation:

There is the answer

The solution of given system of equations is (1/5, 6).

What is system of equation?

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one with two equations and two variables. Linear equations are simpler than non-linear equations because they graph as straight lines.

Given equations : 5x+y=7

                             20x+2=y

We can solve it by using substitution method:

Now, we have 5x+y=7

it can be written as,

         y = 7 - 5x .... equation 1

Similarly, we have 20x+2=y

can be written as,

           y = 20x+2 ..... equation 2

Subtracting equation 1 from equation 2

we get,  20x+2 - ( 7 - 5x ) = 0

             20x + 5x + 2 - 7 = 0

             25x = 5

               x = 1/5

Putting x=1/5 in equation 1,

we get, y = 20 × 1/5 + 2

               = 4 +2

               = 6

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Answer: x = 2

Step-by-step explanation:

x + (x + 1) + (x + 2) = 9

3x + 3 = 9

3x +(3 - 3) = (9 - 3)

3x = 6

x = 2.

Hope this helps

The point (0, -5) lies on the graph of the quadratic equation y = x² - 5. The shape of the graph is a parabola.

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The equation y = x² - 5 represents a quadratic equation. A quadratic equation have the shape of a parabola.

When x = 0;

y = 0² - 5

y = -5

The point (0, -5) lies on the graph of y = x² - 5

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Answer:

The orthocenter of triangle XYZ is (-6,4).

Step-by-step explanation:

To find the orthocenter of triangle XYZ, we need to first find the altitudes of the triangle.

The altitude of a triangle is a line that passes through a vertex of the triangle and is perpendicular to the opposite side.

Let's find the equation of the line passing through X(-9,5) and perpendicular to YZ. The slope of YZ is (8-3)/(-6+6) = 5/0, which is undefined. Therefore, YZ is a vertical line passing through the point (-6,3). The equation of this line is x=-6.

The line passing through X(-9,5) and perpendicular to YZ must be a horizontal line passing through X. Therefore, the equation of this line is y=5.

Similarly, the equation of the line passing through Y(-6,8) and perpendicular to XZ is x=-6.

The equation of the line passing through Z(-6,3) and perpendicular to XY is y=3.

Now, we need to find the intersection of these lines to find the vertices of the triangle's altitude.

The altitude from X passes through the point X(-9,5) and is perpendicular to the line YZ with equation x=-6. Therefore, the intersection of the altitude from X and YZ must have x-coordinate -6. Since the equation of the altitude from X is y=5, we get the point of intersection as (-6,5).

Similarly, the altitude from Y passes through the point Y(-6,8) and is perpendicular to the line XZ with equation x=-6. Therefore, the intersection of the altitude from Y and XZ must have x-coordinate -6. Since the equation of the altitude from Y is y=8, we get the point of intersection as (-6,8).

The altitude from Z passes through the point Z(-6,3) and is perpendicular to the line XY with equation y=3. Therefore, the intersection of the altitude from Z and XY must have y-coordinate 3. Since the equation of the altitude from Z is x=-6, we get the point of intersection as (-6,3).

Now that we have the vertices of the altitudes, we can find the equation of the lines passing through them.

The line passing through (-6,5) and (-6,8) is the line x=-6.

The line passing through (-6,5) and (-6,3) is the line y=4.

The line passing through (-6,8) and (-6,3) is the line x=-6.

Now, we find the intersection of the lines x=-6 and y=4. The intersection point is (-6,4).

Therefore, the orthocenter of triangle XYZ is (-6,4).

Answer:

the interest earned will be $106.38.

Answer:

To convert pounds to rands, you need to know the current exchange rate between the two currencies. Once you have the exchange rate, you can multiply the number of pounds by the exchange rate to get the equivalent amount in rands.

For example, if the exchange rate is 1 GBP = 20 ZAR and you want to convert 100 pounds to rands, you would multiply 100 by 20, which equals 2000 rands.

Step-by-step explanation:

Answer: Let's break down the total cost of dinner into three components: the cost of the meal itself (M), the sales tax (T), and the tip (P).

We know that the sales tax is 8% of the meal cost, so we can write:

T = 0.08M

We also know that the tip is 20% of the total cost, which is the sum of the meal cost and the sales tax, so we can write:

P = 0.20(M + T) = 0.20(M + 0.08M) = 0.20(1.08M) = 0.216M

Finally, we know that the total cost of dinner must be no more than $30, so we can write:

M + T + P ≤ 30

Substituting the expressions for T and P that we derived earlier, we get:

M + 0.08M + 0.216M ≤ 30

Simplifying and solving for M, we get:

1.296M ≤ 30

M ≤ 23.15

Therefore, the most expensive item you can order is $23.15 or less (before tax and tip) to stay within your budget of $30.

Step-by-step explanation:

Answer:

[tex]x \geqslant 2[/tex]

Take 3 from both sides

One true statement about the equation is that if Albert continues to follow his diet and exercise plan, his weight will decrease by 5 pounds per week. Another true statement is that if x is zero, which represents the start of his diet and exercise plan, his weight will be 250 pounds.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides, a left-hand side and a right-hand side, connected by an equal sign "=". The expressions on either side of the equal sign can be numbers, variables, or combinations of both.

Here,

The equation y = 250 - 5x represents a linear model that describes the relationship between Albert's weight (y) and the number of weeks he has been dieting and exercising (x).

The coefficient of x in the equation is -5, which indicates that Albert is losing weight at a rate of 5 pounds per week. The y-intercept of the equation is 250, which represents Albert's initial weight before he started dieting and exercising.

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Complete question:

Albert is trying to lose weight. He has made a linear model to help him keep track of his weight, y, after x weeks of diet and exercise:

y = 250 - 5x

Which statement is TRUE about the equation?

The equation y = 250 - 5x represents a linear model that describes the relationship between Albert's weight (y) and the number of weeks he has been dieting and exercising (x).

The coefficient of x in the equation is -5, which indicates that Albert is losing weight at a rate of 5 pounds per week.

The y-intercept of the equation is 250, which represents Albert's initial weight before he started dieting and exercising.

According to the question the prediction of the prize money distribution is correct.

Prediction is the act of making an educated guess about the future. It is a forecast of what may happen based on current knowledge, trends, and data. Predictions are made in many fields, from weather forecasting to business forecasting. Making predictions is an important part of decision making and planning, as it allows us to anticipate and plan for the future.

First Winner:
The ratio provided states that the first winner will receive 4 parts out of the total of 7 parts.
Therefore, 4/7 of the prize money (R 4 000) will be allocated to the first winner:
(4/7) x R 4 000 = R 2 857.14
Second Winner:
The ratio provided states that the second winner will receive 3 parts out of the total of 7 parts.
Therefore, 3/7 of the prize money (R 4 000) will be allocated to the second winner:
(3/7) x R 4 000 = R 1 142.86
Total:
The total prize money awarded is R 2 857.14 + R 1 142.86 = R 4 000.
Therefore, the prediction of the prize money distribution is correct.

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Answer: v=[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]


I am very sorry if I am wrong but I hope this helps you my friend, Best of luck <3

The probability that Nora will pick a yellow quartz piece on the next selection is 1/9.

To calculate the probability of picking a yellow quartz piece on the next selection, we need to analyze the frequency of yellow quartz pieces relative to the total number of recorded quartz pieces.

Out of the 18 quartz pieces Nora picked, only 2 were yellow.

To find the probability, we divide the number of yellow quartz pieces by the total number of pieces recorded:

Probability = Number of yellow quartz pieces / Total number of recorded pieces

The number of yellow quartz pieces is 2, and the total number of recorded pieces is 18.

So the probability can be calculated as:

Probability = 2 / 18

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2 in this case:

Probability = 1 / 9

It's important to note that this probability assumes the picking process is random and that the distribution of colors in the giant box of quartz pieces remains constant over time.

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Perimeter of the drawing is 22 inches, Perimeter of the garden is 770 inches and the Perimeter of Garden becomes 35 times the Perimeter of drawing when drawing length and breadth is multiply by 35.

A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Perimeter of Rectangle = 2 ( Length + Breadth)

(a) Here Length of Drawing is 7 inches and Breadth of Drawing is 4 inches.

So, Perimeter of the drawing = 2( 7 + 4 )

= 2 * 11

= 22 inches.

(b) According to question , Length and Breadth of actual garden is 35 times of the length and breadth of drawing.

Therefore, Length of Actual garden = 35 * 7 = 245 inches

and, Breadth of Actual garden = 35 * 5 = 140 inches.

So, Perimeter of the garden = 2( 245 + 140 )

= 2 * 385

= 770 inches.

(c) The perimeter of Garden becomes 35 times the perimeter of drawing when drawing length and breadth is multiply by 35.

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The tin's actual diameter is 250 mm.

What do you mean by diameter?

A circular object, like a circle or sphere, has a diameter, which is the length of a straight line that runs through its centre. It is the separation between two locations on an object's edge that are the furthest apart and traverse the object's centre.

Here, if the tin's diameter in the illustration is 10 cm, the actual tin's diameter can be determined as follows:

Real Diameter is 2.5 times the image diameter.

2.5 x 10 cm is the actual diameter.

Real diameter is 25 cm.

To translate the actual dimension to millimetres (mm), we can multiply by 10:

Actual Diameter multiplied by 10 to convert to mm

Real Diameter = 25 cm x 10 in mm.

Actual Diameter is 250 millimetres.

As a result, the tin's actual diameter is 250 mm.

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Answer:

y=1/x-6

Step-by-step explanation:

The answer is 12x³ - 14x² + 18x + 14.

What is the distributive property of multiplication?

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

To multiply (4x + 2)(3x² - 5x + 7), we can use the distributive property of multiplication:

(4x + 2)(3x² - 5x + 7) = 4x(3x² - 5x + 7) + 2(3x² - 5x + 7)

Now we can simplify each term:

4x(3x² - 5x + 7) = 12x³ - 20x² + 28x

2(3x² - 5x + 7) = 6x² - 10x + 14

Putting the terms together, we get:

(4x + 2)(3x² - 5x + 7) = 12x³ - 20x² + 28x + 6x² - 10x + 14

Simplifying further:

(4x + 2)(3x² - 5x + 7) = 12x³ - 14x² + 18x + 14

Therefore, the answer is 12x³ - 14x² + 18x + 14.

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Answer: We know that the function f(x) is an exponential function. An exponential function can be written in the form:

f(x) = a * b^x

where:

a = the initial value (when x = 0)

b = the base of the exponential function

x = the independent variable

To find the values of a and b, we can use the given information:

f(1) = 8, so:

8 = a * b^1

8 = a * b

f(10.5) = 72, so:

72 = a * b^10.5

We can now use the first equation to solve for a:

a = 8/b

Substituting this value into the second equation, we get:

72 = (8/b) * b^10.5

Simplifying:

72 = 8 * b^9.5

9 = b^9.5

b = 9^(1/9.5)

b = 1.4608 (approx.)

Substituting the values of a and b into the exponential function, we get:

f(x) = 8 * 1.4608^x

Now we can find f(3.5):

f(3.5) = 8 * 1.4608^3.5

f(3.5) = 8 * 6.2797

f(3.5) = 50.2376 (approx.)

Therefore, f(3.5) is approximately equal to 50.24.

Step-by-step explanation: