Find the values of a and b. Write your answers in simplest form.

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).

Option 2 is correct. The lines M and N can be said to be parallel. Yes, because angle 1 and angle 2 form a linear pair so (2) 180-129 = 51 and 2 and 7 are alternate interior angles with the same measure.

A linear pair is a pair of adjacent angles formed when two lines intersect. These angles are called a linear pair because they lie on the same line, and their non-common arms are opposite rays, which means they point in opposite directions. Since the sum of the measures of linear pairs is always equal to 180 degrees, these angles are also known as supplementary angles.

To see if the values are parallel we have that

angle 1 and angle 7 when summed have to be equal to 180 degrees

129 + 51 = 180 degrees

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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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The graph of the cubic function y = ∛(x+1) -2 is attached below

A cube root function's graph is a curve that extends to both positive and negative infinity from its origin. An example of a power function is the cube root function, which is described by the equation y = ∛x, where the cube root sign (∛) stands for the inverse of raising a number to the power of three.

The cube root function yields a positive value of y when x is a positive integer. As an illustration, if x = 8, then y = √8 = 2. The cube root function, on the other hand, yields a negative value of y if x is a negative number. As an illustration, if x = -27, y = ∛(-27) = -3

To graph a cube root function, we can create a table of values by choosing several values of x and then calculating the corresponding values of y using the equation y = ∛x. Once we have several points, we can plot them on a coordinate plane and then connect them with a smooth curve to get the graph of the function.

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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:

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:

The inequality shown on the number line is -3<p<2

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality shown on the number line is -3<p<2

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The correct answer is D. They could file for bankruptcy and discharge some of their debt.

What is bankruptcy?

Bankruptcy is a legal process in which a person or business unable to pay outstanding debts to creditors can get a fresh start. It is a form of debt relief in which a debtor is relieved of some or all of their financial obligations and is protected from creditors.

In order to determine this answer, we first need to calculate the couple's monthly income. With an annual income of $86,000, their monthly income would be $7,166.67 ($86,000/12). If one of them loses their job, their monthly income would be reduced by $3,300, leaving them with a monthly income of $3,866.67.

Next, we need to compare this income to the state requirements based on the number of persons in the household. For a four-person household in Virginia, the monthly income requirement is $7,086.25 ($85,939/12). This means the couple's income is below the state requirement and they could file for bankruptcy and discharge some of their debt.

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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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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: 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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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: 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

Answer:

the interest earned will be $106.38.

Answer:

y = 2/3x - 2/3

Step-by-step explanation:

slope m = 2/3, x = 4, y = 2

we have slope-intercept form: y = mx + b

=> 2 = 2/3(4) + b

b = 2 - 8/3 = 6/3 - 8/3 = -2/3

therefore, y = 2/3x - 2/3

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: 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 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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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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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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Answer:

[tex]x \geqslant 2[/tex]

Take 3 from both sides

The following numerals in words are as follows:

3 - three, 4 - four, 5 - five

Numbers are symbols or numbers used to represent numbers.

The most common numerals used in everyday life are the Hindu-Arabic numerals, which include the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

These numbers can be combined to form any number and are used in mathematical operations such as addition, subtraction, multiplication and division.

Roman numerals, which use a combination of letters, are another example of numerals, but they are not as commonly used today as they were in the past.

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Write the following in numerals in words 3/4/5.

Answer:

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

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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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.

Answer:

y=1/x-6

Step-by-step explanation:

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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