How to find the orthocenter of a triangle - example triangle
O Point M is at (1, 3)
O Point R is at (3, 9)
O Point E is at (10, 2)

Answer and Explanation:

Congruent line segments have the same length.

Therefore, to construct a segment congruent to EF that has an endpoint on point G, we simply have to draw a line that is the same length as EF that ends on G.

See the attached image for a sample answer.

The value of f is 0.6.

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the conventional form Ax + By = C. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Given that,

0.25(4f-3) = 0.05(10f - 9)

=> f - 0.75 = 0.5f -0.45

Rearranging the equation and combining like terms we get

f - 0.5f =  -0.45 + 0.75

=> 0.5f = 0.30

=> f = 0.30/0.5

=> f = 3/5

=> f= 0.6

Therefore, the value of f is 0.6.

Correct question: Simplify and solve the following linear equation: 0.25(4f-3) = 0.05(10f - 9)

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Answer:

13

Step-by-step explanation:

If tangent of x degrees equals four-thirds, and measures of triangle is 10. 5 units, and NM measures 2b units then the value of b is equals to seven. So, last option is correct, b = 7 here.

Right angled triangle : A triangle is defined as a regular polygon, with three sides and the sum of any two sides is always greater than the third side. Right angled triangle is one type of triangle. When the angle between a pair of sides is equal to 90 degrees it is called a right-angle triangle. See in above figure ∆LMN is a right angled triangle with m∠LMN = 90° . Also, we have m∠MLN = x° so, m∠LNM = 180° - 90° - x° = 90° - x° ( Since, sum of interior angles of triangle = 180°)

Length of side LM = 10.5

length of side, NM = 2b

tangent of x, tan x = 4/3

We have to determine the value of b. For considering angle x° as centre point then

base of triangle = LM = 10.5

As we know Tangent of any angle is equals to ratio of perpendicular/base.

so, tan x = 4/3 = LM/NM

=> 4/3 = 2b / 10.5

=> 4× 10.5 = 2b × 3

=> b = 42.0/6

=> b = 7

So, the required value is 7.

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yea seven is right. just finished

The graph of an absolue value function is V shaped, symmetric about y-axis or any line parallel to y-axis.

We know that an absolute value of any number describes the distance from zero of that a number is on the number line, without considering its sign (negative / positive number).

Consider an absolute value function f(x)

f(x) = |x|

This means, |x| = x              .......(if x ≥ 0)

            and |x| = -x              .......(if x < 0)

We know that the graph of the absolute value function is V shaped and symmetric about the y -axis or any line parallel to y-axis.

The graph makes a right angle at the origin.

The graph of absolute value consists of two pieces: one with a negative slope and the one with a positive slope.

Also, in the graph of absolute value function a vertex is the point at which the graph of the function changes its direction.

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They are both quadrilaterals and they both have equal and parallel opposite sides.

Rectangles and parallelograms both have four sides, and thus are quadrilaterals.

Quadrilaterals

The definition of a quadrilateral is a 2-D shape with 4 sides and 4 angles. Rectangles and parallelograms both fall under this category. So, they both have all the attributes listed in the definition.

This means 3 shared attributes of rectangles and parallelograms are:

Opposite Sides

Rectangles and parallelograms also have unique relationships between opposite sides. Remember that opposite sides are directly across from each other and not adjacent. In both shapes, opposite sides are parallel. This means that if the sides were to continue forever, they would never intersect. Also, opposite sides are equal. By this, I mean that the lengths of opposite sides are equal. Another way to say this is that opposite sides are congruent.

The ratio of the midpoint of any given line segment is equal to 1 : 1.

As given in the question,

Therefore, the ratio of the midpoint for any given line segment is always equal to 1 : 1.

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The point estimate from a confidence interval can be found by taking the midpoint of the interval.

The formula for the point estimate is (lower bound + upper bound) / 2. For example, the 95% confidence interval for a sample mean of 25 is (23, 27). The point estimate for this sample mean is (23 + 27) / 2 = 25. This point estimate is the best estimate of the true population mean.

In essence, the point estimate is the best guess of the population mean given the data. It is calculated by taking the midpoint of the confidence interval, which is the range of values that is believed to contain the population mean with a certain degree of confidence. The point estimate is usually the most reliable estimate and is used to make decisions in statistical analysis.

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The area of the given triangle is 130.7 cm^2.

What are Triangles?

Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorized into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorized into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now,

Area of a right angle triangle =1/2*base*height

here a=base and let h=height

h^2=b^2-a^2

=23^2-15^2

h^2=304

h=17.43cm

therefore

area=1/2*15*17.43

Area of the triangle=130.7cm^2

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Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

A linear equation in two variables is an equation of the form ax + by = c, where a, b, and c are constants, and x and y are variables. These equations represent a straight line in a two-dimensional coordinate system, and the slope-intercept form of the equation is y = mx + b, where m = -a/b is the slope of the line, and b = -c/b is the y-intercept.

1. (x-1)(y+2)=0: This equation is not a linear equation in two variables as it is a product of two linear equations in one variable, therefore this is not a linear equation in two variables.

2. 2x-3y+7=0: This equation is a linear equation in two variables. The equation is in the form of ax + by + c = 0 where a, b, and c are constants and x and y are variables. This equation is a straight line in a 2D coordinate system and the slope and y-intercept can be calculated using a and b.

7x-3y+2z=0: This equation is not a linear equation in two variables as it has three variables (x, y and z) and it is not possible to graph this equation in a 2D coordinate system as it has three variables.

(y+x)^2-2=0: This equation is not a linear equation in two variables because it is a square of a linear equation. The equation is in the form of (y+x)^2 and we know that any equation in the form of (y+x)^n where n>1 is not a linear equation.

So the correct answer is option 2) 2x-3y+7=0.

Therefore, Of all the given options option 2) 2x-3y+7=0  is a linear equation in two variables.

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Under division, the set of polynomials is not closed. In that, they are closed under addition, subtraction, and multiplication, polynomials constitute a system like the system of integers.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The word polynomial is pronounced as "many terms" since it comes from the Greek words "poly," which means "many," and "nominal," which means "terms." A polynomial is not infinite, although it can have any number of terms.

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Answer:

-49.5

Step-by-step explanation:

3x + 96 = x - 3

2x + 96 = -3 (-x both sides)

2x = -99 (-96 both sides)

x = -49.5 (/2 both sides)

All real numbers except {x = 4} denote the solution set.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = (4⁢x + 8/6⁢x − 24)

The given function is -

y = (4⁢x + 8/6⁢x − 24)

Domain is the set of values for which the given function is defined. The given function is not defined for -

6x - 24 = 0

6x = 24

x = 4

So, all real numbers except {x = 4} denote the solution set.

Therefore, all real numbers except {x = 4} denote the solution set.

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Given condition will be represented by linear equation 5x+10y=90.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Total trail hiked=90miles

mountain trail=5mile

canal-trail=10mile

x represent the number of times Maria hiked the mountain trail, and  y represent the number of times Maria hiked the canal trail

Therefore,

Linear equation will be 5x+10y=90

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Answer:

5/6

Step-by-step explanation:

Alr, so slope of this line is -6/5.

Two lines, which are perpendicular to each other, their slopes' products' is equal to -1.

So, m₁m₂ = -1

or -6/5 m₂ = -1

m₂ = 5/6

Therefore, the slope of that line is 5/6.

Thanks and Cheers!

The quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) is 3x^3 + 6x^2 + 8x + 24.

To find the quotient of (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) we can use polynomial long division method.

First, divide 3x^4 by x and write down the quotient (3x^3)

Now, we multiply (x - 2) by 3x^3 and subtract it from 3x^4 - 4x^2 + 8x - 1

(3x^4 - 4x^2 + 8x - 1) - 3x^3(x - 2)

= 3x^4 - 4x^2 + 8x - 1 - 3x^4 + 6x^3

= 6x^3 - 4x^2 + 8x - 1

Now, we divide 6x^3 by x and write down the quotient (6x^2)

Now, we multiply (x - 2) by 6x^2 and subtract it from 6x^3 - 4x^2 + 8x - 1

(6x^3 - 4x^2 + 8x - 1) - 6x^2(x - 2)

= 6x^3 - 4x^2 + 8x - 1 - 6x^3 + 12x^2

= 8x^2 + 8x - 1

Now, we divide 8x^2 by x and write down the quotient (8x)

Now, we multiply (x - 2) by 8x and subtract it from 8x^2 + 8x - 1

(8x^2 + 8x - 1) - 8x(x - 2)

= 8x^2 + 8x - 1 - 8x^2 + 16x

= 24x - 1

Now, we divide 24x by (x - 2) and write down the quotient (24)

Remainder is

24x - 1 - 24(x - 2) = 47

Finally, we have found that the quotient of the polynomial division is 3x^3 + 6x^2 + 8x + 24 and the remainder is 47. So the final answer is

(3x^4 - 4x^2 + 8x - 1) ÷ (x - 2) = (3x^3 + 6x^2 + 8x + 24)(x - 2) + 47

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Answer: In a parallelogram, opposite angles are congruent, which means they have the same measure. So, if angle g has a measure of (4x - 16)°, then angle h also has a measure of (4x - 16)°. Therefore, the measure of angle h is (4x - 16)°.

So, the answer is 88°.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

6n - n = 5n

13 + 7 = 20

5n = 20

20/5 = 4

n = 4

Answer:

n = 4

Step-by-step explanation:

To solve this, we first have to get the n's on one side:

[tex]6n - 7 = n + 13[/tex]

↓ add 7 to both sides

[tex]6n = n + 20[/tex]

↓ subtract n from both sides

[tex]5n = 20[/tex]

Then, we can divide by 5 on both sides to solve for n.

[tex]n = 4[/tex]

The probability of the spinner is P(not yellow) = 37.5%.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If the spinner is spun once, the probability of not landing on yellow (sections 2 and 3) is equal to the probability of landing on purple (sections 1 and 8), blue (sections 4, 5, and 6), or orange (section 7).

The total probability of these sections is 1- (2/8) = 1-(1/4) = 3/4.

So P(not yellow) = 3/4 = 37.5%.

Hence, the probability of the spinner is P(not yellow) = 37.5%.

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The graph for the given piecewise function is as provided in image.

What is piecewise function?

A piecewise function is a function f(x) which has different definitions in different intervals of x. The graph of a piecewise function has different pieces corresponding to each of its definitions. The absolute value function is a very good example of a piecewise function. Let us see why is it called so. We know that an absolute value function is f(x) = |x| and it is defined as:

f(x)=(x if x≥0 ,

     -x  if x><0)

We should read this piecewise function as

f(x) is equal to x when x is greater than or equal to 0 and

f(x) is equal to -x when x is lesser than 0.

Given piecewise function

f(x)=(3x-5  if x<=-1

       -2x+3 if -1<x<4

        2      if x>=4)

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The study of statistics rests on two major​ concepts probability which  is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions

Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.

Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.

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Answer: the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2) is y = (1/2)x + 5.

Step-by-step explanation:

The slope of the line that is perpendicular to y = -2x + 5 is the negative reciprocal of the slope of y = -2x + 5, which is -2. The negative reciprocal of -2 is 1/2.

To find the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2), we can use the Point-Slope Form: y - y₁ = m(x - X1)

y - 2 = (1/2)(x + 4)

Simplifying, we get:

y = (1/2)x + 5

So the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-4, 2) is y = (1/2)x + 5.

The price per pound that was paid for the apples is $0.85 per pound

An equation shows the relationship between numbers and variables in an expression.

Unit rate is the ratio of two quantities. The denominator of a unit rate is always equal to one.

The apples are 3.4 lbs and their total price is $2.89. hence:

The price per pound is gotten by dividing the total price of apples by the weight of the apple

Price per pound = $2.89 / 3.4 lbs = $0.85 per pound

The price per pound is $0.85 per pound

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The plant is 17/4 inches above the ground

Pam plants the seed 5 1/2 inches below the ground

After a period of one month, the tomato plant has increased to 9 3/4 inches

Therefore the height of the tomato plant above the ground can be calculated by subtracting the height of the seed below the ground from the height of the plant after one month.

9 3/4 - 5 1/2

39/4 - 11/2

= 17/4

Hence the plant is 17/4 inches above the ground

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Answer:

no solution

Step-by-step explanation:

Since you are using substitution, you will plug in one of the variables using one of the equations.

y=x+4

x-y=8

put the y from above into the y below

x-(x+4)=8

Now, solve the equation

x-x-4=8

Put x's together

-4=8

-4 does not equal 8, so this system of equations has no solution

The quotient is 2x^2 + 4x + 5.

The given polynomial is 2x^3 - 3x -10.

As we can see that the given polynomial is a three-degree polynomial but the second degree term is missing, so we can write the polynomial as 2x^3 + 0x^2 - 3x -10.

The divisor is (x-2).

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x) (2x^2) = 2x^3

Thus, we multiply the divisor (x-2) by 2x^2 which gives 2x^3 - 4x^2

Now we subtract this from the polynomial which gives 4x^2 -3x -10.

Repeating the same we multiply the divisor by 4x which gives 4x^2 - 8x. Subtracting the same from 4x^2 -3x -10, we get 5x - 10.

Now we multiply the divisor with 5 to get 5x - 10. Subtracting it from the remaining polynomial 5x -10 leaves the remainder 0.

Thus, we get the quotient as  2x^2 + 4x +5.

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A 95% confidence interval for the mean is (3193, 2607).

Confidence interval in simple words is the range of values that the specific parameter lies within.

Confidence interval for mean is found by the formula,

CI = Х ± t [tex]\frac{s}{\sqrt{n} }[/tex]

where X is sample mean, s is the standard deviation and n is the sample size.

Sample mean = 2900

s = 1300

n = 55

Degree of freedom = n - 1 = 54

t value of degree of freedom 54 with the probability of exceeding the critical value as 1 - 95% = 5% = 0.05 is 1.674.

CI = 2900 ± (1.674)[tex]\frac{1300}{\sqrt{55} }[/tex]

   = 2900 ± 293.44

   = (3193.44, 2606.56)

   = (3193, 2607)

Hence the confidence interval is (3193, 2607).

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The replacement approach refers to determining any variable's value from one equation in terms of another variable. Considering that, the point where the function crosses = (0, 7). The correct answer is c. (3,3).

Considering that the function's intersection point is now = (0, 7) As a result, the point must fulfil the function. We have to check whether these pairs satisfy equation 2x + y = 7 or not.. So, we will put these pairs one by one.

A) (0,7) x=0 & y=7

Than

2×0+7=7

7=7 so, it satisfies.

B) (1,5) x=1 & y=5

Than

2×1+5=7

2+5=7

7=7 so, it satisfies

C) (3,3) x=3 & y= 3

Than

2x3+3= 7

6+3 = 7

9= 7 so, it does not satisfies.

D) (2,3) x=2 & y= 3

Than

2x2+3 = 7

4+3= 7

7=7 so, it satisfies.

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the girl will be scoring a total of 30 goals.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Given, the goal scored

3 times 2

4 times 1

and 5 times 4.

So the total goal scored will be 3*2=6

4*1=4

and 5*4=20

Score = 6+4+20=30

Hence the girl will be scoring a total of 30 goals.

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