How do you write a quadratic function in vertex form from a graph?.

The height of the building is 36 ft.

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, George places a mirror on the ground 45ft from the base of the building. He walks backward until he can see the top of the building in the middle of the mirror. At that point, George’s eyes are 6th above the ground, and he is 7.5ft from the mirror.

As we can see, this arrangement is creating similar triangles,

We know that, similar triangles have corresponding sides in equal ratios,

Therefore,  

x / 45 = 6 / 7.5

x = 6 / 7.5 × 45

x = 36

Hence, the height of the building is 36 ft.

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The equation of line is y = 2x + 8 and the slope of the line is m = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be represented as P ( -2 , 4 )

y = 2x + 7   be equation (1)

On simplifying the equation , we get

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 2

Since , the lines are parallel the slopes of the lines will be equal

So , m = 2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = 2 ( x - ( -2 ) )

On simplifying the equation , we get

y - 4 = 2 ( x + 2 )

y - 4 = 2x + 4

Adding 4 on both sides of the equation , we get

y = 2x + 8

Hence , the equation of line is y = 2x + 8

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A triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex.

There are three angles in a triangle ABC. A triangle is a three-sided polygon and it has three angles. Each angle is formed by the intersection of two sides of the triangle.

In a triangle, the angle between two sides is measured in degrees and these angles are formed by the intersection of the two lines that represent the sides of the triangle. The three angles in a triangle are labeled with the corresponding vertex, for example, angle A, angle B, and angle C.

In a triangle, the sum of the three angles is always 180 degrees. This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

Therefore, In short, a triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex. The sum of the three angles in a triangle is always 180 degrees.

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The height of the triangular prism is 22 meters, having a total surface area of 1192 square meters.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let h represent the height of the triangular prism.

The base are right triangles with side lengths 12 meters, 15 meters, and 19 meters. Hence:

Total surface area = 2 * Area of base + sum of remaining area of surface

Total surface area = 2(1/2 * 15 * 12) + 12*h + 15*h + 19*h

The total surface area of the triangle prism is 1192 square meters. therefore:

1192 = 180 + 46h

46h = 1012

h = 22

The height is 22 meters

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Answer:

1. The discount price of a T-shirt is  $14.40

2. The regular price of a hat is $22.50

3. The discount price is y = x(0.8)

Step-by-step explanation:

1.

20% = 0.2

18 times 0.2 = $3.60

18 - 3.60 = $14.40

So, the discount price of a T-shirt is $14.40

2.

100% - 20% = 80%

18 / 80 = 0.225

0.225 x 100 = $22.50

So, the regular price of a hat is $22.50

3.

Let's y represent the total cost

We have the equation

y = x(0.8)

Answer:

  A. x ≠ -4 or +4

  B. no solution

Step-by-step explanation:

You want the restrictions on x and the solution to the equation ...

  3/(x+4) +2/(x-4) = 16/((x +4)(x -4))

The denominator factors are (x+4) and (x-4). The values of x that make these zero are -4 and +4, respectively.

The variable may not have values -4 or +4.

In order to avoid extraneous solutions, it often works well to rewrite the equation in the form f(x) = 0. We can subtract 16/((x+4)(x-4)) from both sides to make that happen.

  [tex]\dfrac{3}{x+4}+\dfrac{2}{x-4}-\dfrac{16}{(x+4)(x-4)}=0\\\\\\\dfrac{3(x-4)+2(x+4)-16}{(x+4)(x-4)}=0\\\\\\\dfrac{5x-20}{(x+4)(x-4)}=\dfrac{5(x-4)}{(x+4)(x-4)}=\dfrac{5}{x+4}=0[/tex]

There is no value of x that will make this true. The equation has no solution.

The ellipse's equation is [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex] and  [-3, 3] is the ellipse's domain.

The ellipse's equation is (Part A) [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is shown in Part B as [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex]

Part C: [-3, 3] is the ellipse's domain.

The hyperbola's domain lies between [-, -4].

The ellipse and hyperbola's domains do not intersect, hence the system of equations cannot be solved. The origin is the location of the ellipse's centre;8 units make up the vertical main axis. The minor axis equals six units.

Here is a general representation of the ellipse equation:;[tex]$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$[/tex]

a= The semi-major axis, where 8/2 = 4.

The semi-minor axis, b= 6/2 = 3.

Therefore, the ellipse's equation is

[tex]${\frac{-x^2}{3^2}+\frac{y^2}{4^2}=1}$[/tex]

The negative vertex and the domain of the hyperbola are equal.

∴ The hyperbola's domain is [x -4] = [-, -4]

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We can see here that the factor pairs of 16 are:

(1, 16), (2, 8), (4, 4).

The different ways Kevin and his friends could divide into groups are:

(1, 15), (2, 8), (4, 4).

Factors are numbers that can be divided into a larger number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12 because each of these numbers can be divided into 12 with no remainder. Factors are used in mathematics to simplify or evaluate expressions and to find common denominators in fractions.

16 is an odd number of factors because it is a square number.

A square number is a number that can be written as the product of an integer multiplied by itself.

For example, 16 can be written as 4 x 4. Every square number has an odd number of factors because it has one more factor than its square root, which is an integer (e.g 4 in this case). So, 4 x 4 = 16 has 5 factors (1, 4, 2, 8, 16) which is an odd number.

Yes, you can stop checking for factor pairs when you find a pair that repeats. This is because when you find a pair that repeats, you have reached the square root of the number, so you have already found all the factors.

For example, in the case of 16, the square root is 4, so when you find the pair (4, 4), you can stop looking because you have already found all of the factors.

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The provided line's slope and y-intercept are therefore 2, 3. We can use the details provided by the slope-intercept form to graph a linear equation.

For instance, the equation y=2x+3 reveals that the line's slope is 2 and that its y-intercept is located at (0,3).

Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

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Full Question = What is the slope and y-intercept of the line whose equation is y=2x+3?.

A triangle with two equal sides and angles are called isosceles triangle. It can be any measurement for the angles, not necessarily 45, 45 and 90.

An isosceles triangle has two congruent sides. The angles opposite to the congruent sides will also be equal. One angle will no be equal. All the internal angles make a sum of 180. For all these to happen it need not be always 45, 45 and 90. It can be of any combinations with a total sum of 180.

An isosceles triangle could be 40, 40, 100 or 30,30, 120 or 50, 50 , 80. All combinations which have two equal angles and total sum of 180 are possible for an isosceles triangle.

So an isosceles triangle need not be always 45, 45, 90.

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The Z-score of both numbers is equal so both types of grades are better.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

here, z = x - μ / σ

where, μ = mean and σ = standard daviation,

Here,
A. 78 on a test whose mean is 72 and the standard deviation of 6.5,

z = 78 - 72 / 6.5
z = 0.92

B 83 on a test whose mean is 77 and the standard deviation is 8.4

z = 83 - 77 / 8.5
z = 0.92

Thus, the Z score of both numbers is equal so both types of grades are better.

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Answer:

L'ensemble de définition d'une fonction est l'ensemble de tous les éléments d'un ensemble de départ (appelé ensemble de départ ou domaine) pour lesquels la fonction est définie. En d'autres termes, c'est l'ensemble des valeurs qui peuvent être utilisées en tant qu'entrée pour la fonction. Par exemple, si une fonction prend en entrée des nombres réels, l'ensemble de définition serait l'ensemble de tous les nombres réels.

The time that it will take for them to complete the work is given as follows:

2 and 17/20 days.

To obtain the remaining time, we use the together rate, which is the sum of each of the separate rates.

The rates for this problem are given as follows:

Hence the together rate is obtained as follows:

1/x = 1/8 + 1/12

1/x = 5/24

5x = 24

x = 3.8 days.

Ann worked two days, meaning that only 6/8 = 75% of the document has to be completed, hence the time is of:

0.75 x 3.8 = 2.85 days = 2 and 17/20 days.

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The gradient of the line y = x - 10 is 1

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x).

Given the equation of a line is y = x - 10.

The general equation of the line is y = mx + c.

We now get the equation y = x – 10. This will give us the following results when we compare it to the previous line: m = 1 and c = -10.

As a result, the supplied line has a slope of 1.

We must now locate the intercepts. In order to get the y-intercept, let's first enter x = 0 in the equation y = x - 10.

Adding x = 0 to y = x – 10 results in y = – 10.

Therefore, the provided line's y-intercept is equal to -10.

Let's now enter y = 0 to determine the x-intercept in the equation y = x - 10.

By substituting y = 0 for y = x - 10, we obtain x - 10 = 0.

The result of adding 10 from one side to the other is x = 10.

Therefore, the provided line's x-intercept is 10.

∴ m = 1

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No, 6x and 6xy are not like terms; that is, they are two different terms due to different variables.

Like terms can be defined as terms containing the same variable raised to the same power. Only the numerical coefficients differ. We are the only ones who can combine the same terms in expressions. Combining similar terms shortens and simplifies algebraic expressions to make them easier to work with. Consider example 2xy², 12xy², 7xy²and xy²/2, here also all four terms are like terms because xy ² is the common variable. We have, 6xy and 6x terms. First term 6xy, has a varible xy and in second term 6x, only x is a varible i.e., both varibles are different. Therefore, these terms do not have the same set of variables so they are not like terms. Algebraic expressions can be made simpler by combining like words, which makes advantage of some fundamental real number features. The distribution of multiplication over addition is the most frequent use of the distributive property.

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The expression a² - 2ab - 36b², can be factorize as: (a - 6b)^2.

The polynomial expression a² - 2ab - 36b² can be factored as shown below:

This is done by finding two numbers that multiply to -36 and add to -2ab. The numbers are -6b and 6b, and the expression can be written as:

(a - 6b)(a - 6b), which can be simplified to (a - 6b)^2.

Therefore, given the polynomial expression, a² - 2ab - 36b², when factorized, we would get (a - 6b)².

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-4,-3

Step-by-step explanation:

If you reflect over the y axis only the x #

A cow may therefore produce roughly 900 glasses of milk each week, or 3,536 glasses per month.

The unitary technique can be used to solve a problem by first calculating the value of a single unit, then multiplying that value to get the answer. The unitary method is frequently beneficial for multiplication and dividing by fractions because it makes sense immediately and may be executed mentally if the numbers add up. This makes it a helpful strategy to explain or defend the frequently employed textual algorithms for fractions, particularly division by a fraction. The unitary method's formula is to find the value of a single unit and multiply it by the number of units to get the desired value.

given

average cow can produce more than 3,536 glasses of milk in a month

the glasses in each week is as it has 4 weeks :-

3536/4 = 884

A cow may therefore produce roughly 900 glasses of milk each week, or 3,536 glasses per month.

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No, the sides of a triangle cannot have lengths 8, 16, and 18.

What is known as a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

This is because the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides. This is called the triangle inequality theorem.

For a triangle with sides 8, 16, and 18, the side 8 is less than the sum of the other two sides 16+18=34, but greater than the difference of the other two sides 16-18=-2. Therefore, the sides of a triangle cannot have lengths 8, 16, and 18.

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The domain of a logarithm function is the set of all input values (x) for which the logarithm function is defined.

For the natural logarithm function, ln(x), the domain is all positive real numbers, x > 0. This is because the natural logarithm function is defined for input values greater than zero, as the logarithm of any non-positive number is not a real number.

For a logarithm function with a base other than e, such as log_a(x) or logb(x), the domain is also all positive real numbers x > 0. This is because the logarithm function is only defined for input values greater than zero for the same reason as the natural logarithm function.

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Examples of linear equation are x + y = 7, 5x = 3 and nonlinear equations are x^2 - 8x + 3 = 0, x^7 + 5xy - 7 = 0.

The difference between linear and nonlinear equations lie in the degree of polynomial. If the degree of polynomial is 1, it is a linear equation and if the degree of polynomial is 2, it is a non linear equation.  

There can be more than one variable in linear and non-linear equation.

Few examples of linear equations are

3x - 8 = 0

5y - 8x + 2 = 0

Few examples of non-linear equations are

3x² - 8 = 0

5y³ - 8x + 2 = 0

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The 5th equivalent fraction to 1/5 is 5/25.

An equivalent fraction is a fraction that has the same value as another fraction, but a different numerator and denominator. There are an infinite number of equivalent fractions for any given fraction. To find the 5th equivalent fraction to 1/5, you can use the fact that equivalent fractions have a common multiple as a denominator.

The first step is to find a common multiple of the denominators of the fractions you want to compare. In this case, the denominator of the first fraction is 5, and you are looking for the 5th multiple of 5, which is 5*5 = 25.

The next step is to find the numerator that corresponds to the common denominator found in step 1. To do this, you can use the concept of cross-multiplication: the product of the original denominator and the new numerator is equal to the product of the original numerator and the new denominator.

1/5 * 5/5 = 1 * 5/5 * 5 = 5/25

Therefore, the 5th equivalent fraction to 1/5 is 5/25.

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The range of data is calculated by subtracting the lowest value from the highest value.

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Range, which shows statistical dispersion, is the size of the smallest interval in descriptive statistics that encompasses all the data. It is best suited to capturing the dispersion of tiny data sets because it only depends on two observations.

Data is a group of discrete values used to represent information. These discrete values can describe amount, quality, fact, statistics, or other fundamental units of meaning. They can also just be a series of symbols that can be further understood.

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Answer:

BDE

Step-by-step explanation:

congruent triangles have corresponding sides and angles congruent.

from B → A → C along  sides BA → AC →CB

now BD ≅ BA , DE ≅ AC ,  EB ≅ CB , that is

BD → DE → EB

then

BAC ≅ BDE

The parallel sides are 24 units and 25 units, and the distance between them is 10 units (the height of the trapezoid) the area of the shape is 245 square units.

what is trapezoid?

A trapezoid is a geometric shape with four sides, where two of the sides are parallel to each other, but the other two sides are not. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height of the trapezoid is the perpendicular distance between the two bases.

The shape in the image is a trapezoid, which has a formula for its area:

Area = (1/2) x (sum of parallel sides) x (distance between parallel sides)

In this case, the parallel sides are 24 units and 25 units, and the distance between them is 10 units (the height of the trapezoid).

Plugging these values into the formula, we get:

Area = (1/2) x (24 + 25) x 10

Area = (1/2) x 49 x 10

Area = 245 units²

Therefore, the area of the shape is 245 square units.

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Answer:the answer is wrong I did this and i got it wrong

Step-by-step explanation:

The domain is all the values that go into a function i.e., inputs, and the range is all the values that come out, i.e., outputs.

The domain and range are defined as the sets of all x-coordinates and all y-coordinates of ordered pairs. E.g. For considering the below relation set ,

R = {(1, 3), (2, 2), (3, 3), (4, 3)}, then

Domain = set of all x-coordinates

= {1, 2, 3, 4}

Range = set of all coordinates y = {2, 3}

In the case of a function : The domain of a function refers to "all values" that enter the function. The domain of a function is the set of all possible inputs for the function. The range of a function is the set of all its outputs. For example: Consider a function f: A→ B, where f(x) = 5x and each of A and B = {set of natural numbers}. Here we say that A is the domain and B is the co-domain. Then the input values x = {1,2,3,4,...} become the set domain = { natural numbers} and the output of this function is called range of function, Range = {set of natural numbers those multiple of 5}.

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Exponents and logarithms are inverse operations. Or to put it another way, one action undoes another

Logarithmic equation inequality;

Inequalities with a logarithm on one (or both) sides are known as logarithmic inequalities. They are helpful in evaluating situations involving repeated multiplication, such as in the cases of interest and exponential decay, just as exponential inequalities.

Steps to solve logarithmic equation inequality;

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Reason:

1/2 = 4/8

1/4 = 2/8

1/2+1/4+1/8 = 4/8+2/8+1/8 = (4+2+1)/8 = 7/8

The three cats eat a combined 7/8 of a box per day.

Over the course of 7 days, they eat 7*(7/8) = 49/8 = 6.125 boxes of cat food. This value is slightly larger than 6, which means Mr. Dungan did not buy enough cat food. He'll need to buy a 7th box.

Side note: 6.125 = 6 & 1/8 as a mixed number.

a) To find the domain of the equation 3x = 12, we need to solve for x, i.e. x = 4

b) x = 2.83

Divide both sides by 3:

3x/3 = 12/3

x = 4

The domain of this equation will be all real numbers.

b) To find the domain of the equation 1.06x = 3, we need to solve for x.

Divide both sides by 1.06:

x = 3 / 1.06

x = 2.830188679245283

The domain of this equation will be all real numbers.

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