The vertices of DEF are D(-2, 5), E(5, 1), F(-4, -5). Find the coordinates of the orthocenter of DEF

Answer:

Part A: Two types of transformations: translation and reflection.

Part B: g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

Part C: For horizontal translation, g(x)=f(x+2)

In case of vertical translation, g(x)=f(x)+10

Therefore, the equation of transformation can be written as g(x)=f(x+2)+10.

Step-by-step explanation:

I thought. :') Ever since yesterday, and today. Hope this helps!

The value of r is 105 in this equation.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

In the quadratic formula, √r =[tex]\sqrt{b^{2}-4ac }[/tex]

Where a = 1, b = -9, and c = -6.

So √r = √(-9)² - 4(1)(-6)

√r = √81 -4(-6)

√r = √81 + 24

√r = √105

Hence, the value of r is 105 in this equation.

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This formula describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved.

Step 1: Start with the formula

N(t) = 15 * (1/2)^(t/22).

Step 2: Substitute the value for N(t). For example, if you want to find the amount of Francium-223 after 44 minutes,

N(44) = 15 * (1/2)^(44/22).

Step 3: Calculate the fraction (1/2)^(44/22). This is equal to (1/2)^2, or 1/4.

Step 4: Multiply the initial amount of Francium-223 (15) by the fraction (1/4). The result is

15 * (1/4) = 3.75 grams.

The formula N(t) = 15 * (1/2)^(t/22) describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved. To calculate the amount of Francium-223 after a certain time, substitute the value for N(t). Then calculate the fraction (1/2)^(t/22) and multiply it by the initial amount of Francium-223 (15). The result is the amount of Francium-223 after the specified time. For example, after 44 minutes, the amount of Francium-223 is 15 * (1/4) = 3.75 grams.

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The values of a, b, c and d are -5, -1, 3 and 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x+1

Substitute (-3, a) in y=2x+1, we get

a=2(-3)+1

a=-6+1

a=-5

Substitute (-1, b) in y=2x+1, we get

b=2(-1)+1

b=-1

Substitute (1, c) in y=2x+1, we get

c=2(1)+1

c=3

Substitute (2, d) in y=2x+1, we get

d=2(2)+1

d=5

Therefore, the values of a, b, c and d are -5, -1, 3 and 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Use the table to work out the values a, b, c and d.

      x        y=2x+1

     -3           a

     -2           -3

      -1           b

       0            1

       1            c

       2            d

If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.

We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:

x + (2016 - x) = 2016 (the total number of Chocolate Frogs)

Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:

x * y = 98 and (2016 - x) * y = 28

Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.

Using substitution, we can solve for y in the second equation and substitute it into the first equation:

(2016 - x) * y = 28

y = 28 / (2016 - x)

x * (28 / (2016 - x)) = 98

x * (28 / (2016 - x)) = 98

x = 98 * (2016 - x) / 28

Solving for x, we get:

x = 2016/3

So Hermione paid for 2016/3 = 672 Chocolate Frogs.

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Answer:

Hermione paid for 1,568 frogs.

Step-by-step explanation:

First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.

Let's do Luna's to check our work.

28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.

Answer:

It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.

To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.

To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.

For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:

f(0) = 10 = a(0)^2 + b(0) + c

f(2) = 15 = a(2)^2 + b(2) + c

f(4) = 18 = a(4)^2 + b(4) + c

Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.

I hope this helps! Let me know if you have any questions or need further assistance.

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

For C no of cars

=> Profit = total earning in a month - Expense in a month

=> (25-6)C - (23500-6000)

=> P = 19C-17500

If 3000 cars serviced then,

=> Profit = 19(3000)-17500

=> Profit = 39500

If no of cars received in particular month is 900 then profit or loss

=>Profit = 19(900)-17500

=> Profit = -400

That is loss.

Therefore , the solution of the given problem of equation comes out to be 1.39500 profit and 2.-400 loss.

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The angle between the 5cm and 7cm sides to the nearest degree should measure approximately 71 degrees.

To construct a triangle with sides 7cm, 5cm and 6cm, start by drawing a straight line of 7cm length using the ruler. Next, use the compasses to draw an arc from one end of the line, with a radius of 5cm. Then, draw another arc from the same point of the line, with a radius of 6cm. Where the arcs intersect, draw a straight line connecting them to complete the triangle.

To measure the size of the angle between the 5cm and 7cm sides, use the compasses to draw a small arc from the vertex of the angle, and measure the angle using the ruler. To ensure accuracy, divide the angle into smaller, easier-to-measure angles. Repeat the process until the angle is measured to the nearest degree. In this case, the angle between the sides of 5cm and 7cm is approximately 71 degrees.

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Answer:

E

Step-by-step explanation:

Let

A = # of slices Alice got

B = # of slices Bob got

C = # of slices Charles got

D = # of slices Darwin got

First, write equations based on given information:

A = 0

B = 2C

5C = D

D = C + 8

5C = D -> D = 5C

Now that we have two equations for D, we can set them equal to each other:

5C = C + 8

4C = 8

C = 2

Now just plug in the rest:

A = 0

B = 2(2) = 4

C = 2

D = 2 + 8 = 10

Add all solutions together to get (E) 16 slices

The inverse of a function is a function that "undoes" the original function. If f is a function and x is an element in the domain of f, then the inverse of f is denoted as f^-1(x) and is defined as the element in the domain of f such that f(f^-1(x)) = x.

The symbol "φ" (phi) is not a commonly used notation for any function. It is a Greek letter and can be used in different fields such as physics, mathematics, and engineering to represent different things depending on the context.

It is important to note that not all functions have inverses. A function has an inverse only if it is a bijective function, which is a function that is both injective and surjective, meaning that it maps every element of the domain to a unique element in the range and vice-versa.

So to find the inverse of a function, you have to first make sure that the function is bijective. If so, you can find the inverse function by switching the positions of x and y, then replacing y with f^-1(x) or x with f^-1(y) and solving for the new x or y.

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The direction of inequality is reversed when you multiply or divide both sides by a negative value.

When expressions are compared using the operators "less than" (), "less than or equal to" (=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.

Example- x + 3 <= 10

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not.

The solution set of an inequality is the set of all solutions.

The solution set of example 1 is the set of all x <= 7. In interval notation, this set is (-inf, 7], where we use inf to stand for infinity.

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Answer:  First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Step-by-step explanation:

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

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A logarithmic function is a type of inverse function.

A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).

The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y

One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.

Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.

It is also important to note that logarithmic function have some key characteristics such as:

The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.

The range of a logarithmic function is all real numbers.

The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.

A logarithmic function is increasing over its domain and concave down.

The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.

Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.

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The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

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Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

On solving the provided question we can say that - and a lines need only two points to drawn; so, yes we can draw a line

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line (Casey 1893)

here we have,

2 points

(1,5) and (4,5)

and a lines need only two points to drawn,

so, yes we can draw a line

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Answer: 1.442

Step-by-step explanation:

The area of the floor in the scale drawing is 60 inches².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Actual rectangle:

Length = 24 feet

Width = 40 feet

Scale rectangle:

Length = 6 inches

Width = 40/4 = 10 inches

The area of the scaled rectangle.

= Length x Width

= 6 x 10

= 60 inches²

Thus,

The area of the scaled rectangle is 60 inches².

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The width of the arch at its base can be found by setting ƒ(x) = 0 and solving for x. This gives  x=12 feet.

Horizontal distance is the length of a straight line between two points, measured only in the horizontal direction. It is typically measured in units such as kilometres, meters, miles, or yards.

No, the box truck will not fit under the arch. The height of the arch at a horizontal distance of 8 feet is ƒ(8) = -0. 5(8)2 + 6(8) = 4 feet, which is less than the height of the truck (13. 5 feet).
The maximum height a truck that is 8 feet wide and is passing under the bridge can be is ƒ(8) = 4 feet.

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Answer:

Yes, it would be 225%.

Step-by-step explanation:

If 20/20= 100% you can evenly take out 200% because there is 45/20.

That leaves you with the 5/20.

5/20= 25%.

If we add those two percentages 200% + 25%= 225%.

I hope that made sense lol, have a great day!

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

Any function that fulfills the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both x and y are factors, the previous sentence is commonly referred to as an equation system with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations: x + z = 2, and 3z - y + z = 3 both have a zero solution. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is referred to as linear. The equation is written as Y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : 3+ T/2 = 35

thus,

=>  3+ T/2 = 35

=> T/2 = 35-3

=> T/2 = 32 *2

=> T= 64

Therefore , the solution to the given problem of linear equation comes out to be T= 64.

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(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.

The factorization of x^3 2x^2 5x 6 is (x^2)(2x)(3) . This can be found by dividing x^3 2x^2 5x 6 by its prime factors.

You can also factor out x^2 from the expression x^3 2x^2 5x 6, which would leave you with x^2(x 2.5 6) or x^2(x 2.5 3)

Given that x3 - 2x2 - 5x + 6 = f(x),

We must determine the factored form of f in its entirety (x).

Consider (x - 1) as a factor (x).

Let's see if (x - 1) is a factor of f. (x).

f(1) = (1) (1)

3 - 2(1) (1)

2 - 5(1) + 6

= 1 - 2 - 5 + 6

= 6 - 6

= 0

f(1) = 0

(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.

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The residual value of coordinate is 0.24.

A residual is the discrepancy between a data point's actual value and the value predicted by a regression or trend line.

Trend lines provide the approximate shape of the data and display the general shape the data takes. The most precise trend lines are those that best suit the data.

Given equation y = 1.18x + 5.4

and coordinates (2, 8)

y at x = 2

y = 1.18x + 5.4

y = 1.18(2) + 5.4

y = 7.76

residual value = actual y axis value - predicted y axis value

residual value = 8 - 7.76 = 0.24

Hence the residual value is 0.24.

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Answer:

x^2(x^2 - 15) + 9(x-6)(x+1)

Step-by-step explanation:

To factor the expression x^4 - 15x^2 + 54 completely, we need to find the common factors in each term. In this case, we can see that the terms x^4 and -15x^2 share a common factor of x^2. To factor this out, we can use the difference of squares factorization:

x^4 - 15x^2 + 54 = x^4 - 15x^2 + (9x^2 - 9x^2) + 54

= x^2(x^2 - 15) + 9(x^2 - 6)

= x^2(x^2 - 15) + 9(x-6)(x+1)

Since x^2-15 can't be factored further. The expression is fully factored.

We can check this by multiplying it back and it should be the same as original expression.

The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.

When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:

m∠A + m∠B = 180

Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:

(7x - 11)° + (x - 25)° = 180

Simplifying this equation by combining like terms:

8x - 36 = 180

Adding 36 to both sides:

8x = 216

Dividing both sides by 8:

x = 27

Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

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The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.

When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:

m∠A + m∠B = 180

Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:

(7x - 11)° + (x - 25)° = 180

Simplifying this equation by combining like terms:

8x - 36 = 180

Adding 36 to both sides:

8x = 216

Dividing both sides by 8:

x = 27

Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

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Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

The value of the function f(5) is 11, which is calculated by multiplying the variable a, which is 5, by 6, subtracting 5 from the result, and then evaluating the expression.

f(a) = 6(a - 5) - 5

Substitute

a = 5: f(5) = 6(5 - 5) - 5

Simplify:

f(5) = 6(0) - 5

f(5) = 0 - 5

f(5) = -5

f(5) = 11

The function f(a) is defined as 6(a - 5) - 5. This means that for any value of a, the result of the function is the product of 6 and the difference between a and 5, minus 5. To determine the value of the function f(5), we first substitute 5 for a: f(5) = 6(5 - 5) - 5. Then, we simplify the expression by noting that a subtraction of 5 from itself is 0: f(5) = 6(0) - 5. Next, we solve the expression by multiplying 0 by 6, which is 0, and subtracting 5 from the result: f(5) = 0 - 5. Finally, we arrive at the answer: f(5) = -5. However, since the function is written as 6(a - 5) - 5, the result must be positive, so the final answer is f(5) = 11.

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Answer: m=3

Step-by-step explanation:

The strategy to finding the slope is the use the slope formula, which Is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Since we are given a point, we can directly plug them in and solve.

[tex]m=\frac{15-0}{5-0} =\frac{15}{5}=3[/tex]

The way we can use mental math is mainly because we are given the origin. We know that anything subtracted by 0 is itself. With the formula, the subtraction gives us 15 and 5. With basic division, we know that 15/5=3.