Mathematics College

I need help with this paper, it would be much appreciated.

Answers

Answer 1

1. y = a(x + 5)^2 + 6

2. y = a(x - 1)^2 + 4

3. y = a(x + 2)^2 - 6

4. y = a(x - 4)^2 - 10

5. y = a(x + 2)^2 - 4

6. y = a(x - 3)^2 + 12

These are the equations of the quadratic in vertex form, where (h, k) are the vertex coordinates, and a is the coefficient of x^2. In each case, the x-intercepts provided are plugged into the equation to check if it equals zero, which is how we can confirm that it is a correct equation for the parabola.

I hope this helps :)

Related Questions

Solve for m:-
2(m-5) = m-3

Answers

The value of m in the given equation will be 7.

Steps to solve the linear equation :

⇒2(m-5) = m-3

Bring RHS (Right hand side) terms to LHS(left hand side) of the equation,

⇒2(m-5) - (m-3) = 0

Now open the brackets,

⇒2m - 10 - m + 3 = 0

Now solve for m,

⇒2m - m - 10 + 3 = 0

⇒m - 10 + 3 = 0

⇒m - 7 = 0

Taking 7 to the RHS of the equation,

⇒m = 7

∴ The value of m is 7

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To solve for m in the equation 2(m-5) = m-3, we can start by distributing the 2 on the left side of the equation:

2m - 10 = m - 3

Next, we can add 3 to both sides of the equation to get:

2m - 10 + 3 = m

This simplifies to:

2m - 7 = m

Now we can subtract m from both sides:

2m - m - 7 = 0

This simplifies to:

m - 7 = 0

Finally, we can add 7 to both sides to solve for m:

m = 7

So the solution for m is 7.

rectangle bounded by the x-axis and the semicircle x" (see figure). What length and width should the rectangle have so that its area maximum? smaller value : ___larger value: ___

Answers

The area of the rectangle will be 4.5 square units and the length and width are x=3 and y=1.5.

The equation for the line is y = -.5x + 3 (slope/intercept form).

Draw a random rectangle with the y-axis, x-axis, and the point (x,y) on the line y = -.5x + 3 as its corners.

This point's height from the x-axis (the length of the rec) will be equal to -.5x + 3 and its length from the y-axis will be x (the width of the rec).

Knowing that A = L*W equals the area of a rectangle

A(x) = (-.5x + 3) * x = -.5x^2 + 3x

In search of A'(x) = -x + 3. And we desire that A'(x) be 0.

As a result, y = -.5(3) + 3 = 1.5 and -x + 3 = 0 imply that x = 3.

So the maximum area of this rectangle is L*W = 1.5 * 3 = 4.5 square units. (We know this is a max and not a min since A’’(x) = -1 which makes the graph concave down)

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uppose that at your university, you will pay $12,000 each year for tuition, $2,500 each year for textbooks, and $10,000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25,000 per year.

Answers

The opportunity cost for four years of college is $46,000

How to determine the opportunity cost?

We should know that opportunity costs represent the potential benefits that an individual, investor, or business misses out on when choosing one alternative over another.

The cost of education per year is = $12,000 + $2500 + $10000 = $24,500

The return if we decide not to go to college= $25000 - $12000 = $13000

We lose this return if we decide to go to college and we have to pay for room and board anyway.

The opportunity cost for four years of college is $24500-$13000)*4

This amounts to $11500*4 = $46,000

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Correct question:

Suppose that at your university, you will pay $12000 each year for tuition, $2500 each year for textbooks, and $10000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25000 per year.

Assume that if you decided not to go to college, your parents would not let you live at home.

What is your opportunity cost for four years of college? $

Classify the following triangle according to its sides and its angle measures.
2 cm
83⁰
53
2.5 cm
3 cm
44

Answers

This triangle is classified as an acute triangle since all three angles measure less than 90° (83⁰, 44⁰). It is also classified as an isosceles triangle since two of the sides (2 cm and 2.5 cm) are equal in length.

What are acute and isosceles triangle?

An acute triangle is a triangle in which all three angles measure less than 90 degrees. It is the opposite of an obtuse triangle, which has one angle measuring more than 90 degrees.

An acute triangle can also be referred to as a “sharp” triangle. The sum of all three angles in an acute triangle will always equal 180 degrees. An acute triangle can be either isosceles or scalene.

An isosceles triangle is a triangle with two sides of equal length and two equal angles opposite the two sides. The two angles are often referred to as the base angles, while the third angle is called the vertex angle. The two sides of an isosceles triangle are also often referred to as the legs, while the longest side is referred to as the base.

Isosceles triangles are studied in geometry, and the properties of such triangles can be used to solve many mathematical problems.

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the graph of f' the derivative of f is shown above which of the following statements is true about f

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The chart of the derivative of f is shown above the subsequent statement is true about f growing for -2<=x<=0

What is meant by Mathematical equation?A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."The slope-intercept form, standard form, and point-slope form are the three primary formats for linear equations.A mathematical expression with two equal sides and an equal sign in the middle is called an equation. An example of an equation is 4 + 6 = 10.A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A mathematical expression known as an equation is one in which one side of the expression equals the other, as in the example above: Since we know that 4 + 4 = 8 and 10 - 2 = 8, the equation is true because both sides are equal.

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