Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous.
a. All dogs are friendly.
b. All people are happy.
c. Some suspicions were substantiated.
d. Some estimates are accurate.

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 :)

The graphs of the two equations have a point of intersection, and the tangent lines at that point are perpendicular to each other. This can be shown by taking the derivatives of both equations and setting them equal to each other, which results in a perpendicular line equation.

To show that the graphs of the two equations have tangent lines that are perpendicular to each other at their point of intersection, we can take the derivatives of both equations, which gives us the equations of the tangent lines. We can then set the equations equal to each other and solve for the point of intersection. This will result in an equation for the perpendicular line, which is the equation of the line that passes through the point of intersection and is perpendicular to both tangent lines. We can then verify that the two tangent lines are perpendicular to each other at the point of intersection by calculating the slopes of both lines and showing that they are negative reciprocals of each other.

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The value of X is 4/5 if point P is on the unit circle and if the coordinate of P is -3/5 and P is in iV quadrant.

We know that unit circle is the circle of radius 1 unit. We are given the y-coordinate of P, that is y = -3/5. Now if we draw a perpendicular line at x-axis, and we know the length of line joining the P and the origin is 1 unit (h = 1). We can construct a right triangle. Then by pythagorean theorem.

x² + y² = h²

x² = √(h² - y²)

x² = √(1² - (-3/5)²)

x² = √(1 - (9/25))

x² = √(16/25)

x = 4/5

Since X is in the IV quadrant, where x is positive and y is negative.

So x = +4/5

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The correct sample space for the gumballs in Julia's bag is {lemon-lime, watermelon, watermelon, grape, grape, grape} which makes option D correct.

The sample space for the gumballs in Julia's bag would be all the possible outcomes of selecting one gumball from the bag without replacement.

Since there are 1 lemon-lime, 2 watermelon, and 3 grape gumballs in the bag, the sample space would be expressed as:

sample space = {lemon-lime, watermelon, watermelon, grape, grape, grape}.

Therefore,we have 6 total outcomes in the sample space for the gumballs in Julia's bag.

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A single basin of dry rice and beans 20 cups One bag of 40 basins 100 kilogrammes of rice is included in a sack.

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The determinant of the coefficient matrix 3x+4y=0 and -2x+3y=17 is 17.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

A system of equations,

3x+4y=0

-2x+3y=17.

To find the determinant,

we will find the matrix from Cramer's rule,

A =

[tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]

So, determinant of matrix A

ΔA = 3 x 3 -(4 x -2)

ΔA = 9 + 8

ΔA  = 17.

Therefore, the determinant is 17.

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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.

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

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A function is a relation in which each member in the domain is paired with exactly one element in the range.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A phrase: A blank is a relation in which each member in the domain is paired with exactly one element in the range?

We have to find the blank word.

From the function definition,

A relation between a collection of inputs and outputs is known as a function.

A function is a connection between inputs in which each input is connected to precisely one output.

Each function has a range, co-domain, and domain.

Therefore, blank word is a function.

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The complete question:

A blank is a relation in which each member in the domain is paired with exactly one element in the range?

Answer is in attached photo.

Step-by-step explanation:

Solution is in the attached photo, do note that this question tests on the concept of Inequality.

[tex]5a > 5.45[/tex]

Divide both sides by 5:

[tex]\dfrac{5a}{5} > \dfrac{5.45}{5}[/tex]

Answer:

[tex]a > 1.09[/tex]

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.

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

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? $

The square prism's volume is 135 meter

Either the total number of smaller prisms that make up the composite shape, or its volume. the distinction between a larger prism and a smaller prism that was taken out of it.

A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently.

Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape. The triangle and square in the following shape are joined together. The square and the rectangle that make up the blue shape. There are two triangles making up the green shape.

Detailed explanation:

The parameters listed are;

L = 15 meters is the cylinder's length.

D = 7 meters is the cylinder's diameter.

B = 3 meters is the square prism's base length.

Consequently, we have;

The square prism's volume is

= B² x  L

= 3² x 15

= 9 x 15

= 135 meter

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