Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.Shaded area is 0.9599.

Therefore , the solution of the given problem of rational numbers  comes out to be A) 0.75 can be written as 75/100.

Rational numbers are those that may be written as a ratios (or fraction) of 2n. A fraction with a nonzero denominator is said to be rational. A few instances of rational numbers are 1/2, 1/5, and 3/4. As a real function, "0" can also be stated in a number of different ways, such as 0/1, 0/2, etc 0/3. But 1/0, 2/0, 3/0, and so forth. The number seven makes sense. A rational number is produced when three integers are split. To get the rational number 7, divide whole 7 ps by the total number 1. Since 7 can be obtained by dividing two integers, it is referred to as a real function.

Here,

Given :

=> Any number that can be expressed as a straightforward fraction is considered rational. This is the shape of a fraction: => a/b

where the denominator is "b" and the numerator is "a". Since both are integers, b 0.

=>Simple fractions cannot be used to represent irrational values.

So,

A) 75/100 is equivalent to 0.75 rational.

B) √√3 is irrational.

C) √√√9 is irrational.

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Answer:

Step-by-step explanation:

Let x be the number of children Grace babysits. Then, she will earn $50 + $5 per child, or a total of $50 + 5x. To make at least $63, we can write an inequality as follows:

50 + 5x >= 63

To solve for x, we can subtract 50 from both sides:

5x >= 13

And finally, divide both sides by 5:

x >= 2.6

Since Grace needs to babysit at least 2 whole children, she needs to babysit at least 3 children to make $63 or more.

Answer:

Step-by-step explanation:

Well if you do this [tex]$50 + $5=x\\50+5= 55+50+5=110[/tex]you will only have to babysit 2 kids and you will have leftover money.

[tex]65-110=x 65-110=153[/tex]

The way that  the Great Awakening lead to a new American government is that; The Great Awakening helped the colonists realize they needed their own national religion.

The Great Awakening was a period in history characterized by religious revival in the US. There were five major Great Awakenings, that occurred between the beginning of 18th and the end of the 20th century. However, the last of the Great Awakenings lasted until the year 2000.

During the years of 1730s and 1740s, it was clear that the English colonies in America went through the Great Awakening which was a religious resurgence. This movement came into play at a period when there was a very huge emphasis on the idea of secular reason and as a result religious zeal had lost its freshness.

The gospel was usually preached by Christian leaders from town to town to stir up interest in Christianity while emphasizing deliverance from sin. The outcome or result was a reinvigorated commitment to religion.

The Great Awakening, in the opinion of many historians, had a profound effect on the American culture as a whole as well as on different Christian denominations.

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The equation of the axis of symmetry for the function will be x  = -3.

ax²+bx+c=0, with a not, equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given,  the function f(x)= -x²- 6x - 8 Since the given equation is a parabola.

Rewrite the given equation in the vertex form.

f(x) = -x²- 6x - 8

f(x) = -(x² + 6x +8)

f(x) = -(x² + 2 * 3 *x + 9 -1)

f(x) = -(x +3)² +1

Compare this with the general equation of the vertex form

y = a(x - h)²  + k

We get,

a = -1

h = -3

k = 1

Thus the vertex of the given parabola will be (-3, 1)

Since the general form of the focus of the parabola (h, k +p)

Where,

k = 1/4a

k = -1/4

Thus, the coordinates of the focus of the parabola will be (-3, 3/4)

Since the equation of symmetry will be the equation of the line that passes through the points focus and vertex.

Thus, the equation will be x = -3

Therefore, the equation of the axis of symmetry for the function will be x  = -3.

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the angle bisector theorem formula yields the value x=10.

The angle bisector theorem states that RU/RT=US/ST or a/b = x/y. A line or ray known as an angle bisector divides an angle in a triangle into two identically sized parts.

The geometry concept known as the angle bisector theorem examines the ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into. It contrasts their relative lengths with the ratios of the other two sides of the triangle.

Side ratio: RU/RT=US/ST

3x/40 = x+2/16

6x=5x +10

x=10

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Answer: There are 1,000,000 nanoseconds in a millisecond.

Answer:

The answer is 1000000.

Answer: $2.15

Step-by-step explanation: Let x represent the price of a pen.

5x + (x - 1.30) = 11.60

6x - 1.30 = 11.60

6x = 12.90

x = 2.15

A bottle of tomato juice contains 247. 5 mg of vitamin C and A bottle of grape juice contains 258 mg are in one serving of each type of juice is 45mg and 86mg.

A bottle of tomato juice contains 247. 5 mg of vitamin C and has 5. 5 servings so,

247.5/5.5 = 45 mg

A bottle of grape juice contains 258 mg of vitamin C and has 3 servings so,

258/3 = 86 mg

Water-soluble vitamin C, sometimes referred to as ascorbic acid and ascorbate, is present in citrus and other fruits and vegetables. It is also available as a dietary supplement and as an ingredient in topical "serums" used to cure melasma (dark pigment spots) and facial wrinkles. Scurvy is treated and prevented with it.

Vitamin C is a necessary nutrient that aids in collagen development, tissue healing, and the enzymatic synthesis of certain neurotransmitters. It is necessary for the operation of various enzymes and is crucial for the immune system. Additionally, it serves as an antioxidant. The majority of animals can produce their own vitamin C.

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The standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

as given,

r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t₀ = 3

so, [tex]x = 2t^{2}, y = 3t + 4 , z = 2t^{3}[/tex]

[tex]\frac{dx}{dt} = 4t, y=3, z=6t^{2}[/tex]

r'(t) = <4t, 3, [tex]6t^{2}[/tex]>

and at t =3,

r'(t=3) = <12, 3, 54>

we have to find the tangent line to the curve at t=3,

x = 18, y = 13, z = 54

for t=3, (x, y, z) = (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

Thus, the standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

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The standard parameterization for the line tangent to the curve is

x=12t+18 , y=3t+9 , z=54t+54  

In parameterization the variables are independent variables , whereas continuous functions are dependent variables , that is it is dependent on another functions. The given curve is r(t)=(2t^2)i+(3t+4)j+(2t^3)k and given t=t0=3

Given , r(t)=(2t^2)i+(3t+4)j+(2t^3)k

r'(t)=(4t)i+3j+(6t^2)k

and also given t=t0=3

r(t=t0=3) => (18 , 9 , 54)

r'(t=t0=3) => (12 , 3 , 54)

The standard parameterization for the tangent line can be given by using r(t) and r'(t) . so by that we came to know the required standard parameterization.

x=12t+18

y=3t+9

z=54t+54

Therefore, the about mentioned x, y, z are the standard parameterization for the tangent line of given curve.

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The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

Given that,

Natan Nave bought a home with a 13% adjustable rate mortgage for 20 years.

He paid $11. 72 monthly per thousand on his original loan.

At the end of 4 years he owes the bank $75,000.

Now that interest rates have gone down to 10%

The bank will renew the mortgage at this rate or Natan can pay $75,000.

Natan decides to renew and will pay $9. 66 monthly per thousand on this loan.

Per thousand value = 75000/1000 = 75

What was the old monthly payment,

$[tex]11.72*75[/tex] = $879

What is the new monthly payment,

$[tex]9.66*75[/tex] = $724.5

What is the percent decrease in his monthly payment (to the nearest tenth),

= [tex](\frac{9.66}{11.72} )-1 *100[/tex]

= -17.57%

Therefore,

The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

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The value of the function (g o f) (x) = 12x + 49.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Given that the value of f(x) = x + 4 and g(x) = 12x + 1.

The value of (g o f)(x) is:

g(x) = 12x + 1

Substitute the value of f(x) in x for the function of g(x):

(g o f) (x) = 12(x + 4) + 1

(g o f) (x) = 12x + 48 +1

(g o f) (x) = 12x + 49

Hence, the value of the function (g o f) (x) = 12x + 49.

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The value of the function (gof) (x) would be 12x + 49.

The set of all x such that x is in the domain of g and g(x)) is in the domain of f is the domain of f composed with g, as you should be aware of. A composite function's domain is the set of inputs x in the domain of g for which g(x) is in the domain of the function.

A composite function is also known as f of g of x. It is formally represented as f(g(x)) or (f g)(x), which indicates that x = g(x) should be substituted in f. (x). It can alternatively be written as "f circle g of x." It is a process that merges two functions into one new function.

Let the given value be f(x) = x + 4 and g(x) = 12x + 1.

The value of (g o f)(x) is:

Substitute the value of f(x) in x for the function of g(x):

(g o f) (x) = 12(x + 4) + 1

simplifying the above equation, we get

(g o f) (x) = 12x + 48 +1

(g o f) (x) = 12x + 49

Therefore, the value of the function (gof) (x) be 12x + 49.

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Answer: 32

Step-by-step explanation:

Answer:

She had 32 pairs.

Step-by-step explanation:

Subtract 2 from 18 and then times that answer by 2.

The center is called rectangle point X. The distance from the corner of the rectangle to the center (BX) can be found using the Pythagorean theorem is 21.74 to the nearest tenth be 21.7.

The Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse. So, we can apply the Pythagorean theorem as follows:

        BX² = AB² + BC²

Plugging in the values for AB and BC:

        BX²= 12² + 18²

        BX² = 144 + 324

        BX² = 468

Finally, taking the square root of both sides gives us the length of BX:

        BX = √(468)

        BX = 21.74 to the nearest tenth = 21.7

The description above involves finding the length of the diagonal of a rectangle that goes from one corner of the rectangle to its center. This length is similar to as BX in the definition. To find BX, the Pythagorean theorem is used.

The Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse.

By substituting the values of AB and BC, the equation BX² = AB² + BC² can be solved to find the length of BX. Finally, taking the square root of the solution gives the length of BX to the nearest tenth.

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The value of the limit is [tex]\lim_{x \to \frac{\pi}{4} } \frac{tan(x) - 1}{x - \frac{\pi}{4} } = 2[/tex].

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.

Given that the limit is:

[tex]\lim_{x \to \frac{\pi}{4} } \frac{tan(x) - 1}{x - \frac{\pi}{4} }[/tex]

When the limit is substituted the limit is in an indeterminate form.

Using the L'Hospital rule we have:

[tex]\lim_{x \to \frac{\pi}{4} } \frac{tan(x) - 1}{x - \frac{\pi}{4} }\\\\\lim_{x \to \frac{\pi}{4} } \frac{1 + tan^2(x)}{1 }\\[/tex]

Substitute the value of limit in the equation:

[tex]\lim_{x \to \frac{\pi}{4} } \frac{tan(x) - 1}{x - \frac{\pi}{4} } = 2[/tex]

Hence, the value of the limit is [tex]\lim_{x \to \frac{\pi}{4} } \frac{tan(x) - 1}{x - \frac{\pi}{4} } = 2[/tex].

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The following equations are organized for P as a function of Q

1) P = 20-8Q

2) p = [tex]\dfrac{12-Q}{3}[/tex]

3) p = 9 - 4Q

A function in mathematics is, technically speaking, a relation between a set of inputs and a set of potential outputs, where each input is related to exactly one output. Examples of functions in mathematics typically range from integers to integers or from real numbers to real numbers.

Additionally, it is a relation or a process that links each element x of a set X to the codomain of the function and to a single element y of a different set Y (typically the same set).

1) Q = 20-P

Q + P = 20

P = 20-Q

2) Q=12-3P

Q +3P = 12

3P = 12-Q

p = [tex]\dfrac{12-Q}{3}[/tex]

P = 4 - 1/3Q

3) 8Q = 18 -2p

8Q + 2p = 18

2p = 18 - 8Q

p =  [tex]\dfrac{18-8Q}{2}[/tex]

p = 9 - 4Q

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Complete question:

Let's call the amount of Deep Thought granola mixed "x" (in pounds). The amount of Oat Dream granola mixed would then be 20 - x (in pounds).

We know that Deep Thought granola is 25% nuts and dried fruit and Oat Dream granola is 10% nuts and dried fruit. We also know that the desired mix of 20 pounds of granola should be 19% nuts and dried fruit.

Therefore, we can set up the following equation to find the amount of Deep Thought and Oat Dream granola to be mixed:

0.25x + 0.10(20 - x) = 0.19 * 20

Expanding the right side of the equation and solving for x, we get:

0.25x + 2 - 0.1x = 3.8

0.15x = 1.8

x = 12

So, we would mix 12 pounds of Deep Thought granola and 8 pounds of Oat Dream granola to get 20 pounds of granola that is 19% nuts and dried fruit.

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The required function is continuous at x = -5 when c = 4.

If it is possible to draw the curve without encountering any breaks, the function is considered to be continuous in the interval. If every point in the interval satisfies the function, the function is said to be continuous.

For the function to be continuous at x = -5, the value of the function f(-5) must be equal to the value of c. That is,

f(-5) = c

Since f(x) = 4 when x = 1, we have

f(-5) = 4

Therefore,

c = 4

So the function is continuous at x = -5 when c = 4.

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The system of equation y = −8x − 9 and y = 6x + 5. So the point of the specified is (-1, -1).

These are the specified parameters:

y = −8x − 9 and y = 6x + 5

Substitute the equation

y = −8x − 9

6x + 5 = −8x − 9

6x + 8x = -9 - 5

14x = -14

  x = -14/14

  x = -1

Substitute x = -1 into the equation

y = 6x + 5

y = 6 (-1) + 5

y = -6 + 5

y = -1

So the poin (x, y) is (-1, -1).

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The two points that would line of fit go through to best fit the data is (1, 9) and (10, 1).

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Given a scatterplot.

There are 10 points which are marked in the scatterplot.

We have to identify the points which are closely related to the general trend of the line.

Those points will be best passing through the line of best fit.

Here the graph will be negative, since the values on the vertical line are decreasing with the increase in the values on horizontal.

Hence the two points are (1, 9) and (10, 1).

Hence the two points are (1, 9) and (10, 1).

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All such strings if no repeats are allowed, meaning each of A, B, or C is used once then the total number of combinations is 13.

An array is a collection of elements that are ordered and can be accessed through indices.

In this case, we are dealing with arrays of character strings, where each string is a sequence of letters. In this problem, there are three possibilities for the characters that can appear in each string: A, B, or C.

(a) Three character strings where repeats are allowed:

Tree:

List: AAA, AAB, ACC, ABA, ABC, ACA

Number of items on list: 6

(b) Three character strings where repeats are not allowed in a row:

List: AB, AC, BAC, BCA, CAB, CBA

Number of items on list: 6

(c) Three character strings with no repeats allowed:

Tree:

ABC

List: ABC

Number of items on list: 1

So, the total number of items on the list is calculated as,

=> 6 + 6 + 1.

=> 13

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The y-intercept represents the initial temperature, and the rate of change gives how the temperature changes per minute.

So the correct options are A and D.

Here we have a relation that shows how the temperature changes as a function of time.

So if F(x) is the temperature and x is the time, the y-intercept is given by:

F(0)

So the y-intercept is the initial temperature, the correct option is A.

And the rate of change tells us how the temperature changes as the time passes, so we can define the rate as "the change in temperature per minute" like on option D.

These are the correct options.

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Answer:

x = -1

y = -7

Step-by-step explanation:

y=9x+2`

-2x+7y=-47  ==> isolate y

Equation 1: 7y = 2x - 47  ==> add 2x on both sides

Equation 2: y = 9x + 2

7 * (y = 9x + 2)

Equation 3: 7y = 63x + 14

Equation 1: 7y = 2x - 47

Subtract equation 1 from equation 3:

  7y = 63x + 14

- (7y = 2x - 47)

7y-7y = 63x-2x + 14-(-47)

0 = 61x + 14 + 47

0 = 61x + 61  ==> solve for x

-61 = 61x  ==> subtract 61 on both sides to isolate x

x = -1

Now solve for y

y = 9(-1) + 2  ==> plugin -1 for x in y=9x+2`

y = -9 + 2  ==> simplify

y = -7

`

Leon found the sum of 5/6 and 2/3 to be 11/12, you can tell that his answer is incorrect without calculating by seeing that after doing denominator same we do not get 11 as addition.

The sum of 5/6 and 2/3 will be calculated as,

= 5/6 + 2/3

= 5/6 + 2(2)/3(2)

= 5/6 + 4/6

= 9/6

= 3/2

So, the sum of 5/6 and 2/3 is 9/6.

Therefore, you can tell that his answer is incorrect without calculating by seeing that the given answer is not equivalent to the 11/12.

Since a fraction has a numerator and a denominator that are separated by a bar, adding fractions is a little different than adding integers normally. If the denominators are equal, adding fractions can be done with ease. Like fractions are transformed to like fractions because they share a common denominator, which makes addition simpler.

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The value of angles ∠A and ∠B is equal to 40°.

Given is that ∠A = 5x − 5 and ∠B = 3x + 13

We can write -

∠A = ∠B            {Vertically opposite angles}

5x − 5 = 3x + 13

5x - 3x = 18

2x = 18

x = 9

So, we can write -

∠A = 5x − 5 = 40°

∠B = 3x + 13 = 40°

Therefore, the value of angles ∠A and ∠B is equal to 40°.

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Answer: a/c

Step-by-step explanation: cancel out the common factor b. to find the excluded values would be b = 0, c = 0

The polynomial that satisfies the conditions is: p(t) = (1/4)(t - 1)² (t - 2)³

This polynomial has a root of multiplicity 2 at t = 1 and a root of multiplicity 3 at t = 2, and also satisfies p(0) = 2 and p'(0) = 1.

The other root of p(t) can be found by factoring the polynomial further, but since the degree of the polynomial is 6, it will have 3 additional roots, which can be found using various mathematical methods such as the Rational Root Theorem or numerical methods.

Polynomials are mathematical expressions that involve variables raised to a power and are combined using addition and subtraction operations. The degree of a polynomial is the highest power of the variable in the expression.

A zero of a polynomial is a value of the variable for which the polynomial evaluates to zero. The multiplicity of a zero is the number of times the factor (t - zero) appears in the polynomial's factorization.

Given the conditions that the polynomial p(t) has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, we can write p(t) as the product of factors (t - 1)² and (t - 2)³:

p(t) = a(t - 1)² (t - 2)³

where a is some constant. To find the value of a, we use the fact that p(0) = 2 and p'(0) = 1. We evaluate p(0) and p'(0) using the polynomial expression above, then solve for a.

First, we find p(0):

p(0) = a(0 - 1)² (0 - 2)³ = a(-1)² (-2)³ = a * 8

Next, we find p'(0):

p'(t) = 2a(t - 1)(t - 2)³ + a(t - 1)² * 3(t - 2)²

p'(0) = 2a(-1)(-2)³ + a(-1)² * 3(-2)² = 16a + 12a = 28a

Now that we have expressions for p(0) and p'(0), we can solve for a:

p(0) = a * 8 = 2 => a = 1/4

p'(0) = 28a = 1 => 28 * 1/4 = 1

So the polynomial that satisfies the conditions is:

p(t) = (1/4)(t - 1)² (t - 2)³

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The values are 0,27,27,1000 and dependent values.

A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.

f(0) = |0|^3 = 0^3 = 0

f(-3) = |-3|^3 = 3^3 = 27

f(3) = |3|^3 = 3^3 = 27

f(-10) = |-10|^3 = 10^3 = 1000

f(a-3) = |a-3|^3 = (a-3)^3 if a >= 3, and -(a-3)^3 if a < 3

f(ah) = |ah|^3 = (ah)^3 if h >= 0, and -(ah)^3 if h < 0

So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|^3 = 8 and f(ah) = f(-5) = |-5|^3 = 125.

Therefore, The values are 0,27,27,1000 and dependent values.

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The values are 0,27,27,1000 and dependent values.

A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.

f(0) = |0|³= 0³ = 0

f(-3) = |-3|³ = 3³ = 27

f(3) = |3|³ = 3³ = 27

f(-10) = |-10|³ = 10³ = 1000

f(a-3) = |a-3|³ = (a-3)³ if a >= 3, and -(a-3)³ if a < 3

f(ah) = |ah|³ = (ah)³ if h >= 0, and -(ah)³ if h < 0

So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|³ = 8 and f(ah) = f(-5) = |-5|³ = 125.

Therefore, The values are 0,27,27,1000 and dependent values.

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The solution is Option A.

The value of the equation is x = -13/15 and x = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

15x² + 13x = 0   be equation (1)

On simplifying the equation , we get

Subtracting 13x on both sides of the equation , we get

15x² = -13x

Divide by x on both sides of the equation , we get

15x = -13

Divide by 15 on both sides of the equation , we get

x = - ( 13/15 )

So , when x = 0

0 = 0

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = -13 ± √ ( 169 - 4 ( 15 ) ( 0 ) ) / 2 ( 15 )

x = -13 ± √ ( 169 - 0 ) / 30

x = ( -13 ± 13 ) / 30

So , we have 2 solutions to x ,

x = ( -13 - 13 ) / 30

x = -26 / 30

x = -13/15

And , x = ( -13 + 13 ) / 30

x = 0/30

x = 0

Hence , the solutions to the equation is x = -( 13/15 ) and x = 0

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After calculations, it is determined that the segments do not form a right-angled triangle.

we need to calculate the distances between the points as the side lengths of the triangle.

these side lengths must satisfy the Pythagoras principle :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.

the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.

this is then caked the distance formula, but it is all Pythagoras again.

AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =

= 8² + 0² = 8²

AB = 8

AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20

AC = sqrt(20)

BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52

BC = sqrt(52)

as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.

if this is a right-angled triangle, then

8² = sqrt(20)² + sqrt(52)²

must be true.

but

64 = 20 + 52 = 72 is wrong.

so, the segments do not form a right-angled triangle.

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