What is the discriminant of the polynomial below 9x2 - 18x + 9?

The number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The decimal number is 0.66 which is non-terminating.

As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We can write the number 0.66 as:

= 66/100

= On simplification:

= 33/50

Thus, the number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.

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Answer:

The exact value is [tex]\cfrac{\sqrt{3}}3[/tex]

Step-by-step explanation:

Since 60 degrees is an angle we can find on the unit circle, the goal to get an exact value is to use the elements of the unit circle, which are exact values of sine and cosine.

Writing cotangent in terms of sine and cosine

We can use the trigonometric identity

[tex]\cot \theta = \cfrac{\cos \theta }{\sin \theta }[/tex]

Thus for the exercise we will have

[tex]\cot 60^\circ = \cfrac{\cos 60^\circ }{\sin 60^\circ }[/tex]

Identifying the known exact values.

From the unit circle that you can see on the attached image below, we have to identify the exact values of cosine and sine of 60  degrees.

So first try to look for the angle 60 degrees, there you will see a point that has a pair of values,  those represent (cosine, sine), thus we get:

[tex]\cos 60^\circ=\cfrac 12 \\\\\sin 60^\circ = \cfrac{\sqrt3}2[/tex]

Finding the exact value of cot 60 degrees.

We can replace the exact values of sine and cosine on the trigonometric identity for cotangent.

[tex]\cot 60^\circ = \cfrac{\cfrac 12 }{\cfrac{\sqrt 3}2 }[/tex]

Working with the reciprocal we get

[tex]\cot 60^\circ = \cfrac 12\times \cfrac2{\sqrt 3}[/tex]

Simplifying we get

[tex]\cot 60^\circ = \cfrac 1{\sqrt 3}[/tex]

Rationalizing since we usually do not want square roots on the denominator we get

[tex]\cot 60^\circ = \cfrac 1{\sqrt 3} \times \cfrac{\sqrt 3}{\sqrt 3}\\\boxed{\cot 60^\circ = \cfrac {\sqrt 3}3}[/tex]

And that is the exact value of cotangent of 60 degrees.

The exact value of cot(60°) is √3 / 3.

To find the exact value of cot(60°), we can use the identity:

cot(θ) = 1 / tan(θ)

Since tan(θ) = sin(θ) / cos(θ), we need to find the values of sin(60°) and cos(60°).

In a 30-60-90 degree triangle, the sides are in the ratio 1 : √3 : 2. Since the angle is 60°, the opposite side (opposite the 60° angle) has length √3 and the adjacent side (adjacent to the 60° angle) has length 1.

Using these values, we can calculate the sine and cosine of 60°:

sin(60°) = opposite/hypotenuse = √3/2

cos(60°) = adjacent/hypotenuse = 1/2

Now, we can find cot(60°):

cot(60°) = 1 / tan(60°)

= 1 / (sin(60°) / cos(60°))

= 1 / (√3/2 / 1/2)

= 1 / (√3/1)

= 1 / √3

= √3 / 3

Therefore, the exact value of cot(60°) is √3 / 3.

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Answer: Letter B.

Step-by-step explanation:

The expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is 64c¹⁵-d²⁷. the expression will be written in the power of a cube as below:-

64c¹⁵-d²⁷ = (4c⁵)³ - (d⁹)³

Therefore, the expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.

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Answer:

(3,3)

Step-by-step explanation:

The optimal least squares fit for the given data is y = 0.2732x² - 0.6452. This curve minimizes the sum of squared errors, providing an accurate representation of the data.

The provided data points are (-1, 0), (5, 5), and (6, 10), denoted as {x} = [-1, 5, 6] and {y} = [0, 5, 10]. The goal is to find the least squares fit for the curve y = ax² + b. To minimize the sum of squared errors between the data and the curve, the normal equations are derived.

The normal equations are given by:

(x₁⁴ + x₂⁴ + x₃⁴)a + (x₁² + x₂² + x₃²)b = x₁²y₁ + x₂²y₂ + x₃²y₃ (Equation 1)

(x₁² + x₂² + x₃²)a + 3b = y₁ + y₂ + y₃ (Equation 2)

By substituting the given data, the equations become:

1922a + 62b = 485

62a + 3b = 15

Solving these equations yields the values: a = 0.2732 and b = -0.6452. Therefore, the curve of the best least squares fit is y = 0.2732x² - 0.6452.

In conclusion, the curve that minimizes the sum of squared errors for the provided data points is y = 0.2732x² - 0.6452. The graph of this curve, along with the given data, visually represents the accuracy of the least squares fit.

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Answer:

401 students voted for the trip .

Step-by-step explanation:

As given in the question

535 students of the senior class voted to take a field trip[tex]\frac{3}{4}[/tex] of the class voted .

Thus

[tex]Students\ voted\ for\ the\ trip = \frac{3}{4}\times Total\ students[/tex]

Put value in the above

[tex]Students\ voted\ for\ the\ trip = \frac{3\times 535}{4}[/tex]

[tex]Students\ voted\ for\ the\ trip = \frac{1605}{4}[/tex]

                                                        = 401

Therefore 401 students voted for the trip .

Final answer:

△RST is a right triangle because the slope of line RS is 3/2 and the slope of line RT is 0, indicating that RS is perpendicular to RT.

Explanation:

To determine whether △RST is a right triangle, we can calculate the slopes of the sides to check for perpendicularity. A right triangle will have one pair of sides that are perpendicular to each other, meaning their slopes will be negative reciprocals.

The slope of line RS is calculated using the coordinates R(-3,1) and S(-1,4) as:

Slope of RS = (4 - 1) / (-1 + 3) = 3 / 2

The slope of line RT is calculated using the coordinates R(-3,1) and T(3,1) as:

Slope of RT = (1 - 1) / (3 + 3) = 0 / 6 = 0

Since the slope of RS is a non-zero finite number and the slope of RT is zero, they are perpendicular to each other because the slope of a line perpendicular to a horizontal line (slope of 0) is undefined, which is the negative reciprocal of 0.

Therefore, the correct statement is:

△RST is a right triangle because RS‾ is perpendicular to RT‾.

Final answer:

Upon calculating the slopes of the sides of △RST, it is concluded that none of the sides are perpendicular to one another, which means that △RST is not a right triangle.

Explanation:

To determine if △RST is a right triangle, we need to calculate the slopes of the sides to check for perpendicularity because perpendicular lines have slopes that are negative reciprocals of each other. Let's calculate the slopes of line segments RS, ST, and RT.

Slope of RS is given by (4 - 1)/(-1 + 3) = 3/2.
Slope of ST is (4 - 1)/(-1 - 3) = 3/-4 = -3/4.

Slope of RT is (1 - 1)/(3 + 3) = 0/6 = 0.

Since the slope of RT is 0, it means that RT is a horizontal line. The slope of RS is 3/2, and the slope of ST is -3/4. These slopes are not negative reciprocals of each other. Hence, none of the lines are perpendicular to each other, and we can conclude that △RST is not a right triangle because no two of its sides are perpendicular.

Answer:

[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.

Step-by-step explanation:

Mass of mulch sold = x pounds

Mass of gravel sold = y pounds

Total mass of mulch and gravel sold = 173 pounds

x + y = 173 ...[1]

Supplier sells [tex]2\frac{1}{4}[/tex] pounds of mulch for every [tex]1\frac{1}{3}[/tex] pounds of gravel.

That is for [tex]\frac{9}{8}[/tex] pounds of mulch for every [tex]\frac{4}{3}[/tex] pounds of gravel.

Then gravel sold for 1 pound mulch = [tex]\frac{4}{3}\times \frac{8}{9}=\frac{32}{27} pounds[/tex]

Then for x pounds of mulch the gravel sold will be:

[tex]\frac{32}{27} pounds\times x[/tex]

Mass of gravel sold = [tex]y = \frac{32}{27} pounds\times x[/tex]

Putting value of y in [1] :

[tex]x + \frac{32}{27} pounds\times x = 173[/tex]

x =[tex]\frac{4,671}{59} pounds[/tex]

y = [tex]173 pounds -\frac{4,671}{59} pounds=\frac{5,536}{59}pounds[/tex]

[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.

Answer:

P is True and q true is , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is false .

Explanation:

The table of conjunctions show:

The first statement, "A square root of 16 is 4," (p), is true.

The second statement, "a square root of 9 is -3," (q), is true.

The value of k, which forms a line perpendicular to y=3x-9 passing through the points (2,1) and (k,5), is -2. This is determined by using the slope formula and the property that the slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope.

The subject of this question is linear equations in mathematics, specifically about finding the slope and working with perpendicular lines. The given equation, y=3x-9, represents a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this given equation, the slope (m) is 3 and the y-intercept (b) is -9.

If another line is perpendicular to this line, its slope is the negative reciprocal of the given line's slope. Therefore, the slope of the line that passes through the points (2,1) and (k,5) would be -1/3.

The slope formula, (m = (y2 - y1) / (x2 - x1)), can be used to find the value of k. So, we have -1/3 = (5 - 1) / (k - 2). From this, you can solve for k to find that k = -2.

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Answer:

She bought 6 bag of chips.

Step-by-step explanation:

Let the price of bag of chips be s.

Each sandwich cost three times as much as a bag of chips.

Cost of sandwich = 3s

She bought 5 sandwiches for $6.

That is cost of sandwich = 3s = 6

                      s = 2$

Cost of bag of chips = s = 2$

Price of 5 sandwiches = 5 x 6 = 30 $.

She spent $42, remaining money = 42 - 30 =12 $

Number of bag of chips can be bought with 12 $

                 [tex]n=\frac{12}{2}=6[/tex]

She bought 6 bag of chips.

Answer:

g>5

Step-by-step explanation:

g-6>-1

+6 to both sides

g is left alone :)

Answer:

the anwser is A

Step-by-step explanation:

if you didnt understand the top

Answer:

The pair which are inverse of each other are:

Option: C

[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]

Step-by-step explanation:

Two functions f(x) and g(x) are said to be inverse of each other if:

fog(x)=gof(x)=x

i.e. the composition of two functions give identity no matter what the order is.

A)

[tex]f(x)=\dfrac{x}{12}+15[/tex] and [tex]g(x)=12x-15[/tex]

Now we calculate fog(x):

[tex]fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x[/tex]

Hence, option: A is incorrect.

B)

[tex]f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}[/tex]

Now we calculate fog(x):

[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x[/tex]

Hence, option: B is incorrect.

D)

[tex]f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3[/tex]

Now we calculate fog(x):

[tex]fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)[/tex]

[tex]fog(x)=9+\sqrt[3]{9-x^3}\neq x[/tex]

Hence, option: D is incorrect.

C)

[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]

Now we calculate fog(x):

[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})[/tex]

[tex]fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x[/tex]

Similarly,

[tex]gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x[/tex]

Hence, option: C is the correct option.

Answer:

D.f(x)=8x³+6 and g(x)=³x-6/8

Step-by-step explanation:

apex

Answer:

As Given :The coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .

⇒As we can see the two triangles are congruent because length of sides are equal.i.e By SSS  ΔJKL and ΔJ'K'L' are congruent.

⇒ As you can see from the figure depicted below the triangle JKL is rotated by an angle of 180° then translation of y coordinate by 1 unit up has taken place.

So , Option (3) is correct which is :△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.

Hidemi will receive a tip approximately amount of $13.50 which is the correct answer would be option (C).

Hidemi works as a waiter. He serves a table of four with a bill of $90.27. If Hidemi gets a 15% tip which is given in the equation.

The percentage is defined as a ratio stated as a fraction of 100.

For example, if Shekharaman received a 57% on his quiz, she received a 67 out of 100. It is written as 57/100 in fractional form and 57:100 in ratio form.

We have to determine the evaluation of 15% of $90.27.

⇒ 15% of 90.27

15% is described as 15/100 in fractional form

⇒ (15/100)(90.27)

15/100  is expressed as 0.15 in decimal form

⇒ (0.15)(90.27)

Apply the multiplication operation, and we get

⇒ 13.540 ≈ 13.50

Therefore, He will receive a tip approximately amount of $13.50.

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Answer:     4 1/2 in

Step-by-step explanation: correct on gradpoint