Draw the image of A ABC under a dilation whose center is A and scale factor is 1/4

To make the polynomial monic, divide even by leading term first.

Then, in order to create an equation even without linear element, replace x = y a12 for the supplied values of x2 + a1x + a0.

A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.

x3=y3 and y2=x2+xy+y2.

Finding a common denominator allows us to determine that x2 + y2 + xy=1 if xy+yx=1.

By multiplying by xy:

x2+y2=−xy

move every term to the left:

x2+xy+y2=0

Consequently, x3y3=(xy)(x2+xy+y2)=(xy)

x/y+y/x+1=0

=>(x²+y²+xy)/xy=0/1

=>x²+xy+ y²=0——(1)

Now, Since,x³-y³=(x-y)(x²+xy+y²)

=>x³ -y³=(x-y)(0). [from equation (1)]

=>x³ -y³=0,Ans.

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For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.

The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.

This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.

For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

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a) The velocity and position functions are given as follows:

b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...

The acceleration function for this problem is defined as follows:

a(t) = cos(t).

The velocity function is the integral of the acceleration function, hence it is given as follows:

v(t) = sin(t).

(as the integral of cos(t) is sin(t).)

The particle will be at rest when:

v(t) = 0.

Hence:

sin(t) = 0

t = arcsin(0)

t = kπ, k = ± 1, ± 2, ± 3, ...

The position function is the integral of the velocity function, hence it is given as follows:

s(t) = -cos(t) + 3.

As:

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A function that depends on another function is referred to as a composite function.

Let's say the price of an item is $1

Scenario #1 - 40% off $1  = 40 cents OFF

The discounted price = 60 cents

Now the 10% off of 60 cents

60-6 = 54 cents.

Scenario #2 - 10% of $1

The discounted price = 10 cents

100(cents) - 10 = 90 cents

Now the 40% off of 90 cents

90-36 = 54 cents

Let's try another value to confirm

Let's say the price of an item is $2

Scenario #1  - 40% off $2 = 80 cents OFF

200-80= 120 = $1.20

Now the 10% off of $1.20

120-12= 108 = $1.08

Scenario #2 - 10% off $2 = 20 cents OFF

200-20 = 180= 1.80

Now the 40% off of $1.80

180-72 = 108 = 1.08

The complete question is,

A store offers a discount of 40 off any one regular-priced item. employees also get 10% off any purchases. in which order should the discounts apply so that the employee pays the least amount?

A. Employee discount then store discount

B. They are both the same

C. Store discount then employee discount

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Answer:

Sin A / A = Sin B / B         Law of Sines

Sin 73 / X = Sin 59 / 18     Application of Law of Sines

X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1

The true statement is:

The asymptote of g(x) is the asymptote of f(x) shifted three units down.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = [tex](2/5)^x[/tex]

and, g(x) ==  [tex](2/5)^x[/tex] - 3

Now, Using translation the '-3' in g(x) shows the Vertical Translation down by 3 units.

Hence, The asymptote of g(x) is the asymptote of f(x) shifted three units down.

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The sample correlation coefficient, is represented as  r, measures the strength of correlation  and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the  positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.

The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.

A positive correlation tells us  that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.

So, the value of the sample correlation coefficient between the  rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as  correlated and how strong is this correlation occurs.

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[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]

Answer: X stands for 10

Step-by-step explanation:

If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4

To convert a fraction to a decimal, you simply divide the numerator by the denominator.

The quadratic equation written in the vertex form is:

y = 2*(x - 3)^2 - 1

We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:

f(x) = a*(x - h)^2 + k

Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)

Then the values that we have are:

a = 2

h = 3

k = -1

Then we can write the quadratic equation in the vertex form as:

y = 2*(x - 3)^2 - 1

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Answer:

tenth

Step-by-step explanation:

Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

Answer:

Here are the answers in fraction form.

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x < - \frac{11.7}{0.7}[/tex]

Here are the answers in decimal form.

[tex]x > 2.43[/tex]

[tex]x < -16.71[/tex]

Step-by-step explanation:

We will have 2 answers.

Answer 1

[tex]0.7x+5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]0.7x > 6.7-5\\0.7x > 1.7[/tex]

Divide both sides by [tex]0.7[/tex].

[tex]\frac{0.7x}{0.7} > \frac{1.7}{0.7}\\[/tex]

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x > 2.43[/tex]

Answer 2

[tex]-0.7x-5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]-0.7x > 6.7+5\\-0.7x > 11.7[/tex]

Divide both sides by [tex]-0.7[/tex].

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

[tex]\frac{-0.7x}{-0.7} < \frac{11.7}{-0.7}[/tex]

[tex]x < \frac{11.7}{-0.7}[/tex]

[tex]x < -16.71[/tex]

The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

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By using the properties of real numbers the given expression can be written as  -8y.

What is solving an expression?

Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

Given:

The given expression is, [tex]\frac{4}{3}(-6y)[/tex]

According to the distributive property of real numbers, if a, b, c are three real numbers the,

a(bc) = (ab)c

Using the associative property of multiplication, the given expression can be written as,

[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]

Hence, by using the properties of real numbers the given expression can be written as  -8y.

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A quadratic equation has two roots.

A function can have two roots. A root of a function is a point at which the function's value is equal to zero. This means that the function crosses the x-axis, and two roots means that it crosses the x-axis twice. Depending on the type of function, these two points can be either real or complex numbers. For example, the quadratic equation x2-3x+2 has two real roots, namely x = 1 and x = 2.A quadratic polynomial may have one, two, or zero roots. Quadratic polynomials have a degree of two.

Let's consider a quadratic polynomial

[tex]ax^2+bx+c=0[/tex]

where [tex]a\neq 0[/tex]

The quadratic polynomial is of degree two. Therefore, a quadratic equation has no more than two roots.

There is a formula to find the roots of quadratic polynomials, which is called the quadratic formula.

[tex]x=\frac{-b\frac{+}{-}\sqrt{b^2-4ac} }{2a}[/tex]

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Answer:

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the polynomial is 4w - 1. The highest power of the variable w is 1, so the degree of the polynomial is 1.Therefore, the correct answer is A) 1

Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

The weighted average of the numbers −1 and 1 is 0.3. Hence option A is the correct option.

What is the weighted average?

A weighted mean is similar to an average. Rather than contributing equally to the final mean, some data points contribute more "weight" than others. If all of the weights are equal, the weighted mean equals the arithmetic mean (the familiar "average").

Given numbers are  -1 and 1.

The first number is -1 and the second number is 1.

Two third of the first number is

= -1 × (2/3)

= -2/3

The one third of second number is

= 1 × (1/3)

= 1/3

The average weight is the sum of two third of the first number and one-third of the second number is -2/3 + 1/3 = -1/3 = -0.33.

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The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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The volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

Rectangular Prism:

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here.

The Volume of a Rectangular Prism Formula is,

The volume of a Rectangular Prism (V) = l × b × h

Where,

“b” is the base length of the rectangular prism

“l” is the base width of the rectangular prism

“h” is the height of the rectangular prism

The formula for the volume of a rectangular prism is length x width x height. So, the volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

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The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.

The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.

1. List the variables

b = cupcakes

c = brownies

4.50 = price of the cupcakes

1.75 = price of the brownies

50 = total money

2. Relate the variables

1.75b + 4.50c ≤50

Each product should be multiplied by its price

The total money can be equal to or less than 50 (≤)

The products should be added

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The age of my sister and her three children in 4 years will be 70 years

The age is added in 6 years to get 90 years> the addition is done as follows

Sister + 6 + Child1 + 6 + Child2 + 6 + Child3 + 6 + Child4 + 6 = 90 years

Sister + Child1 + Child2 + Child3 + Child4 + 6 + 6 + 6 + 6 + 6 = 90

Sister + Child1 + Child2 + Child3 + Child4 + 6 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 30

Sister + Child1 + Child2 + Child3 + Child4 = 60

In 4 years the age will be

Sister + Child1 + Child2 + Child3 + Child4 + 4 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 20

Sister + Child1 + Child2 + Child3 + Child4 = 70

in 4 years the ages will be 70 years

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Answer: the answer is negative  5

Step-by-step explanation:

Simplest radical form means the radical form of a number or algebraic expression in simplest terms.

The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2.

Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.

16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4.

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By using trigonometric relations, we can see that the angle x on the right triangle is:

x = 62.96°

On the image, we can see a right triangle, and we want to find the value of x, which is the measure of an angle on the right triangle.

On the given triangle we can see that the hypotenuse measures 77 units, and the adjacent cathetus to the angle has a measure of 35.

Then we can use the trigonometric relation:

cos(x) = (adjacent cathetus)/(hypotenuse)

Replacing the values that we know:

cos(x) = 35/77

Now we can apply the inverse cosine function in both sides:

Acos(cos(x)) = Acos(35/77)

x = Acos(35/77) = 62.96°

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The surface area of the hemispherical vessel is 715.92 square centimeter and the cost to paint is Rs. 3579.62.

An object's surface area is the total area that all of its surfaces occupy. Different 3D shapes in geometry have various surface areas. There are two groups for the surface area:

Surface area of the lateral Surface that is curved Surface area overall.

Given that the external diameter of the hemispherical vessel is 16cm, hence the radius is 8cm.

The internal diameter of the hemispherical vessel is 12cm, hence the radius is 6cm.

The total surface area of the vessel is given by the following formula:

[tex]SA= 2\pi R^2 + 2\pi r^2 + \pi (R^2 - r^2)\\\\SA= 2(3.14)(8)^2 + 2(3.14)(6)^2 + (3.14)(8^2 - 6^2)\\\\SA= 401.92 + 226.08 + 87.92\\\\SA= 715.92[/tex]

The total surface area of the vessel is 715.92 square centimeters.

The cost to paint 1 square centimeter is Rs. 5, hence the cost to paint 715.92 square centimeters is:

C = (715.92)(5)

C = 3579.6

Hence, the cost to paint 715.92 square centimeters is Rs. 3579.62.

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To use substitution to determine which value of x makes the inequality true, we need to have an inequality with x as one of the variables. Without more information on the inequality, it is not possible to determine which value of x makes the inequality true. The set {10, 18, 21} does not contain any variable x.

Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.

Step-by-step explanation: