A 10 ft. tree casts a 14 ft. shadow. If a building casts a 280 ft. shadow, how tall is the building?

What is polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..

This leads to a polynomial of ...

p(x) = (x - 5)(x - (4+i))(x - (4-i))

Now we can simplify...

(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17

Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...

p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85

So p(x) = x3 + 3x2 + 57x - 85

p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested

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Answer:

  x = 14

Step-by-step explanation:

You want the value of x in ∆OPQ, where ∠O = (2x − 5)°, ∠P = (3x − 8)°, and ∠Q = (10x – 17)º.

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...

  ∠O +∠P +∠Q = 180°

  (2x -5)° +(3x -8)° +(10x -17)° = 180° . . . . . use the given expressions

  15x -30 = 180 . . . . . . divide by °, collect terms

  x -2 = 12 . . . . . . . . . divide by 15

  x = 14 . . . . . . . . . . add 2

The value of x is 14.

__

Additional comment

The measures of the angles are ...

  O = 23°, P = 34°, Q = 123°

The roots of the Given quadratic equation are 0.57 and -2.9 solved using the algebraic method.

The given equation is a quadratic equation because the degree of the given equation is 2.

How can one tell whether or not a given equation is a quadratic equation?

A quadratic equation is a two-variable polynomial equation of degree two of the form [tex]f(x) = ax^2+bx+c = 0[/tex] with the variables a, b, and c being real numbers and a not equal to 0. With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x). The values of x that fulfil the quadratic equation are known as the roots.

The given equation is 3x²+7x - 5 =  0 a =3,b=7, c =-5

lets roots of the given equation is (α, β).

roots can be found using  Shreedhara Acharya's formula.

[tex](\alpha, \beta) = [-b \± \sqrt(b^2 - 4ac) ]/2a[/tex]

α = [-b + √(b^2 – 4ac)]/2a

β = [-b - √(b^2 – 4ac)]/2a

b^2 – 4ac = 49-4*3*(-5) = 49+60 = 109

α = (-7+[tex]\sqrt{109}[/tex])/2*3

α = (-7+10.44)/6

α = 0.57

β  = (-7 - 10.44)/6

β  = -2.9

So the roots of the Given quadratic equation are 0.57 and -2.9.

-- The given question is incomplete, the complete question is

"What will be the roots of the equation 3x^2+7x-5=0" --

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The mean deviation of the scores is 2 when the mean value is 15.

In the statistics, mean deviation indicates the average deviation relative to the mean value of a given statistical data. While calculating mean deviation mean value is subtracted from each data value. After that all these values are added and divided by the total amount of data.

We are given three score 12, 15 and 18

Number of scores, N = 3

mean of the scores = (12+15+18)/ 3

                                =15

Let, mean score is denoted by X

List of scores X1    12

                      X2   15

                      X3    18

Now, we calculate X1 -X= 12- 15 = -3

                             X2-X = 15-15 = 0

                           X3-X = 18- 15 = 3

Absolute value of X1-X = |X1-X| = |-3| = 3

Absolute value of X2-X =|X2-X|= |0| = 0

Absolute value of X3-X = |X3-X| = |3| = 3

Sum of absolute value= ∑|Xi-X| = 6

Hence, mean deviation = ∑|Xi-X|/N = 6/3

mean deviation =2

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The domain is {9, 8, -9, 3, 7}, the range is {-8,-9, 5, 8} and the relation is a function

From the question, we have the following parameters that can be used in our computation:

{(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }

The domain is the set of the x values

So, we have the following representation

x = {9, 8, -9, 3, 7}

Remove repeated entries

x = {9, 8, -9, 3, 7}

So, the domain is {9, 8, -9, 3, 7}

Similarly, we have

Range = {-8,-9, 5, 8}

Also, the relation is a function

This is because the no x value has several y values

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The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let [tex]Wi[/tex] and [tex]Li[/tex] denote whether the game '[tex]i[/tex]' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [[tex]W1W2[/tex]] + P [[tex]W1L2W3[/tex]] + P [[tex]L1W2W3[/tex]]

        = [tex]p(1-p)[/tex] + [tex]p3[/tex] + [tex]p(1-p){2}[/tex]

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

Answer:

  P(-0.2, 2.2)

Step-by-step explanation:

You want the coordinates of point P that divides AB into segments with the ratio AP/PB = 3/7. The end points are A(-2, 1) and B(4, 5).

The point that divides AB in the ratio m/n is ...

  P = (mB +nA)/(m+n)

  P = (3(4, 5) +7(-2, 1))/(3+7) = (12 -14, 15 +7)/10

  P = (-0.2, 2.2)

Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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The vertices of the image of quadrilateral ABCD, after a dilation with a scale factor of 3, are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.

The vertices of the quadrilateral ABCD in this problem are given as follows:

A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2).

The scale factor of the dilation is given as follows:

k = 3.

Then the coordinates of the image, given by the answer at the beginning of the answer, were obtained multiplying the coordinates of each of the vertices by 3.

The problem asks for the coordinates of the image of quadrilateral ABCD after the dilation with the given scale factor.

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The correct analysis would be 3 option

Describe statistics using an example.

A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.

The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.

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The simultaneous equations 2x + 3y = 8 and 4x + 6y = 7 supplied do not have a solution  

A collection of two or more equations, each of which contains two or more variables, each of whose values can simultaneously fulfil one or more of the equations in the collection, with the total number of variables in the collection being equal to or fewer than the total number of equations.

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously.

Here are a few examples of simultaneous equations:

2x + 4y = 14

4x − 4y = 4.

Given,

2x + 3y = 8 and 4x + 6y = 7

We get,

2x + 3y = 8 ….. (i)

4x + 6y = 7 ….. (ii)

Then we have Multiply (i) by 4

4x + 6y = 16..... (iii)

Therefore, LHS of (ii) and (iii) are same but RHS is different. As a result, the answer is false.

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Tim puts two pickles in each of the five lunch bags, leaving him with three pickles.

If Tim puts the same number of pickles in each of the lunch bags and as many as possible, only a maximum of two can be put in each of the bags:

Dividing 13 pickles by 5 lunch bags, the answer is 2 pickles with a reminder of 3 pickles

13 ÷ 5 = 13/5

Therefore, Tim puts two pickles in each of the five lunch bags and is left with three pickles.

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Answer:

B

Step-by-step explanation:

the order of a matrix are given as

m × n ( m is the number of rows and n the number of columns

matrix A is of order 2 × 3

matrix B is of order 3 × 2

for the matrices to be conformable for multiplication then

the number of columns in A is equal to the number of rows in B

This is the case here , then the order of the resulting product is

AB :  2 × 3 × 3 × 2 the outer values , that is 2 × 2

The expressions represent the length of side, HI are sqrt(161) and 15 sin(90°- 75°) . So, option (a) and (c) are right answers.

A geometry theorem : the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides ( i.e base and prependicular) .

Mathematically, (GH)² + (HI)² = (GI)²

We have , provide a triangle GHI , since measure of angle H is 90° so it is a right angled triangle.

We have to calculate the length of side HI , for this we can use either triangular formulae or Pythagoras theorem. Here, we are using Pythagoras theorem,

As we have, GH (prependicular) = 8 unit , GI (hypotenuse) = 15 unit , HI ( base) = ?

(prependicular)²+( base)² = (hypotenuse)²

=> (GH)² + (HI)² = (GI)²

=> (8)² + (HI)² = (15)²

=> (HI)² = (15)² - (8)²

=> (HI)² = 225 - 64 = 161

=> HI = sqrt(161) = 12.68

Using Trigonometric functions,

measure of angle G = 180° - 90° - 75° = 15°

In right triangle GHI, sin 15° = HI /15

=> HI = 15 sin 15° = 15 sin(90°- 75°)

So, the length of side HI is sqrt(161) or 15 sin 15° .

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Complete question:

Consider right triangle ∆GHI present above. Which expressions represent the length of side HI? Choose 2 answers:

a)15 sin(90° - 75°)

b)15 cos(90° - 75°)

c) sqrt(161)

d)tan(90° -

The numeric value of the expression c = 5a + 6b is given as follows:

c = 759.5.

The expression in this problem is defined as follows:

c = 5a + 6b.

To obtain the numeric value of the expression, the values of a and b have to be known, and they are discovered solving the system of equations presented as follows:

In standard format, the system is given as follows:

Multiplying the first equation by 6 and the second by -5, we have that:

Adding the two equations, we have that the variable b is given as follows:

-2b = -119

b = 119/2

b = 59.5.

Then the variable a is obtained as follows:

5a + 8 = 7(59.5) - 6

a = (7(59.5) - 6 - 8)/5

a = 80.5.

Thus the numeric value of the expression is given as follows:

c = 5(80.5) + 6(59.5)

c = 759.5.

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Answer:

11.2

Step-by-step explanation:

15x + 32 = 200       Subtract 32 from both sides

15x + 32 - 32 = 200 - 32

15x = 168  Divide both sides by 15

[tex]\frac{15x}{15}[/tex] = [tex]\frac{168}{15}[/tex]

x = 11.2

Answer:

i think the answer is x= 11.2

Step-by-step explanation:

15x= 200-32

15x=168

x=168/15

x=11.2

A closed under addition can be proved if the sum of any two members of the set also belongs to the set.

We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

For example,

A = {( x, y) , y = 0 }

B= { (x, y) , x+ y = 1 }

Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is  (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.

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The root of the quadratic equation x² + 5x = -6 are -2 and -3.

Given that,

The quadratic equation x² + 5x = -6 with the variable x.

We have to find what are the root of the quadratic equation.

We know that,

Take the quadratic equation x² + 5x = -6

x² + 5x = -6

x² + 5x +6=0

Now find the factors for 6

6=2×3

So,

2+3=5

We get

x² + 2x + 3x+6=0

Taking the common terms

x (x+2) + 3(x+2)=0

(x+2) (x+3)=0

Now

x+2=0

x=-2

And

x+3=0

x=-3

Therefore, The root of the quadratic equation x²+5x = -6 are -2 and -3.

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Answer:

A. It is a decrease in assets.

Step-by-step explanation:

The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits. The business increased its credit score since it paid the exact amount it got a loan for back to the Loan Company.

That money was the payable loan depicted in the Debit section.

Answer:

OptionA) Decrease in assets

Step-by-step explanation:

The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits.

The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

a piece of a geometric figure that has been removed by one or more points, lines, or planes is known as segment.

The formula that we used is:

[tex]P(x,y)=\frac{mx2+nx1}{m+n},\frac{my2+ny1}{m+n}[/tex]

x = m(x₂) + n(x₁)/(m + n)

⇒ 2 = m(-1) + n(3)/(m + n)

⇒ 2(m + n) = 3n - m

⇒ 2m + 2n = 3n - m

⇒ m/n = 3/2

Therefore, The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).

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Answer:

The level of irritation for both groups can be compared to see if the new cream had a significant effect.

Step-by-step explanation:

In this experiment, the purpose of having two groups is one being the control group, and one being the group being experimented on. The control group is needed in order to know for sure that it is the cream that is beneficial, instead of an outside factor such as the poison ivy being bad.

By comparing the level of irritation for both groups, it will become apparent if the new cream has a side effect.

Answer:

The level of irritation for both groups can be compared to see if the new cream had a significant effect.

Step-by-step explanation:

the phrasing is a bit strange.

but I think the first one means "overall" in the sense of outside and inside the 2 test groups.

the third one would object compare results only inside the group that got the active ingredient.

the 4th one is just nonsense.

so, only the second answer option makes sense. these 2 groups are created so that their results can be compared. that is the whole point.

Of the given options the one that is true is if two variables are very strongly associated then the correlation between them will be near 1.0 or -1.0. Hence, option A is correct.

Correlation of 1.0 indicates that the variables are directly related while a correlation of -1.0 indicates that the variables are inversely related.

The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It's a typical technique for explaining direct connections without explicitly stating cause and consequence.

However, we utilise correlation to indicate a link between two quantitative variables in statistical terms.

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To find the asymptotes and holes of a rational function, factor the denominator of the function and set it to zero. This will give you the x-values of the holes. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote.

To find the asymptotes and holes of a rational function, you must first factor the denominator of the function and set it to zero. This will give you the x-values of the holes, or the values where the function is undefined. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote. For example, if the numerator is a second degree polynomial and the denominator is a third degree polynomial, the asymptote will be a first degree polynomial. To find the equation of the asymptote, divide the numerator and denominator by the highest degree term of the denominator. The resulting quotient will be the equation of the asymptote. The asymptotes will be straight lines, so the equation will be in the form of y = mx + b. The holes will be the x-values of the points where the denominator equals zero. The asymptotes and holes will divide the graph of the rational function into distinct regions, and can be used to analyze the behavior of the function.

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We can construct a 30-degree angle by bisecting a 60-degree constructed angle.

By following the given steps we can create a 30-degree angle,

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The value of c square when the given equation y = 4x - 10 is written in standard form is equal to 100.

As given in the question,

Given equation is equal to :

y = 4x - 10

Standard form of the equation in the slope intercept form is written as:

y = mx + c

Here value of m represent slope is equal to 4

And value of c represents the y-intercept form is equal to -10.

Value of c square is given by :

c = -10

Squaring both the sides we get,

⇒c² = ( -10 )²

⇒c² = 100

Therefore, the value of c square in the given equation is equal to 100.

The given question is incomplete , the complete question is :

When the equation y = 4x - 10 is written in the standard form the value of C Square will be?

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The plums that remain with George after sharing 22 with Jude will be equal to 50.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data mentioned in the question,

We first need to determine how many plums Jude received. Decide to round everything to the sixteenth.

George is having 3/8 = 6/16

Terry is having 1/4 = 4/16

Samuel is having 3/16

So, remaining will go to Jude = (16 - (6 + 4 + 3))/16 = 3/16

Consequently, if Jude received 3/16 of the plums, and she received 36 plums, 1/16 of the total plums is,

= 36/3 = 12 plums (As a side note, there were 192 plums in total).

George has got 6/16 plums = 6 × 12 = 72

Then, he gave 22 plums to Jude, so he has left with,

72–22 = 50 left.

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The graph of which the function has an axis of symmetry at x = 3 is the graph of

The axis of symmetry of a quadratic function is the line that bisects the curve into two.

The formula for the axis of symmetry is of the form

x = -b / 2a

for the function y = x² - 6x - 1

b = -6

a = 1

the axis of symmetry, x = -(-6/(2 * 1))

= - (-3)

= 3

hence the axis of symmetry is x = 3

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Answer: 5

Step-by-step explanation: If n is the exponent and the base is 10, 6.72342 is to be multiplied by 10 power 5 to give the answer as 672342.

6.72342 * 10^5 = 6.72342 * 100000

                          = 672342

If at a local sandwich shop, 45% of customers preferred white bread over whole wheat bread. The  percentage of customers chose whole wheat bread with turkey is: D. 26%.

First step is to find the percentage of customers who preferred ham with whole wheat bread

Percentage = ( 1- .45)

Percentage = .55

Second step is to find the percentage of customers who preferred whole wheat bread

Percentage = (1- .52)

Percentage  = .48

Now let find the  percentage of customers chose whole wheat bread with turkey

Percentage = .48 × .55

Percentage = .26 ×100

Percentage =26%

Therefore the correct option is D.

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Formula for solving mean deviation is [tex]\frac{[\sum |X-\mu|]}{N}[/tex].

Mean Deviation Definition:

The mean deviation is defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set. The mean deviation of the data values can be easily calculated using the below procedure.

Step 1: Find the mean value for the given data values

Step 2: Now, subtract the mean value from each of the data values given (Note: Ignore the minus symbol)

Step 3: Now, find the mean of those values obtained in step 2.

Mean Deviation Formula

The formula to calculate the mean deviation for the given data set is given below.

Mean Deviation = [tex]\frac{[\sum |X-\mu|]}{N}[/tex]

Here,

Σ represents the addition of values

X represents each value in the data set

µ represents the mean of the data set

N represents the number of data values

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