cting Polynomials: Practice
Question 1 of 5
Select the correct answer.
Let p(x) be a polynomial as shown below, and let b be an integer.
p(=) = a₁ + a₁ + a₂=² + ... + an In
Which of the following is true regarding the sum and difference of p(x) and b?
O
The sum-and difference of p(x) and b are integers.
The sum and difference of p(x) and b are polynomials.
The sum of p(x) and b is a polynomial, and the difference is an integer.
The sum of plx) and b is an integer, and the difference is a polynomial.
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Answer:

the mean and the median of the set of scores are the same.

Step-by-step explanation:

median = 89

mean = 96+77+86+97+89 = 445 / 5

= 89

mode = none

The mean and the median of the set of scores are the same.

Introduction to Mean, Median, and Mode: In statistics, we frequently choose a representative value to roughly characterise the entire collection of data. The name "measure of central tendency" denotes that this representative value is one around which the data is centred. The mean, median, and mode are these central tendencies. The most typical way to measure central tendency is with the mean. In actuality, it represents the mean of the specified set of data. Both continuous and discrete data can be used with it. In most cases, the median shows the midpoint of the given set of data when it is arranged in a specific order.

Mean: - Average value

Median: - Middle term (after arranging in either accending or descending order)

Mean = 445/5 = 89

Median = Middle term = 3rd term = 89

Mean and median are equal.

Hence, option D is correct

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[tex]m = \frac{ - u}{v} = \frac{ - 9}{3} = - 3 [/tex]

[tex]km = - 1 \\ k = - \frac{1}{m} = \frac{ - 1}{-3}=1/3 [/tex]

The slope of the perpendicular line will be 1/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

9x + 3y = 36

3y = 36 - 9x

y = 12 - 3x

The slope of the given equation is - 3.

Let m be the slope of the perpendicular line. Then the slope of the perpendicular line will be 1/3.

m (-3) = -1

Simplify the equation, then we have

m (-3) = -1

3m = 1

m = 1/3

The slope of the perpendicular line will be 1/3.

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Answer:

Length = 120 ft

Total cost = 1500$

Step-by-step explanation:

First, to find the length of the backyard we reverse the formula (A = l * w) and divide 10,800 by 90.

10,800 ft^2 / 90 ft = 120 ft.

we can check this by plugging the length of 120 ft into the formula:

120 ft * 90 ft = 10,800 ft^2.

Next, to find the cost of the single length of fence we multiply our length (120 ft) by the cost ($12.50):

120 * 12.50 = $1500

Recall the Pythagorean identity,

[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]

Since [tex]\theta[/tex] belongs to Q3, we know both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are negative. Then

[tex]\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}[/tex]

Recall the half-angle identities for sine and cosine,

[tex]\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2[/tex]

[tex]\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2[/tex]

Then by definition of tangent,

[tex]\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}[/tex]

[tex]\theta[/tex] belonging to Q3 means [tex]180^\circ < \theta < 270^\circ[/tex], or [tex]90^\circ < \theta < 135^\circ[/tex], so that the half-angle belongs to Q2. Then [tex]\sin\left(\frac\theta2\right)[/tex] is positive and [tex]\cos\left(\frac\theta2\right)[/tex] is negative, so [tex]\tan\left(\frac\theta2\right)[/tex] is negative.

It follows that

[tex]\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}[/tex]

Answer:

Step-by-step explanation:

hello :

f(x) = a(x+h)²+k

(h;k) the vertex    so : h=3   and k= 5

now calculate  a   given f(0) = 12

means : a(0+3)²+5 = 12

9a=7   so : a=7/9

the equation is : y= (7/9)(x+3)²+5

Answer:

T [1;11].

Step-by-step explanation:

x-coordinate of the point T is:

x(T)=2*x(W)-x(S); ⇒ x(T)=2*(-3)+7=1;

y-coordinate of the point T is:

y(T)=2*y(W)-y(S); ⇒ y(T)=2*1+9=11.

Finally, T(1;11).

We currently have two fractions: y / 1 and (y - 3) / 3.

In both cases, we are only concerned with the denominator. Yes, the numerator will change when we change the denominator, but that will not affect the answer to this question.

As such, we need to find the least common multiple of 1 and 3. That is 3. Therefore, the common denominator is 3.

Hope this helps!

Answer:

8.2

Step-by-step explanation:

We can find the unit rate of this problem by dividing 18.68 by 24 to get .82. .82*10 is equal to 8.2.

Answer:

34.2°

Step-by-step explanation:

sinB/b = sinA/a

sinB/7 = sin(40°)/8

sinB = 7sin(40°)/8

B=arcsin(7sin(40°))/8

So, to the nearest tenth, B is 34.2°.

Answer:

3

Step-by-step explanation:

AD/AB = AE/AC

8/10 = 12/AC

AC = 12(10/8) = 15

EC = 15 - 12 = 3

he difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be –3x² + 7x – 18. Then the correct option is D.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The expressions are given below.

(2x² + 6x – 11) and (5x² – x + 5)

Then the difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be

⇒ (2x² + 6x – 11) - (5x² – x + 5)

⇒2x² + 6x – 11 – 5x² + x – 5

⇒ –3x² + 7x – 18

Then the correct option is D.

The complete expression is given below.

(2x² + 6x – 11) and (5x² – x + 5)

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The length of the rectangle that makes the area to be 273 square feet is 21 feet.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the length of the rectangle, hence:

Length * width = area

13 * x = 273

x = 21 feet

The length of the rectangle that makes the area to be 273 square feet is 21 feet.

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Substituting into vertex form, we can write the equation of the parabola as

[tex]y=a(x-0)^{2}+9\\\\y=ax^{2}+9[/tex]

To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).

[tex]0=a(3)^{2}+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}[/tex]

The statement which best explains whether the student is correct is: D. the student is completely incorrect because there is "no solution" to this inequality.

An inequality refers to a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Since |x-9| is greater than or equal (≥) to zero (0), we can logically infer that this student is completely incorrect because there is "no solution" to this inequality.

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Complete Question:

A student found the solution below for the given inequality.

|x-9|<-4

x-9>4 and x-9<-4

x>13 and x<5

Which of the following explains whether the student is correct?

A. The student is completely correct because the student correctly wrote and solved the compound inequality.

B. The student is partially correct because only one part of the compound inequality is written correctly.

C. The student is partially correct because the student should have written the statements using “or” instead of “and.”

D. The student is completely incorrect because there is “ no solution “ to this inequality.

Answer:

[tex]dy \ = \ 0.1[/tex]

Step-by-step explanation:

Considering the Leibniz notation to represent the derivative of [tex]y[/tex] with respect to [tex]x[/tex], suppose [tex]y \ = \ f\left(x\right)[/tex] is a differentiable function, let [tex]dx[/tex] be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable [tex]dy[/tex] as

                                                  [tex]dy \ = \ f'\left(x\right) \ dx[/tex],

where [tex]dy[/tex] is the function of both [tex]x[/tex] and [tex]dx[/tex]. Hence, the terms [tex]dy[/tex] and [tex]dx[/tex] are known as differentials

Dividing both sides of the equation by [tex]dy[/tex], yield the familiar expression

                                                         [tex]\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)[/tex].

Given that [tex]f\left(x\right) \ = \ x[/tex] and [tex]dx \ = \ 64.1 \ - \ 64 \ = \ 0.1[/tex], hence

                                                 [tex]f'\left(x\right) \ = \ 1[/tex].

Subsequently,

                                               [tex]dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1[/tex].

The 5 number summary are

Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19

The complete question is in the attached image

The 5 number summary of box plot are:

Each of these summaries are represented by the vertical lines of the box plot

From the attached box plot, we have:

Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19

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To solve this problem, just use multiplication.

[tex]7\text{ pairs of pants}*3\text{ shirts}*5\text{ ties}*6\text{ jackets}=\large\boxed{630\text{ outfits}}[/tex]

You can somewhat think of this situation as a sort of tree. You start with 7 large branches representing the pants, then for every one of those you have 3 medium-sized branches to represent the pairs of pants. Each one of those has 5 sticks for the ties, which in turn each have 6 leaves to represent the jackets and therefore a complete outfit. The solution is found by getting the total number of leaves on the tree.

Answer: ( C ) the average would approach a set value.

The translation of the question is:

The solar park is a concentrated zone of development of solar power generation projects and provides developers an area that is well characterized, with proper infrastructure and access to amenities and where the risk of the projects can be minimized.

How many solar parks are there in China?

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The surface area of the given triangular prism is 960 yd²

From the question, we are to calculate the surface area of the given figure

The given figure is a triangular prism

Surface area of the triangular prism =

[tex](26 \times 12 )+ 2(\frac{1}{2} \times 10\times 24) + (24 \times 12) + (12 \times 10)[/tex]

= 312 + 240 + 288 + 120

= 960 yd²

Hence, the surface area of the given triangular prism is 960 yd²

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Step-by-step explanation:

So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get

Opportunity Loans:

 [tex]A = 1600(1+\frac{0.0345}{12})^{(12)(1)}[/tex]

 [tex]A = 1600(1.002875)^{12}[/tex]

 [tex]A \approx 1600(1.035)[/tex]

 [tex]A = \$1,656.08[/tex]

  Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount

 [tex]Interest=1656.08-1600\\Interest=56.08[/tex]

General Loans:

 [tex]A = 1600(1+\frac{0.042}{4})^{(4)(1)}[/tex]

 [tex]A = 1600(1.0105)^4[/tex]

 [tex]A \approx 1600(1.042)[/tex]

 [tex]A = 1,668.27[/tex]

 To find the interest we do the same thing we did in the previous problem

 [tex]interest = 1668.27-1600\\interest=68.27[/tex]

Opportunity loans has the least amount of interest after a year

Step-by-step explanation:

1A

the travel paths of the plane build a right-angled triangle.

one travels north, which creates the vertical leg.

the other travels west, which creates the horizontal leg.

their distance is the Hypotenuse (the baseline opposite of the 90° angle), which we can get via Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

how long are the legs ?

the plane going north travels at 240 km/h for 90 minutes.

the plane going west travels at 180 lm/h for 90 minutes.

90 minutes = 1.5 hours (1 hour 30 minutes).

so,

plane 1 went 240×1.5 = 360 km.

plane 2 went 180×1.5 = 270 km.

distance² = 360² + 270² = 129600 + 72900 = 202500

distance = sqrt(202500) = 450 km

2A

again Pythagoras :

130² = 80² + (2nd leg)²

16900 = 6400 + (2nd leg)²

10500 = (2nd leg)²

2nd leg = 102.4695077... m

so, the full perimeter is

130 + 80 + 102.4695077... = 312.4695077... m

312.4695077... = 100%

1% = 100%/100 = 3.124695077... m

how many % are 220 m ? well as many as how often 1% fits into 220 m :

220 / 3.124695077... = 70.40686998... %

3A

again Pythagoras :

the legs of that inner right-angled triangle are (as you correctly wrote) 40 m and 45 m.

the fence is the Hypotenuse, and we get

fence² = 40² + 45² = 1600 + 2025 = 3625

fence = 60.20797289... m ≈ 60 m

please burn that into your brain forever for any right-angled triangle situations :

a² + b² = c²

Pythagoras

Answer:

The set notation for the diagram is P-Q

Answer:

The diagonal length of the desk is 7.42462120246 inches.

Step-by-step explanation:

Since it is a square then all sides are equal which means we can easily formulate the pythagorean theorem on the diagonal length of the desk.

a^2 + b^2 = c^2

A and B are the same (width and length) since it is a square.

5.25^2 + 5.25^2 = c^2

27.5625 + 27.5625 = c^2

55.125 = c^2

Put c^2 under a square root (apply to both sides)

square root of 55.125 = 7.42462120246 = c

Answer:

(m+n) [x-y]

Step-by-step explanation:

(m+n) (2x-y)-x(m+n)

We can factor out (m+n)

(m+n) [(2x-y)-x]

Combine like terms

(m+n) [2x-x-y]

(m+n) [x-y]

Answer:

one sixth plus 4 sixths

Step-by-step explanation:

from one sixth you have to add 4/6 to get to 5 sixths(5/6)

Answer:

1/2 = c*8 or c*8=1/2

Step-by-step explanation:

It says 1/2 is equal to which means 1/2 is on the side for one of the equations. It doesn't really matter. It says is equal to a number, c and eight. Its implying that you multiply c and 8 together because if it meant for another number to be multiplied then a third symbol would be in the operation.

Answer:

x = 47°

y = 27°

Explanation:

The angles lie on parallel lines which sum ups to 180 degrees.

2x + 1 + 85 = 180

2x = 180 - 86

2x = 94

x = 47

2y + 126 = 180

2y = 180 - 126

2y = 54

y = 27

Answer:

[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]

Step-by-step solution:

[tex]0=x^4-4x^2-5[/tex]   [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex]  [tex]u=-1[/tex]
[tex]x^2 =5[/tex]    [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex]   [tex]x = +-i[/tex]