Find the quotient and remainder using synthetic division for
1³ + 31² + 8x + 14
------------------------
x + 2
The quotient is
The remainder is​

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].

For part f:

Plug in the value of the limit, 2,

[tex](2)^{2} =4[/tex]

Thus we proved the limit.

For part g:

Plug in the value of the limit, -1,

[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]

Thus we proved the limit.

For part h:

Plug in the value of the limit, 1,

[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]

Thus we proved the limit.

The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f'(x) = x² - 2 - 3xcosx.

We know a function f(x) is decreasing if f'(x) is < 0.

Therefore,

x² - 2 - 3xcosx < 0.

x² - 3xcosx < 2.

x(x - 3cosx) < 2.

Now, 3cosx can be [- 3, 3].

x(x - 3) < 2 and x(x + 3) < 2.

x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.

x < 2 Or x < 5 and x < 2 or x < - 1.

But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).

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Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer:

3.8 ,6.16 , 9.24

Step-by-step explanation:

Answer:

60/s or s/60

Quotient means divide so you divide the following, s and 6 by each other.

Step-by-step explanation:

Hope it helps! =D

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Use similar triangles,

BAC and DAB are similar

therefore

CA/AB = BA/AD

CA/20 = 20/10

cross multiply

AC = CA = 20*20/10 = 40

Or use metric relations

CA*AD = BA^2

CA = BA^2/AD = 20^2/10 = 40

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

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The lines FE and GH are parallel to each orther.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Given that

ΔPEI = ΔGHI

here ∠pie = ∠gih

PI =HI

GI=EI

So both triangles are congruent

So the FE║GH.

Hence the lines FE and GH are parallel to each orther.

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Answer:

1 circle

Step-by-step explanation:

Angle bisectors will meet at one specific point. Radius taken from centre to one side of triangle is the radius of the incircle. There can be no other configuration to form an incircle so only one incircle can be inscribed in a triangle.

The cost of the shirts after the discount is $43.20.

A 5% tax adds an additional $2.16 so the total bill comes to  45.36.

Kayla does not have enough money to buy the three shirts.

The first step is to determine the total cost of the three shirts.

Total cost of the three shirts = cost of one shirt x total number of shirts

$18 x 3 = $54

Cost of the shirt after the sale = (1 - discount/100) x total cost of the shirt

(1 - 20/100) x $54

(1 - 0.2) x $54

= 0.8 x $54

= $43.20

Price after the tax : (1 + tax/100) x cost of the shirt after the discount

(1 + 5/100) x $43.20

(1 + 0.05) x $43.20

1.05 x $43.20 = 45.36

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Answer:

8 hours and 45 minutes.

Step-by-step explanation:

The rate of inflation of potatoes is 0.019.

The rate of inflation of Oranges is 0.019.

The rate of inflation of Ground beef is 0.019.

Inflation is an increase in the level of prices of the goods and services that households buy. It is measured as the rate of change of those prices.

Given:

Here, the annual rate of inflation r (in decimal form) is given by

r = [tex](p_2/ p_1)^{1/n[/tex] - 1

Now, The average price of a  potatoes increased from $0.620 in 2009 to $0.749 in 2019.

Thus, The required rate of inflation,

r = [tex](0.749/ 0.620)^{1/10[/tex] - 1

r = 1.019 - 1

r = 0.019

Now, The average price of a Oranges increased from $0.910 in 2009 to $1.280 in 2019.

Thus, The required rate of inflation,

r = [tex](1.280/ 0.910)^{1/10[/tex] - 1

r = 1.034 - 1

r = 0.034

Now, The average price of a Ground beef increased from $2.251 in 2009 to $3.375 in 2019.

Thus, The required rate of inflation,

r = [tex](3.775/ 2.251)^{1/10[/tex] - 1

r = 1.0321 - 1

r = 0.0321

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Answer:

5. 6 appointments are cancelled

6. 80  more spots

Step-by-step explanation:

5. Jasmine has 36/24 = 1.5 times as many appointments as cancellations each day.

Since 1.5 times 4 is 6, Jasmine has 6 cancellations each day.

6. Kendrick's kennel has 2 spots for cats for every 7 spots for dogs. If he has a total of 144 spots for both cats and dogs;

Spots for cats = 2x ;

So, spots for dogs will be = 7x ;

Total spots for cats and dogs will be = 2x + 7x = 144 ;

x = 144/9 = 16 ;

So, spots for cats = 2 * 16 = 32 ;

Spots for dogs = 7 * 16 = 112 ;

spots for dogs more than cats are = 112 - 32 = 80 .

Kendrick kennel has 80 more spots for dogs than cats.

Answer: 4/27 or 0.148148

First you solve for any grouping symbols ( absolute value, parentheses, brackets, etc.) Since there aren’t any you move on to exponents, 4^3 is the same as 4*4*4 which equals 64. Next you do multiplication 6*2 is 12 so our problem is currently

64-60 over 15+12. Next you simplify, which make the problem 4/27. You can divide which makes your problem 0.148148 but most of the times you keep it as a fraction.

=======================================================

Explanation:

I'm assuming your teacher meant to say "same number or letter" instead of "same number of letter" at the very end of the problem.

The best case scenario is that the person selecting the cards is very lucky to select say a king of hearts and king of clubs. This shows that 2 cards is the lowest amount of cards to select here.

----------

Of course, such a scenario is not that likely. That person is likely to get some other card compared to the 1st selection.

Let's assume the person selecting the cards has the worst luck possible. This means they select each card 1,2,3,...,10,J,Q,K exactly once in any order. If this happens, then the person does not have any pairs just yet. The person has selected 13 cards so far with this worst case scenario.

The 14th card is guaranteed to pair up with some other card previously chosen. There simply aren't any other options left once you've exhausted all possibilities. See the pigeonhole principle for more information.

So this is why you would need to select 14 cards to guarantee having at least two pair up together (i.e. you would have 2 or more pairs).

Answers:  

Explanation:

The angles TSO and QRP are marked with the same double angle arc markers. This signifies they are congruent or the same measure. For example, they both could be 30 degrees each.

The naming "angle TSO" is the same as saying "angle OST". The order of the letters does not matter as long as point S is in the middle. Similarly, saying "angle QRP" is the same as "angle PRQ".

Answer:

If the pharmaceutical sales representative meets her target for Medication A, she will receive 60% of the $20,800 bonus, or $12,480. When added to her base salary of $68,400, her total compensation for the year would be $80,880.

Step-by-step explanation:

Answer:

The total would be 99,620

Step-by-step explanation:

29400*0.80=23520

Add the amount to the base salary

76100+23520=99,620

Answer: To find out how much medication the patient receives each day, you need to determine the patient's weight in kilograms and then calculate the total dosage per day.

You can convert the patient's weight from pounds (lb) to kilograms (kg) by dividing the weight by 2.2.

So,

315/2.2 = 142.72 kg

Next, we can use this weight to determine the dosage per day:

3 mg/kg * 142.72 kg = 428.16 mg

Now, since the physician ordered twice a day, we will multiply the dosage per day with 2:

428.16 mg * 2 = 856.32 mg

So the patient receives 856.32 mg of medication each day.

Step-by-step explanation:

The constant cost call c is $0.7 and the cost of per minute call m is $0.93.

In algebra, a system of equations consists of two or more equations and looks for ways to solve them all together. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.

Let the constant cost be c and the per minute cost be denoted by m.

The equation for 5 minutes of the call is:

5.91 = 5m + c

c = 5.91 - 5m

The equation for 10 minutes of the call is:

10.06 = 10m + c

Substitute the value of c in the above equation:

10.06 = 10m + 5.91 - 5m

10.06 - 5.91 = 5m

4.69 = 5m

m = 0.93

Substitute the value of m:

10.06 = 10(0.93) + c

c= 0.7

Hence, the constant cost call c is $0.7 and the cost of per minute call m is $0.93.

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Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

the formula is written as x3 -10x = 100.

We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.

We've made multiple tries and have:

x = 5.4 (roughly) (approximately)

In x3 -10x = 100, replace x with 5.4.

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100

Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given  equation problem.

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Answer:

[tex]20\ln(5)-16\approx16.18876[/tex]

Step-by-step explanation:

[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]

The inequality that can be used to determine the inseam sizes that best fit a medium size bike is 25 < x < 28.32.

Solving the equation the original cost of the shoes before the discount will be obtained as $385.

To find the original cost of the shoes before the discount, you can use the following equation:

original cost = final cost÷ (1 - discount percentage)

In this case:

original cost = $135 ÷  (1 - 0.65)

To find the final cost you need to multiply 135 by 1 - 0.65.

0.65 is the equivalent to 65% when it's represented as a decimal.

0.65 represents the proportion of the original price that was removed (65% or 0.65)

So:

original cost = $135 ÷ (1 - 0.65)

original cost = $135 ÷ (1 - 0.65) = $135 ÷  0.35 = $385

The original cost of the shoes before the discount was $385.

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The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.

The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.

The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:

20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35

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Answer:

y = [tex]\frac{3}{4}[/tex]x + 3

Step-by-step explanation:

find the slope m

m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]

m = [tex]\frac{3 - 0}{0 - - 4}[/tex]

m = [tex]\frac{3}{4}[/tex]

y = mx + b

find b

insert y1 and x1 into the equation

0 = [tex]\frac{3}{4}[/tex](-4) + b

0 = -3 + b

b = 3

y = [tex]\frac{3}{4}[/tex]x + 3

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x [tex]\geq[/tex] 3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x [tex]\geq[/tex] 3/2 and it's output that is y exists between  (-∞ , 2).

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Answer:

------------------------------

Given equation:

Its solutions are:

The product of the solutions is -15:

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

Step-by-step explanation:

You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.

When the constant is zero, the equation becomes ...

  ax² +bx = 0

Factoring out x, we have a factored form as ...

  x(ax +b) = 0

showing that the equation can always be factored.