What is the quotient (x3 – 3x2 + 5x – 3) ÷ (x – 1)?















What is the quotient (x3 + 3x2 + 5x + 3) ÷ (x + 1)?

Answer:

x ≥ -3

Step-by-step explanation:

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -4x - 12  =   -4 • (x + 3)

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  -4

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2      Subtract  3  from both sides

           x ≥ -3

Inequality Plot :

2.3      Inequality plot for

        -4.000 X  - 12.000  ≥  0

Answer:

5 ≤x

Step-by-step explanation:

3x + 9 ≤7x -11

Subtract 3x from each side

3x-3x + 9 ≤7x-3x -11

9 ≤4x -11

Add 11 to each side

9+11  ≤4x -11+11

20 ≤4x

Divide each side by 4

20/4 ≤4x /4

5 ≤x

The area of w is 289 pi m². Find the circumference of w A. c=17 pi m B. c= 34 pi m C. c=68 pi m D. c=289 pi m

Answer: 34 pi

Step-by-step explanation:

1/tan^2(x)=cot^2(x)

csc^2(x)-1=cot^2(x)"trigonometric identity"

o see what is going on, we simply draw a triangle. Since the tower is 125 feet high, but the guy wire is 20 feet from the top, the triangle is 125 - 20 = 105 feet high, then 80 feet long.

Using the pythagorean theorem, 105^2 + 80^2 = g^2

g^2 = 11025 + 6400 = 17425

g = sqrt(17425)

g = 132.0038 feet = 132 feet

Hope this helps!

The length of the guy wire is 132 ft, determined by using the Pythagorean theorem with the given vertical and horizontal distances.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore, the length of the guy wire is 132 ft.

Complete question:

The top of an antenna tower is 125 ft. above level ground. The tower is to be guyed 20 ft. from its top to a point on the ground 80 ft. from the base of the tower· What is the length of the guy wire?

Explanation:

One formula for the area of a triangle is ...

Area = (1/2)ab·sin(C)

This presumes you know the measures of two sides and the angle between them. The Law of Sines is typically used where you know all the angles and only one side measure.

You would use the law of sines to find an additional side measure, then make use of the above formula for area.

To find the area of a triangle using the Law of Sines, you need to determine the lengths of two sides and the measure of the angle opposite one of those sides. Plug those values into the Law of Sines formula and solve for the missing side or angle.

The area of a triangle can be found using the Law of Sines by following these steps:

Final answer:

The probability that Mark spends a night at Rutgers University, the University of Miami, and Clemson University is 1/720, or approximately 0.00139.

Explanation:

To find the probability that Mark spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University, we assume that these choices are made without replacement from the 10 colleges he is considering. As he can only spend the night at 3 of them, his first choice has a 1 in 10 chance of being Rutgers University, his second choice a 1 in 9 chance of being the University of Miami, given that his first choice was Rutgers, and his third choice a 1 in 8 chance of being Clemson University, given that his first two choices were Rutgers and the University of Miami.

The overall probability is the product of these independent probabilities:

Probability = (1/10) × (1/9) × (1/8) = 1/720

Therefore, the probability is 1/720, or about 0.00139 when rounded to five decimal places.

Answer: D.

Step-by-step explanation: Your Answer Is D. This Does Not Represent A Function.

A table that does not represent a function include the following; D. table D.

In Euclidean Geometry, a function refers to a mathematical expression which is used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set P) to an output variable (Set Q).

In this context, we can logically deduce that table D does not represent a function because the same input value is mapped to different output values;

0 ↔ -1

0 ↔ 4

0 ↔ 6

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The opposites of the numbers 5, -2.5, 1.15, and 915 are -5, 2.5, -1.15 and -915 respectively. The opposite of a number is its value, but it is in the opposite direction on a number line.

The opposite of a number is the value that is exactly as far from 0, but in the opposite direction on a number line. Thus, the opposite of a positive number is the same number, but negative. Similarly, the opposite of a negative number is the same number, but positive. So the opposites of the given numbers 5, -2.5, 1.15, and 915 would be -5, 2.5, -1.15, and -915 respectively.

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ANSWER

96 yd

EXPLANATION

Let the width of the rectangle be w, then, the length of the rectangle will be:

[tex]l = 5w[/tex]

The area of a rectangle is calculated using the formula:

[tex]Area=l \times w[/tex]

[tex]Area=5w \times w[/tex]

[tex]Area=5 {w}^{2} [/tex]

It was given that, the area of the rectangle is 320yd²

[tex]320=5 {w}^{2} [/tex]

Divide both sides by 5.

[tex]64 = {w}^{2} [/tex]

Take square root of both sides to get:

[tex]w = 8yd[/tex]

This means the length is

[tex]l = 5 \times 8 = 40yd[/tex]

The perimeter of a rectangle is given by:

P=2(w+l)

We plug in the values to get:

[tex]P=2(40 + 8) = 2 \times 48 = 96yd[/tex]

The perimeter is 96yd

Well... for starters:

[tex]

\frac{5}{2}=5\times\frac{1}{2} \\

\frac{5}{2}=\frac{5}{1}\times\frac{1}{2}

[/tex]

And the rule is [tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]

Therefore:

[tex]\frac{5}{2}=\frac{5\times1}{1\times2}\Longrightarrow\boxed{\frac{5}{2}=\frac{5}{2}}[/tex]

Answer:

$126

Step-by-step explanation:

First, use the general percent equation (y is x% of z, y being your part percentage, x being your percent, and z being your whole base).

y = 40% x 90 --> .4 x 90 = 36

y = 36

Now, simply add the part percentage (36) to the original whole base.

90 + 36 = 126

The markup price of the model is equal to $126.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a toy store's per cent of markup is 40%. A model train costs the store $90.

First, use the general per cent equation (y is x% of z, y being your part percentage, x being your per cent, and z being your whole base).

y = 40% x 90 --> .4 x 90 = 36

y = 36

Now, simply add the part percentage (36) to the original whole base.

90 + 36 = 126

The markup price of the model is $126.

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Answer:

WR = 26

Step-by-step explanation:

Givens

UT = 10

VS = 18

WR = ??

Formula

(WR + UT) / 2 = VS

Solution

Substitute

(WR + 10) /2 = 18

Multiply both sides by 2

(WR + 10/2 * 2 = 18 * 2

Do the multiplication

WR + 10 = 36  

Subtract  10 from both sides

WR + 10 - 10 = 36 - 10

WR = 26

Answer:

D. 914 feet

Step-by-step explanation:

We are given the distance that a person can see on a clear day from the upper observation platform of the Eiffel tower in Paris. We are then required to estimate the height of the upper observation platform using the formula;

[tex]d=\frac{5}{6}\sqrt{h}[/tex]

Where d is the distance and h the height of the upper observation platform. The first step would be to solve for h, that is make h the subject of the formula in the above equation;

We multiply both sides of the equation by the reciprocal of 5/6 which is 6/5;

[tex]\sqrt{h}=\frac{6}{5}d[/tex]

The next step is to eliminate the square root on the Left Hand Side of the equation by squaring both sides;

[tex]h=1.44d^{2}[/tex]

Given d is 25.2, h becomes;

[tex]h=1.44*25.2^{2}\\h=914.4576[/tex]

To the nearest whole number, h becomes 914

The correct option is D. The height of the upper observation platform is approximately 914 feet

To estimate the height  h  in feet of the upper observation platform using the given formula  [tex]d = \frac{5}{6} \sqrt{h}[/tex] , follow these steps:

1. Given:

d = 25.2 miles

We need to solve for  h .

2. Substitute the given  d  into the formula:

[tex]25.2 = \frac{5}{6} \sqrt{h}[/tex]

3. Isolate [tex]\sqrt{h}[/tex]:

Multiply both sides by [tex]\frac{6}{5}[/tex] to get rid of the fraction:

[tex]25.2 \times \frac{6}{5} = \sqrt{h}[/tex]

4. Calculate the left side:

[tex]25.2 \times \frac{6}{5} = 25.2 \times 1.2 = 30.24[/tex]

So,

[tex]\sqrt{h} = 30.24[/tex]

5. Square both sides to solve for  h :

[tex](\sqrt{h})^2 = 30.24^2 \\\\h = 30.24^2[/tex]

6. Calculate  30.24^2 :

[tex]30.24 \times 30.24 = 914.0576[/tex]

7. Round to the nearest whole number:

[tex]h \approx 914 \text{ feet}[/tex]

Therefore, the height of the upper observation platform is approximately 914 feet, which matches option D.

Answer: D. 914 feet

Answer:

V = 3408 pi  unit^3

Step-by-step explanation:

Volume  of a cone is given by

V = 1/3 pi r^2 h

We know the radius is 12 and the height is 71

V = 1/3 * pi * (12)^2 *71

V = 1/3 * pi * 144 *71

V = 3408 pi  unit^3

Answer:

[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]

Step-by-step explanation:

Given that radius of the cone is r = 12 units

Given that height of the cone is h = 71 units

Now question says to find the volume of the given cone.

So plug these values into formula of volume of the cone.

[tex]Volume=\frac{1}{3}\pi r^2h[/tex]

[tex]Volume=\frac{1}{3}\pi (12)^2(71)[/tex]

[tex]Volume=\frac{1}{3}\pi (144)(71)[/tex]

[tex]Volume=\frac{1}{3}\pi (10224)[/tex]

[tex]Volume=\frac{10224 \pi}{3}[/tex]

[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]

Hence correct choice is D.

Answer:

12, 13, 4

Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE

6, 4, 11

LONGEST SIDE GREATER THAN OR EQUAL TO THE SUM OF THE OTHER TWO SIDES - NO TRIANGLE.

7, 6, 5

Sum of the squares of the smaller 2 sides > longest side squared - ACUTE SCALENE TRIANGLE

3, 14.5, 17

Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE

Step-by-step explanation:

Final answer:

To determine if a set of three lengths can be the side lengths of a triangle, we need to apply the triangle inequality theorem.

Explanation:

In order for a set of three lengths to be the side lengths of a triangle, they must satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This can be represented as:

a + b > c

a + c > b

b + c > a

For example, if the given lengths are 3, 4, and 7, we can check if they satisfy the inequality:

3 + 4 > 7

3 + 7 > 4

4 + 7 > 3

Since all of these inequalities are true, the lengths 3, 4, and 7 can indeed be the side lengths of a triangle.

Bar graphs are easy to understand, widely used, and can show changes over time. That gives them an advantage over other graphs that are difficult to read or can only show a single data set.

They use vertical or horizontal bars to represent data along both an x-axis and a y-axis visually. Each bar represents one value, so it'll be an advantage for Peter because he can add as many colours he wants and the graph would still be easy to read. When the bars are stacked next to one another, the viewer can compare the different bars, or values, at a glance.

Answer:

option A

2/4 = 0.5

Step-by-step explanation:

Given in the questions that,

number of student in chess club = 4

P(B) = 4/10

number of student in karate club = 6

P(A) = 6/10

number of students who are both in chess and karate club = 2

P(A∩B) = 2/10

total number of students 10

Formula to use

Answer:

P(A/B) = P(A∩B) / P(B)

          = 2/10 / 4/10

          = 2/4

          = 1/2

          = 0.50

Step-by-step explanation:

Answer:

Option A. is even so both ends of the graph go in the same direction.

Step-by-step explanation:

Graphing the function give we can recognize the factor is even, but at the same time both the ends go in the same direction.

Answer:

Subtraction Property on Equality.

Step-by-step explanation:

2. 15x + 6 = -24

15x + 6 - 6 =  -24-6

15x = -30

Subtraction Property on Equality.

-11a^2+1ab+4b^2; P-Q would mean you rearrange the equation to where (-4a^2-2ab+9b^2)-(7a^2-3ab+5b^2). Don't forget to distribute the negative for Q since you plugged it into a variable.

-4a^2-2ab+9b^2-7a^2+3ab-5b^2

Add/Subtract like terms

-11a^2+1ab+4b^2

Answer:

yes these functions are inverse

Step-by-step explanation:

so heisjsksbKjsbkaosbdjskms

Answer:

The probability that exactly one switch is good is

[tex]P(x) =0.0392[/tex]

Step-by-step explanation:

The probability that a switch is defective is:

[tex]P(D) = \frac{2}{100} =0.02[/tex]

The probability that a switch is not defective is

[tex]P(D') = 1-P(D)=0.98[/tex]

Therefore, if two switches are selected, the probability that exactly 1 is good is:

[tex]P(1=1)=P (D) P (D ') + P (D') P (D)[/tex]

[tex]P(x)=(0.02)(0.98) + (0.98)(0.02)[/tex]

[tex]P(x) =0.0392[/tex]

Answer:

P (exactly one good switch) = 0.0392

Step-by-step explanation:

We know that 2% of all switches are defective.

P (defective) = [tex]\frac{2}{100} =0.02[/tex]

So P (not defective) = 1 - P (defective) = [tex]1-0.02=0.98[/tex]

Now we have to find the probability of one good switch out of 2 that are used in a device.

P (exactly one good switch) = [tex] (0.02 \times 0.95) + (0.02 \times 0.95) [/tex] = 0.0392

roughly 1.5

since it says the limit as x approaches 2- it means that you are going from the left (from the negative ie 2-). If it said 2+ you would go from the right. So you should start on the left at the end of that line and follow it until it gets essentially at where 2 is. Then record that value which in this case about 1.5

The limit of the function as x approaches 2 is 3.

In mathematics, a limit is a value that a function 'approaches' as the input (or variable) 'approaches' some value. To find the limit using the given graph, we need to examine the behavior of the function as it approaches a particular value. In this case, we look for the value the function approaches as x approaches a specific number.

From the graph, we can see that as x approaches 2 from the left side, the y-values approach 3. Similarly, as x approaches 2 from the right side, the y-values also approach 3.

Therefore, the limit of the function as x approaches 2 is 3.

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Answer: Option A.

Step-by-step explanation:

You need to use this formula for calculate the surface area of the right cylinder:

[tex]SA=2\pi r^2+2\pi rh[/tex]

Where "r" is the radius and "h" is the height.

You can identify in the figure that:

[tex]r=8units\\h=3units[/tex]

Knowing this, you can substitute these values into the formula [tex]SA=2\pi r^2+2\pi rh[/tex], therefore you get that the surface area of this right cylinder is:

[tex]SA=2\pi (8units)^2+2\pi (8units)(3units)[/tex]

[tex]SA=176\pi\ units^2[/tex]

Answer:

Step-by-step explanation:

The last three situations involve "descriptive statistics," which could mean measures of central tendency and measures of the spread of data.  The first one does not, since no exploratory work has yet been done.  

It's important that you look up terms such as this one and be able to come up with examples on your own.

ANSWER

[tex]g(x) = - 3x[/tex]

EXPLANATION

The given function is

f(x)=x

If this function is vertically stretched by a factor of 3 and flipped over the x-axis then the new function is

[tex]g(x) = - 3x[/tex]

The negative sign means there is a reflection in the x-axis.

The correct choice is A.

Answer:

  B.  1/392 cubic yard

Step-by-step explanation:

The volume is the product of base area and height:

  V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³

Answer:

B. 1/392 cubic yard

Step-by-step explanation:

Given,

The base area of the pillar, B = [tex]\frac{1}{28}[/tex] square yard ,

Its height, h = [tex]\frac{1}{14}[/tex] yd

Thus, the volume of the pillar would be,

[tex]V=B\times h[/tex]

[tex]=\frac{1}{28}\times \frac{1}{14}[/tex]

[tex]=\frac{1}{28\times 14}[/tex]

[tex]=\frac{1}{392}\text{ square yard}[/tex]

Since, the concrete he needs to cast the pillar = Volume of the pillar

= [tex]\frac{1}{392}\text{ square yard}[/tex]

Option 'B' is correct.

Answer:

See below in bold.

Step-by-step explanation:

Area of a circle with radius 2 cm = πr^2 =  π * 2^2 = 4π cm^2.

Area of a circle with radius  4 cm = πr^2 =  π * 4^2  = 16π cm^2.

Answer:

x^2 + y^2 = 8^2

Step-by-step explanation:

The general equation in standard form here is x^2 + y^2 = r^2.

Replace r with 8, obtaining:

x^2 + y^2 = 8^2

The standard form equation of a circle with a radius of 8 and centered at the origin is x² + y² = 64.

The equation for a circle centered at the origin with a given radius can be written in standard form. For a circle with a radius of 8, which is centered at the origin, the standard form equation is x² + y² = 64. This equation is derived from the general formula for a circle's equation in standard form, which is (x - h)² + (em)(y - k)² = R², where (h, k) is the center of the circle and R is the radius. Since the center is at the origin, h and k both equal zero.

Answer:

[tex]g(x)=8(2^x)[/tex]

Step-by-step explanation:

Here we are given with parent function [tex]f(x)=2^x[/tex] and the graph which shows that the function g(x).

We are asked to guess the function g(x).

We are given the two coordinates on g(x)

(0,8) and (2,32)

Hence for x = 0 , g(x)= 8

And for x=2, g(x)= 32

Let us say that the translated function is represented by

[tex]g(x)=a2^x+b[/tex]

[tex]g(0)=a\times 2^0+b[/tex]

Hence

[tex]a \times 2^0+b=8[/tex]

[tex]a +b=8[/tex] --------------- (i)

also

[tex]g(2)=32[/tex]

Hence

[tex]a\times 2^2+b=32[/tex]

[tex]4a+b=32[/tex] -------------------(ii)

Subtracting (i) from (ii) we get

[tex]3a=34[/tex]

Hence a = 8

Now putting this value of a in (i)

[tex]8+b=8[/tex]

B=0

Hence [tex]g(x)=8 \times 2^x +0[/tex]

[tex]g(x)=8(2^x)[/tex]