Tom paid $245.97 for a laptop. This was 3/5 of the original price. What was the original price?

1. Factor x^3 + 9x^2 + 6x - 16 using Polynomial Division

(x^2 + 10x + 16)(x -1)

2. Factor x^2 + 10x + 16

(x + 2)(x + 8)(x - 1)

Answer: x - 1

Answer:

x - 1

Step-by-step explanation:

width = volume / height * length

= x^3 + 9x^2 + 6x - 16 / (x + 2)(x + 8)

Since the volume ends in -16  and  last term of denominator

= +2 * + 8 = +16  the least term of the width will be - 1.

Also x^3 / x^2 = x

so the answer is (x - 1)

Answer: So, the probability will be

[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]

Step-by-step explanation:

Since we have given that

Number of blue balls =30

Number of red balls = 40

Number of white balls = 30

Since there are 100 balls in total ,

As we have given that there is no white ball chosen.

So, only 70 balls are left with us , from which we choose a blue ball

So, the probability will be

[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]

The conditional probability of picking a blue ball given that a white ball was not picked is 0.43. This is calculated by dividing the number of blue balls by the total remaining balls after excluding the white balls.

To solve this question, we need to understand the concept of conditional probability. Given that we have 30 blue balls, 40 red balls, and 30 white balls, we have a total of 100 balls in the bag. The problem states that a white ball was not chosen. From that, we have eliminated the 30 white balls from the total, leaving us with 70 balls (30 blue and 40 red).

In the case of the conditional probability of choosing a blue ball, given that a white ball was not chosen, we are just focused on the remaining 70 balls. So, the probability is calculated by dividing the number of blue balls by the total remaining balls. Hence, the conditional probability is 30/70 = 0.43 (approximately).

https://brainly.com/question/32171649

#SPJ3

The answer is C: Associative Property of Addition.

Hope this helps! :)

The total number of people that all the cars can hold is greater than 480 and less than 500 people.

A:  According to the given situation, where both the number of trolley cars and the number of people in each car must have two digits and be less than 30.

Hence, the possible number of trolley cars in the park = 22 and a possible number of people in each car= 22

B: explain how you found your answer.

Lets suppose the number of cars be =c and the number of persons be= p

As the number of cars and number of person are same, so c=p

so, [tex]c\times c[/tex] should lie the given range of 480 to 500.

Now, the nearest perfect square that lies between 480 and 500 is 484.

The square root of 484 is 22. So, the number of cars and people are 22.

C: This is the only hit and trial method for solving this question.

y < -3x - 2

y = -3x - 2

for x = 0 → y = -3(0) - 2 = 0 - 2 = -2 → (0, -2)

for x = -2 → y = -3(-2) - 2 = 6 - 2 = 4 → (-2, 4)

y > -3x + 8

y = -3x + 8

for x = 0 → y = -3(0) + 8 = 0 + 8 = 8 → (0, 8)

for x = 2 → y = -3(2) + 8 = -6 + 8 = 2 → (2, 2)

Answer:

The system of inequalities  y < –3x – 2 y > –3x + 8 doesn't have any solution because their regions are non intersecting.

explanation:

Here given equations are y < –3x – 2 , y > –3x + 8

[tex]$$\begin{aligned}&y < -3 x-2 \\&y=-3 x-2\end{aligned}$[/tex]

For [tex]$x=0 \Rightarrow y=-3(0)-2=0-2=-2 \Rightarrow(0,-2)$[/tex]

For [tex]$x=-2 \Rightarrow y=-3(-2)-2=6-2=4 \Rightarrow(-2,4)$[/tex]

[tex]$$\begin{aligned}&y > -3 x+8 \\&y=-3 x+8\end{aligned}$[/tex]

For [tex]$x=0 \Rightarrow y=-3(0)+8=0+8=8 \rightarrow(0,8)$[/tex]

For [tex]$x=2 \Rightarrow y=-3(2)+8=-6+8=2 \rightarrow(2,2)$[/tex]

Therefore by analyses of graph we can say  that the system of inequalities  y < –3x – 2 ,  y > –3x + 8 doesn't have any solution because their regions are non intersecting.

Learn  more about the Graphical representation here-

https://brainly.com/question/1288364

#SPJ2

C = 14π cm ( in terms of π )

the circumference (C) of a circle is calculated using the formula

C = πd ( where d is the diameter )

C = 14π cm ≈ 3.14 × 14 - 43.96 cm

[tex]-10 < -2x+4\leq8\ \ \ \ |-4\\\\-14 < -2x\leq4\ \ \ \ |\text{change the signs}\\\\14 > 2x\geq-4\ \ \ \ |:2\\\\\boxed{7 > x\geq-2}\to\boxed{-2\leq x < 7}[/tex]

A table represents a function if each input in the table is paired with exactly one unique output. To affirm if a table represents a function, one would have to ensure there are no repeated inputs with different corresponding outputs. Without the actual data, we cannot conclusively decide whether a given table is a function.

To determine if a table represents a function, we must assess if each input (domain element) corresponds to exactly one output (range element). A function is a set of ordered pairs where no two distinct pairs have the same first element. If a table has rows where the first entry (the input or 'x' value) repeats with different second entries (outputs or 'y' values), it does not represent a function since it fails to assign a single unique value to that input.

For a geometric representation, if a graph passes the vertical line test, it is a function. This means that a vertical line drawn through any point on the graph only crosses it once. If the acceleration, velocity, or any other variable changes over time and can be represented in a table with unique outputs for every time instant, that table exemplifies a function of time.

Without specific table data, we cannot definitively answer whether the provided table represents a function. If a table shows a unique output for each input without repetition, then it indeed represents a functional relationship.

Answer:

Step-by-step explanation:

[tex]\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\\\\leg=a=3b\\leg=b\\hypotenuse=2\sqrt{10}\\\\\text{Substitute}\\\\(3b)^2+b^2=(2\sqrt{10})\qquad\text{use}\ (ab)^n=a^nb^n\\\\3^2b^2+b^2=2^2(\sqrt{10})^2\qquad\text{use}\ (\sqrt{a})^2=a\ \text{for}\ a\geq0\\\\9b^2+b^2=4(10)\qquad\text{combine like terms}\\\\10b^2=40\qquad\text{divide both sides by 10}\\\\b^2=4\to b=\sqrt4\\\\b=2[/tex]

1 [tex]\frac{1}{2}[/tex] dozen

1 dozen = 12

to convert to dozen, divide 18 by 12

[tex]\frac{18}{12}[/tex] = [tex]\frac{3}{2}[/tex] = 1 [tex]\frac{1}{2}[/tex] dozen

Sarah bought 1.5 dozen of eggs as 1 dozen of eggs has 12 eggs as defined "Twelve objects, twelve shapes, or twelve numbers make up a dozen. Doz or dz are used to shorten it. One of the oldest common units of measurement is the dozen".

Comparing a physical quantity to a known standard quantity of the same kind is the process of measurement. For instance, measuring length with Vernier Calipers and determining wire diameter with a screw gauge.

One of the most basic and straightforward traditional units of measurement is the dozen. The 12-base number system is referred to as duodecimal or dozenal. A dozen is a collection of precisely twelve figures, shapes, or things. You can spell it out as doz or dz. So, a dozen is equal to twelve. The counting of the finger bones with the thumb is thought to have marked the beginning of the dozen. It has to do with nature. Twelve moon cycles or zodiac signs, 12 months, and two cycles of 12 hours each make up a day. These days, many household items and other items are sold by the dozen.

12 eggs=1 dozen

18 eggs=

=18*1/12

=18/12

=3/2

=1.5 dozen.

Given that a dozen of eggs has 12 eggs by definition, Sarah purchased 1.5 dozen eggs. "A dozen is made up of twelve things, twelve shapes, or twelve numbers. It can be abbreviated with doz or dz. The dozen is one of the earliest common units of measurement ".

To know more about measurement,

https://brainly.com/question/2384956?referrer=searchResults

#SPJ9

Answer:

 Length of one side of Keisha's kitchen = 15 feet.

Explanation:

  Let the side of square be a. The area of a rectangle is breadth x width. Here breadth = width = side of square

 Area of square = a x a = [tex]a^2[/tex]

It is given that area of Keisha's kitchen is known, so she can find side of the square by finding square root of the area.

So we have area = 225 feet squared = [tex]a^2[/tex]

So length of one side of Keisha's kitchen = [tex]\sqrt{225} =15[/tex]feet

The length of one side of Keisha's kitchen is 15 feet, as the area of a square is found by squaring the side length and the square root of 225 is 15.

Keisha's kitchen is shaped like a square, which means all four sides of the kitchen are of equal length. Given that the area of the kitchen is 225 square feet, we need to find the length of one side. The formula below is used to find the area of a square:

So, let’s set up the equation:

Or in mathematical terms:

To find the side length, we need to take the square root of 225:

Knowing that [tex]\sqrt{225}[/tex] = 15, we have:

Therefore, each side of Keisha's kitchen is 15 feet long.

For this case we have the following expression:

[tex]k (x) = x (x + 2) ^ 3 (x + 4) ^ 2 (x-5) ^ 4\\[/tex]

The roots are:

[tex]x = -2\\\\x = -4\\\\x = 5\\\\x = 0\\[/tex]

For example: For x = 0 we have

[tex]k (0) = 0 (0 + 2) ^ 3 (0 + 4) ^ 2 (0-5) ^ 4\\\\k (0) = 0 (2) ^ 3 (4) ^ 2 (-5) ^ 4\\\\k (0) = 0 (8) (16) (625)\\\\k (0) = 0\\[/tex]

so it is shown that [tex]x = 0[/tex] is a root.

By definition, multiplicity represents the number of times a root is repeated in a polynomial, in turn it is given by the degree of the term that contains the root.

Thus:

The multiplicity of 0 is 1

The multiplicity of -2 is 3

The multiplicity of -4 is 2

The multiplicity of 5 is 4

Answer:

The multiplicity of 0 is 1

The multiplicity of -2 is 3

The multiplicity of -4 is 2

The multiplicity of 5 is 4

GGGGGGGGGGGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOTTTTTTTTTTTTTTTTTTTAAAAAAAAAAAAAAAAAAA snatch a lil bit of points rq

Answer:

Correct choice is D

Step-by-step explanation:

Consider regular 60 sided polygon (regular means all sides are of equal length). Connect the center of this polygon with each polygon's vertex. You get 60 equal isosceles triangles with base that is polygon's side. The measure of the angle opposite to the base is

[tex]\dfrac{360^{\circ}}{60}=6^{\circ}.[/tex]

Rotating the polygon by 6° over the center, each such triangle will map onto the previous triangle. Thus, the least angle by which a regular 60-gon can be rotated so that it maps onto itself is 6°.

Formula: P(A or B)=P(A)+P(B)-P(A or B)  

p(c)=7/18

p(s)=6/18

p(c or s)=2/18

0.39+0.33-0.11=

answer:0.61

Formula: P(A or B)=P(A)+P(B)-P(A or B)  

p(c)=7/18

p(s)=6/18

p(c or s)=2/18

0.39+0.33-0.11=

answer:0.61

Answer: AA'+BB'+CC'+DD'+EE'=31.5 inches.

Step-by-step explanation:

As we know a translation is a transformation that maintain distance.

therefore ,if line segment YZ was used to translate ABCDE then

⇒ YZ=AA'=BB'=CC'=DD'=EE'=6.3 inches

Thus AA'+BB'+CC'+DD'+EE' =5 times YZ=5×6.3=31.5 inches.

Translation is a function that moves an object for a particular distance such that every point of the object must be moved in the same direction and for the same distance.

Answer,

1) -2

2) 3/b (Reciprical means flipping the fraction)

3) -5 for number (Question 11)

4) Number 12 I couldn't tell if the sign was a dividing sign or a plus sign.

5) I'm not very good with word problems so, I won't be much help. But, I think they want you to subtract the highest temperature from the lowest.

Answer:

The right graph is A.

Step-by-step explanation:

When x=0, -5y=15, y=-3

That means (0,3) is on that line.

When y=0, 4x=15, x=15/4

That means (15/4,0) is on that line too.

Based on the two points, the graph is A.

Answer:

ans is A

Step-by-step explanation:

heres another way to solve this

convert the eqn to standard form:

4x-5y = 15

15+5y = 4x

5y = 4x - 15

y = 4x/5 - 3

with y=mx+C, where m is slope and C is y-intercept

slope is 4/5 positive and y-intercept is -3

the ans is a

Answer:

2.897

Step-by-step explanation:

Let us find the mean and variance for the sample first.

105 104 110 112

114 106 108 109

Mean = sum/8 = 108.5

Variance = 12

Std dev = sq rt of variance = 3.464

Std error = std dev/ sq rt n

since n =8, we get std error = 1.225

Since sample size is small, df =8-1 =7

For 95% confidence intervals, t critical value for two tailed=2.365

Margin of error = std error x t critical = 1.225(2.365)

=2.897

Final answer:

To estimate the cost of 7.8 pounds of potatoes at a price of $3.25 per pound, multiply the price by the number of pounds, resulting in a total estimated cost of $25.35.

Explanation:

We need to estimate the cost for 7.8 pounds of potatoes given that potatoes cost $3.25 per pound. To do this, we multiply the price per pound by the number of pounds:

Cost = Price per pound × Number of pounds

Cost = $3.25 × 7.8 pounds

After performing the multiplication, we find that:

Cost = $25.35

Therefore, the estimated cost for 7.8 pounds of potatoes at a price of $3.25 per pound is $25.35.

Let [tex] x,y [/tex] be the lengths of the original legs. The original area is thus

[tex] \dfrac{xy}{2} [/tex]

Now, we triple the legs, so we have [tex] (x,y)\mapsto(3x,3y) [/tex]

The new area is

[tex] \dfrac{(3x)(3y)}{2} = \dfrac{9xy}{2} = 9\dfrac{xy}{2} [/tex]

which is 9 times the original area.

So, if you triple both legs, the area will be nine times as much as the original one.

Answer:

[tex]36.1[/tex] square feet of floor was carpeted.

Step-by-step explanation:

Number of Square feet = Length of the room * Width of the room

Now we have to substitute the values to the above equation,

Number of square feet = [tex]20\frac{1}{2} *15\frac{3}{5}[/tex]

                                      =[tex]\frac{41}{2} +\frac{78}{5}[/tex]

                                      =[tex]\frac{205+156}{10}[/tex]

                                      =[tex]\frac{361}{10}[/tex]

                                      =[tex]36.1[/tex] feet

[tex]x^3+8y^6\\\\=x^3+2^3y^{2\cdot3}\\\\=x^3+2^3(y^2)^3\qquad|\text{used}\ (a^n)^m=a^{nm}\\\\=x^3+(2y^2)^3\qquad|\text{used}\ (ab)^n=a^nb^n\\\\=(x+2y^2)(x^2-x\cdot2y^2+(2y^2)^2)\qquad|\text{used}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(x+2y^2)(x^2-2xy^2+2^2(y^2)^2)\\\\=(x+2y^2)(x^2-2xy^2+4y^4)[/tex]

Answer:

K12 Here 100% verified

Step-by-step explanation:

Answer: YES!

Step-by-step explanation:

Assuming ABCD is a parallelogram, the opposite sides are parallel

AB║DC     and       AD║ BC

Lines a and d, and b and c are not parallel in a quadrilateral with given angles A = 2x, B = 90, C = x, and D = 3x degrees. None of the pairs of opposite sides show consecutive interior angles summing to 180 degrees, which would be required if they were parallel.

When determining if lines a and d, and b and c are parallel in a figure where the angles have been given as A = 2x degrees, B = 90 degrees, C = x degrees, and D = 3x degrees, we must use the properties of angles and parallel lines to justify the answer.

First, let's establish the relationship between the angles. Since B is a right angle, we know that the figure at least has one right angle. The sum of the angles in any quadrilateral is 360 degrees. Therefore, we can set up the equation 2x + 90 + x + 3x = 360 to find the value of x.

Combining like terms gives us 6x + 90 = 360. Subtracting 90 from both sides gives us 6x = 270. Dividing both sides by 6 gives us x = 45 degrees.

The value of A is 2x, which means A = 90 degrees. The value of C is x, which means C = 45 degrees. The value of D is 3x, which is 135 degrees. Since A + D = 90 + 135 = 225 degrees, which is not equal to 180 degrees, lines a and d are not parallel. Similarly, since the value of B is 90 degrees, and C is 45 degrees, B + C = 90 + 45 = 135 degrees, which is also not equal to 180 degrees and hence lines b and c are not parallel.

According to the consecutive interior angles formed by a transversal cutting across parallel lines, these angles should add up to 180 degrees if the lines are parallel. Since our calculations show that A + D and B + C do not add up to 180 degrees, we have sufficient proof that lines a and d and lines b and c are not parallel.

Use the order of operations (PEMDAS):

Parentheses, Exponents, Multiplication & Division, and then Addition & Subtraction

************************

1) (8 - 2) + 18 x 6

Parentheses (8 - 2)          

6 + 18 x 6    

Multiplication (18 x 6)

6 + 108

Addition (6 + 108)

114

**************************

2) (15 + 29 - 4) x 4

Parentheses (15 + 29 - 4)  

40 x 4

Multiplication (40 x 4)

160  

******************************

3) (13 + 5) x (13 - 5)

Parentheses (13 + 5) and (13 - 5)

18 x 8

Multiplication (18 x 8)

144

*********************************

Answers: 114, 160, 144

The correct answer is x=-3.

Given equation:

[tex]\frac{4}{3}x-7 = -11[/tex]  ----- (A)

To solve the above equation, follow these steps:

Step-1:

Add 7 on both sides of equation (A):

(A)=> [tex]\frac{4}{3}x -7 + 7 = -11 + 7 \\ \frac{4}{3}x = -4[/tex]

Step-2:

Multiple 3 on both sides, you will get:

[tex]\frac{4}{3}x * 3 = -4 * 3 \\ 4x = -12 \\ x = -3[/tex]

Hence the correct answer is x=-3.

Answer:

The value of x is -3.

Step-by-step explanation:

Given equation:

4/3 x-7=-11

By adding 7 to both sides of equation:

= 4/3x - 7 + 7 = -11 + 7

= 4/3x = -4

By multiplying 3 on both sides

= 4/3x × 3 = -4 × 3

= 4x = -12

By dividing 4 on both sides of equation:

= 4x/4 = -12/4

= x = -3

Hence by solving equation, the value of x out to be -3.