The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length c width, what is the length of the rectangle?

Answer:

rational number

Step-by-step explanation:

written as a fraction p/q, where p and q are integers and q is not equal to zero, is called as rational numbers. Example - 4/5, 2, 100, 1/7 etc all are rational numbers.

ANSWER

[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]

EXPLANATION

The given equation is:

[tex] {x}^{ - 2} + 4 {x}^{ - 1} + 3 = 0[/tex]

Recall that:

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

[tex] \frac{1}{ {x}^{2} } + \frac{4}{x} + 3 = 0[/tex]

Or

[tex] {( \frac{1}{x} )}^{2} + 4( \frac{1}{x} ) + 3 = 0[/tex]

Let

[tex]u = \frac{1}{x} [/tex]

Our equation then becomes:

[tex] {u}^{2} + 4u + 3 = 0[/tex]

The factors of 3 that add up to 4 are:

[tex] {u}^{2} + 3u + u + 3[/tex]

[tex]u(u + 3) + 1(u + 3) = 0[/tex]

[tex](u + 1)(u + 3) = 0[/tex]

[tex]u + 1 = 0 \: or \: u + 3 = 0[/tex]

[tex]u = - 1 \: or \: u = - 3[/tex]

This implies that:

[tex] \frac{1}{x} = - 1 \: or \: \frac{1}{x} = - 3[/tex]

[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]

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Answer:

[tex]t=280\ minutes[/tex]

Step-by-step explanation:

Let's call "v" the speed of the commercial airplane and call "t" at the travel time of the commercial plane

The distance in kilometers of the trip is: 1730 km

Then we know that:

[tex]vt=1730[/tex]

Then for the jet we have that the speed is:

[tex]2v[/tex]

The flight time for the jet is:

[tex]t-140[/tex]

Therefore:

[tex](2v)(t-140) = 1730[/tex]

Substituting the first equation in the second we have to:

[tex](2*\frac{1730}{t})(t-140) = 1730[/tex]

[tex](\frac{3460}{t})(t-140) = 1730[/tex]

[tex]3460-\frac{484400}{t} = 1730[/tex]

Now solve for t

[tex]\frac{484400}{t} = 3460 - 1730[/tex]

[tex]\frac{484400}{t} =1730[/tex]

[tex]\frac{t}{484400} =\frac{1}{1730}[/tex]

[tex]t=\frac{484400}{1730}[/tex]

[tex]t=280\ minutes[/tex]

Answer:

Range = (-∞, 5)

Step-by-step explanation:

This is the absolute value function with transformation.

The parent function is f(x) = |x|

This function has a "negative" in front, so it makes it reflect about x axis

The -4 after x makes horizontal translation of 4 units right

the +5 at the end makes the function translate 5 units UP

The graph is shown in the attached picture.

Looking at the graph, we can clearly see the range. The range is the allowed y-values. Hence, we can see that the range is  -infinity to 5

answer is not properly given, so i can't choose from the options, but the answer is -∞, 5 to 5

Final answer:

To determine if one triangle is a dilation of another, ratios of corresponding sides must be compared and set up as proportions to see if they are equivalent. When the proportions are equivalent, it indicates a consistent scale factor, confirming a dilation.

Explanation:

To determine if one triangle is a dilation of the other, we compare the ratios of corresponding sides from each triangle. A dilation occurs when all sides of one triangle are in proportion with the sides of a second triangle by the same scale factor. For example, if one triangle has sides of length 3, 4, and 5, and the second triangle has sides of length 6, 8, and 10, then the ratios of the corresponding sides (3/6, 4/8, 5/10) all simplify to 1/2, indicating that the second triangle is a dilation of the first.

To use ratios to determine if one triangle is a dilation of another, you need to set up proportions. For instance, we can express the ratios of corresponding lengths as fractions, and then set each of these ratios equal to the unit scale to form proportions. If the lengths of the triangles are given as 1 inch to 50 inches and 0.5 inches to 5 inches, we can set up the proportion 1/50 = 0.5/5 to show that they are equivalent.

In problems like this, proper notation and maintaining consistency across corresponding dimensions (e.g., width to width and length to length) is essential for accurate comparison.

[tex]g(x)=\sqrt x-5\\h(x)=-2x^2+3[/tex]

Step-by-step answer:

The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n.  Pascal's triangle will start with (1,1)  = coefficients of (p,q)^n =1.  For n=2, we add successive terms of the previous value of n.  Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:

(1,1)

(1,2,1)

(1,3,3,1)

(1,4,6,4,1)

(1,5,10,10,5,1)

meaning for n=5, the binomial expansion for (P+Q)^5 is

P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5

Setting P=2x, Q=y in the term 10P^3Q^2, we get a term

10(2x)^3(y)^2

=10(8x^3)(y^2)

=80x^3y^2

So the required coefficient is K=80.

We can also find the coefficient 10 by binomial expansion of

n=5, x=3 in

C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10

Then again substituting 10(2x)^3(y)^2 = 80x^3y^2

to get the coefficient K=80.

Answer: 80

Step-by-step explanation: cuz

There is no picture of the parallelogram needed to answer this question.

Answer:

Mean: 4.44 add up every number and divide it by how many there is.

Median: 3 put from least to greatest and count till the middle.

Mode: 3 because it appears the most

Answer:

A. Mean = $41900

B. Median = $37000

C. Mode = $37000

Step-by-step explanation:

A. Mean

Here

n=40

Mean = Sum of values/n

[tex]Mean = \frac{(3)(18000)+(3)(22000)+(3)(25000)+(5)(34000)+(17)(37000)+(2)(45000)+52000+(5)(80000)+140000}{40}\\=\frac{54000+66000+75000+170000+629000+90000+52000+400000+140000}{40} \\=\frac{1676000}{40}\\=41900[/tex]

Mean = $41900

B. Median:

As the number of salaries is even,

the median will be mean of middle two terms

[tex]Median= \frac{1}{2}(\frac{n}{2}th\ term+ \frac{n+2}{2}th\ term)\\=  \frac{1}{2}(\frac{40}{2}th\ term+ \frac{40+2}{2}th\ term)\\=\frac{1}{2} (20th + 21st)}\\[/tex]

The 20th and 21st term will be 37000

So their mean will be same

So,

Median = $37000

C. Mode

Mode is the value which occurs most of the time in data.

the occurrence of 37000 is highest in the given data.

So,

Mode = $37000 ..

Step-by-step explanation:

hi I have answered ur question

Answers:

1. 75/w=5/6

5*w=75*6

5w=450

Divide by 5 for 5w and 450

5w/5=450/5

w=90

2. 1/5=11/p

1*p=5*11

p=55

3. 9/z=3/13

3z=13*9

3z=117

Divide by 3 for 3z and 117

3z/3=117/3

z=39

4. 210=15m

Divide by 15 for 210 and 15m

210/15=15/15m

m=14

5. 22n=11*19

22n=209

22/22n=209/22

n=9.5

6. 9p=180

9p/9=180/9

p=20

7. 100=5x

100/5=5x/5

x=20

8. 4*x=3*24

4x=72

x=18

9. 10*y=14*7

10y=68

10y/10=68/10

y= 68/10

10. 16x=8*15

16x=120

16x/16=120/16

x=7.5

Final answer:

The five number summary for the ages of best actress Oscar winners is composed of the minimum (21), first quartile (Q1 - 30), median (Q2 - 33), third quartile (Q3 - 41), and maximum (81) values.

Explanation:

The first step to finding the five number summary is to identify the minimum, first quartile (Q1), median (second quartile Q2), third quartile (Q3), and the maximum from the sorted dataset of best actress Oscar winners.

Minimum: The smallest number in the dataset is 21.

Q1: The first quartile is the median of the first half of the data. Since we have an odd number of data points (91), we split the data into two parts of 45 values each. The first quartile is the median of the first 45 ages, which is the 23rd data point in the sorted list when counting from the smallest age. In our case, Q1 is 30.

Median (Q2): The median is the middle value, which is the 46th data point for our 91 data points. The median is also the age of 33.

Q3: The third quartile is the median of the second half of the data. The third quartile is the 68th data point, which is the age of 41.

Maximum: The largest age in the dataset is 81.

Therefore, the five number summary of the ages of best actress Oscar winners is 21, 30, 33, 41, and 81.

Answer:

D

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 2, 4 ]

From the table

f(b) = f(4) = 16

f(a) = f(2) = 4, hence

average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6

The average rate of change for a function is calculated using the change in y-values divided by the change in x-values.

The average rate of change for a function is the change in the y-values (output) divided by the change in the x-values (input) over a given interval. To calculate the average rate of change for the function from x = 2 to x = 4, we need to find the change in y-values and the change in x-values for this interval.

Let's assume the function is f(x). We can calculate the average rate of change using the formula:

Average Rate of Change = (f(4) - f(2)) / (4 - 2)

Replace f(4) and f(2) with the corresponding y-values for x = 4 and x = 2, respectively, to get the final result.

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Answer:

48+14i

Step-by-step explanation:

So squaring (i+7) looks like this

(i+7)^2

(i+7)(i+7)

Use foil.

First: i(i)=i^2=-1

Outer: i(7)=7i

Inner: 7(i)=7i

Last: 7(7)=49

____________Add the terms.

48+14i

After solving the expression, the result of squaring value of a will be equal to 14i + 48.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data provided by the question,

i² = -1

a = (i + 7)

Squaring the value of a,

a = (i + 7)(i + 7)

a = i² + 7i + 7i +49

a = -1 + 14i + 49

a = 14i +48

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Answer:

No.

Step-by-step explanation:

Direction variation is of the form y = kx.

This is not direct variation.

The equation 3y = 5x + 4 does not represent a direct variation because it includes a constant term '+4'. A direct variation would only have the form y = kx without any added or subtracted constants.

The equation 3y=5x+4 represents a direct variation, and if so, to find the constant of variation. A direct variation is when one variable is a constant multiple of another, expressed in the form y = kx, where k is the constant of variation. In this case, the equation 3y = 5x + 4 is not a direct variation because of the additional constant term '+4'. For it to be a direct variation, y must be alone on one side of the equation, and there should be no constant term added or subtracted with the term that is a multiple of x.

To be a direct variation, the equation needs to have the form y = kx. In the practice equation y + 7 = 3x, if we solve for y, we get y = 3x - 7 which still would not be a direct variation because of the -7. The other example equation 4y = 8 is not in the form of direct variation either since it has no variable x in it; it represents a horizontal line where y is a constant.

Answer:

12

Step-by-step explanation:

Consider the list of multiples

multiples of 4 are 4, 8, 12, 16, 20, ....

multiples of 6 are 6, 12, 18, 24, ....

The least common multiple is 12

Answer:

The surface area of the pyramid is 0.6625 inches²

Step-by-step explanation:

* Lets explain how to find the surface area of the square pyramid

- The square pyramid has 5 faces

- A square base

- Four triangular faces

- Its surface area is the sum of the areas of the five faces

- Area of the square = L × L , where L is the length of its sides

- Area of the triangle = 1/2 × b × h , where b is the length of its base

 and h is the length of its height

∵ The length of the side of the square is 0.25 inches

∴ Area of the base = 0.25 × 0.25 = 0.0625 inches²

∵ The length of the base of the triangle is 0.25 inches and the length

  of its height is 1.2 inches

∴ The area of its triangular face = 1/2 × 0.25 × 1.2 = 0.15 inches²

∵ The surface area of the pyramid = the sum of the areas of the 5 faces

∵ The area of the four triangular faces are equal

∴ The surface area = 0.0625 + (4 × 0.15) = 0.0625 + 0.6

∴ The surface area = 0.6625 inches²

* The surface area of the pyramid is 0.6625 inches²

Answer:

rotated

Step-by-step explanation:

The triangle MNO has already been dilated and therefore, the answers were left to 3: rotated, reflected and translated. Triangle YHQ is not an image of triangle MNO. Thus, leaving only 2 choices: rotated and translated. If triangle MNO was translated, triangle YHQ was supposed to be in the same position as triangle MNO is and leaving only 1 option which is rotated.

Answer:

rotated

Step-by-step explanation:

the correct answer is rotated

when triangle Δ M N O was dilated to create Triangle Δ Y H Q

we can clearly see that the length of the sides of the triangle is increased and from the figure we can clearly see that the largest side is rotated.

marked angle is also rotated.

so, we can clearly say that to make  Triangle Δ Y H Q triangle Δ M N O is dilated and rotated.

Answer:

x=4/7

Step-by-step explanation:

6 - 2/3(x+5) = 4x

First I want to clear the fraction so I will multiply everything by 3

3*6 -3* 2/3(x+5) = 3*4x

18 - 2(x+5) =12x

Distribute

18 - 2x-10 =12x

Combine like terms

8 -2x = 12x

Add 2x to each side

8 -2x+2x =12x+2x

8 = 14x

Divide each side by 14

8/14 =14x/14

8/14=x

Divide top and bottom by 2

4/7=x

Answer:

c

Step-by-step explanation:

You can find that 22-6=38-22=54-38=70-54=16

so the answer is c 16

Answer:  The correct opion is

(C) 16.

Step-by-step explanation:  Given that the values in the following table represent a linear function.

x:       1,     2,    3,     4,    5

y:       6,    22,  38,  54,  70.  

We are to find the common difference of the associated arithmetic sequence.

If y = f(x) is the given function, then we see that

f(1) = 6,  f(2) = 22,  f(3) = 38,  f(4) = 54 and f(5) = 70.

So, the common difference of the associated arithmetic sequence is given by

[tex]f(2)-f(1)=22-6=16,\\\\f(3)-f(2)=38-22=16,\\\\f(4)-f(3)=54-38=16,\\\\f(5)-f(4)=70-54=16,~~~\cdots.[/tex]

Thus, the required common difference of the associated arithmetic sequence is 16.

Option (C) is CORRECT.

Answer:

D

Step-by-step explanation:

To find the critical values , that is the zeros

Solve the quadratic

x² - x - 20 = 0 ← in standard form

Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)

The factors are - 5 and + 4, since

- 5 × 4 = - 20 and - 5 + 4 = - 1, hence

(x - 5)(x + 4) = 0

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 4 = 0 ⇒ x = - 4

Thus the critical values are - 4, 5 → D

Answer:

D. -4, 5

Step-by-step explanation:

x² - x - 20 factorised = (x - 5) (x + 4)

In order to get the answers, you have to make each bracket equal zero.

(x - 5) = x = 5

(x + 4) = x = -4

The crucial numbers are -4 and 5.

Hope this helps!

Answer:

Step-by-step explanation:

The number of grains of wheat on the n(th) square is 2^(n-1), or 2 to  

the power of n-1.  This is because the first square has 2^0 = 1 grain,  

the second has 2^1 = 2, and the n(th) square has twice as many as the  

previous. Thus the total number of grains of wheat is

    S = 1 + 2 + 4 + 8 + ... + 2^63.

Since this is a geometric sequence with common ratio 2, the sum is

        2^64 - 1

    S = -------- = 2^64 - 1 = 18446744073709551615.

          2 - 1

Answer:

D is 36080

Step-by-step explanation:

D is the largest since A is 3.608, B is 360.8, C is 36.08

When dividing, the smaller decimal points will be larger, but if you multiple, the numbers shrink.

Answer:

1) 55 degrees

2) 90 degrees

3) 105 degrees

Step-by-step explanation:

All triangles equal to 180 degrees. So to find the missing angle measure you have to subtract the two given measures by 180.

First triangle:

180 - 50 - 75 = 55 degrees

Second triangle:

180 - 60 - 30 = 90 degrees

Third triangle:

180 - 45 - 30 = 105 degrees

Answer: The radius is the distance between the center and the circumference of a circle and is half of the diameter of the circle .

Hopefully, this helps!

A line segment that joins the center of a circle to any point on the circle is called the radius of the circle. Whichever point on the circle we choose, the distance to the center of the circle will always be the same.

Answer:

14

Step-by-step explanation:

Assuming the die is 6 sided, there are only 6 possible rolls she can get. And assuming that this is a perfect world where probability is perfect, she will roll each number 14 times, because 84/6 is 14.

Final answer:

Kayla can expect to roll a number 3 approximately 14 times out of 84 rolls of a fair six-sided die, since each roll has a 1 in 6 chance of landing on any given number.

Explanation:

When Kayla rolls a die 84 times, she can expect to roll a 3 in a proportion equal to the probability of rolling a 3 on a single die. A fair six-sided die has a 1 in 6 chance of landing on any given number, including the number 3. Since each roll of the die is independent, we can calculate the expected frequency of rolling a 3 by multiplying the total number of rolls by the probability of rolling a 3.

The calculation is straightforward:

Therefore, Kayla can expect to roll a 3 approximately 14 times in 84 rolls.

Answer:

Jagdish is 27 years old

Step-by-step explanation:

Jagdish=x

Resham=x+3

Rajesh=x+5

(x+3)(x+5) = 960

x²+8x+15=960

x²+8x=945

x²+8x-945=0

now factor this to solve

(x-27)=0 (x+35)=0

which means

x=27 and x=-35

obviously, we cannot have negative ages so we use x=27

so, Jagdish=27

Resham=30

Rajesh=32

and we can check this by doing 30x32 which does equal 960 so it is correct

The age of Jagdish for the condition is 27 years.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

Given Jagdish is 3 years younger than Resham

and  Rajesh is 5 years older than Jagdish

let age of Jagdish be x

Resham = x + 3

Rajesh = x + 5

according to conditions,

(x + 3)(x + 5) = 960

x² + 8x + 15 = 960

x² + 8x = 945

x² + 8x- 945=0

now factor this to solve

(x - 27)(x + 35) = 0

(x - 27) = 0, (x + 35) = 0

which means

x=27 and x=-35

obviously, we cannot have negative ages so we use x = 27

Therefore, the age of Jagdish is 27 years.

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Answer:

y=-6x+3

Step-by-step explanation:

Answer:

y=-6x+3

Step-by-step explanation:

because the slope will always have the X and in the middle you can put them together to get your answer

Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]

b₁, b₂ - bases

h - height

We have b₁ = 20in, b₂ = 6in and h = 7in.

Substitute:

[tex]A=\dfrac{20+6}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)=91\ in^2[/tex]