The height of the parallelogram, h, can be found by dividing the area by the length of the base. If the area of the parallelogram is represented by 4x2 – 2x + 5 and the base is 2x – 6, which represents the height? 2x + 5 + 2x – 7 – 2x – 7 + 2x + 5 –

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

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.

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

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

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:

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:

u + v = <7 , 1>

║u + v║ ≅ 7

Step-by-step explanation:

* Lets explain how to solve the problem

- We can add two vector by adding their parts

∵ The vector u is <-4 , 7>

∵ The vector v is <11, -6>

∴ The sum of u and v = <-4 , 7> + <11 , -6>

∴ u + v = <-4 + 11 , 7 + -6> = <7 , 1>

∴ The sum u and v is <7 , 1>

* u + v = <7 , 1>

- The magnitude of the resultant vector = √(x² + y²)

∵ x = 7 and y = 1

∵ ║u + v║ means the magnitude of the sum

∴ The magnitude of the resultant vector = √(7² + 1²)

∴ The magnitude of the resultant vector = √(49 + 1) = √50

∴ The magnitude of the resultant vector = √50 = 7.071

* ║u + v║ ≅ 7

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:

[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:

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:

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:

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:

90 degree clockwise rotation about (0,0).

Step-by-step explanation:

That would be a clockwise rotation of 90 degrees about the origin (0,0).

The rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To find the rotation that maps point K(8,-6) to K(-6,-8), we can use the following steps,

Plot the points K(8,-6) and K(-6,-8) on a coordinate plane.

Since point K(8,-6) is being mapped to point K(-6,-8), the rotation must be counterclockwise. As rotation about the origin with angle 90 gives the transformation equation,
(x, y) ⇒ (y, -x)

Therefore, the rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).

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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 ..

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: 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:

A: 0

B: There is one real root with a multiplicity of 2.

Step-by-step explanation:

[tex]\bf{x^2+2x+1=0}[/tex]

The discriminant of the quadratic equation can be found by using the formula: [tex]b^2-4ac[/tex].

In this quadratic equation,

I found these values by looking at the coefficient of [tex]x^2[/tex] and [tex]x[/tex]. Then I took the constant for the value of c.

Substitute the corresponding values into the formula for finding the discriminant.

Simplify this expression.

The answer for part A is [tex]\boxed{0}[/tex]

The discriminant tells us how many real solutions a quadratic equation has. If the discriminant is

Since the discriminant is 0, there is one real root so that means that the first option is correct.

The answer for part B is [tex]\boxed {\text{There is one real root with a multiplicity of 2.}}[/tex]

Answer:

A: 0  

B: There is one real root with a multiplicity of 2 .  

Step-by-step explanation:

Given a quadratic equation:

 [tex]ax^2+bx+c=0[/tex]

You can find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

In this case you have the following quadratic equation:

[tex]x^2+2x+1=0 [/tex]

Where:

[tex]a=1\\b=2\\c=1[/tex]

Therefore, when you substitute these values into the formula, you get that the discriminant is this:

[tex]D=(2)^2-4(1)(1)\\\\D=0[/tex]

Since [tex]D=0[/tex], the quadratic equation has one real root with a multiplicity of 2 .

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.

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:

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:

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

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

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]

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:

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:

34 square units

Step-by-step explanation:

Step 1 : Write the formula for area of rectangle

Area of rectangle = length x breadth

From the graph:

AB = DC

AD = BC

Step 2 : Find the distance between AB and AD to find the length and breadth.

Coordinates : A (-1, 4), B (3, 3)

Distance between two points on AB

Formula : √(x2-x1)² + (y2-y1)²

= √(3-(-1))² + (3-4)²

= √17

Distance between two points on AD

Coordinates of A (-1, 4), D = (-3,-4)

Formula : √(x2-x1)² + (y2-y1)²

= √(-3-(-1))² + (-4-4)²

= √68

Area of rectangle = length x breadth

Area of rectangle = √17 x √68

Area of rectangle = 34

Therefore the area of rectangle = 34 square units

!!

Answer:

34

Step-by-step explanation:

Answer:

The dimensions of the living room is the scale drawing are 16 in by 10 in

Step-by-step explanation:

we know that

The scale drawing is equal to

[tex]\frac{4}{6}\frac{in}{ft}[/tex]

That means ----> 4 inches in the drawing represent 6 feet in the real

so

Find the dimensions of the living room in the scale drawing

using proportion

For 24 ft

[tex]\frac{4}{6}\frac{in}{ft}=\frac{L}{24}\frac{in}{ft}\\ \\L=4*24/6\\ \\L=16\ in[/tex]

For 15 ft

[tex]\frac{4}{6}\frac{in}{ft}=\frac{W}{15}\frac{in}{ft}\\ \\L=4*15/6\\ \\W=10\ in[/tex]

therefore

The dimensions of the living room is the scale drawing are 16 in by 10 in

Answer:

-3± √5

Step-by-step explanation:

It is given that,

m² + 6m = -4

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± v(b² - 4ac)]/2a

To find the solution of given equation

m² + 6m = -4

⇒ m² + 6m  + 4 = 0

Here a = 1, b = 6 and c = 4

m =  [-b ± v(b² - 4ac)]/2a

  =  [-6 ± √(6² - 4*1*4)]/2*1

  = [-6 ± √(36 - 16)]/2

  = [-6 ± √20]/2

  = [-6 ± 2√5]/2

 = -3± √5