4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z

The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of  option c.  [1,5].

Length of the cardboard box = x + 1

Width of the cardboard box = 5  - x

Height of the cardboard box = x - 1

Volume of the box V (x) =  length × width × height

Substitute the values we have,

V(x) = (x+1)(5-x)(x-1)

Expanding this expression gives,

V(x) = -x³ + 5x² + x - 5

To know where Volume is changing at the fastest average rate,

Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.

Taking the derivative of V(x), we get,

V'(x) = -3x²+ 10x + 1

Taking the absolute value of this expression, we get,

|V'(x)| = 3x² - 10x - 1

Now, we can calculate the maximum value of |V'(x)| over each interval,

At [1,2]

|V'(1)| = 8

|V'(2)| = 9

[1,3.5]

|V'(1)| = 8

|V'(3.5)| = 0.75

[1,5]

|V'(1)| = 1

|V'(5)| = 24

[0,3.5]

|V'(0)| = 1

|V'(3.5)| = 0.75

The maximum value of |V'(x)| occurs on interval [1,5].

Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].

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The above question is incomplete, the complete question is:

A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

Answer: 5:9

Step-by-step explanation:

Hope this helps! :)

The probability distribution for X is given below:

Probability of no even number, (X = 0)= 1/2

Probability of one even number, (X = 1) = 1/2

Probability of two even numbers, (X = 2) = 1/8

The probability distribution for X is found as follows:

The probability that an even number is not selected i.e. X = O

P(X = 0) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 0) = 1/2

The probability that an even number is selected once i.e. X = 1

P(X = 1) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 1) = 1/2

The probability that an even number is selected twice i.e. X = 2

P(X = 2) = 2/4 * 2/4

P(X = 2) = 1/8

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Answer:

This has no answer. Whats the question? Please tell me so I can help you

Is it probability ???

Answer:

I believe it is B. always

Because Adding, subtracting or even multiplying will always give you a new polynomial not the same polynomial.

Im sorry if i am wrong

Answer:

k = 1

Step-by-step explanation:

given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0

here the polynomial is divided by (x + 1)

then substitute x = - 1 into the polynomial and equate to zero

k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0

- k + 1 + 5 - 5 = 0

- k + 1 = 0 ( subtract 1 from both sides )

- k = - 1 ( multiply both sides by - 1 )

k = 1

The model y = 200(0.65)ⁿ represents exponential decay because the value of the bike decreases over time as t increases.

The value of the bike decreases by approximately 40.67% per year.

The value of the bike will be $50 approximately 5.2 years after it was purchased.

a. A = Peⁿ = 200e⁻⁰.⁴³⁰⁷≈ 118.66

The value of the bike after one year is approximately $118.66.

b. percent decrease = (initial amount - final amount) / initial amount * 100%

percent decrease = (200 - 118.66) / 200 * 100% ≈ 40.67%

c. We can set y = 50 in the model and solve for t:

50 = 200(0.65)ⁿ

0.65ⁿ = 0.25

Taking the natural logarithm of both sides, we get:

ln(0.65ⁿ) = ln(0.25)

t ln(0.65) = ln(0.25)

t = ln(0.25) / ln(0.65) ≈ 5.20

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Answer:

the answer is true

The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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The Area of Kitchen is 120 square feet.

We have,

Area of living room = 144 square feet

So, the dining room

= 1/3 (area of living room)

= 1/3 (144)

= 48 square feet

and, Area of Dining room = 2/5 x Area of kitchen

48 =  2/5 x Area of kitchen

Area of kitchen = 48 x 5/2

Area of Kitchen = 24 x 5

Area of Kitchen = 120 square feet

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The answer is  960in² (Option C) This is a geometry prompt involving hexagonal shape.

Since there are 6 congruent triangles, you find the area of 1 of the triangles and multiply by 6

Area of 1 triangle:

1/2bh = 1/2 (9 in) (10 in)

=1/2 (90 sq in.)

= 45 sq in.

Area of 1 hexagon is 6 (45 sq. in) = 270 sq. in.

There are 2 hexagons in the net, so multiply by 2

Area of 2 hexagons is...

2 (270 sq. in) = 540 sq. in.

Then find the area of the rectangular sides...which will be the 6 small squares shown on the first picture

**the rectangles each have 1 side that is equal to 1 side of the hexagon and 1 side is equal to the height of the prism.

Area of 1 rectangle side

lw = (10 in) (7in.)

= 70 sq. in.

multiply all of the 6 sides of the area

=6 (70 sq.in)

=420 sq. in

Then add the area of the 2 hexagons to the area of the 6 rectangular sides

Total area = 540sq. in + 420sq. in

= 960sq. in.

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Answer:

Large Number = 34 & Smaller Number = 20

Step-by-step explanation:

1. Define Variables

     Large Number = n

     Smaller Number = s

2. Equations

     n + s = 54

     n - s = 14

3. Combine the Equations

     n + s + n - s = 54 + 14

     2n = 68

     n = 34

4. Find s

     34 + s = 54

     s = 20

Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer: -2

Step-by-step explanation:

You can see it clearly passes through an origin consisting of -2

Answer:

Step-by-step explanation:

A -5        

Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.

The formula used is:


Exposure Time = 8/ 2^((dBA-85)/3)

Since the decibel (dBA) given is 106


Exposure Time = 8/ 2^((106-85)/3)

= 8/2^1
= 8/ 128

= 0.0625 hours or 3 minutes, 75 seconds.

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1)  Total time elapsed = 4 hours 59 minutes.

2)  Total time elapsed =  6 hours 12 minutes

3)  Total time elapsed =   6 hours 2 minutes

1) Time difference from 12:00 noon to 4:00 p.m = 4 hours

Time difference from 4:00 p.m to 4:59 p.m. = 59 minutes

So, the total time elapsed = 4 hours 59 minutes.

2) The time difference from 1:23 a.m. to 2:00 a.m. = 37 minutes

The time difference from 2:00 a.m to 7:00 a.m. = 5 hours

The time difference from 7:00 a.m. to 7:35 a.m. = 35 minutes

Here, the minutes elasped = 37 + 35

                                             = 72 minutes

                                             = 1 hour 12 minutes

So, So, the total hours elapsed = 5 + 1

                                                    = 6 hours

Thus, the total time elapsed = 6 hours 12 minutes

3) Time difference from 11:28 p.m. to 12:00 midnight = 32 minutes

Time difference from 12:00 midnight to 5:30 a.m. = 5 hours 30 minutes

Here, the minutes elasped = 32 + 30

                                             = 62 minutes

                                             = 1 hour 2 minutes

So, the total time elapsed =  6 hours 2 minutes

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The line plot is not symmetric because the numbers of siblings range from 0 to 8.

a. The line plot is not symmetric because the numbers of siblings range from 0 to 8. The number of students with 0 siblings is much greater than the number of students with 8 siblings.

b. The distribution is skewed left, meaning that the majority of students have fewer siblings than the average.

c. Since the distribution is skewed left, the median would be a better measure of the center because it is not affected by the outliers. The median number of siblings is 0. To measure the spread of the distribution, we can use the range, which is 8.

Therefore, the line plot is not symmetric because the numbers of siblings range from 0 to 8.

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In 5 seconds of free fall at a speed of 165 feet per second, the parachute user will drop around 122.5 meters.

To convert feet per second (ft/s) to meters per second (m/s), we can use the following conversion factor:

1 m/s = 3.3 ft/s

Therefore, the parachutist's rate of 165 ft/s is equivalent to:

165 ft/s × (1 m/3.3 ft) = 50 m/s

Next, we can use the kinematic equation:

d = 1/2 * a * t²

Here d is the distance traveled (in meters), a is the acceleration due to gravity (9.8 m/s²), and t is the time (in seconds).

For 5 seconds of free fall, we have:

d = 1/2 * 9.8 m/s² * (5 s)² = 122.5 m

Therefore, the parachutist will fall approximately 122.5 meters during 5 seconds of free fall at a rate of 165 ft/s.

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The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.

First, we can factor out a common factor of z:

z(20z² - 11z - 3) = 0

Now we need to factor the quadratic expression in the parentheses.

We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:

z(20z² - 11z - 3) = 0

z(4z - 3)(5z + 1) = 0

Setting each of the factored terms equal to zero, we have:

z = 0, 3/4, -1/5

Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.

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Answer:

    [tex]\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1[/tex]

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
[tex]m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}[/tex]

So line z will have an equation of the form
[tex]y = -\dfrac{3}{5}x + b[/tex]

We know that a line perpendicular to this line will have a slope of
[tex]- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}[/tex]

So the equation of the perpendicular line is
[tex]y = \dfrac{5}{3}x + b[/tex]

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

[tex]y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1[/tex]

This corresponds to Choice A

To determine what percentage of working adults in your neighborhood regularly ride the bus to work, the best sampling method and survey question are D. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"

The best sampling method involves random sampling of the population.

A random sample gives each member of the population an equal chance of being selected as a participant in the survey.

It is also described as a probability sampling method.

Thus, in this instance, the correct option is D.

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The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)

we need to solve for x in terms of y, where y = f(x).

Replace f(x) with y

Function y = -(1/2) - log₃√(9-x)

Solve for x

First, isolate the logarithmic term on one side of the equation.

y + (1/2) = -log₃√(9-x)

[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]

[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]

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To find the circumscribed side of a triangle, the steps to follow are:

1. Construct the perpendicular bisector of one of the sides of the triangle.

2. Construct the perpendicular bisector of the second side of the triangle.

3. Identify the point of intersection for the two perpendicular bisectors. This is the circumcenter of the triangle and the center of the circumscribed triangle.

4. Construct a circle that has a radius that is the length from the circumcenter to one of the vertices of the triangle.

A circumscribed triangle is one in which a circle is drawn in the center of the triangle and the circle goes round while touching only three vertices of the triangle.

To draw the circumscribed side of a triangle, you can start by constructing the perpendicular bisector of one of the sides and then the second side. Next, identify the point of intersection, and finally construct the circle.

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Öncelikle verilen A ve B ifadelerinin değerlerini hesaplayalım:

A = (sin x . sec x)² - (tan x . cosec x)²

A = (sin x / cos x)² - (sin x / cos x)²

A = sin² x / cos² x - sin² x / cos² x

A = 0

B = 2 - 2cos² x + cos⁴ x - sin⁴ x

B = 2 - 2cos² x + (cos² x)² - (sin² x)²

B = (cos² x)² - 2cos² x + 2

Şimdi 2A + 3B'yi hesaplayalım:

2A + 3B = 2(0) + 3[(cos² x)² - 2cos² x + 2]

2A + 3B = 3cos⁴ x - 6cos² x + 6

Bu şekilde 2A + 3B ifadesinin ayrıntılı hesaplanması tamamlanmış oldu.

Comparing all the numbers, we can see that (d) 21/2500 is not equal to the other numbers, since it is a fraction and all the other numbers are decimals. Therefore, (d) is the answer.

To determine which of the numbers is not equal to the other, we can convert all the numbers to the same form and compare them.

a) 0.84% can be written as 0.0084 in decimal form.

b) (0.21)(0.04) equals 0.0084.

c) 8.4 x 10⁻² can be written as 0.084 in decimal form.

d) 21/2500 can be simplified by dividing both the numerator and denominator by 21 to give 1/119.

e) 21/2500 x 10⁻² can be simplified by dividing both the numerator and denominator by 21 and multiplying by 100 to give 0.084.

In conclusion, to determine which number is not equal to the other, we need to convert all the numbers to the same form and compare them. In this case, we converted all the numbers to decimal form except for (d), which is a fraction. By comparing the numbers, we found that (d) is not equal to the other numbers.

Therefore, (d) is the answer.

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Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

The equivalent expression to the given expression [tex]2^{3x}[/tex] - 4  is equal to 8ˣ - 4.

The expression is equal to,

[tex]2^{3x}[/tex] - 4

Simplify the expression using the law of exponent we get,

yᵃᵇ = (yᵃ)ᵇ

Here  in the expression the value of y = 2,

Value of a = 3

and the value of b = x

Substitute the value in the formula we get,

= ( 2³ )ˣ - 4

value of the exponent 2³ = 2 × 2 × 2

                                          = 8

This implies the equivalent expression is,

= 8ˣ - 4

Therefore, the value of the given expression is equivalent to 8ˣ - 4.

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Te polynomials are closed under addition and subtraction

This is calculated as

Length 1 and 2 = 8x^2 − 5x − 2 + 7x − x^2 + 3

Evaluate

Length 1 and 2 = 7x^2 + 2x + 1

This is calculated as

Third side = Perimeter - Length 1 and 2

So, we have

Third side = 4x^3 − 3x^2 + 2x − 6 - 7x^2 - 2x - 1

Evaluate

Third side = 4x^3 − 10x^2 − 7

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction

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The surface area of the square pyramid using given dimensions is given by option a.  3,456m².

In the square pyramid,

Using Pythagoras theorem,

Height of the square pyramid is equal to,

In a right angled triangle,

Base = 18m

Hypotenuse = 30m

Height = √ Hypotenuse ² - base ²

Substitute the values we have,

⇒ height = √ 30² - 18²

⇒ height = √576

⇒ height =  24m

Dimensions of square pyramid are,

Base edge 'b' = 36m

height of the pyramid 'h' = 24m

Surface area of square Pyramid = b² + 2b√(b²/4) + h²

Substitute the values we have,

⇒Surface area of square Pyramid

= 36² + 2(36)√((36)²/4) + (24)²

= 1296 + 72√324 + 576

= 1296 + 2160

= 3,456m²

Therefore, the surface area of square Pyramid is equal to option a.  3,456m².

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)