Solve for x.
=(x-1)= 9(x + 2)
x = -8
x = -3
x = 3
O x = 8
7
8
Co
10
A

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

m = 12

Step-by-step explanation:

Given

18 - m = 6 ( subtract 18 from both sides )

- m = - 12 ( multiply both sides by - 1 )

m = 12

Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:\(\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\]\) Multiplying the equation by the least common multiple of the denominators, we get:\(\[16 + 8 = 2x\]\) Simplifying, we get:\(\[2x = 24\]\)Dividing both sides by 2, we get:\(\[x = 12\]\)Therefore, it takes Cindy 12 hours to rake the yard alone.

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a. i. There are 27,040,000 different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive  (so 123AB is the same as 123aB)

ii. There will be 99,532,800  different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive

b. i. The probability that all 4 randomly selected students were math majors is  0.520

ii. There are 4,725 different pairs of math majors that could be chosen for the committee.

a. i) There are 10 choices for each of the first 3 digits, and 26 choices for each of the last 2 letters. Since the password is not case sensitive, we can choose either uppercase or lowercase letters, so there are 26 + 26 = 52 choices in total for each letter. Therefore, the total number of different passwords is:

10 x 10 x 10 x 52 x 52 = 27,040,000

ii) There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit (since we can't repeat the first two digits), and 52 choices for the first letter. For the second letter, there are 51 choices left (since we can't repeat the first letter), but we need to distinguish between uppercase and lowercase letters, so there are 52 x 51 = 2,652 choices for the two letters in total. Therefore, the total number of different passwords is:

10 x 9 x 8 x 52 x 2,652 = 99,532,800

b) i) The total number of ways to select a 4-student committee from 20 students is:

20 choose 4 = 4,845

The number of ways to select a committee consisting of 4 math majors is:

10 choose 4 = 2,520

Therefore, the probability that all 4 randomly selected students were math majors is:

2,520 / 4,845 = 0.520

ii) The number of ways to select a 4-student committee with exactly two math majors is:

(10 choose 2) x (10 choose 2) x (15 choose 0) = 4,725

(We choose 2 math majors from 10, and 2 non-math majors from 15, since there are 5 biology majors and 5 music majors to choose from.)

Therefore, there are 4,725 different pairs of math majors that could be chosen for the committee.

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Answer:

15.14%

Step-by-step explanation:

The formula for APR is stated thus:

APR=fees+interest/principal/n*365*100

principal is the loan amount of $700

fees is the processing fees on the loan which is $50

interest amount=principal*interest %=$700*8%=$56

n is the number of days of the loan which is a year i.e 365 days

APR=($50+$56)/$700/365*365*100

APR=$106/$700/365*365*100

APR=0.151428571 /365*365*100

APR=0.151428571 *100=15.14%

The annual percentage rate on the loan is 15.14% which represents the actual cost on the loan not just the interest cost of 8% annually

To compare the greater pay between a salary of $74,000 per year and an hourly rate of $40 for 80 hours every fortnight, we need to calculate the total earnings for each option.

Salary per year:

To calculate the total earnings for the salary option, we simply take the annual salary of $74,000.

Total earnings = $74,000 per year

Hourly rate:

To calculate the total earnings for the hourly rate option, we need to determine the total number of hours worked in a year. Since there are 26 fortnights in a year, and the lawyer works 80 hours per fortnight, the total number of hours worked in a year would be:

Total hours worked per year = 26 fortnights * 80 hours/fortnight = 2,080 hours

Now we can calculate the total earnings:

Total earnings = Hourly rate * Total hours worked per year

= $40/hour * 2,080 hours

= $83,200

Comparing the two options, we find that the greater pay is $83,200 from the hourly rate, which exceeds the $74,000 salary per year.

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Answer:

6:05 is the answer it should be obvious

Answer:

Hello,

x=5

Step-by-step explanation:

\(Since\ \overrightarrow{AD}=\overrightarrow{BC}, ABCD\ is\ a\ parallelogramm\\\\12x+60=150-6x\\\\18x=90\\\\x=\frac{90}{18} \\\\\boxed{x=5}\\\)

Answer: Firstly the area of parallelogram is. = b×h. so value of base is 9cm and height is 45cm . So area is equal to. base×height. = 9×45= 405² cm.

405cm²

Attitude, beliefs, and knowledge shape a teacher's delivery: attitude affects engagement, beliefs influence instructional decisions, and knowledge enables effective communication and learning facilitation.

Attitude, beliefs, and knowledge play crucial roles in shaping how a teacher delivers a lesson. Here's a detailed explanation of their impacts:

Attitude:

Attitude refers to a teacher's mindset, emotions, and approach towards teaching. A positive attitude fosters enthusiasm, motivation, and a genuine passion for the subject matter. This translates into an engaging and dynamic teaching style, creating an environment conducive to learning. Conversely, a negative attitude can lead to disinterest, lack of enthusiasm, and a disengaged teaching approach, which can hinder students' engagement and comprehension.

Beliefs:

A teacher's beliefs influence their instructional decisions and pedagogical strategies. Beliefs about students' capabilities, learning styles, and the purpose of education can shape the teacher's approach to delivering a lesson. For example, if a teacher believes that all students have the potential to succeed, they may employ differentiated instruction techniques to cater to diverse learning needs. Conversely, if a teacher holds limiting beliefs about students' abilities, they may adopt a one-size-fits-all approach, which may hinder student progress.

Knowledge:

A teacher's knowledge encompasses both subject matter expertise and pedagogical content knowledge. Profound knowledge of the subject allows a teacher to effectively structure and present the lesson, answer student queries, and provide relevant examples. Pedagogical content knowledge helps in selecting appropriate instructional strategies, adapting to student needs, and assessing learning effectively. Without a strong knowledge base, a teacher may struggle to deliver accurate information, engage students, or address misconceptions.

Collectively, attitude, beliefs, and knowledge significantly impact a teacher's delivery of a lesson. A positive attitude enhances student motivation and engagement. Strong beliefs in students' potential and individualized instruction foster a supportive learning environment. Adequate subject knowledge and pedagogical skills enable effective communication and facilitate meaningful learning experiences. By combining these elements, teachers can create an impactful and effective learning environment that nurtures student growth and achievement.

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The slope of the line from the equation is 2/3.

The line:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

The formula of a line:

y = mx + c

m = slope

c = y-intercept

Here we are provided with the equation:

8x - 12y = 108

12y = 8x - 108

y = 2/3x - 9

So by equating we get the slope:

m = 2/3

Therefore the slope is 2/3.

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The measure of ∠POX  = 160°  The length of XOA = 16.95 mm ,We know that PM¯, PN¯, and PO¯ are angle bisectors of triangle MNO, so they divide the opposite sides in two equal parts. Let x = MY, y = NY, and z = OY. Then, we have:

MX / NO = MY / NY (by the angle bisector theorem)

MX / (MX + XO) = x / (x + y)

MX(x + y) = x(MX + XO)

MXy = XOx

NO / OX = NY / OY (by the angle bisector theorem)

(OX + XO) / OX = y / z

1 + XO/OX = y/z

XO/OX = (z - y)/y

Now, we can use these equations to solve the problem:

To find PX¯, we need to find MX. Using the angle sum property of triangles, we have:

m∠M = 180 - m∠MON = 140°

m∠PMX = m∠M/2 = 70°

m∠PMO = m∠MON/2 = 20°

m∠XMO = m∠PMX + m∠PMO = 70° + 20° = 90°

Therefore, PX¯ is the altitude from M to XO¯, so we have:

tan(30°) = PX / MX

MX = PX / tan(30°)

= 23 / √(3)

= 13.31 mm

To find m∠PMX, we can use the fact that PM¯ is an angle bisector:

m∠PMX = m∠M + m∠PMO

= 140° + 20°

= 160°

To find m∠POX, we can use the fact that PO¯ is an angle bisector:

m∠POX = m∠O + m∠PNO

= 180° - m∠MON + m∠PNO

= 180° - 40° + 20°

= 160°

To find XO¯, we need to find y and z. Using the fact that PX¯ is an angle bisector, we have:

PY / OY = PM / OM

23 / z = 52 / (x + y + z)

y + z = 52z / 23

z = 23y / (52 - 23)

Using the equation XO/OX = (z - y)/y, we have:

XOA / 52 = (23y / (52 - 23) - y) / x

XOA= 52 * 23y / ((52 - 23) * x - 23y)

Substituting MX = 23/√(3) - PX = 23/√(3) - 13.31, we get:

y = NO * PY / (PM + PN + PO) = 56.17 mm

z = OY + PY = 79.17 mm

XOA = 16.95 mm

Therefore, the answers are:

Length of PX¯: 13.31 mm

Measure of ∠PMX: 160°

Measure of ∠PO

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Answer:

r = 8

Step-by-step explanation:

\(\frac{3.6}{3.15}\) = \(\frac{r}{7}\) ( cross- multiply )

3.15r = 3.6 × 7 = 25.2 ( divide both sides by 3.15 )

r = \(\frac{25.2}{3.15}\) = 8

Answer:

8

Step-by-step explanation:

Answer:

.5 and .5, .75 and .25, ect

Answer:

0.5

Explanation:

Take one, divide that by two. You get a decimal number, which is .5.

(Not the only two numbers which go into one, but eh, it'll do)

Elena and Marc both drive the same number of miles per year in their respective vehicles, hence the mileage will never be the same.

Elena's mileage = 9000

She drives 22000 miles each year.

So mileage each year will form an arithmetic progression.

9000, 31000 , 53000, 75000 ....

Marc's mileage = 22000

he drives 22000 miles each year

So mileage each year will form an arithmetic progression.

22000 , 44000 ,66000, 88000 ...

Hence we can see that the mileage of both the cars will never be equal.

In an arithmetic progression (AP) sequence of numbers, the difference between these two consecutive integers is always the same. It is also known as an arithmetic sequence.

For instance, a progression in arithmetic is the natural number series 1, 2, 3, 4, 5, 6,... Between two succeeding terms, let's say 1 and 2, it has a common difference of 1. (2 -1). We can see that in both the case of odd and even integers, the common differences between two succeeding words will equal 2.

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Answer:

The correct expression that can be represented by n decreased by thirty-one is n - 31

let

The unknown number = n

n decreased by thirty-one

= n - 31

If n = 29

n - 31

= 29 - 31

= -2

The correct expression is 31-n.

False

This is a subtraction expression.

True

This is an addition expression.

False

To evaluate, substitute 29 for the variable in the expression

True

To evaluate, substitute 31 for the variable in the equation.

False

To evaluate the expression, add 31 to 29.

False

The correct expression is n - 31

True

To evaluate the expression, subtract 31 from 29.

True

Step-by-step explanation:

the answer is a b e g f hop this helps u

The given series is 1 3 9 27 81

here, all the numbers are the multiplication of three.

it is the series of function f(x) = 3^x

substitute x= 1, 2 , 3 , 4 , 5......

If the dimensions of trapezoid JKLM are multiplied by a scale factor of f to create trapezoid J'K'L'M' "The area of trapezoid J'K'L'M' is f times the area of trapezoid JKLM." Therefore, option A is correct.

When you multiply the dimensions of a trapezoid by a scale factor, the area of ​​the resulting trapezoid is equal to the square of the scale factor multiplied by the area of ​​the original trapezoid. In this case, the scaling factor is f, so the area of ​​trapezoid J'K'L'M' is f² times the area of ​​trapezoid JKLM.

When scaling a trapezoid, the base perimeter, angle, and length can change, depending on the specific value of the scale factor and the dimensions of the original trapezoid. 

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We can use this equation to graph the semicircle of radius 20 on the upper half of the plane. We can use the trigonometric substitution to find the integral of sqrt(400 - x²) dx. Thus, the solution to the given problem is10 θ + 5 sin 2θ + C (where C is the constant of integration).

To evaluate the given integral using trigonometric substitution sqrt(400 - x²) dx, we need to use the substitution x

= 20 sin θ.Using Trigonometric Substitution square root(400 - x²) dxLet x

= 20 sin θ dx

= 20 cos θ dθ√(400 - x²)

= √(400 - 400 sin²θ)

= √(400 cos²θ)

= 20 cos θNow substitute the above equations to the given integral:integral of square root(400 - x²) dx

= integral of 20 cos²θ dθ

= 20 integral of (1 + cos 2θ)/2 dθ

= 10 θ + 5 sin 2θ + C (where C is the constant of integration)To get back to x, we can use the identity sin²θ + cos²θ

= 1. Thus, when x

= 20 sin θ,x² + y²

= 400sin²θ + cos²θ

= 1 ⇒ y²/400 + x²/400

= 1.We can use this equation to graph the semicircle of radius 20 on the upper half of the plane. We can use the trigonometric substitution to find the integral of square root(400 - x²) dx. Thus, the solution to the given problem is10 θ + 5 sin 2θ + C (where C is the constant of integration).

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Answer: whats the uqestion

Step-by-step explanation:

\(\pi\) measures to both of those degrees as seen on the unit circle.

sorry that its handwritten, I'm on my ipad so its easier. Let me know if you have any questions, I'm  happy to help

In the case of Typical behavior of the sales prices of houses median is the best term. In the case of Ages of 1st graders mean is the best way of central tendency and for Heights of women mode is the best measure.

First of all we have to know the Mean, median and mode. The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

In the case of typical behavior of the variable sales price of houses, the Median will be the best measure of central tendency because the median will not get affected by the higher/lower prices of houses.

The age of each kid will be almost the same.  In order to represent the typical behavior of the variable Age of 1st graders, the mean will be the best measure of central tendency.

Incase of Heights of women, the mode will be the best measure of central tendency as it will describe the height that most of the females have. 

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The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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For a survey of 320 homeless persons showed that 78 were veterans. A 99% confidence interval for the population proportion of homeless persons who are veterans is: (0.182, 0.306). The correct answer is Option (c) "I am 99% confident that the proportion of all homeless persons who are veterans is between 0.182 and 0.306."

It is given that a survey of 320 homeless persons showed that 78 were veterans and a 99% confidence interval for the population proportion of homeless persons who are veterans is (0.182, 0.306). Now, we have to determine the correct statement from the given options.

a. With 90% confidence, the mean number of homeless veterans is between 18.2 and 30.6.

This statement is incorrect. The interval (0.182, 0.306) is a confidence interval for the proportion of homeless persons who are veterans and not for the mean number of homeless veterans. Hence, option (a) is incorrect.

b. I am 99% confident that the proportion of the sampled homeless persons who are veterans is between 0.182 and 0.306.

This statement is also incorrect. The 99% confidence interval is for the population proportion of homeless persons who are veterans and not for the sample proportion. Hence, option (b) is incorrect.

c. I am 99% confident that the proportion of all homeless persons who are veterans is between 0.182 and 0.306.

This statement is correct. The given confidence interval is for the population proportion of homeless persons who are veterans and it is a 99% confidence interval. Therefore, option (c) is the correct statement.

d. 99% of veterans are homeless between 18.2% and 30.6% of the time.

This statement is incorrect. The confidence interval is for the population proportion of homeless persons who are veterans and not for the proportion of veterans who are homeless. Hence, option (d) is incorrect

.e. Between 18.2% and 30.6% of veterans are homeless.

This statement is incorrect. The confidence interval is for the population proportion of homeless persons who are veterans and not for the proportion of veterans who are homeless. Hence, option (e) is incorrect.

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Answer: it’s the second one

Step-by-step explanation:

Answer:

10, 7.2, 8 2/3

Step-by-step explanation:

My strategy is dividing the number of click by the time in seconds. By doing this, I got 10 from 30/3, 7.2 from 36/5, and lastly 8 2/3 from 26/3.

Answer:

maybe 2-5-9

Step-by-step explanation:

The axis of Symmetry and the vertex of the quadratic equation will be: x = 2 and

Given is a function f(x) = 2x²-8x+5, we need to find the axis of symmetry and the vertex of the function,

The standard form of a quadratic equation, which is represented by f(x) = ax² + bx + c, can be used to determine the axis of symmetry and the vertex of the function f(x) = 2x²-8x+5.

When compared to the function, we get a = 2, b = -8, and c = 5. The equation for a quadratic function's vertex and axis of symmetry in this form is:

Axis of Symmetry (x = h): x = -b / (2a)

Vertex (h, k): h = -b / (2a) and k = f(h)

Let's change the values of a and b in the formulas to determine the vertex and the axis of symmetry:

Axis of Symmetry (x = h):

x = -(-8) / (2 * 2)

x = 8 / 4

x = 2

Therefore, the axis of symmetry is x = 2.

Vertex (h, k):

h = -(-8) / (2 * 2)

h = 8 / 4

h = 2

Now, substitute h = 2 into the original function to find k:

f(2) = 2(2)² - 8(2) + 5

f(2) = 2(4) - 16 + 5

f(2) = 8 - 16 + 5

f(2) = -3

Therefore, the vertex is (2, -3).

Hence:

Axis of Symmetry: x = 2

Vertex: (2, -3)

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