Karen was trying to factor 6x^2+106x 2 +106, x, squared, plus, 10. She found that the greatest common factor of these terms was 222 and made an area model:.

Answer:

60

Step-by-step explanation:

900 divided by 15 is 60

The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.

What is the equation of a line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

The equation of a line that passes through the point (2, 6) and has a slope of -1/2 can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the equation of the line, we can use the point-slope form of a line, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Substituting the values for the point and the slope into this equation, we get:

y - 6 = (-1/2)(x - 2)

y - 6 = -1/2x + 1

y = -1/2x + 7

Hence, The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.

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The orthogonal basis produced using the Gram-Schmidt process for W is[tex]y_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right], y_2=\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right][/tex]

What is orthogonal ?

The concept of orthogonality in mathematics is an extension of perpendicularity in geometry. By extension, the term "orthogonality" is also used to describe the division of particular system properties. The phrase also has specific applications in other disciplines, such as chemistry and painting.

[tex]$$x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \quad \text { and } \quad x_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]$$[/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]$$y_1=x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]$$[/tex]

Now we know [tex]$X_1, X_2$[/tex] and [tex]$Y_1$[/tex]

Lets solve for [tex]$Y_2$[/tex]

[tex]y_2=x_2-\frac{x_2+y_1}{y_1+y_1} y_1$$[/tex]

[tex]y_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}{\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right][/tex]

[tex]\begin{aligned}y_2 & =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{7+28-0+1}{1+16+0+1}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{36}{18}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-2\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\left[\begin{array}{c}2 \\-8 \\0 \\2\end{array}\right] \\y_2 & =\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right]\end{aligned}[/tex]

Complete question: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2

1 7

-4 -7

0 -6

1 1

The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)

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The value of 'a'  in the system of equations will be;

⇒ a = - 4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are;

⇒ ax + 12y = - 6

⇒ 2x - 6y = 4

Now,

By the condition of No solution for the system, we get;

⇒ a / 2 = 12 / - 6

⇒ a / 2 = - 2

⇒ a = - 4

Thus, The value of 'a'  in the system of equations will be;

⇒ a = - 4

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What we have here in the picture is a graph of a segment. The goal is to find the segment's length, which we can do by using the distance formula:[tex]d^2=\left(x_2-x_1\right)^2-\left(y_2-y_1\right)^2[/tex].

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Note that the distance between two points is equal to the length of the line segment that joins them.

So now we already have answers for two of the boxes.

The difference in the x-coordinates gives us the horizontal distance between the two points, while the difference in the y-coordinates gives us the vertical distance between the points.

So, the other two boxes should contain:

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Answer:

Option A

Step-by-step explanation:

(x + 7)2 = 102 + (x + 3)2

(Tangents from the external point are equal)

⇒ x = 7.5cm ⇒ OB = x + 3 = 10.5 cm

The account's APY is 5.12%.

Annual Percentage Yield, or APY, is the rate that may be earned on an account over the course of a year and includes compound interest.

The annual percent yield, or APY, accounts for interest compounding. Because it takes into account the interest you earn on your money, it accurately reflects the interest rate you really receive on an investment.

Consider the previous illustration, where a $100 investment generates a 5% quarterly compounded return. On the $100, you receive interest throughout the first quarter. However, in the second quarter, you also receive interest on the $100 in addition to the first quarter's interest.

The APY (Annualized Percentage Yield) formula is:

APY = [tex](1+i/N)^{N} -1[/tex]

where, i = Nominal rate = 5%, N = Number of compounding periods = 12

putting the values in the above formula, we get,

APY = (1 + 5% / 12)^12 - 1

APY = (1 + 0.4167%)^12 - 1

APY = (1 + 0.0041667)^12 - 1

APY = (1.0041667)^12 - 1

APY = 1.051161897 - 1

APY = 0.051161 or 5.12%

The APY for this account 5.12%

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We can solve this question by using Pythagoras Theorem . The value of x in the given question is 8√3.

The well-known Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle, states that the square on the hypotenuse (the side opposite the right angle) is equal to the square on the legs of a right triangle. Pythagorean Theorem is written as a2 + b2 = c2. Alternatively, the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two legs.

From the given triangle using Pythagoras theorem,

       Assume the triangle as ABC where AB=y BC=z and AC=28

        D is the altitude from B and BD=x

         AD=12 so CD=16

Now using Pythagoras theorem,

           (y)2 = (12)2 + (x)2 - eq1

           (z)2 = (x)2 + (16)2 -eq2

           (y)2 + (z)2 =(28)2 -eq3

  Substitute eq 1 and 2 in 3

        ⇒2(x)2 + (12)2 + (16)2 =(28)2

        ⇒(x)2 =192

        ∴x =8√3

We can solve this question by using Pythagoras Theorem . The value of x in the given question is 8√3.

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Answer:

b

Step-by-step explanation:

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

Inequality is the unequal distribution of resources, opportunities, or rewards among individuals or groups in society. It can occur in many forms, such as unequal access to healthcare, education, employment, or other resources, or unequal treatment based on race, gender, ethnicity, and other factors. Inequality can also manifest as unequal income and wealth distribution, as well as unequal access to political power and decision-making. Inequality can be caused by a variety of factors, including structural factors and personal or individual-level factors, such as discrimination. Inequality can have a negative effect on both individuals and societies, leading to social and economic inequities that can be difficult to overcome.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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18 first-year teachers were in the meeting.

In this question, we have been given that a school staff meeting had 60 teachers in attendance, 30% of whom were the first-year teachers.

We need to find the number of first-year teachers present in the meeting.

Let x be the number of first-year teachers present in the meeting.

As 30 percent of school staff are the first-year teachers, we need to find the 30 percent of 60.

Using the formula of percentage,

x = 60 * (30/100)

x = 18

Therefore, the number of first-year teachers present in the meeting = 18

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Answer:

50% increase

Step-by-step explanation:

If we call the number of people x;

On the first afternoon, everyone plants 8x (Average 8 per person)

In the future, the plan to plant 12x trees (Average 12 per person)

From 12x to 8x is a 50% increase, (12/8 = 1.5)

Hope this helps,

:]

Answer:

(1, 1)

Step-by-step explanation:

x+y=2

y=5x-4

x + 5x - 4 = 2

6x - 4 = 2

6x = 6

x = 1

x + y = 2

1 + y = 2

y = 1

(1, 1)

Given :  55.7796

To Find : rounded off to 3 decimal places

Solution:

55.7796

To round off to   3 decimal places need to check digit at

4th decimal place

if  digit is 5 or greater than 5 then digit at 3rd decimal place has to be increased by  1  and all decimal places after that to be removed

if  digit is  less than 5 then digit at 3rd decimal place remains same and all decimal places after that  to be removed

55.7796

Digit at 4th decimal place is 6 which is greater than 5

Hence digit at 3rd decimal place has to be increased by 1

9 + 1 = 10  Hence 1 to be carried forward to digit at 2nd decimal place

7 + 1 = 8

Hence  number rounded off to 3 decimal places  is

55.780

55.7796 rounded off to 3 decimal places is  55.780

Answer: The correct equation to find the cost, c, of each cello lesson is: 15c + 35 = 425

Step-by-step explanation:

This equation represents the total cost of the cello lessons and the cello rental, which is 425 dollars. The cost of the cello lessons is represented by 15c, and the cost of the cello rental is represented by 35 dollars. By solving this equation for the variable c, we can find the cost of each cello lesson.

To solve this equation, we can use the following steps:

Subtract 35 from both sides of the equation: 15c = 425 - 35

Simplify the right side of the equation: 15c = 390

Divide both sides of the equation by 15: c = 390/15

Simplify the right side of the equation: c = 26

Therefore, the cost of each cello lesson is $26.

Answer:

[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]

Step-by-step explanation:

Given equation:

[tex]t^2-10t+6=7[/tex]

When completing the square for a quadratic equation, the first step is to move the constant to the right side of the equation:

[tex]\implies t^2-10t+6-6=7-6[/tex]

[tex]\implies t^2-10t=1[/tex]

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies t^2-10t+\left(\dfrac{-10}{2}\right)^2=1+\left(\dfrac{-10}{2}\right)^2[/tex]

Simplify:

[tex]\implies t^2-10t+\left(-5\right)^2=1+\left(-5\right)^2[/tex]

[tex]\implies t^2-10t+25=1+25[/tex]

[tex]\implies t^2-10t+25=26[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (t-5)^2=26[/tex]

Square root both sides:

[tex]\implies \sqrt{(t-5)^2}=\sqrt{26}[/tex]

[tex]\implies t-5=\pm \sqrt{26}[/tex]

Add 5 to both sides:

[tex]\implies t-5+5=\pm \sqrt{26}+5[/tex]

[tex]\implies t=5 \pm \sqrt{26}[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]

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Answer:

1. 2(x-2) = 2x -4 = -7 + 6x -4x +3

2. (x+14) - (8-2x) = 3x + 6 = 9x - 2(3x-3)

3. 3(x+5) = 3x + 15 = -2x + 9 + 5x + 6

4. -4(x+1) + 5x = x - 4 = (7-2x) + (3x -11)

5. (7 + 5x) + (-4x - 1) = 6 + x = -3x + 6 + 4x

Step by step:

For number 1:

2(x-2) = 2x - 4

-7 + 6x -4x + 3 = (-7 + 3) + (6x - 4x) = 2x - 4

For number 2:

(x+14) - (8-2x) = x + 14 - 8 + 2x = (14-8) + (2x + x) = 3x + 6

9x - 2(3x-3) = 9x - (6x - 6) = 9x - 6x +6 = 3x + 6

--

Have a nice day!!

Answer:

4

1

2

5

3

Step-by-step explanation:

we should simplify them first

we will keep the first column the same and call them by numbers 1-5 and the second column will be labled by letters A-E

1- 2(X-2)

 2X-4

2- X+14-(8-2X)

X+14-8+2X

3X+6

3 - 3(x+5)

    3x+15

4: -4(x+1)+5x

   -4x-4+5x

  x-4

5. (7+5x)+(-4x-1)

x+6

A: 7-2x+3x-11

x-4

A=4

B: -7+6x-4x+3

   -7+2x+3

2x-4

B=1

C: 9x-6x+6

3x+6

c= 2

D: -3x+6+4x

    x+6

D= 5

E-2x+9+5x+6

 3x+15

E= 3

hopes this helps and im sorry for the mess i had to write a lot please mark brainliest

As a new cell phone plan charges a flat monthly fee of $24 and allows for an unlimited number of text messages, but charges $0.15 per minute (m) used for phone calls, the equation that will represent the problem is C=24+0.15m.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let m be the minutes talked on phone,

C=24+0.15m

The problem is represented by the equation C=24+0.15m since the new cell phone plan charges a fixed monthly fee of $24 and permits unlimited text messages, but each minute (m) utilized for phone calls costs $0. 15.

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Answer:

x = 5

Step-by-step explanation:

Find the scale factor from figure B to A

let x = the scale factor

5x = 2  Divide both sides by 5

x = [tex]\frac{2}{5}[/tex] or .4

12.5 x .4 = 5

Answer:

(x+3, y-3)

Step-by-step explanation:

10) The second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).

11) The second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).

When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.

Given,

Line q passes through (3, 5), (-2, 4)

(y-y₁)=m(x-x₁)

(y-5)=((4-5)/(-2-3))(x-3)

(y-5)=(-1/-5)(x-3)

-5y+25=-x+3

x-5y+22=0

10) Given point is (0,1)

Slopes are equal for parallel lines.

So, (y-1)/(x-0)=(-1/-5)

-5y+5= -x

x-5y+5=0Let y=0 then,

x= -5

Therefore, the second pair of coordinate on the line parallel to q and passes through the point (1, 0) is (-5, 0).

11) The equation of a line perpendicular to q is,

(y-y₁)=(-1/m)(x-x₁)

(y-5)=5(x-3)

y-5=5x-15

5x-y-10=0

Let y=0 then,

5x-10=0

x=2

Therefore, the second pair of coordinate on the line perpendicular to q and passes through the point (3, 5) is (2, 0).

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0.5 x 0.11 is equal to 0.055 because of the zeros and the decimal placements.

Even though it would seem like the answer would be 0.55, the decimal placement of 0.5 makes it so that the number would change to an extra zero in the final result.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The likelihood that the number is 3 or 5 is 0.47.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

There are 15 identical spaces. Once the spinner has been spun,

Probability is determined by dividing the number of potential outcomes by the number of possible positive outcomes.

5 times: 5, 10, and 15

3 times, 6, 9, 12, and 15.

Different results (3, 5, 6, 9, 10, 12, and 15) (stop doing them).

a variety of successful results 7

3) There are 15 possible outcomes.

4) Probability is equal to 7/15, or 0.47

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According to the Central Limit Theorem for proportions, the property does dˆ exhibit is the statistic is biased.

Central line theorem:

In statistics, central limit theorem states that when the large sample size has a finite variance, the samples will be normally distributed and the mean of samples will be approximately equal to the mean of the whole population.

Given,

A certain statistic dˆ is being used to estimate a population parameter d. The expected value of dˆ is not equal to d.

Here we need to find the property does dˆ exhibit.

As per the Central Limit Theorem establishes that for a proportion p in a sample of size n:

Expected value μ = p

Standard error s = √p(1 - p) /n

Here the expected value is different of the expected, hence, the statistic is biased.

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The amount of money that Kaylee will have left after spending to by meat in Ruby's market would be = $5.01.

The total amount of money Kaylee has to spent in the market = $11

The quantity of sausage she ordered = 1/2pound

The price of per pound of sausage = $3.25

Therefore 1/2 pound = 3.25 × 1/2 = $1.63

The quantity of chicken she ordered = 1¾ pounds

The price per pound of chicken = $2.50

Therefore 1¾ pounds = 2.50 × 1¾ = $4.36

The total money spent on meat = 1.63 + 4.36 = $5.99

The amount that Kaylee would have left = 11-5.99=$5.01.

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The installment price is $55.

This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Here, you buy an I-phone for $800 or pay $75 down and the balance in 12 monthly payments of $65. The total amount will be:

= 75 + (12 × 65)

= $855

The installment will be:

= $855 - $800

= $55

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Roger Federer's record-tying run of five consecutive Wimbledon Championships was ended in 2008 when he was defeated in the final by Rafael Nadal.

Swiss tennis player Roger Federer, born in Basel, Switzerland, on August 8, 1981, dominated the sport in the early 21st century with his superb all-around performance.

At Wimbledon 2008, Federer made an effort to beat Borg's mark and become the first male player to win six straight Wimbledon championships in the Open Era.

Federer's 41-match winning streak was snapped at Wimbledon when Nadal upset him in his most successful major.

Roger federer's run of 5 consecutive wimbledon championships, a record tied with bjorn borg, was halted when he was defeated in the final in 2008 by Rafael Nadal

The following year, Federer repeated the feat, and in 2010, Nadal once again won the double.

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Answer:

eat dog haha ok thats my answer

Answer:

$220

Step-by-step explanation:

Because, from 1 to 20 there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) so it is said that for one odd number you win $22, as for 10 odd numbers, that is $22 x 10 which is $220