Write the slope-intercept form of the equation of each line.
7) y - 9 =2/3 (x + 6)
8) y + 4 = 8(x - 2)

Both equations are satisfied, so the solutions to the equations are correct.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

\begin{bmatrix}
1 & 4 & 5 & -10 \\
2 & 8 & 6 & -20
\end{bmatrix}

The corresponding equations are:

1x + 4y = -10
2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10
2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Both equations are satisfied, so the solutions to the equations are correct. This can be solved using the concept of matrix.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

[tex]\left[\begin{array}{cccc}1&4&5&-10\\2&8&6&-20\end{array}\right][/tex]

The corresponding equations are:

1x + 4y = -10

2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10

2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Answer: a. in the step by step explanation.  b. 20x - 15

Step-by-step explanation:

I think that Denise thought that the 5 only appplied to 4x since they were closer and since she multiplied them both, she thought there would be no use of it.

Example - 2 (3x+2)

                 2 x 3x = 6x

                 6x + 2

Of course this is wrong since the real answer should be 6x + 12 but someoneone like Denise may see it that way, only multiplying the ones closest and not opening it fully.

It must be less effective than 100%. Any time you switch from one source of energy to another, especially if there is effort involved, there is a cost.

An enzyme is a protein that must retain its three-dimensional structure in order for it to function as a "lock and key." A little alteration to the enzyme structure might render it inoperative.

Denaturation of proteins is common. The protein's structure can change as a result of environmental factors including pH and temperature. An increase in temperature should hasten the process, but an excessive increase might harm the enzyme. Therefore, the situation in which there is no change to the enzyme structure would be the "ideal" one.

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Note : The complete question could be as bellow,

A second set of measurements were taken, and the efficiency was found to be greater than 100%. What reasons most likely explain why the second set had a different efficiency? Select all that apply:

Used the reciprocal of the efficiency formula

Raised the resistance force in a shorter amount of time

Used the incorrect conversion factor from pounds to Newtons for force Incorrect values for the resistance distance

Inaccurate readings from force sensor for effort force

Increase efficiency from reduced friction

Answer:

they always go smallest to largest!

7.65 x 2= 3.21

Step-by-step explanation:

The unit rate of the relationship between the amount of water pumped and time is the amount of water pumped in one minute for 14 hours.

To calculate unit price, you need to divide the first term (quantity) by the second term (unit). The resulting value is the unit price.

For example, if you want to calculate the unit price for a bag of 4 $3 apples, divide the total cost ($3) by the number of apples (4).

$3 / 4 apples = $0.75 / apple

In this example, the unit price is $0.75 per apple. So the price per apple is $0.75.

Given by the equation:

The unit rate of water pumped versus time is the amount of water pumped in one minute, so:

28/2=14

That means 14 gallons of water is being pumped every minute.

Now you can calculate the water pumped in 3/2 minutes like this

14*3/2=21

So in total, water pumped in 12 minutes plus 3/2 minutes gives water pumped in 15/2 minutes.

14*15/2=105

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On solving the provided question, we can say that length of the rectangle pool is  is = 17.58

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

[tex](30+2x)(40+2x)-1200=3696\\1200+60x+80x+4x^2 -1200=3696\\4x^2 +140x-3696=0\\x=17.58 or -52.58\\[/tex]

length is = 17.58

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Three minutes equal 180 beats on the double number line. three minutes of 270 beats 2:180=90 , 3:270=90

In music, a beat is a pulse that occurs repeatedly. Simple meters are those in which the beat first breaks into two, and subsequently into four. There are two beat groups in double meters, three beat groups in triple meters, and four beat groups in quadruple meters.

For double, triple, and quadruple meters, there are several conducting patterns. One group of beats equals one measure (duple, triple, or quadruple). Bar lines divide the measures. Simple meters' time signatures specify two things: the beat unit, or note value that represents the beat, and the number of beats in each measure (the top number). Notes are graphically grouped by beat and connected by a beam.

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Answer:

46

Step-by-step explanation:

The type of angle below is called an alternate angle where the opposite angle is the equal size.

As the angle given is 46 the alternating angle would be 46!

Have a lovely day :)

Answer:

46 because 46 is alternative angle

Answer:

There are 4 quarts in a gallon, so 3 1/2 gallons is equal to 3.5 x 4 = 14 quarts.

Since the shop packages its ice-cream in 1-quart containers, the shop will need 14 containers to fulfill the order.

Step-by-step explanation:

Answer:

[tex]\textsf{1)} \quad 10000(1.06)^t[/tex]

2)   €17,908.48

3)  0.5%

4)  120

[tex]\textsf{5)} \quad 10000(1.005)^{120}[/tex]

6)  €18,193.97

7)  More money.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the compound interest formula to write an expression that describes the given scenario over t years:

[tex]\implies A=10000(1+0.06)^t[/tex]

[tex]\implies A=10000(1.06)^t[/tex]

To calculate how much money will be in the fund after 10 years, substitute t = 10 into the equation from question 1:

[tex]\implies A=10000(1.06)^{10}[/tex]

[tex]\implies A=10000(1.79084769...)[/tex]

[tex]\implies A=17908.4769...[/tex]

Therefore, there will be €17,908.48 in the emergency fund after 10 years.

If the annual rate is 6%, the monthly interest rate is the annual rate divided by 12 (since there are 12 months in a year):

[tex]\implies \dfrac{6\%}{12}=0.5\%[/tex]

Given that are 10 years in the scenario, the exponent will be the number of months in 10 years:

[tex]\implies 10 \times 12 = 120[/tex]

0.5% = 0.005

Therefore, the complete expression that describes the scenario, given an annual interest rate of 6% that compounds monthly over 10 years is:

[tex]\implies 10000(1 + 0.005)^{120}[/tex]

[tex]\implies 10000(1.005)^{120}[/tex]

To calculate how much money will be in the emergency fund after 10 years if the interest compounds monthly, calculate the expression from question 5:

[tex]\implies 10000(1.005)^{120}[/tex]

[tex]\implies 10000(1.81939673...)[/tex]

[tex]\implies 18193.9673...[/tex]

Therefore, there will be €18,193.97 in the emergency fund after 10 years.

Amount in fund when compounded annually = €17,908.48

Amount in fund when compounded monthly = €18,193.97

Therefore, there is more money in the emergency fund when it is compounded monthly as the compounding frequency is greater (interest is earned on both the principal and the interest, so the more frequent the compounding periods are, the more interest is earned).

The general rule about compounding in exponential functions is the higher the number of compounding periods, the greater the amount of compound interest.  

In terms of compounding interest in investment:

The coating thickness distribution is normal and has a mean value of 1.245.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

To calculate the data's coating thickness, sample mean is employed.

The following formula is used to determine the mean value's point estimate:

[tex]\bar x = \frac{1}{n} \sum x_i[/tex]

The typical probability plot shown there has a rather straight pattern. Assume right now that the coating thickness distribution is normal and has a mean value:

[tex]\bar x = \frac{19.92}{16}\\\\\bar x = 1.245[/tex]

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Colton can rent the car for a total of 6 days while still staying within his means.

We are aware that hiring a car costs $72.37 per day, and that each mile travelled costs $0.06. We also know that Colton has a $450 spending limit and intends to go 275 miles.

We may set up the following inequality to determine how long Colton can afford to hire the car for:

72.37d + 0.06(275) <= 450

This inequality indicates that the entire cost must be less than or equal to Colton's $450 budget. It represents the cost of renting the car as well as the cost of the miles driven.

We must isolate d on one side of the inequality in order to solve for it. To calculate the cost of the miles driven, first multiply 0.06 by 275:

72.37d + 16.5 <= 450

After that, we will take 16.5 away from either side of the inequality:

72.37d <= 433.5

A final division of 72.37 will be applied to both sides of the inequality:

d <= 6

Therefore, Colton can rent the car for a total of 6 days while still staying within his means.

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Answer:

13 times

Step-by-step explanation:

lol, I actually did this right now. I got 13 times for both coins being heads, 9 times for each coin being tales, and exactly 30 times both were uneven. I hope this helps :)

The value of x in the simplest radical form is 3.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: Let the triangle be ΔABC

The triangle ABC is a right-angled triangle and the angles inside the triangles are 45°, 45° and 90°

tan θ = x / 3

Now , θ = 45°

So, tan 45° = x / 3

The value of x is 3.

Hence, the value of x is 3.

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6

Step-by-step explanation:

um7

No, the conditions for inference have not been met. The two samples must be independent, meaning that the individuals in the college sample should not also be in the high school sample. Without independent samples, it is not possible to construct a 95% confidence interval for the true mean difference.

1. Collect data from the two samples of seniors in high school and college.

2. Calculate the mean difference in the number of hours of sleep for the two samples.

3. Calculate the standard deviation of the differences in hours of sleep for the two samples.

4. Calculate the standard error of the mean difference.

5. Calculate the critical value for a 95% confidence interval.

6. Calculate the lower and upper bounds of the confidence interval by

adding and subtracting the critical value from the mean difference.

7. Interpret the confidence interval to determine the true mean difference in the number of hours of sleep for seniors in high school and colleg

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It is simpler to compute the likelihood of the complement event when calculating probabilities since you can then just subtract it from 1 to determine the probability.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. It is simpler to compute the likelihood of the complement event when calculating probabilities.

the variety of strategies for success. all events that could possibly occur.

Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.

P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).

where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.

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1) The definition of function F(x) is: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of the cubic function is: A. F(x) = ax³ + bx² + cx + d.

4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

From the graph, the roots of the function are given as follows:

Meaning that the cubic function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept of the function, numerically, is given as follows:

F(0) = a(2² x (-2))

F(0) = -8a.

The y-intercept is positive, meaning that the leading coefficient is negative, and thus the option B is the correct option.

The general format of a cubic function, with leading coefficient a and constant d positive, is given as follows:

y = ax³ + bx² + cx + d.

Meaning that the correct option for item 2 is given by option A.

The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.

From the graph given by the image presented at the end of the answer, using rounding, the approximate solution for item 4 is given by option A.

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Answer:

148

Step-by-step explanation:

first plug in w(x) into u(x):

u(w(x)) = 5(-5(x)+4)+3

then plug in -5 for x:

u(w(-5)) = 5(-5(-5)+4)+3

solve:

= 148

This is a composite function:

Composite functions are are functions that are written within each other like f(g(x).

To solve this problem, first solve the function within u(x), which would be w(x)

w(-5) = -5(-5) -4

        = 25 - 4

       = 21

Now, plug in that value into u(x) to get your final answer:

u(21) = 5(21) +3

         = 105 +3

       = 108

Answer: u(w(-5) = 108

In graph theory, a 2-factor is a subgraph of a given graph that includes every vertex of the original graph and has the property that every vertex has even degree (i.e. degree is a multiple of 2).

The term "2-factor" is used because it is a factor of the original graph that is made up of edges and every vertex has degree 2.

A 2-factor can also be defined as a set of cycles that cover all vertices of the graph. In other words, it is a collection of cycles such that every vertex belongs to exactly one cycle. A 2-factor can also be thought of as a cycle cover of a graph.

A graph that has a 2-factor is called a 2-factorizable graph. Not all graphs are 2-factorizable, for example a graph with an odd number of vertices can't have a 2-factor.

2-factors have many applications in various fields such as scheduling, coding theory, and computer science. They are also used to study the connectivity and robustness of graphs.

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So, the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.

The probability of selecting a Japanese restaurant menu from Zach's collection of 18 menus is found by taking the number of Japanese restaurant menus (4) and dividing it by the total number of menus in the collection (18). This can be written mathematically as:

p(japanese) = 4/18

So the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.

In other words, if Zach selects a menu at random from his collection, there is a 2/9 chance that it will be from a Japanese restaurant.

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The speed of the current is 1 mile per hour.

To calculate we can start by using the formula: distance = speed x time.

Let's call the speed of the current "c" and the speed of Sarah's rowing "r".

When Sarah rows down the river with the current, her speed is the sum of her rowing speed and the current speed: distance = (r + c) * time

When she rows back against the current, her speed is the difference between her rowing speed and the current speed: distance = (r - c) * time

We know that the distance is four miles in both cases, and the time is one hour and two hours respectively.

So we can set up the following two equations:

(r + c) * 1 = 4

(r - c) * 2 = 4

Solving the first equation:

r + c = 4

Solving the second equation:

r - c = 2

Adding the two equations:

r = 3

We know that Sarah is rowing at a constant speed, so we can substitute this value back into one of the original equations:

(3 + c) * 1 = 4

c = 1

So the speed of the current is 1 mile per hour.

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Answer:

The radius of the circle is 5.1, and the diameter of the circle is 10.2

Step-by-step explanation:

In the shown circle, the point from the center to the edge is 5.1, so that is the radius. Then, the diameter of a circle is twice its radius, so we have:

5.1 * 2 = 10.2

So the diameter of the circle is 10.2.

The radius of the circle is 5.1, and the diameter of the circle is 10.2.

Hope this helped!

The perimeter of the triangle is 96, rounded to the nearest hundredth.

To calculate the perimeter of the triangle, we need to first calculate the length of the hypotenuse.

The hypotenuse of a right triangle is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two sides.

Therefore, for this triangle, we have:

(Hypotenuse)² = (24)² + (32)²

Therefore, the Hypotenuse = √(24² + 32²)

Hypotenuse = √(576 + 1024)

Hypotenuse = √1600

Hypotenuse = 40

To calculate the perimeter, we need to add up all three sides of the triangle.

the perimeter = 24 + 32 + 40

the perimeter = 96

Therefore, the perimeter of the triangle is 96, rounded to the nearest hundredth.

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Answer:

5:4

Step-by-step explanation:

girls = 4

boys = 5

ratio = boys:girls = 5:4

HOPE THIS HELPED

The cost of pair of gloves is $8.5 and cost of hat is $6.5. The solution has been obtained by using linear equation.

What is a linear equation?

The equation with the biggest degree of one is one that is linear. The lack of variables in a linear equation with an exponent larger than one is demonstrated by this. A straight line is produced by such an equation on the graph.

Let the cost of pair of gloves be 'x' and cost of hat be 'y'.

We are given that Cody bought two pairs of gloves and four hats for $43.00.

This can be represented as 2x + 4y = $43.00

Tori bought two pairs of gloves and two hats for $30.00.

This can be represented as 2x + 2y = $30.00

On subtracting both the equations, we get

⇒ 2y = 13

⇒ y = 6.5

Substituting this value in the equation, we get

⇒2x + 2(6.5) = $30.00

⇒x + 6.5 = 15

⇒x = 8.5

Hence, the cost of pair of gloves is $8.5 and cost of hat is $6.5.

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Since, there are multiple questions, so the question answered above is attached below.

She reportedly invested $6600 at 3% and $3400 at 2.5%, according to the statement.

Investing is a smart way to put your money to work and could make you richer. If you make smart investing choices, your money may increase in value as outpace inflation. The major factors contributing to investment's increased growth potential are the possibility of compounding and the trade-off amongst risk and return.

Simple interest is calculated as follows: deposit amount multiplied by time and interest rate.

Let "a" represent the money placed in the account earning 3% interest.

Let's use the symbol to represent the amount deposited into the account earning 2.5% interest (10,000 - a)

a * 0.03 plus (10,000 - a) * 0.025 = 283

0.03a + 250 - 0,025a = 283

Collect like terms

0.03a - 0.025a = 283 - 250

0.005a = 33

a = $ 6600

What was put into the 2.5% account = 1000 - 6600 = $ 3400

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Answer:

159

Step-by-step explanation:

The angle below is a co-interior angle

This means that both angle should add up to 180

Have a lovely day :)

Answer:

Step-by-step explanation:

Because we know that the two lines going diagonal are equivalent, we also know that they are parallel because equivalent lines have the same slope, meaning they are parallel. We also know that the two interior angles should add to 180. Follow the steps in the image for the rest.

-Hope this helped

Answer: 6x - 5

Step-by-step explanation:

    Given:

1/6 (12x - 30) + 4x

    Distribute:

2x - 5 + 4x

    Combine like terms with addition:

6x - 5

Answer:

6x - 5

Step-by-step explanation:

Given expression,

→ (1/6)(12x - 30) + 4x

Let's simplify the expression,

→ (1/6)(12x - 30) + 4x

→ ((12x - 30)/6) + 4x

→ 2x - 5 + 4x

→ (2x + 4x) - 5

→ 6x - 5

Hence, the answer is 6x - 5.

Answer:

53

Step-by-step explanation: