[(1/15−2/5)⋅(−3/4)³]÷(−9)

Answer:

f = 40

Step-by-step explanation:

0.25f = 10

f = 40

Let's check

0.25(40) = 10

10 = 10

So, f = 40 is the correct answer.

The value of x in the simplest radical form is 6.633

What is value ?

Value in mathematics can refer to a number of concepts that are closely related. Any specific mathematical object can be a mathematical value in general. In elementary mathematics, this is typically a number, such as a real number like or an integer like 42.

The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. For illustration, let's look at the number 45.

The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.

cos Ф = adjacent / hypotenuse

cos 45° = √22 / x

x = √22 / cos 45°

  = (√22* √2 )

  = √44

  = 6.633

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Answer: Just 1

Step-by-step explanation:

The absolute value is always positive, so there is just 1.

Answer:

See attachment.

Step-by-step explanation:

If CD and MB are parallel, triangle CDE is similar to triangle MBE.

In similar triangles, corresponding sides are always in the same ratio.

[tex]\implies \sf CD:MB=DE:BE=EC:EM[/tex]

From inspection of the given diagram, EM is approximately 0.35 times the length of EC.  Therefore, let EC = 10 and EM = 3.5.

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, let CD = 7 and let DE = 12.

Substitute these values into the created ratio equation:

[tex]\implies \sf 7:MB=12:BE=10:3.5[/tex]

[tex]\implies \sf \dfrac{7}{MB}=\dfrac{12}{BE}=\dfrac{10}{3.5}[/tex]

Calculate BE:

[tex]\implies \sf \dfrac{12}{BE}=\dfrac{10}{3.5}[/tex]

[tex]\implies \sf \dfrac{12 \cdot 3.5}{10}=BE[/tex]

[tex]\implies \sf BE=4.2[/tex]

Calculate MB:

[tex]\implies \sf \dfrac{7}{MB}=\dfrac{10}{3.5}[/tex]

[tex]\implies \sf \dfrac{7 \cdot 3.5}{10}=MB[/tex]

[tex]\implies \sf MB=2.45[/tex]

Therefore:

[tex]\implies \sf CM=EC-EM[/tex]

[tex]\implies \sf CM=10-3.5[/tex]

[tex]\implies \sf CM=6.5[/tex]

[tex]\implies \sf DB=DE-BE[/tex]

[tex]\implies \sf DB=12-4.2[/tex]

[tex]\implies \sf DB=7.8[/tex]

Zach is trying to find out the hypotenuse value of the right-angle triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".

Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.

In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.

Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.

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The confidence interval will be narrower and would involve a larger risk of being incorrect.

A 95% confidence interval and a 99% confidence interval must be compared.

The confidence level is lower for a 95% confidence interval compared to a 99% confidence interval.

The margin of error would be smaller if the confidence level were lower.

As a result, the 95% confidence interval is smaller than the 99% confidence interval.

Because a 95% interval is narrower, fewer values that could provide the parameter with the correct estimate are included in the interval.

Therefore, we can say,

A 99% confidence interval will be shorter than a 95% confidence interval and carry a higher risk of being inaccurate.

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The exact value of the trigonometric expression sin(x - y) is given as follows:

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

The trigonometric expression in the context of this problem is defined as follows:

sin(x - y).

The identity used to obtain the sine of the subtraction of two angles is given as follows:

[tex]sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

Considering the sine of x, the cosine of x is obtained as follows:

[tex]\sin^2{x} + \cos^2{x} = 1[/tex]

[tex]\left(\frac{\sqrt{28}}{6}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\frac{28}{36} + \cos^2{x} = 1[/tex]

[tex]\cos^{2}{x} = \frac{7}{9}[/tex]

[tex]\cos{x} = \frac{\sqrt{7}}{3}[/tex]

The angle y, with a tangent of [tex]\frac{1}{\sqrt{3}}[/tex], is the angle of 30º, hence the sine and cosine are given as follows:

Hence the trigonometric expression is given as follows:

[tex]\sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

[tex]\sin{(x - y)} = \left(\frac{\sqrt{28}}{6}\right) \times \frac{\sqrt{3}}{2} - \frac{\sqrt{7}}{3} \times \frac{1}{2}[/tex]

[tex]\sin{(x - y)} = \frac{\sqrt{84}}{12} - \frac{2\sqrt{7}}{12}[/tex]

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

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Answer:

C. 8 : 1

Step-by-step explanation:

A unit rate is a ratio of a number to one.

To make both sides of the given ratio:

[tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex]

whole numbers (and make the right side 1), simply multiply both sides by the Least Common Multiple (LCM) of the denominators.

To find the LCM of two numbers, list out their prime factorizations and then multiply the highest power of each distinct prime number present.

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5 = 5

20 = 4 * 5

LCM(5, 20) = 4 * 5 = 20

The LCM of 5 and 20 is 20.

Next, we need to multiply 20 by both sides of the ratio.

[tex]20\left(\dfrac{2}{5}\right) : \left(\dfrac{1}{20}\right)20[/tex]

Then, simplify.

[tex]\dfrac{40}{5} : 1[/tex]

[tex]8 : 1[/tex]

So, the unit ratio of [tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex] is 8 : 1.

The slope-intercept form of the given equation is y = -3/5x - 5

From the question, we are to write the given equation in the slope-intercept form

From the given information,

The given equation is

3x + 5y = -25  

The general form for the slope-intercept form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form of a line

3x + 5y = -25

5y = -3x - 25

Divide through by 5

5y/5 = -3/5x - 25/5  

y = -3/5x - 5

The equation is y = -3/5x - 5

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This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

What is probability ?

Probability is a measure of the likelihood of an event occurring, represented as a number between 0 and 1. 0 indicates that an event is impossible, and 1 indicates that an event is certain to happen. It is the ratio of number of favorable outcomes to the total number of possible outcomes.

In this case, the number of favorable outcomes is the number of women in the class, which is 63. The total number of possible outcomes is the total number of students in the class, which is 63 women + 86 men = 149 students. Therefore, the probability of selecting a woman is,

P(woman) = 63/149

So , This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

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Margin of error is 0.017 pound(approximately.)

Now, According to the question:

We know that:

Formula of margin of error :

E = [tex]z^*[/tex] × [tex]\frac{s}{\sqrt{n} }[/tex]

where:

z* = critical value for confidence interval

s= standard deviation

n= sample size.

We have:

s= 0.15 pound

n= 300

Critical value for 95% confidence = 1.96

Then, Margin of error for 95% confidence interval will be :

E = (1.96)[tex]\frac{0.15}{\sqrt{300} }[/tex]

E = 0.0169740971 ≈ 0.017

Hence, Margin of error is 0.017 pound (approximately.)

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On solving the provided question we can say that the polynomial is x² + 6x + 8  by factorization are x(x-5) - 1(x-5) ⇒ (x-1)(x-5) ⇒ x = 5, 1

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x2 – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the polynomial is

by factorization are

x(x-5) - 1(x-5)

(x-1)(x-5)

x = 5, 1

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Answer:

The total number of pencils is 76 x 3 = 228 pencils

If each teacher receives an equal amount of pencils, we can divide the total number of pencils by the number of teachers to find how many pencils each teacher receives:

228 pencils / 4 teachers = 57 pencils/teacher

Each teacher receives 57 pencils.

When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.

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When Claire and Megan meet, they will be [tex]13\frac{1}{2}[/tex] miles away from the outpost. This can be solved by applying the concept of speed.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone [tex]8\frac{1}{2}[/tex] miles. When they meet, they will have gone a total of [tex]17\frac{1}{2}[/tex] miles, leaving them [tex]13\frac{1}{2}[/tex]miles away from the outpost.

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The distance between base of ladder and the building should be

4.4 meter.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC² = AB² + BC²

Given,

Height of the window from the ground AB = 9 meter

Length of the ladder AC = 10 meter

Distance between base of ladder and building BC = ?

By Pythagorean theorem,

In the right ΔABC

AC² = AB² + BC²

10² = 9² + BC²

BC² = 10² - 9²

BC² = 100 - 81

BC² = 19

BC = √19

BC = 4.359 meter

BC = 4.4 meter

Hence, base of ladder should be 4.4 meter away from the building.

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The loop is 4112.16 kilometers long.

To solve this problem, we can set up the following equation:

distance = speed x time

We know that Sarah's current speed is s km/hr, and that the loop is d kilometers long. We also know that her current time is 2 hours and 40 minutes, or 160 minutes.

From the information given, we know that if Sarah increases her speed by 1 km/hr, her time around the loop would be reduced by 6 minutes. Therefore, we can set up the following equation:

d = (s + 1)(160 - 6) = (s + 1)154

We also know that Sarah's current speed is s km/hr, and that the loop is d kilometers long and the time she takes is 160 minutes. Therefore, we can set up the following equation:

d = s * 160

We can now solve for s by substituting the first equation into the second equation:

d = s * 160

d = (s+1)154

s160 = (s+1)*154

We can now solve for s

s = 154/6 = 25.66 km/hr

Now we can plug in s into the first equation we have:

d = s * 160

d = 25.66 * 160

d = 4112.16 km

The loop is 4112.16 kilometers long.

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The amount of food eaten was the dependent variable in this experiment.

Everything that track in the study and what is impacted by it are both considered dependent variables. Depending on the independent variable, the dependent variable will change. Because it "depends" on the independent variable, it is known as a dependent variable. The dependent variable on other measurable variables As a result of an experimental modification of the independent variable or variables, these variables should change.

The amount of study one did, how much sleep one got the night before the test, or even how hungry he or she were can all affect your test result, which makes it a dependent variable. As an example, the test score might be a dependent variable.

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Answer:

a. The area of the square is 25 feet x 25 feet = 625 square feet.

b. To find the percent of points that landed in the pond, we divide the number of points that landed in the pond by the total number of points generated and multiply by 100.

3,200 points / 5,000 points = 0.64

0.64 x 100 = 64%

so 64% of the points landed in the pond.

c. To find the area of the pond, we multiply the proportion of points that landed in the pond by the area of the square.

64% of the points landed in the pond = 0.64

Area of the pond = 0.64 x 625 square feet = 400 square feet. So, the area of the pond, to the nearest square foot, is 400 square feet.

Step-by-step explanation:

Answer: We can use the formula for the sum of an arithmetic series to find the number of pages in the Funny Book. The formula is:

S = n/2 (2a + (n-1)d)

Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, the series is the page numbers, a = 1, d = 1, and we know that there is no page numbered "21" but the page numbered "20" is there.

The number of pages numbered 20 is 20, and the number of pages numbered 19 is 19. So n = 20 + 19 = 39

By substituting the values into the formula

S = 39/2 (2*1 + (39-1)1) = 3920 = 780

The greatest number of pages that the Funny Book can have if it contains a page numbered 20 but not any that are numbered 21 is 780.

Step-by-step explanation:

The p-value is a probability and it should be between 0 and 1.

The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.

Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.

It is also important to note that the p-value is a probability and it should be between 0 and 1.

Therefore,  The p-value is a probability and it should be between 0 and 1.

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No, the given measurement of the sides of a triangle does not forms a right angled triangle.

As given in the question,

For the given triangle,

Length of the sides of the triangle is given by :

8cm , 5 cm , and 10cm

In the given triangle longest side is equal to 10cm

Condition for a right angled triangle:

Longest side is the hypotenuse of the right angled triangle.

By Pythagoras theorem we have,

( Hypotenuse )² = ( Side1)² + ( Side 2)²

R.H.S. ( Right hand side )

= ( 8 )² + (5 )²

= 64 + 25

= 89

≠ 10²

Here given length side of a triangle does not satisfies the Pythagoras theorem .

Therefore, the given sides of a triangle is not representing a right angled triangle.

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Answer:

Step-by-step explanation:

Uh sorry but there is no picture here

Answer:

no graph is attached

Step-by-step explanation:

Using half angle formula,

Half angle formulas are equations that contain the half angles of the trigonometric ratios.

Given that tanα = -1/2 and π/2 < α < π

To find sin(α/2), we use the half angle formula

sin(α/2) = √[(1 - cosα)/2]

Also, tan²α + 1 = sec²α = 1/cos²α

⇒ cosα = ±1/√(1 + tan²α)

Since π/2 < α < π

cosα = -1/√(1 + tan²α)

Substituing this into the equation for sin(α/2), we have

sin(α/2) = √[(1 - cosα)/2]

sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]

Substituting  tanα = -1/2 into the equation, we have

sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]

sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]

sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]

sin(α/2) = √[(1 + 1/√(5/4))/2]

sin(α/2) = √[(1 + 1/√5/2)/2]

sin(α/2) = √[(1 + 2/√5)/2]

sin(α/2) = √[(√5 + 2)/√5)/2]

sin(α/2) = √[(√5 + 2)/2√5

sin(α/2) = √[(√5 + 2)/2√5 × √5/√5

sin(α/2) = √[5(√5 + 2)]/2 × 5

sin(α/2) = √[5(√5 + 2)]/10

So, sin(α/2) = √[5(√5 + 2)]/10

Using the half angle formula,  

tan(α/2) = sinα/(1 + cosα)

Using the trigonometric identity cosα = ±1/√(1 + tan²α)

cosα = ±1/√(1 + (-1/2)²)

cosα = ±1/√(1 + 1/4)

cosα = ±1/√(5/4)

cosα = ±1/√5/2

cosα = ±2/√5

Since π/2 < α < π

cosα = -2/√5

Also, since the trigonometric identity sinα = ±√(1 - cos²α)

So, sinα = ±√(1 - (-2/√5)²)

sinα = ±√(1 - 4/5)

sinα = ±1/√5

Since π/2 < α < π

sinα = +1/√5

Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have

tan(α/2) = sinα/(1 + cosα)

tan(α/2) = +1/√5/(1 + (-2/√5))

tan(α/2) = +1/√5/(1 - 2/√5)

tan(α/2) = +1/√5/(√5 - 2)/√5)

tan(α/2) = 1/(√5 - 2)

So, tan(α/2) = 1/(√5 - 2)

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The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.

Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:

(h(2) - h(-2)) / (2 - (-2))

First, we have to find h(2) and h(-2) by substituting these values in the function:

h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5

h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5

So, the average rate of change is:

(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25

Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25

The greatest possible error for 25 miles is 12.5 miles.

Half of the unit of measure to which a measurement is rounded is the largest possible error. The maximum error is 2 units when a measurement is taken to the nearest whole unit 4.

Given, A value of 25 miles.

Now, we know the greatest possible error is half of the unit of measure.

Therefore, The greatest possible error for 25 miles is,

= (25/2) miles.

= 12.5 miles.

As 12.5 miles is half the value of 25 miles.

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Answer: Please use this method
Periods N = 8 years x 12 = 96 periods
The interest rate I = 4.5 % per year, compounding, divided by 12 = 0.375 % for each period.
Present value PV = minus $ 6,981.46
Future value FV = $ 10,000.20

Step-by-step explanation:

The object will travel 639.36 yards in one minute.

Formula: Yards = Feet x 0.3333

The question is asking how many yards an object will travel in one minute when it is moving at a constant rate of 32 feet per second.

We can use the formula above to calculate the number of yards the object will travel in one minute. We know that the object is traveling at a rate of 32 feet per second.  To find the number of yards traveled in one minute, we need to multiply 10.6667 yards per second by 60 seconds in a minute. Therefore, in one minute (60 seconds), the object will travel 32 x 60 = 1920 feet. We can now use the formula to convert this to yards: Yards = 1920 x 0.3333 = 639.36 yards. Therefore, the object will travel 639.36 yards in one minute.

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A degree 3 polynomial has either 1 real root, 2 real roots, or 3 real roots. It is possible for the polynomial to have imaginary roots as well, but these are not counted.

A polynomial of degree 3 is a equation in the form of ax3 + bx2 + cx + d = 0. For a polynomial of degree 3, the number of roots it has depends on the value of the discriminant, which is calculated using the formula b2 - 4ac.  If the discriminant is positive, the polynomial has three real roots. If the discriminant is equal to zero, the polynomial has two real roots. If the discriminant is negative, the equation has one real root and two imaginary roots. In the case of one real root, the polynomial can be factored into (x - r) (ax2 + bx + c). In the case of two real roots, the polynomial can be factored into (x - r1) (x - r2). In the case of three real roots, the polynomial can be factored into (x - r1) (x - r2) (x - r3).

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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:

6-y^2 can be factored by using the difference of squares formula which states that:

a^2 - b^2 = (a+b)(a-b)

We can factorize 6-y^2 by using the following:

6 - y^2 = (sqrt(6) + sqrt(-y^2))(sqrt(6) - sqrt(-y^2))

= (sqrt(6) + yi)(sqrt(6) - yi)

where i is the imaginary unit.

So, 6-y^2 = (sqrt(6) + yi)(sqrt(6) - yi) is the factored form of 6-y^2

Please note that the factorization is only true for real values of y, when y is not real the expression can't be factorized.