Rectangle a has side lengths of 6 cm and3.5 cm. The side lengths of rectangle B are proportional to the side lengths of rectangle a

With placing positive integers around the circle. Yes, there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.

What exactly is a circle?

A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.

The equation for a circle in the plane is:

(x-h)^²+ (y-k)² = r²

When the coordinate points are (x, y)

(h, k) is the coordinate of a circle's center.

where r is the circumference of a circle.

where circle area = πr²

Circle circumference=2πr

Now,

First 10 positive integers

that are 1,2,3,4,5,6,7,8,9,10

after putting these in circle 1 and 10 will be adjacent

and

To prove :-there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17 .

Now as sum of =5+6+7=18

6+7+8=21

7+8+9=24

Hence,

           There exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.

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The maximum area is 900 square meters

Given that

Perimeter, P = 120

So, we have

P = 2(l + w) = 120

This gives

l + w = 60

Make l the subject

l = 60 - w

The area is

A = lw

So, we have

A =w(60 - w)

Expand

A = 60w - w^2

Differentiate and set to 0

60 - 2w = 0

So, we have

w = 30

Recall that

A =w(60 - w)

So, we have

A = 30(60 - 30)

Evaluate

A = 900

See attachment

This is represented as follows

Length (l) | Width (w) | Area (A)

30 | 30 | 900

35 | 25 | 875

40 | 20 | 800

45 | 15 | 675

50 | 10 | 500

55 | 5 | 275

See attachment

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Answer:

900 m²

Step-by-step explanation:

The maximum possible area of a rectangle is when the width and length are equal, i.e. it is a square.

To find the side length of a square, divide its perimeter by 4. Therefore, the width and length of a rectangle with perimeter 120 m is:

[tex]\implies \sf \dfrac{120}{4}=30\;m[/tex]

The area of a square is the square of its side length, so the maximum area for a rectangle with perimeter of 120 m is:

[tex]\implies \sf Area=30^2=900\;m^2[/tex]

The formula for the perimeter of a rectangle is:

[tex]\boxed{\sf Perimeter=2(width+length)}[/tex]

Therefore, if the perimeter is 120 m:

[tex]\implies \sf 120=2(width+length)[/tex]

[tex]\implies \sf width+length=60[/tex]

So the width and length must sum to 60 m.

Sketch various rectangles where the sum of their width and length is 60 m.  For example:

The formula for the area of a rectangle is:

[tex]\boxed{\sf Area=width \times length}[/tex]

A table with the width, length and areas (in increments of 5 m for the lengths) is as follows:

[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \sf width\;(m)&\sf length\;(m)& \sf area\;(m$^2$)\\\cline{1-3}\vphantom{\dfrac12}5&55&275\\\vphantom{\dfrac12}10&50&500\\\vphantom{\dfrac12}15&45&675\\\vphantom{\dfrac12}20&40&800\\\vphantom{\dfrac12}25&35&875\\\vphantom{\dfrac12}30&30&900\\\vphantom{\dfrac12}35&25&875\\\vphantom{\dfrac12}40&20&800\\\vphantom{\dfrac12}45&15&675\\\vphantom{\dfrac12}50&10&500\\\vphantom{\dfrac12}55&5&275\end{array}[/tex]

Let x be the length of the rectangle (in meters).

Let y be the area of the rectangle (in meters squared).

From inspection of the values of area from the table from part (b), the function is quadratic, since the second differences between the y-values is constant.  The maximum point (vertex) is (30, 900).  Therefore, the graph is a parabola that opens downwards.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

As the vertex is (30, 900) and the parabola opens downwards (so the value of "a" is negative):

[tex]\implies y=-a(x-30)^2+900[/tex]

To find the value of a, substitute one of the other points into the equation:

[tex]\implies -a(10-30)^2+900=500[/tex]

[tex]\implies -a(-20)^2=-400[/tex]

[tex]\implies -400a=-400[/tex]

[tex]\implies a=1[/tex]

Therefore, the equation of the parabola is:

[tex]y=-(x-30)^2+900\qquad \{x|\;0 < x < 60\}[/tex]

Note: If the measure of one side of the rectangle is 60 m, then the measure of the adjacent side will be 0 cm, which is impossible. Therefore, the domain of the function must be set to (0, 60).

From inspection of the table, the maximum area of a rectangle that has a perimeter of 120 m is when its width and length are both 30 m.

From the graph of the relationship between length and area of a rectangle with a perimeter of 120 m, the maximum area is when the length is 30 m ⇒ max area = 900 m².

Therefore, the maximum area of the rectangle is 900 m².

The value of the segment JK in the given triangle is 7.40 units.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

The trigonometric function cos is given as:

Cos A = adjacent side / hypotenuse

Using the function of cos:

Cos J = adjacent side / hypotenuse

Cos 22 = x / 8

0.927 (8) = x

x = 7.40

Hence, the value of the segment JK in the given triangle is 7.40 units.

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The solution is, the value of x= 12.4.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

radius = 22

so, from the given diagram we get,

height of the right angle triangle = √22²-19.8²

                                                      =9.59

so, x = 22- 9.59

       = 12.41

Hence, The solution is, the value of x= 12.4.

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Answer: P'(50) = -200 means that the derivative of P(t) with respect to t, evaluated at t = 50, is equal to -200. The derivative of a function represents the rate of change of the function. In this case, P'(50) = -200 represents the rate of change of the number of individuals infected by the disease 50 days after it was first detected.

Since P'(50) = -200, this means that the number of individuals infected by the disease is decreasing at a rate of 200 individuals per day when t = 50. In other words, 200 individuals are recovering or being treated each day, so the total number of infected individuals is decreasing.

Step-by-step explanation:

Answer: [-3, 13)

A square bracket [] means it includes the number, and a round bracket () means that value is not included.

Answer:

The equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.

Step-by-step explanation:

Given the points (4, 2) and (2, 4), we can use the point-slope form of a line, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

To find the slope m, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values for the two points, we get:

m = (4 - 2) / (2 - 4) = 2 / -2 = -1

Next, we'll substitute one of the points and the slope into the point-slope form:

y - 2 = -1 (x - 4)

Expanding the right-hand side, we get:

y - 2 = -x + 4

Adding x and 2 to both sides, we get:

y = -x + 6

So, the equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.

Step-by-step explanation:

college level question ???? what the ...

oh my.

16 : 20 = 16 / 20 = 16 ÷ 20

16/20 = 4/5 = 0.8

The homeowner will need 43 packages of flooring material and it will cost him $388.29.

What is the arithmetic?

Arithmetic is a branch of mathematics that deals with the study of numbers, including their properties, operations, and calculations. It involves performing basic mathematical operations, such as addition, subtraction, multiplication, and division, on numbers to solve mathematical problems.

The first room requires 24 ft * 15 ft = 360 square feet of flooring.

The second room requires 12 ft * 13 ft = 156 square feet of flooring.

So, the total amount of flooring material required is 360 + 156 = 516 square feet.

The homeowner will need 516 square feet / 12 square feet per package = 43 packages of flooring material.

So, the cost will be 43 packages * $9.03 per package = $388.29.

Hence, The homeowner will need 43 packages of flooring material and it will cost him $388.29.

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The slope of the line through the points is 4/7 and the graph is given below.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that, the points ​(14​,8​) and ​(28​,​16) form a proportional relationship.

A proportional relationship will be of the form y = kx, where k is the slope or constant of proportionality.

We have two points ​(14​,8​) and ​(28​,​16).

Slope = (16 - 8) / (28 - 14) = 8/14 = 4/7

Equation of the line is y = 4/7 x

When x = 0, y = 0

When x = 7, y = 4/7 × 7 = 4

When x = 14, y = 4/7 × 14 = 8

When x = 21, y = 4/7 × 21 = 12

and so on.

So the points are (0, 0), (7, 4), (14, 8), (21, 12), (28, 16) and so on.

Hence the slope of the line is 4/7.

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The equation of the line perpendicular to 5x - 3y = 12 is y = -3/5x + 64.

Given that two lines are perpendicular, their slopes are negative reciprocals of each other.

The equation 5x - 3y = 12 can be rearranged to find the slope:

y = (5/3)x - 4

So the slope of the line is 5/3.

The slope of a line perpendicular to it would be the negative reciprocal of 5/3:

-3/5

Since both lines intersects at x = 30, find a point on both lines by substituting x = 30 into 5x - 3y = 12:

5(30) - 3y = 12

150 - 3y = 12

-3y = 12 - 150

-3y = -138

y = 46

Write the equation of the perpendicular line by substituting (a, b) = (30, 46) and m = -3/5 into y - b = m(x - a):

y - 46 = -3/5(x - 30)

Rewrite in Slope-intercept form:

y - 46 = -3/5x + 18

y = -3/5x + 18 + 46

y = -3/5x + 64

The equation is: y = -3/5x + 64

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Answer:

[tex]\displaystyle y=\frac{1}{1-4e^{-x}}[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{1}{1+C_1e^{-x}}\\\\-\frac{1}{3}=\frac{1}{1+C_1e^{-0}}\\\\-\frac{1}{3}=\frac{1}{1+C_1}\\ \\ 3=-1-C_1\\\\4=-C_1\\\\-4=C_1[/tex]

Thus, the specific solution to the IVP given the initial condition is [tex]\displaystyle y=\frac{1}{1-4e^{-x}}[/tex]

The solution to the system of equations is 6kg of 15 % chromium and 3kg of 18 % stainless steel

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of chromium be x

Let the amount of stainless steel be y

The percentage of amount of chromium = 15 % of x

The percentage of amount of stainless steel = 18 % of y

Now , the amount of mixture = 9 kg

The percentage of amount of mixture = 17 %

So , the equation will be

x + y = 9   be equation (1)

0.15x + 0.18y = 0.17 ( 9 )

On simplifying the equation , we get

15x + 18y = 153  

Divide by 3 on both sides of the equation , we get

5x + 6y = 51   be equation (2)

Multiply equation (1) by 5 , we get

5x + 5y = 45   be equation (3)

Subtracting equation (3) from equation (2) , we get

y = 6 kg

So , the value of x = 3 kg

Hence , the mixture contains 6kg of 15 % chromium and 3kg of 18 % stainless steel

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a)  v(t) = -32t + 80 feet/second  and a(t)= -32 feet/second²

b. t = 3 seconds.

c. 24 feet/second > 0).

d.  the time at which the rock reaches its highest height is 2.5 seconds and 80 feet respectively.

e. the acceleration is given by a(2.5) = -32 feet/second²

The velocity, v(t), of the rock is given by the derivative of the position function s(t) with respect to time,

v(t) = ds(t)/dt = -32t + 80 feet/second.

The acceleration, a(t) = dv(t)/dt = -32 feet/second²

b) v(3) = -32*3 + 80 = 24 feet/second.

This quantity represents the velocity of the rock at t = 3 seconds.

c) At t = 3 seconds, the rock is rising up because the velocity is positive (v(3) = 24 feet/second > 0).

d) the time at which the rock reaches its highest height,

v(t) = 0, we get -32t + 80 = 0, so t = 80/32 = 2.5 seconds.

The height of the rock will be found using the position function s(t), so s(2.5) = -16(2.5)^2 + 80(2.5) = 80 feet.

e) At the highest height, the velocity of the rock is 0, so the acceleration is given by a(2.5) = -32 feet/second².

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Answer:

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5.

6.

7. imaginary number

Step-by-step explanation:

i think this is it I'm so sorry if its wrong

i cant figure out 5 and 6 so sorry

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5. real irrational root

6. real ration root, whole number

7. imaginary number

The coordinates of the vertex will be (-1/12, 23/24).

ax²+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, a quadratic equation F( x )=6 x²+ x +1

Compared with the general formula of the quadratic equation ax²+bx+c=0,

a = 6

b = 1

c = 1

Solving the equation:

F( x )=6 x²+ x +1

F( x ) - 1 =6 x²+ x

f(x) - 1 = 6(x² + x/6)

f(x) -1 = 6(x² + x/6 + 1/144 - 1/144)

f(x) - 1 = 6(x + 1/12)² - 1/24

f(x) = 6(x + 1/12)² - 1/24 + 1

f(x) = 6(x + 1/12)² + 23/24

From the general formula of a quadratic equation to vertex form will be

F(x) = a(x-h)² + k

h will be -1/12 and k  will be  23/24

therefore, The coordinates of the vertex will be (-1/12, 23/24).

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The formula to calculate the number of books donated by Hannah would be: bbb/150150150 = 333.

Essentially, we are taking the total number of books that were donated, bbb, and dividing it by the total number of students at Hannah's school, 150150150. The result of this equation is 333, which represents the number of books Hannah donated. To calculate this number we would first divide bbb by 150150150. Then, we would multiply the result by 333 to get the total number of books Hannah donated. For example, if the total number of books donated was 300,000, the number of books Hannah donated would be 49,950. This can be calculated by dividing 300,000 by 150150150 and then multiplying the result by 333.

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The coordinate of the quadrilateral DEFG after trnaslation, reflection and dilation is mention on the graph.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The vertices of the quadrilateral DEFG (Red) is given as,

D(2, 2), E(6, 2), F(8, 4), G(2, 4)

The vertices of the quadrilateral D'E'F'G' after translation (Green) is given as,

D'(2, -4), E'(6, -4), F'(8, -2), G'(2, -2)

The vertices of the quadrilateral D"E"F"G" after reflection (Purple) is given as,

D"(-2, -4), E"(-6, -4), F"(-8, -2), G"(-2, -4)

The vertices of the quadrilateral D'''E'''F'''G''' after reflection (Black) is given as,

D'''(-1, -2), E'''(-3, -2), F'''(-4, -1), G'''(-1, -2)

The coordinate of the quadrilateral DEFG after trnaslation, reflection and dilation is mention on the graph.

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A) There are 100 * 99 * 98 * 97 ways to award the prizes, since there are 100 choices for the first prize, 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize..

What is the combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects, such as numbers, sets, and permutations.

B) If the person holding ticket 47 wins the grand prize, there are 99 * 98 * 97 ways to award the remaining prizes, since there are 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.

C) If the person holding ticket 47 wins one of the prizes, there are 100 * 99 * 98 * 97 ways to award the prizes.

D) If the person holding ticket 47 does not win a prize, there are 99 * 98 * 97 * 96 ways to award the prizes, since there are 99 choices for the first prize, 98 choices for the second prize, 97 choices for the third prize, and 96 choices for the fourth prize.

E) If the people holding tickets 19 and 47 both win prizes, there are 98 * 97 * 96 * 95 ways to award the remaining prizes, since there are 98 choices for the third prize, 97 choices for the fourth prize, 96 choices for the fifth prize, and 95 choices for the sixth prize.

F) If the people holding tickets 19, 47, 73, and 97 all win prizes, there are 96 * 95 * 94 * 93 ways to award the remaining prizes, since there are 96 choices for the fifth prize, 95 choices for the sixth prize, 94 choices for the seventh prize, and 93 choices for the eighth prize.

G) If none of the people holding tickets 19, 47, 73, and 97 wins a prize, there are 96 * 97 * 98 * 99 ways to award the prizes, since there are 96 choices for the first prize, 97 choices for the second prize, 98 choices for the third prize, and 99 choices for the fourth prize.

H) If the grand prize winner is a person holding ticket 18, 47, 73, or 97, there are 3 * 99 * 98 * 97 ways to award the remaining prizes, since there are 3 choices for the grand prize winner (18, 47, or 73), and 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.

I) If the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes, there are 98 * 97 * 96 * 95 ways to award the prizes, since there are 98 choices for the first prize, 97 choices for the second prize, 96 choices for the third prize, and 95 choices for the fourth prize.

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The upper critical value to be used in constructing a 94% confidence interval is 1.88.

What is meant by confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. At a specified level of confidence, a confidence interval is calculated. The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

In statistics, confidence is another word for probability. The most typical level of confidence is 95%, however, higher levels, such as 90% or 99%, are occasionally employed.

The confidence interval is given as 94% = 0.94

Based on the normal population, a confidence interval for a population proportion is calculated, and a normal probability table is then used to determine the critical value.

So if the confidence interval is 94%, the rest 6% of the data will be present outside the given confidence interval.

Out of the 6%, 3% of data will be present on either side of the interval.

So the critical value will be the value of [tex]z_{\frac{\alpha }{2} } = z_{0.03 }[/tex] = 1.88.

Therefore the upper critical value to be used in constructing a 94% confidence interval is 1.88.

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Value of angle x = 70°

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Given,

ACD = 35

BCE = 105

ABC = x

By, the figure

BA || CD

⇒ ACD = BAC (alternate angles on AC)

⇒ BAC = 35°

BCE = 105

Exterior angle is equal to sum of two opposite interior angles in the triangle.

BCE = BAC + ABC

105 = 35 + x

x = 105 - 35

x = 70°

Hence,

70° is measure of x.

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I identified the Atmospheric conditions such as air pressure, temperature, and relative humidity conditions that cause snow, rain, thunderstorms, fog, and clear sky in the lab. I discovered that low-pressure zones typically have snow, rain, and stormy weather, and high-pressure areas typically have foggy or bright weather.

Atmospheric conditions, such as temperature, pressure, humidity, wind direction, and the presence of fronts, greatly influence weather patterns.

Changes in air pressure result in winds, which can transport warm or cold air, moisture, and storms. High humidity leads to clouds and precipitation, while low humidity often results in clear skies.

Note that temperature differences between different air masses can create fronts, which are boundaries separating different air masses, leading to changes in weather.

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Full Question:

"How do atmospheric conditions influence weather patterns?

Statements about the mean that are true-It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.

It is also known as the arithmetic mean, arithmetic average, or simply average. The mean measure of central tendency is also known as these terms.

When there are even numbers of data points rather than odd numbers, there might be more than one median when the two middle numbers are divided by two.

When there are scores that are uncertain, it can be located: With uncertain scores, the median can be discovered.

The mode is a real number in the data that occurs more frequently than other values, hence it correlates to an actual score in the data.

There can be more than one: there are multiple modes (bimodal, trimodal, and multimodal) where two or more values appear the same number of times.

Hence, the statements that are true about means are -It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.

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Answer:

Step-by-step explanation:

To calculate the amount of interest earned by Amelia's investment, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt), where

A = amount after t years

P = principal amount ($9810)

r = annual interest rate (2.7%)

n = number of times the interest is compounded per year (quarterly, so n = 4)

t = number of years (13)

Plugging in the values, we get:

A = $9810 * (1 + (0.027/4))^(4 * 13)

A = $9810 * (1.00675)^52

A = $9810 * 1.8972436

A = $18561.61 (rounded to nearest cent)

Therefore, the interest earned by Amelia's investment is $18561.61 - $9810 = $8751.61.

The values of the compositions of the functions are.

Here we have two graphs for functions f(x) and g(x), and we need to use these to find the values of some compositions.

First, we want to find the value of:

f(g(5))

Using the second graph we can see that g(5) = 0, then:

f(g(5)) = f(0)

and using the first graph we can see that f(0) = 4, then

f(g(5)) = 4.

The second expression is:

g(f(1))

And we cans ee that f(1) = 3, then:

g(f(1)) = g(3) = 1

So:

g(f(1)) = 1

And so on, for the next two we have:

f(f(4)) = f(2) = 0

g(g(3)) = g(1) = 5

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Answer:

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by adding 1/2 (12x - 2) to both sides of the equation:

-1/2 (12x - 2) + 1/2 (12x - 2) = -6x - 1 + 1/2 (12x - 2)

Combining like terms on the right side of the equation, we get:

0 = -6x + 12x - 1 + (12x - 2) / 2

Simplifying further:

0 = 6x - 1 + 6x

Combining like terms again:

0 = 12x - 1

Adding 1 to both sides:

1 = 12x

Finally, dividing both sides by 12:

x = 1/12

Step-by-step explanation:

Answer: No solution.

Step-by-step explanation:

1.) Distribute -1/2

-6x + 1 = -6x - 1

2.) Move over terms to combine

0 = -2

There is no solution to this equation.

Answer:

Step-by-step explanation:

2-A

3- trapezium

4 - perpendicular

6- A

Answer:

13.9873

Step-by-step explanation:

This problem can be solved using long division, use the picture for reference below.

First, change the divisor 6.3 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

881.2 ÷ 63 = 13.9873

and therefore:

88.12 ÷ 6.3 = 13.9873

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