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The solutions to the equatiοn [tex]2x^2 + 2x - 12 = 0[/tex] are x = 2 and x = -3.

It is a secοnd-degree quadratic equatiοn, an algebraic equatiοn in x. The quadratic equatiοn in its standard fοrm is written as Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term. An equatiοn must have a zerο-terminal term (a 0) fοr the x²  cοefficent in οrder tο qualify as a quadratic equatiοn.

When cοnstructing a quadratic equatiοn in standard fοrm, the x²  term is written first, fοllοwed by the x term, and finally the cοnstant term. The numerical values οf letters a, b, and c are typically expressed as integral values rather than fractiοns οr decimals.

[tex]x = (-b \± \sqrt{ (b^2 - 4ac)}) / 2a[/tex]

where a = 2, b = 2, and c = -12. Substituting these values, we get:

[tex]x = (-2 \± \sqrt{(2^2 - 4(2)(-12))) / 2(2)[/tex]

[tex]x = (-2 \± \sqrt{(100)}) / 4[/tex]

[tex]x = (-2 \± 10) / 4[/tex]

Sο the sοlutiοns are:

x = (-2 + 10) / 4 = 8/4 = 2

x = (-2 - 10) / 4 = -12/4 = -3

Therefore, the solutions to [tex]2x^2 + 2x - 12 = 0[/tex] are x = 2 and x = -3.

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1. Option 1 multiply 18 m by 0.09361 yd is the correct answer.

2. The cost of the wallpaper will be $1013.

A conversion factor is a ratio used to convert a measurement in one unit to the equivalent measurement in another unit.

In order to convert 18 meters to yards, we must multiply 18 m by 0.09361 yd.

This is because when converting from one unit to another, we must use the conversion factor to multiply, rather than divide.

In this case, the conversion factor is 0.09361 yd/m.

Therefore, we must multiply 18 m by 0.09361 yd to get the answer.

Therefore, the correct answer is option 1, which is to multiply 18 m by 0.09361 yd.

2. To answer the second question, Ken is buying wallpaper. It costs $6.49 per meter.

He needs 512 feet.

To calculate how much the wallpaper will cost, first convert 512 feet to meters.

1m = 3.28ft,

therefore 512ft ÷ 3.28ft = 156.1m.

Then multiply the cost of wallpaper per meter, $6.49, by the number of meters needed, 156.1m.

156.1*$6.49=$1013.07.

To round the nearest half dollar, the cost of the wallpaper will be $1013.

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The equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

What is the rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity. It is expressed as a ratio of two different units, and it indicates how fast or slow one quantity is changing in relation to another quantity.

If we assume that a person's height decreases by 0.06 cm per year starting at age 30,

we can use the following equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

where h(30) represents the person's height at age 30.

This equation assumes that the rate of height decrease is constant and linear over time.

Hence, the equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

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After answering the provided question, we can conclude that Therefore, trigonometry the helicopter's horizontal distance to the hiker is approximately 388 feet.

The study of the relationship between triangle wall lengths and angles is known as trigonometry. The topic first emerged in the Hellenistic era, around the third century BC, because of the utilization of geometry in astronomical studies. The branch of mathematics known as precise methods deals with certain quaternion functions and about there potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, buying new furniture, secant, and cosecant are their person names and acronyms (csc). The study of triangle properties, specially those of right triangles, is known as trigonometry. As a result, geometry is really the study of the properties of all geometric shapes.

We can use trigonometry to solve this problem. Let's start by drawing a diagram:

             Hiker

               /|

              / |

             /  | 1500 ft

            /   |

           /θ   |

          /     |

         /14°   |

        /_______|

     Helicopter

We are looking for the horizontal distance between the helicopter and the hiker, which we can call x. We know the altitude of the helicopter (1500 ft), and we know the angle of depression (14°).

From the diagram, we can see that:

tan(14°) = x / 1500

We can solve for x:

x = 1500 * tan(14°)

x ≈ 387.7 ft

Therefore, the helicopter's horizontal distance to the hiker is approximately 388 feet.

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The specified circle's center is at (-7, 4). The revised center will therefore be (-7 - 3, 4 - 4) = (-10, 0).

We must deduct 3 from x and 4 from y in order to move the circle 3 units to the right and 4 units below. The revised center will therefore be (-7 - 3, 4 - 4) = (-10, 0).

By inserting the new center and simplifying, it is possible to find the equation for the resulting circle. The equation for a circle has the conventional form[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the circle's center and r is its radius. Since the original equation is[tex](x+7)^2+(y-4)^2=36[/tex], we may substitute the new center (-10, 0) and the radius 6 to obtain [tex](x + 10)^2 + y^2 = 36[/tex]as the equation of the translated circle.

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The 43rd term of the sequence is -4,930.

A recursive formula is one that defines each term in a sequence by reference to the one before it (s). The following parameters are defined using the recursive formulas:

The opening phrase of the series

The formula to calculate any phrase from its previous term

In the given series we have, a_1 = 1,916 and a_n = a_{n-1} - 163.

Thus,

a_1 = 1,916

a_2 = a_1 - 163 = 1,753

a_3 = a_2 - 163 = 1,590

a_4 = a_3 - 163 = 1,427

Here, each term is 163 less than the previous term.

Thus,

a_{43} = a_{42} - 163 = a_1 - 42(163) = 1,916 - 6,846 = -4,930

Hence, the 43rd term of the sequence is -4,930.

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The circumference of the circle with a radius of 6 feet would be approximately 37.7 feet.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter of the circle, which is the total length of the boundary that encloses the area of the circle.

The formula for the circumference of a circle is

C = 2πr

Where C is the circumference, r is the radius, and π is approximately 3.14.

If a circle has a radius of 3 feet, the circumference would be

C = 2πr

C = 2π(3)

C ≈ 18.85 feet

When the radius doubles to 6 feet, the circumference would be

C = 2πr

C = 2π(6)

C ≈ 37.7 feet

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Answer:

double, and 36

Step-by-step explanation:

Mc graw hill

Q...

The solutions for the equation [tex]y=-4(x-2)^2+6[/tex] are as follows [tex]x = 2 + \sqrt{(6 - Y) / 4}[/tex] or [tex]x = 2 - \sqrt{(6 - Y) / 4}[/tex].

The given equation is in standard form for a quadratic equation, where the coefficient of [tex]x^2[/tex] is negative. This means the graph of the equation is a downward-opening parabola, and the vertex of the parabola is (2, 6).

To solve the equation, we can first isolate the variable Y on one side:

[tex]Y - 6 = -4(x - 2)^2[/tex]

Then we can divide both sides by -4:

[tex](Y - 6) / -4 = (x - 2)^2[/tex]

Next, we can take the square root of both sides:

[tex]\sqrt{[(Y - 6) / -4] }= x - 2[/tex]

[tex]\pm \sqrt{(Y - 6) / -4}= x - 2[/tex]

So the solutions are:

[tex]x = 2 + \sqrt{(6 - Y) / 4}[/tex] or [tex]x = 2 - \sqrt{(6 - Y) / 4}[/tex]

These equations give the x-coordinates of the points on the graph of the equation for a given value of Y.

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Caleb's yearly expense for his internet service and Netflix subscription is $695.76.

To write an equation for Caleb's yearly expenses, we need to first determine his total monthly expense and then multiply it by 12 to get the yearly expense.

Caleb's monthly expense can be calculated as the sum of the internet and Netflix costs, which is:

$14.99 + $14.99 = $29.98

To include the initial setup fee of $28, we can add it to the monthly expense to get

$29.98 + $28 = $57.98

This is Caleb's total monthly expense, and to find his yearly expense, we can multiply it by 12

$57.98 x 12 = $695.76

Therefore, the equation for Caleb's yearly expense is

Yearly expense = 12 x (monthly internet cost + monthly Netflix cost + initial setup fee)

Yearly expense = 12 x ($14.99 + $14.99 + $28)

Yearly expense = $695.76

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The given question is incomplete, the complete question is:

Caleb got internet service at home from a company called "Inter-What??". The company charged him $28 to hook it up. Then joined Netflix. He pays $14. 99 a month to keep the internet connected and he also pays the same amount for Netflix. Write an equation and find the yearly expense

Answer:

For the second set of numbers, 23, 16, 4, 10, 16, 65, 8:

Mean: To find the mean, we add up all the numbers and divide by the total number of numbers:

(23 + 16 + 4 + 10 + 16 + 65 + 8) / 7 = 142 / 7 = 20.2857 (rounded to 4 decimal places)

Median: To find the median, we need to first arrange the numbers in order from smallest to largest:

4, 8, 10, 16, 16, 23, 65

There are an odd number of numbers (7), so the median is the middle number, which is 16.

Mode: The mode is the number that appears most frequently in the set. In this case, 16 appears twice, which is more than any other number, so the mode is 16.

Range: To find the range, we subtract the smallest number from the largest number:

65 - 4 = 61

So the mean is 20.2857, the median is 16, the mode is 16, and the range is 61.

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The product of -10(15 + 25h) is -150 - 250h.

In mathematics, a product is the result of multiplying two or more numbers or quantities together. The product is a fundamental operation in arithmetic and algebra, and it is denoted by the symbol "×" or "." or by placing the numbers or quantities next to each other without any symbol.

In the given question,

To use the area model to multiply -10(15+ 25h),We can label the dimensions of the rectangle as 15 and 25h, and we can label the value we want to multiply by (-10) as -10. Then, we can find the area of each of the smaller rectangles by multiplying the corresponding dimensions together:

To find the product of -10(15 + 25h), we can add the areas of the two smaller rectangles:

-10(15 + 25h) = -150 - 250h

Therefore, the product of -10(15 + 25h) is -150 - 250h.

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Answer:

A = 47 degrees

Step-by-step explanation:

cosineA = adjacent/hypotenuse

cosineA =  34/50

cosineA = 0.68

reverse cosine

A = 47 (rounded to the nearest whole number)

If they are equal, then the methods are consistent; if not, they yield different solutions, possibly due to varying techniques or assumptions.

Hi! Based on the information provided, it seems you are comparing two methods for finding the altitude of a triangle.

The previous activity gave an altitude of 9,000. If the new method also results in an altitude of 9,000, then both methods give the same solution.

To determine if they are the same, compare the calculated values from each method.

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Answer:

3(y-2)=2(y-1)-3

or, 3y-6 =2y-2-3

or, 3y-6 =2y-5

or 3y-2y =6-5

or y=1

hence, the value of y is 1

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Of the company's customers, the number that would be expected to experience pain relief from the shoes is 2832.

An experiment is a process done by scientific and mathematical methods.

Analysis:

The number of people in each group is:

in the first group "60x70% = 672

in the second group 960X 60% =576

in the third group 960x 450 x 8432

in the fourth group 960 x 55% =528

in the fifth group 960x65% =62e

The total number of five experimental groups of customers is

2832.

Therefore, the total number of five experimental groups of customers is

2832.

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Answer:

b = 6(x - 3)

Step-by-step explanation:

Answer: 4[tex]\sqrt{13}[/tex]

Step-by-step explanation:

pythagrean's therom: a^2 +b^2 = c^2

(8)^2 +(12)^2 = c^2

64 +144 = c^2

[tex]\sqrt{208}[/tex] = c

[tex]\sqrt{(4)^2 (13)}[/tex] = c

4[tex]\sqrt{13}[/tex] = c

Median is 67. We see comparing the medians that the Allstars are likewise taller on average than the Champs. Conclusion is that the Allstars have taller players than the Champs based on central tendency from data.

We may compare the measures of central tendency of the heights of the players on both teams to see which team normally has the tallest players. The median and mean are the two often used measurements of central tendency based on data.

We add together all the heights and divide by the total number of players to determine the mean height for Allstars:

(73+62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15 = 1006 / 15 = 67.1 inches

We add together all the heights for the Champs and divide by the overall player count:

(15) = 996/15 = 66.4 inches (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)

We can observe from comparing the means that the Allstars are taller on average than the Champs.

Outliers or extremely high or low numbers in the data, however, can have an impact on the mean. We may determine the median, which is the midpoint value when the data is sorted in either ascending or descending order, to further evaluate the data.

We order the data according to Allstars:

60 60 62 63 65 66 67 68 69 70 70 71 71 72 73

The centre number, or median, is 68.

We order the information for the Champs:

58 60 60 62 65 66 67 68 69 70 70 75

The centre number, or median, is 67.

We can observe from comparing the medians that the Allstars are likewise taller on average than the Champs.

We can therefore draw the conclusion that the Allstars typically have taller players than the Champs based on the metrics of central tendency.

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Answer:

80

Step-by-step explanation:

First, let's mark all animals as x. Now we can form an equation:

[tex] \frac{1}{3} x + \frac{1}{4} x + \frac{1}{5} x + \frac{1}{6} x + 4 = x[/tex]

Then, let's multiply this whole equation by 60, since it's a common denominator:

20x + 15x + 12x + 10x +240 = 60x

57x = -240 + 60x

57x - 60x = -240

-3x = -240 / : (-3)

x = 80

[tex] \texttt{2(x + 2) = - 8} \\ \: \: \: \: \texttt{2x + 2 = - 8} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 8 - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{x = \cancel\frac{ - 10}{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\texttt \purple{ x = - 5} \: }[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps-

The required equation of change is : C= $40 - 10x, where x is the highest price of gas and C is the change.

Let's start by finding the total cost of the 10 gallons of gas. Let's assume that the price of gas is x dollars per gallon at the gas station with the highest price. Then, the total cost of 10 gallons of gas is:

10x dollars

Since Steve paid with two $20 bills, the total amount he paid is:

$40

Therefore, the equation we need to solve to find Steve's change is:

$40 - 10x = C

where C is the amount of change that Steve will receive. We can simplify this equation by subtracting 10x from both sides:

$40 - 10x - 10x = C - 10x

$40 - 20x = C - 10x

Then, we can simplify further by adding 10x to both sides:

$40 - 20x + 10x = C

$40 - 10x = C

Now, we have an equation that relates the price of gas to the amount of change that Steve will receive. To solve for C, we need to know the price of gas at the gas station with the highest price. Once we know that value, we can substitute it into the equation and solve for C.

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The complete question is :

Steve bought 10 gallons of gas at the gas station with the highest price. He paid with two $20 bills. Write and solve an equation to find his change.

To compare the two accounts, we need to calculate the final amount in each account after the given period.

For the simple interest account:

I = P * r * t

I = 250 * 0.03 * 3 = $22.50

Final amount = P + I = $272.50

For the compound interest account:

Final amount = P * (1 + r/n)^(nt)

Final amount = 250 * (1 + 0.04/2)^(22) = $276.16

Therefore, the compound interest account earns more by $3.66 ($276.16 - $272.50).

Answer:4% over 2 years

Step-by-step explanation:

Step-by-step explanation:

1) v=πr^2×h

v= π 1.5^2×3

v=21.205750411731

to 2dp v= 21.21

2) v=πr^2×h

v=π×1.5^2×3.5

v=24.740042147019

to 2 dp v= 24.74

Answer:

1.  6.75π or 21.2 cubic inches (nearest tenth)

2. 7.875π or 24.7 cubic inches (nearest tenth)

Step-by-step explanation:

The formula to find the volume of a cylinder is:

[tex]\boxed{V=\pi r^2 h}[/tex]

where:

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\pi r^2 h\\&=\pi \cdot 1.5^2 \cdot 3\\&= \pi \cdot 2.25 \cdot 3\\&=6.75 \pi \\&=21.2\; \sf in^3\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 6.75π or 21.2 cubic inches.

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies V&=\pi r^2 h\\&=\pi \cdot 1.5^2 \cdot 3.5\\&= \pi \cdot 2.25 \cdot 3.5\\&=7.875\pi \\&=24.7\; \sf in^3\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 7.875π or 24.7 cubic inches.

Answer:

it 50°

Step-by-step explanation:

D is the reflection of x

Answer:

85 points per minute

Step-by-step explanation:

the points earned per minute is calculated as

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₂, y₂) = (200, 17007) and (x₁, y₁ ) = (100,8507) ← 2 ordered pairs from table

points earned per minute = [tex]\frac{17007-8507}{200-100}[/tex] = [tex]\frac{8500}{100}[/tex] = 85

Answer: 4 2/5

Step-by-step explanation:

1 divided by 2 is 1/2, so if 1/2 times 2 equals one cup, then all we have to do is times 2 1/5 by two. 2 x 2 is 4, and 1/5 times 2 is 2/5.  Add them together, and you get 4 2/5. Alex will need 4 2/5 cups of dip.

Answer:

We can use ratios to set up a system of equations and solve for a, b, and c. Since a:b = 3:8, we can write:

a = 3x

b = 8x

Similarly, since b:c = 6:11, we can write:

b = 6y

c = 11y

Now we have two expressions for b, so we can set them equal to each other and solve for y:

8x = 6y

y = 4x/3

Substituting y back into the expression for c, we get:

c = 11y = 44x/3

To find the smallest possible values of a, b, and c, we want to choose values of x that are as small as possible while still being positive integers. Since x must be a multiple of 3 (because a = 3x is a multiple of 3), let's try x = 3. Then we get:

a = 3x = 9

b = 8x = 24

c = 44x/3 = 44

So the smallest possible values of a, b, and c are 9, 24, and 44, respectively.

Step-by-step explanation:

Answer: 5 1/12

Step-by-step explanation:

1. Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

2. Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3 = 10/3

3. Add: 7/4 + 10/3 = 7 · 3/4 · 3 + 10 · 4/3 · 4 = 21/12 + 40/12 = 21 + 40/12 = 61/12 

Answer: 17y - 12

Step-by-step explanation:

By distributing the 3 with the numbers inside the parentheses (2y - 4),

you would get: 6y - 12

You are left with: 11y + 6y - 12

Finally, by adding like terms, your answer would be 17y - 12