Domain: -4 BOOKMARK
Determine the domain and range for the following graph.

The 38 square feet increase in the area of the patio following the increase in the length and width by 2 feet and the 2 square feet increase following the increase in the length by 2 feet and decrease in the width by 2 feet indicates that the area of the patio is 70 square feet.

The area of a plane figure is the space occupied by the figure of a specified surface upon which it is placed.

Let L represent the length of the patio, and let W represent the width of the patio, we get;

Area of the patio = L × W

(L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = Area + 38

Therefore; (L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = L × W + 38

2·L + 2·W + 4 = 38 (subtraction property)

2·L + 2·W = 38 - 4 = 34

2·L + 2·W = 34...(1)

(L + 2) × (W - 2) = L·W - 2·L + 2·W - 4 = Area + 2 = L·W + 2

L·W - 2·L + 2·W - 4 - L·W = L·W + 2 - L·W (Subtraction property)

2·W - 2·L - 4 = 2

2·W - 2·L - 4 + 4 = 2 + 4 = 6 (Addition property)

2·W - 2·L = 6...(2)

The simultaneous equations (1) and (2) are solved as follows;

Adding equation (1) to equation (2), we get;

2·L + 2·W + 2·W - 2·L = 34 + 6 = 40

4·W = 40

W = 40 ÷ 4 = 10

W = 10

The width of the patio, W = 10 feet

2·W - 2·L = 6, therefore;

2 × 10 - 2·L = 6

2·L = 2 × 10 - 6 = 14

L = 14/2 = 7

The length of the patio, L = 7 feet

The area of the patio = L × W

L × W = 7 feet × 10 feet = 70 square feet

The area of the patio = 70 square feet

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The solution for the quadratic equation; x squared + 8 x + 16 = 0 as required to be determined using a numerical approach is; Choice C; x = -4.

It follows from the task content that the solution of the quadratic equation is to be determined by using a numerical approach as stated.

On this note, since the standard form quadratic equation takes the form; ax² + bx + c = 0.

To solve, it is important to determine two numbers whose product yields c and sum is; b.

Therefore, for the equation; x² + 8x + 16 = 0; the numbers are; 4 and 4.

Therefore, we have;

x² + 4x + 4x + 16 = 0.

x (x + 4) + 4 (x + 4)

(x + 4) (x + 4) = 0

x = -4.

On this note, the correct answer choice is; Choice C; x = -4.

Complete question; The correct question syntax is; x² + 8x + 16 = 0.

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Distributive Property

Addition Property of Equality

Simplifying

Division Property of Equality

Simplifying

Answer:

3 and 3/11

Step-by-step explanation:

[tex]\frac{8}{2 \frac{4}{9} } \\\\\frac{8}{ \frac{22}{9} } \\\\= 8 / \frac{22}{9} \\\\= \frac{8}{1} / \frac{22}{9} \\\\= \frac{8}{1} * \frac{9}{22} \\\\[/tex]

[tex]=\frac{72}{22} \\\\= 3 \frac{6}{22} \\\\= 3 \frac{3}{11}[/tex]

Step-by-step explanation:

8 ÷ 2 4/9

so, as always with operations involving fractions I recommend to convert mixed numbers to full fractions first :

2 4/9 = (2×9 + 4)/9 = (18 + 4)/9 = 22/9

the division looks then like this :

8 ÷ 22/9

or

8 / 22/9 = 8/1 / 22/9

remember, when we divide by a fraction, then this is the same as a multiplication with the upside-down fraction :

8/1 × 9/22 = 8×9 / 1×22 = 72/22 = 36/11 =

= (3×11 + 3)/11 = 3 3/11

8 ÷ 2 4/9 = 3 3/11

the symbols ÷, /, : have a little bit different semantic meaning in their context, but they all do the same thing : divide.

and they are therefore interchangeable.

Answer:

the digit will be 0 so to get divisible by 10

This method is valid since it produces an interval that contains the true difference 95% of the time. The interval for the gender difference in U.S. teen depression rates is between 3.2% and 8.5%, with girls having higher rates.

The confidence interval method is a valid way of estimating a population parameter based on a sample statistic. In this case, the sample statistic is the 6% difference observed in the study. The confidence interval is used to estimate the true difference between the two groups in the population. This method produces an interval that contains the true difference 95% of the time. In this case, the 95% confidence interval for the gender difference in U.S. teen depression rates is between 3.2% and 8.5%, with girls having higher rates. This means that there is a 95% chance that the true difference in depression rates between boys and girls is somewhere between 3.2% and 8.5%. This method is considered valid because it produces an interval that contains the true difference 95% of the time.The 95% confidence interval for the gender difference in U.S. teen depression rates is calculated as follows:

Lower bound: 6% - 1.96*(Standard Error)

Lower bound: 6% - 1.96*(1.5%)

Lower bound: 3.2%

Upper bound: 6% + 1.96*(Standard Error)

Upper bound: 6% + 1.96*(1.5%)

Upper bound: 8.5%

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It is not possible to determine how many cigarettes someone would smoke based on how long they can hold their breath. The ability to hold one's breath is not related to the number of cigarettes smoked per day

x=12.0; y=19.6

Option 4 is the right answer.

What are the properties of tangent of the circle?

A tangent is correctly formed only if touches the circle at only one point. A tangent never passes through a circle, that is, it never crosses the circle while entering its interior. A tangent is also not known for intersecting the circle at the two different points.

Since, in a circle the radii are equal.

So, OA=OB=x=12

Tangent to a circle is the line that touches the circle at only one point.

The length of tangents from an external point to a circle are equal.

By the theorem,

If two tangents are drawn from an external point of the circle, then they are of equal lengths.

So, AC =BC (by the theorem)

AC and BC look to be tangents- tangents to a circle from a point are congruent.

So, AC is congruent to BC.

Thus, AC=BC=y=19.6

Hence, x=12.0 and y=19.6

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During boarding and deplaning, the minimum number of flight attendants mandated by the FAA for dispatch must be present on the aircraft.

Before a pilot can work for an airline that operates scheduled flights with aircraft that have 30 or more seats under Part 121, the FAA mandates that they have logged at least 1,500 flying hours. There are a few exclusions, such as the possibility of reducing this requirement by half, to only 750 hours, for former military pilots.

Republic requested that the FAA relax the 1,500-hour requirement for employing pilots due to the severe pilot shortage. The airline said that after 750 hours, pilots will be more than capable of taking the controls of a regional plane because Republic had its own aviation academy.

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The linear approximation of function f(x) = √1-x at a = 0: L(x) = 1 - x/2

√0.9 = 0.95

and √0.99 = 0.995

In this question we need to find  the linear approximation of the function f(x) = √(1 - x) at a = 0 and use it to approximate the numbers √0.9 and √0.99

Consider a given function f(x) = √(1 - x)

The slope of given function would be,

f'(x) = -1/2√(1 - x)

We know that the linear approximation function based at 0 is defined by the equation of the tangent line at 0.

so, at x = 0,

f(0) = 1

and slope of the tangent line at 0 : f'(0) = -1/2

The formula to find the linearization at x = a is: L(x) = f(a) + f’(a)(x - a)

the linearization of f(x) = √(1 - x) at a = 0 is L(x) = 1 - x/2

Now we find √0.9

√0.9

= √(1 - 0.1)

= 1 - (0.1/2)

= 0.95

and √0.99

= √(1 - 0.01)

= 1 - (0.01/2)

= 0.995

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10-(x+3)/2=8 => correct answer is - 8

=> 10 - (x+2) = 8x2

=> 10 - x - 2 = 16

=> 10 - x = 16 + 2

=> 10 - x = 18

=> -x = 18 - 10

=> x = -8

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Answer: sequences 1,5,7,9,10

Step-by-step explanation:

An arithmetic sequence is defined by a sequence of numbers with a common difference between terms. Technically if x=0 in q9 we have a constant sequence, which by definition is arithmetic. However if x does not equal 0 it is not arithmetic.

The shape of JKL is an Isosceles triangle

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, add up to 180 degrees.

The three vertices of shape JKL  \which are J(3, 0), K(6, 8) and L(-5, 3), points that the shape is a triangle since triangles have 3 vertices.

The shape is plotted and attached and the graph which is a pictorial representations represents the shape to be a triangle

The plot shows that LJ = JK = 8.5

Also, distance between points J(3, 0) and K(6, 8)  is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(3 - 6)² + (0 - 8)²}

d =√{9 + 64}

d = √73

d = 8.54 units

distance between point J(3, 0) and L(-5, 3)

d =√{(3 - (-5))² + (0 - 3)²}

d =√{64 + 9}

d = √73

d = 8.54 units

distance between point K(6, 8) and L(-5, 3)

d =√{(6 - (-5))² + (8 - 3)²}

d =√{121 + 25}

d = √146

d = 12.08 units

since LJ = JK, the triangle is isosceles

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The maximum km's you travel if your cost is not more than Birr 1350. is 130 kilometers.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the ride service charges Birr 50 to pick you up from the hotel and Birr 10 per km for the trip.

Let the number of kilometers be x.

50 + 10x = 1350

Collect the like terms

10x = 1350 - 50

10x = 1300

Divide

x = 1300 / 10

x = 130

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Answer:

B. x=2 and D. x=-10

Step-by-step explanation:

We have the quadratic formula: [tex]x=\frac{-b\sqrt{b^{2} -4ac} }{2a}[/tex]

Quadratic equations are in the form [tex]ax^2+bx+c[/tex]

We have to get the equation equal to zero before we can use the quadratic formula so subtract 20 from both sides and we get [tex]x^2+8x-20=0[/tex]

[tex]a=1, b=8, c=-20[/tex]

Now we plug these values into the quadratic equation

[tex]x=\frac{-8\sqrt{8^{2}-4(1)(-20) } }{2(1)}[/tex]

Now we solve for x

[tex]x=\frac{-8\sqrt{64+80} }{2}[/tex]

[tex]x=\frac{-8\sqrt{144} }{2}[/tex]

Now we get two equations because the square root gives us both a positive and a negative answer.

[tex]x=\frac{(-8)+12}{2}[/tex] and [tex]x=\frac{(-8)-12}{2}[/tex]

Let's solve the first one now

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

[tex]x=2[/tex]

Now the second one

[tex]x=\frac{-20}{2}[/tex]

[tex]x=-10[/tex]

so [tex]x=2[/tex] and [tex]x=-10[/tex]

so the answers are B and D.

Hope this helps!

Answer: C) $3,780.00

Step-by-step explanation:

1 year = 7% interest rate

3 years = 21% interest rate

21% = 0.21

Take 18000 times 0.21 = $3,780.00

Answer:

No solution

Step-by-step explanation:

We calculated the odd ratio for the given data set is 1.2.

An odd ratio refers to the ratio of the number of the favorable incident to the ratio of the number of unfavorable incidents. In this calculation one ratio is divided by another ratio.

we can determine an odd ratio by dividing the odds of first group by the odds in the second group. In the exposed situation, the cases are divided by controls and for the unexposed situation cases are also divided by controls. Finally, exposed is divided by unexposed.

The above question stated the following data

exposed   498 cases   controls 872

unexposed 622 cases   controls 1309

We have two group first one is cases and the other is control.

Now odd ratio = (498/872)/(622/1309)

                      Odd ratio = 1.2

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The first derivative of quadratic function is obtained as a linear function.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

It can also be described as the slope of the tangent of function at a given point.

The general form of a quadratic function is as below,

f(x) = ax² + bx + c

Its first derivative can be written as below,

f'(x) = 2ax + b

The degree of the function f'(x) is 1.

Thus, it is a linear function.

Hence, the function to describe the derivative of quadratic function is linear.  

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To calculate the perimeter of the figure, I first calculated the area and the breadth of each rectangle which is 4/18m2 and 1/9m respectively.

The perimeter of the figure can be calculated by adding the perimeter of each rectangle.

Perimeter = 4 x (2 x (1/9 m) + 2 x (4/18 m))

Perimeter = 8 x (1/9 m + 4/18 m)

Perimeter = 104/18 m

Perimeter = 5.78 m

The figure I made up consists of four identical rectangles that form a square at the center. To calculate the perimeter of the figure, I first calculated the area and the breadth of each rectangle which is 4/18m2 and 1/9m respectively. As the four rectangles are identical, I multiplied the perimeter of one rectangle by 4 to get the perimeter of the entire figure. Perimeter of one rectangle is calculated by adding the length and breadth of the rectangle. I multiplied the sum of the length and breadth of a rectangle (1/9 m + 4/18 m) by 8 to get the perimeter of the figure. Finally, I simplified the result to get the perimeter of the figure which is 5.78 m.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

send the question compeletly .

Answer:

b

Step-by-step explanation:

Maintaining same number of bulbs and changing the ratio the number of blue bulbs will be 90

From the problem we can deduce

Frank has white and blue bulbs with the ratio of 3 : 5

white, w = 3

blue, b = 5

The number of blue bulbs

3 parts = 45

5 parts = ?

cross multiplying

3 * ? = 5 * 18

? = 75

total number of bulbs = 75 + 45 = 120

new ratio is 1 : 3 sum of the ratio is 4

120 / 4 = 30

1 part = 30

3 parts = 3 * 30 = 90

blue bulbs are 90

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Nolan stops reading at time 2:05 am.

To calculate this,  first, calculate the amount of time elapsed since he began reading. Since he started reading at a quarter to 11, then subtract 11:45 pm (a quarter to 12) from the time he began reading, which was 11:45 pm. This gave me an elapsed time of 0 hours and 15 minutes.  then added this elapsed time to the total time Nolan read, which was 3 hours and 5 minutes. This gave us a total elapsed time of 3 hours and 20 minutes. Finally, then added this total elapsed time to the start time of 11:45 pm. This gave me the result of 2:05 am as the time Nolan stopped reading.

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The probability that both candies are of same color is 0.22

Probability:

                Probability means possibility.The value is expressed from zero to one.In other words probability is simply how likely something is to happen.

The distribution of colors of candies in a bag is as follows.

    Brown      0.1

    Red         0.3

   Yellow      0.2

   Green      0.2

   Orange    0.2

The probability for both candies are Orange.

                = 0.2 x 0.2

                = 0.04

The probability for both candies are Brown.

               =  0.1 x  0.1

               = 0.01

The probability for both candies are Yellow.

               = 0.2 x 0.2

               = 0.04

The probability for both candies are Green.

              = 0.2 x 0.2

              = 0.04

The probability for both candies are Red.

             = 0.3 x 0.3

             = 0.09

Now,

       The total probability  that they are the same color

                    = 0.04 + 0.01 + 0.04 + 0.04 + 0.09

                    = 0.22

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By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:

Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:

m∠B + m∠C + m∠D = 180°

Then:

13x - 35 + 5x - 19 + 2x + 14 =180

20x -40 = 180

20x = 180 + 40

20x = 220

x = 220/20

x = 11

Now that we know the value of x, we can find the measures of the angles.

m∠B = (13x- 35)° = (13*11 - 35)° = 108°

m∠B = (5x - 19)° = (5*11 - 19)° = 36°

m∠D = (2x + 14)° = (2*11 + 14)° = 36°

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