median home price in the west fell from 203400 to 192300 find the percent decrease

Answer:

When it crosses y-axis it means that x coordinate must be 0 so let substitute 0 to x, y=5-2*0

So coordinates are [0,5]

The path should be 6.38 feet wide

Let x be the width of the path.

Since the rectangular plot has an area with dimensions 15 ft by 10 ft, we add x to each dimension to give the dimensions of the rectangular plot plus uniform path.

So, the dimensions are 15 + x by 10 + x respectively.

So, the area of the rectangular plot plus uniform path is A

A = (15 + x)(10 + x)

Since the combined area of the path is 350 square feet, A = 350 ft²

So, (15 + x)(10 + x) = 350

Expanding the brackets, we have

150 + 15x + 10x + x² = 350

x² + 25x + 150 = 350

x² + 25x + 150 - 350 = 0

x² + 25x - 200 = 0

Using the quadratic formula, we find x, the width of the path

So,

\(x = \frac{-25 +/-\sqrt{25^{2} - 4X1 X (-200)} }{2 X1 } \\x = \frac{-25 +/-\sqrt{625 + 800)} }{2}\\x = \frac{-25 +/-\sqrt{1425} }{2}\\x = \frac{-25 +/-37.75 }{2}\\x = \frac{-25 + 37.75 }{2} or x = \frac{-25 - 37.75 }{2}\\x = \frac{12.75 }{2} or x = \frac{-62.75 }{2}\\x = 6.375 or x = -31.375\)

Since x cannot be negative, we choose the positive answer.

x = 6.375 ft

x ≅ 6.38 ft

So, the path should be 6.38 feet wide

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Answer:5

Step-by-step explanation:

Let x represent the width of the path. Then the dimensions of the combined garden and path are 15+2x and 10+2x.

(15+2x)(10+2x)-15(10)=350

Simplify the left side.

150+30x+20x+4x^2-150=350

Combine like terms and set one side to zero.

4x^2+50x-350=0

Factor out the common factor, 2.

2(2x^2+25x-175)=0

Factor the resulting trinomial.

2(2x+35)(x-5)=0

Set each factor equal to zero and solve.

2x+35=0\rightarrow x=-35/2 or x-5=0\rightarrow x=5

The only solution that makes sense in this context is 5. Therefore, the path should be 5 ft wide.

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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Given:

To find the solutions:

Let us find three points to plot the graph.

From equation (1),

From equation (2),

Then, the graph is,

Hence, the solution is (-3, -5).

The equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

The first equation is given as

y = 8x - 4

The slope of the above equation is

m = 8

Parallel lines have equal slope

So, the slope of the other line is

m = 8

The equation is then calculated as

y = m(x - x1) + y1

Where

m = 8

(x1, y1) = (-7, -4)

So, we have

y = 8(x + 7) - 4

Expand

y = 8x + 56 - 4

Evaluate the difference

y = 8x + 52

Hence, the equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

Answer:

$ 3125.00

Step-by-step explanation:

P=\(\frac{SI * 100 }{R*T}\)=

\(\frac{500*100 }{4*4}\) = \(\frac{50000}{16}\) = $3125.00

P(A or B) =

Formula: P(AUB)=P(A)+P(B)-P(A n B)

We roll six-sided die.

Then sample space ={1,2,3,4,5,6}

And

Event A: Roll an odd number.

Odd numbers are {1,3,5}

Event B: Roll a number less than 5

Number less than 5 are {1,2,3,4}

So, Probability P(A)=

Probability P(B)=

Now, the odd number which is less than 5 are {1,3}

So, P(A n B)=

Since P(AUB)=P(A)+P(B)-P(A n B)

Therefore, P(A or B) = 1/6

We are given the following function:

Part A. We are asked to determine the slope of the tangent line at "x = 4".

To determine the slope of the tangent line at a point "x = a" we use the following limit definition:

Now, we substitute the value of "x = 4" in the limit definition, we get:

Now, we determine the value of f(4) from the given function;

Solving the operations:

Now, we substitute the values in the limit:

Now, we take 7 as a common factor:

Now, we factor de denominator, we get:

Now, we cancel out the "x - 4":

Now, we substitute the values of "x = 4", we get:

Therefore, the slope is 49.

Part B. We are asked to determine the equation of the tangent line. We have that the general form of a line equation is:

From part A we have that the slope is 49, therefore, we have:

Now, we need to determine a point on the line to determine the value of "b". We already have that the point "x = 4" is part of the line. To determine the corresponding value of "y" we substitute in the given function:

Solving we get:

Therefore, the point (x, y) = (4, 84) is on the line. Substituting we get:

Solving the product:

Now, we subtract 196 from both sides:

Now, we substitute the value in the line equation:

Thus we have determined the equation of the tangent line.

Answer:

a)   Number of laundries he can do with this box  = 78 laundries.

b)   Price he paying for each load =  0.26 $

Step-by-step explanation:

y≤−5x−10 and y>x+2 The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

To graphically solve this system of linear inequalities, we can start by graphing each inequality on the same coordinate system:

First, let's graph the inequality y ≤ -5x - 10. We can start by graphing the line y = -5x - 10, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,-10), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y ≤ -5x - 10. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y ≤ -5x - 10 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 ≤ -5(0) - 10

0 ≤ -10

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, let's graph the inequality y > x + 2. We can start by graphing the line y = x + 2, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,2), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y > x + 2. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y > x + 2 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 > 0 + 2

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, we can shade the region that satisfies both inequalities. The shaded region is the region that is below the line y = -5x - 10 (including the line itself) and above the line y = x + 2 (excluding the line itself).

The shaded region is shown below:

Graph of y≤−5x−10 and y>x+2

The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

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Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

Answer:12

Step-by-step explanation: I multiplied 3 times 4

The Lateral Surface Area of cone is 12  π  ft³

The lateral area of a cone is defined as the area covered by the curved surface of the cone. It is also called lateral surface area (LSA) or curved surface area (CSA) of a cone. A cone is a 3-D object which tapers smoothly from the flat circular base to a point. In other words, it is a shape formed by a set of line segments coming from the base that connects to a common point

example:

Find the lateral area of a cone having base radius of 21 units and height of 20 units. (Use π = 22/7)

Solution: Given that r = 21 units and h = 20 units

Thus, slant height of the cone, l = √(r2 + h2) = √(212 + 202) = √(441 + 400) = √841 = 29 units

We know, the lateral area of the cone = πrL

Lateral area of a cone = (22/7) × 21 × 29

= 22 × 3 × 29

= 1914 units2

Answer: The lateral surface area of the given cone is 1914 units2

Given:

l= 4 ft

r= 3 ft

Lateral area = πrl

Lateral area = π * 3 * 4

Lateral area = 12 π  ft³

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Answer:

v ≈ 4 cm

Step-by-step explanation:

using the Sine rule in Δ VWX

\(\frac{v}{sinV}\) = \(\frac{w}{sinW}\)

where v = WX and w = VX

∠ W = 180° - (126 + 21)° = 180° - 147° = 33° , then

\(\frac{v}{sin21}\) = \(\frac{6}{sin33}\) ( cross- multiply )

v × sin33° = 6 × sin21° ( divide both sides by sin33° )

v = \(\frac{6sin21}{sin33}\) ≈ 4 cm ( to the nearest cm )

Answer:

Step-by-step explanation:

-5i+6j=x(1i+2j)+y(3i+4j)

-5=x+3y(multiply by 2)

6=2x+4y

-10=2x+6y

subtract

16=-2y

y=-8

-5=x+3(-8)

x=-5+24=19

-5i+6j=19(i+2j)-8(3i+4j)

so we can write (-5,6) as a linear combination of (1,2) and (3,4)

As per the given line segments, the work done by the particle is 78N.

Line segments:

In meth, then bounded by two distinct points on a line is called as line segment.

Given,

Here we have a particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field below.

And we need to find the work done.

While we have the function in the given question as,

=> F(x,y,z) = z²i + 3xy j + 4y²k

Here we have consider that, If C is the path the particle follows, then work done is ∫ₓᵃ F dx.

Then according to the question the force F(x,y,z) = z²i + 3xy j + 4y²k and all four points are in the plane is written as,

z = 1/4 y

So, if S is the at surface with boundary C, so that S is the portion of the plane  over the rectangle is calculated as,

=> D=[0,2] x [0,4].

Then as per the stroke's theorem,

=> ∫∫[2z(0) + 3z(1/4) + 4y]

=> ∫∫3z/4 + 4y

=> [39]₀²

=> 78

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The 1st one/Top one.

X value is different each time. Function can have the same y-value (3, 1), (2, 1) but can't have the same x-value (3, 1) (3, 3)

The slope of the equation of the line described is equal to 1/3.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

y + 2 = 1/3(x-8)

y + 2 = 1/3x - 8/3

y = 1/3x - 8/3 - 2

y = 1/3x - 2/3

Therefore, the slope of the equation of the line described is equal to 1/3.

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The algebric expression \(cot(sin^{(-1)}\sqrt{(x^2}\)simplifies to sqrt(1 - |x|^2) / |x|.

The expression "cot(sin^(-1)(sqrt(x^2)))" involves trigonometric and square root functions. Let's break it down step by step to simplify the expression.

Inside the square root: x^2.

The square root of x^2 is |x| (the absolute value of x), as the square root eliminates the square and keeps the positive value.

The expression sin^(-1)(sqrt(x^2)) is equivalent to arcsin(sqrt(x^2)).

Since we already know that the square root of x^2 is |x|, we can rewrite the expression as arcsin(|x|).

Now, we have cot(arcsin(|x|)).

The cotangent (cot) of an angle is equal to the reciprocal of the tangent (tan) of the same angle.

So, cot(arcsin(|x|)) can be written as 1 / tan(arcsin(|x|)).

Using the inverse trigonometric identity, tan(arcsin(x)) = x / sqrt(1 - x^2), we can simplify further.

In our case, x = |x|.

Therefore, tan(arcsin(|x|)) = |x| / sqrt(1 - |x|^2).

Substituting this result back into the expression, we have 1 / (|x| / sqrt(1 - |x|^2)).

To divide by a fraction, we multiply by its reciprocal.

Hence, the final simplification of the expression is sqrt(1 - |x|^2) / |x|.

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

161700 ways.

Step-by-step explanation:

The order in which the transistors are chosen is not important. This means that we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

3 transistors from a set of 100. So

\(C_{100,3} = \frac{100!}{3!(100-3)!} = 161700\)

So 161700 ways.

Answer:

4

Step-by-step explanation:

5/8 x 4 =2.5

2.5 is also 2 1/2

21 divided by 3 equals 7

7 pencils in each holder

:]

Ryan will put 7 pencils in each pencil holder.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in "m" in different ways and if following it, a second event can occur in "n"  ways; then the two events in succession can occur in m × n  ways.

Given that Ryan has 21 pencils, wants to put the same number of pencils in each of the 3 pencil holders.

Pencil = 21

Pencil holder = 3

Therefore, we will do as 21 divided by 3

21/3 = 7

Hence, there are 7 pencils in each pencil holder.

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Answer:

As a claustrophobia, I can ????

O 35°, 35°, 20°

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

D

Step-by-step explanation: