An oil refinery is located 1 km north of the north bank of a straight river that is 3 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 5 km east of the refinery. The cost of laying pipe is $300,000/km over land to a point P on the north bank and $600,000/km under the river to the tanks. To minimize the cost of the pipeline, how far downriver from the refinery (in km) should the point P be located? (Round your answer to two decimal places.)

The simplified form of the expression; 16^¾ as given in the task content is; 8.

It follows from the task content that the simplified form of the expression as given in the task content is to be determined.

Since the given expression is; 16 ^ ¾.

It follows from the rational exponents law of indices that we have;

⁴√16³

where 16³ = 4096

Therefore, we have; ⁴√4096

The result is therefore; ⁴√4096

= 8.

On this note, the simplified form of the expression 16^¾ is; 8.

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Answer:

concave down: ( negative infinity, 0)

concave up: (0, positive infinity)

minimum: x = 4

maximum: x=-6

Step-by-step explanation:

Area of circle =  1764 pi in² in terms of pi .

area of circle = pi  r²

                      = 42 * 42 pi²

                      = 1764 pi in²

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Since Jane has $5.00 and purchased a biscuit and soda for $1.30. The amount that she receive as change is $ 2.91.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

Note that An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol is used to denote subtraction,

So  5.00 - 0.79 - 1.30

= 2.91

Therefore, one can say her reminder as change is  2.91 dollars.

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The expenditure of the man in percent is 40%   and his savings is  Rs16200  .

In the question ,

it is given that ,

amount earned by the man = Rs 27000

amount spend by the man = Rs 10800

So , the expenditure in percent can be calculated using the formula ,

we get ,

= (expenditure)/(total earning)  × 100

= 10800/27000 × 100

= 0.4 × 100

= 40%

the savings = earning - expenditure

savings = 27000 - 10800

= 16200

Therefore , The expenditure of the man in percent is 40%   and his savings is  Rs16200  .

The given question is incomplete , the complete question is

A man earns Rs 27,000 and spends Rs 10,800 every month. Express her expenditure in percent also calculate his savings .

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The unit rate of orange could be found by Sara and Daniel by ratio to be $1.50

If Sara's mother bought 8 large oranges for $12.00

Sara may have thought of it like if $12 is for 8 oranges the how much is for 1

12 : 8 then X : 1

12/8 then x/1

12/8 = x/1

x = $1.50

Daniel would have taken this method, if 8 oranges costs $12 then 1 orange would cost ?

8 oranges : $12 then 1 orange : ?

8 : 12 = 1 : ?

8/12 = 1/?

8 * ? = 1 * 12

? = 12/8

? = $1.5

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The number of proper subsets of Z = 255.

Subsets are a subset of the mathematical idea known as Sets. A set is a group of items or components that are enclosed in curly braces, such as "a,b,c,d." Set B is said to be a subset of A if set A is a collection of even numbers and set B contains the numbers 2, 4, and 6. B is designated as BA and A is the superset of B.

The number of proper subsets can be calculated by the formula 2 raise ti the power n where n represents the number of elements in the set

Here, n = 8

thus [tex]2^{n} = 2^{8}[/tex]

which is equal to 256

However since one of the subsets of Z is itself it is not a proper subset

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Answer:

4

Step-by-step explanation:

Welcome to Gboard clipboard, any text you copy will be saved here.

The length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.

According to the question,

We have the following information:

Jessica found that the perimeter of her kitchen table was 18 feet she found the area of her kitchen table to be 18 ft.²

Now, let's take the length of the table to x ft and the width of the table to be y ft.

So, we know that following formulas are used to find the perimeter and area of rectangle:

Perimeter = 2(length+width)

2(x+y) = 18 ...(1)

Area = length*width

xy = 18

x = 18/y

Putting this value of x in equation 1:

2(18/y+y) = 18

18/y + y = 9

([tex]y^{2}[/tex]+18) = 9y

[tex]y^{2}[/tex]-9y+18 = 0

[tex]y^{2}[/tex]-6y-3y+18 = 0

y(y-6)-3(y-6) = 0

(y-6)(y-3) = 0

y-6 = 0 and y-3 = 0

y = 6 ft and y = 3 ft

Now, putting this value of y in x = 18/y:

x = 18/6

x = 3 ft

x = 18/3

x = 6 ft

Hence, the length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.

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The equation representing the perimeter is 6x + 2

The number of bricks for the width is 12 the number of bricks for the length is 25

The length would be 200 inches, the width would 96 inches

1. The perimeter of the garden bed is the perimeter of a rectangle

= 2( L + B)

where L = 2x + 1

B = x

we have to put the values in the formula

2((2x + 1) + (x))

2(3x + 1)

= 6x + 2

2. To get the length of each side we have

total bricks = 6x + 2

74 = 6x + 2

72 = 6x

x = 72 / 6

x = 12

length = 2x + 1

= 2 * 12 + 1

= 25 bricks

hence the width = 12 bricks

length = 25

c. The length would be 25 bricks x 8 inches

= 200 inches

The width = 12 x 8

= 96 inches

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complete question

(Image: Rectangle with one side equaling x and the other side equaling 2x+1)

Assessment Instructions Show and explain all steps in your responses to the following parts of the assignment.

Part 1: Write an equation representing the perimeter of the garden bed.

Part 2: Calculate how many bricks are used on each side.

Part 3: Determine the length of each side.

Answer:

Step-by-step explanation:

The are 6 possibilities for each dice, so the number of outcomes is:

Outcomes with the sum of 10:

Probability of getting 10 is 3 out of 36:

The value of angle z in the triangle illustrated is C. 131°.

It should be noted that the value of the total angles in a triangle is 180°. In this case, the other two angles are given as 97° and 34°.

The other angle will be:

= 180° - (97° + 34°)

= 180° - 131°

= 49°

Therefore, the value of the angle z will be:

= 180° - 49° (angle on a straight line)

= 131°

Therefore, the correct option is C.

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Answer: C 131

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

I'm assuming this is rise over run. The rise is 1 and the run is 2.

Remember, [tex]\frac{rise}{run}[/tex]

Peter plans to 480 percent increase for his shirts.

According to the question,

We have the following information:

Peter plans to start his own business selling T-shirts. Each T-shirt costs him $2.50 to make. He plans on selling each T-shirt for $14.50.

We know that the following formula is used to find the percent increase when the final price and initial price is given:

Percent increase  = 100*(final-initial)/initial

(More to know: the same formula can be used to find the percent decrease for a product.)

Percent increase = 100*(14.50-2.50)/2.50

Percent increase = 100(12)/2.50

Percent increase = 480%

Hence, Peter plans 480% of increase for his shirts.

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Answer:

y = 15

Step-by-step explanation:

the triangle has congruent base angles of 50°

This means the triangle is isosceles with the 2 legs being congruent, so

3y - 10 = y + 20 ( subtract y from both sides )

2y - 10 = 20 ( add 10 to both sides )

2y = 30 ( divide both sides by 2 )

y = 15

A graph which represents the system of inequalities is: B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality plotted on a graph and these include the following:

Additionally, the y-value for this inequality graph intersects the x-axis at -1.5 and the boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be represented with the greater than (>) inequality symbol.

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Based on the residual plot, the linear model is appropriate as C. Yes, there is no clear pattern in the residual plot.

A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.

The residual plot depicts the difference between the observed and fitted response values. The ideal residual plot, also known as the null residual plot, depicts a random scatter of points forming a band.

In this case, no clear pattern was detected.

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Answer:

it seems like the person above me is correct.

Step-by-step explanation:

Answer:

Question 1: We need to know whether Angles P and N are congruent or not.

Question 2: Cannot be proven congruent

Question 3: AAS Congruence Theorem

Question 4: ASA Congruence Postulate

Step-by-step explanation:

Background info: The information (congruence lines on sides and angles) is read counterclockwise (starting from the very left to right).

Question 1: In order to prove the triangles congruent with the AAS, we need two pairs of congruent angles and one pair of congruent sides. We still need one more pair of congruent angles. Since the triangle is read counterclockwise, the angle to the left of the current congruent angle given needs to be given to us. This is angles P and N.

Question 2: For this answer, the triangles cannot be proven congruent because we are only given three congruent angle pairs. This means that it should be the "AAA" Theorem, however, it doesn's exist due to the fact that the triangles could still be two different sizes despite the fact that the angles are the same. In order to prove this congruent, we would need info on congruent sides.

Question 3: Reading the triangle left to right, we see a congruent angle pair (A), another congruent angle pair (A), and a congruent side pair (S). Putting this together, we get AAS.

Question 4: Reading the triangle left to right, we see an angle pair (A), a side pair (S), and an angle pair (A). Putting this together, we get ASA.

Hope this helps! (No guarantees it's 100% correct)

⇒Perimeter is the summation of all the sides of a shape

⇒Note for some sides I will not be able to explain because I cannot draw to show you.

P=S+S+S+S+S+S

P=4+8+12+2+8+4

P=38

⇒For the Area Divide the shape into two shapes Note it will results into two rectangles with the 1st rectangle having measurements L=12 and W=2

and the 2nd rectangle having L=8 and W=4 After finding the areas of both these rectangles ADD  the areas for they will give you the area of the whole shape

[tex]1^{st} _{rectangle area} =L*W\\1^{st} _{rectangle area}=12*2\\\\\\1^{st} _{rectangle area}=24[/tex]

⇒[tex]2^{nd} _{rectangle area}=L*B\\2^{nd} _{rectangle area}=8*4\\2^{nd} _{rectangle area}=32\\\\total_{shape \\area}=24+32\\[/tex]

The Area of the shape is 56

note if you were to insert the unit of measurement you were going to put in the square measurement.

Please do not hesitate to ask failure to understand.

The equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

Given:

3y = -12x + 4 and point (1,1)

3y = -12x+4

divide by 3 on both sides

3y/3 = -12x/3 + 4/3

y = -4x + 4/3.

m = -4.

y = mx + c

substitute m and (1,1)

1 = -4*1 + c

1 = -4 + c

c = 1 + 4

c =5

substitute c and m value in y = mx+c

y = mx + c

y = -4x + 5.

Therefore the equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

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Answer:

-3

Step-by-step explanation:

x= -18 + 15 = -3

The distance between the points is 17

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes are defined as coordinates. The x- and y-values are commonly represented by (x,y).

Given that

Points G (-5,-8) and H (3,7) are plotted on a coordinate grid

We have to find the distance between points G and H

The formula for calculating the distance between two points is given by

= √((3-(-5))2 + (7-(-8)2)

= √((3+5)2 + (7+8)2)

= √((8)2 + (15)2)

= √(64 + 225)

= √289

=17

Therefore the distance between the points is 17

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10. The coordinates of the point W on the y-axis that makes VW + XW a minimum which is on the straight line joining V and X is  W(0, 1)

A straight line is a line without a curve, and the equation of a straight line in mathematics is y = m·x + c

10. The given points are V(2, 3) and X(-2, -1)

The location of the point W is on the y-axis

The shortest distance between two points is a straight line.

When VW + XW is a minimum, W is on the straight line joining V and X, such that by the segment addition postulate, VX = VW + XW

The slope of the line joining V and X, m, is found as follows;'

[tex]m=\dfrac{-1- 3}{-2 - 2} =1[/tex]

The equation of the line in point and slope form is therefore;

y - 3 = 1 × (x - 2) = x - 2

y = x - 2 + 3 = x + 1

The equation of the line VW in the slope and intercept form, y = m·x + c  is y = x + 1

The y-intercept is therefore, c = 1

The x-coordinates of a point on the y-axis is x = 0

The x-coordinate of W is 0

The y-coordinate of the point W on the line VX is given by the y-intercept of the line VX

The y-intercept of the line VX = 1 = The y-coordinate of the point W

The coordinate point W so that VW + XW is a minimum is W = (0, 1)

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x-7 is not a factor of [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex].

In long division method, we divide  [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex] by x-7

x-7 )  [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex]  (  [tex]x^{3}-10x^{2} +71x-495[/tex]

        [tex]x^{4}+7x^{3}[/tex]

  -----------------------------

              [tex]-10x^{3}+x^{2} +2x+1435[/tex]

             [tex]-10x^{3}-70x^{2}[/tex]

          --------------------------

                        [tex]71x^{2} +2x+1435[/tex]

                        [tex]71x^{2} +497x[/tex]

                   ----------------------------

                                  [tex]-495x+1435[/tex]

                                  [tex]-495x-3465[/tex]

                               ----------------------------

                                                 [tex]4900[/tex]

As 4900 is a remainder, x-7 is not a factor.

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Answer:

a) WS, ZV, YU

b) VU

c) ZW

d) WXY

e) None

f) TU, TV, UV, XY, XZ, YZ

g) SW, VX, VZ, WX, WZ, YZ

Step-by-step explanation:

A prism is a polyhedron that has:

From inspection of the give diagram, the figure appears to be a quadrilateral prism with bases STUV and WXYZ.

Parallel line segments

a) Segments parallel to XT:

b) Segments parallel to ZY:

c) Segments parallel to VS:

Planes

d) Planes parallel to plane STU:

e) Planes parallel to plane UVZ:

Skew lines

Skew lines are a pair of non-coplanar lines that:

f) Segments skew to SW:

g) Segments skew to UT:

Applying the midsegment theorem:

a. x = 17; y = 2

b. Length of DF is: 20 units.

According to the midsegment theorem:

Length of GH = half the length of EF

Given the following:

GH = 1/2(EF)

Substitute:

x - 3 = 1/2(28)

x - 3 = 14

x - 3 + 3 = 14 + 3

x = 17

DH = HF

DH = y + 8

HF = x - 7

Therefore:

y + 8 = x - 7

Plug in the value of x

y + 8 = 17 - 7

y + 8 = 10

y = 10 - 8

y = 2

Length of DF = y + 8 + x - 7

Plug in the values of x and y:

Length of DF = 2 + 8 + 17 - 7

Length of DF = 20 units.

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In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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