Edwina measured the length of this swimming pool by drawing similar triangles as shown. What is the best estimate of p, the length of the swimming pool?

The midpoint of the segment given (5,5) and (1,1) is (3, 3).

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Coordinates of the midpoint of the line joining the points (x₁,y₁) and (x₂,y₂)= [(x₁ + x₂)/2 , (y₁ + y₂)/2].

The midpoint of the line segment with endpoints (5,5) and (1,1)

= [ ( 5 + (1))/2 , ((5) + 1)/2 ]

= [ (6)/2 , 6/2 ]

= [ 3, 3

Therefore, the midpoint of the line segment with endpoints is (3, 3).

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Answer:

x = -3

y = -4

Step-by-step explanation:

2x - 5y = 14 ⇒ ( 1 )

y = 3x + 5 ⇒ ( 2 )

First, let us find the value of x.

For that let us use equation ( 1 ) and replace y with (3x + 5 ).

2x - 5y = 14

2x - 5 ( 3x + 5 ) = 14

Solve the brackets.

2x - 15x - 25 = 14

Combine like terms.

-13x - 25 = 14

Add 25 to both sides.

-13x = 14 + 25

- 13x = 39

Divide both sides by -13.

x = -3

Let us find the value of y.

For that, use equation (2) and replace x with (-3).

y = 3x + 5

y = 3 × -3 + 5

y = - 9 + 5

y = -4

Answer: 1. y = 6

2. x = -2

3. X = -10.29

4. n = -5.165

Step-by-step explanation:

1. -2y + 7 = -5

-2y + 7 - 7 = -5 - 7

-2y = -12

y = 6

2.-3(x + 5) = -9

3(x+5) = 9

x+5 = 3

x = 3 - 5

x = -2

3. X+2.5= -7.79

X= -7.79 - 2.50

X = -10.29

4. 3.33 + 2n = -7

3.33 - 3.33 + 2n = -7 - 3.33

2n = -10.33

n = -5.165

Answer:

The second company should get the contract.

Question

The project manager for the state department of highways has two beds for the resurfacing of a 10 mile stretch of highway.

Reason

Based on the least expensive price per mile per year, the second company should get the contract. This is because the price per mile per year for the second company is lower than the price per mile per year for the first company.

The first company gives a bit of $120,000 per mile and will guarantee the web for eight years. The second company bids the word for $150,000 per mile using a new asphalt material made from used tires.

The second company will guarantee the work for 12 years. Determine the price per mile per year for each company and decide which company should get the contract based on the least expensive price per mile per year.

The project manager for the state department of highways has two beds for the resurfacing of a 10 mile stretch of highway. The first company gives a bit of $120,000 per mile and will guarantee the web for eight years.

The second company bids the word for $150,000 per mile using a new asphalt material made from used tires. The second company will guarantee the work for 12 years.

Determine the price per mile per year for each company and decide which company should get the contract based on the least expensive price per mile per year

The percent gain in the number of wolves is 90%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

From the information, in a wildlife park, there were 20 gray wolves. after a few years, there were 38 gray wolves.

The percent gain will be:

= Increase in wolves / Previous number × 100

= (38 - 20) / 20 × 100

= 18/20 × 100

= 90%

Therefore, it should be noted that based on the information illustrated above, the percentage gain will be 90%.

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Answer: y = 1x+4

the related between the x and y is x plus one and y plus 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3x+4y<12

The amount that each employee will get out of the bonus to your department will be $3,000.

What will each employee get?

You manage a staff of 9 employees in your department which means that there are 10 people in total.

The amount that each person will get from the bonus will therefore be:

= 30,000 / 10 employees

= $3,000

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Answer:

16/41 or 39%

Step-by-step explanation:

add both boys and girls and divide boys by that number

The nth term of the given quadratic sequence is 2n².

What is quadratic sequence?

The ordered sets of numbers known as quadratic sequences are based on the rule n^2 = 1, 4, 9, 16, 25,.... (the square numbers). Every quadratic sequence has a n^2 term.

Consider, the given quadratic sequence

2, 8, 18, 32, 50, ...

we have to find nth term of this quadratic sequence ; 2 , 8 , 18 , 32, 50, ...

To find the nth term, we have to find the relation between the given terms.

here we see,

1st term = 2 = 2 × 1 × 1 = 2 × 1²

2nd term = 8 = 2 × 2 × 2 = 2 × 2²

3rd term = 18 = 2 × 3 × 3 = 2 × 3²

4th term = 32 = 2 × 4 × 4 = 2 × 4²

similarly 5th term = 2 × 5² = 2 × 25 = 100

...........

so nth term = 2 × n² = 2n²

Hence, the nth term of the given quadratic sequence is 2n².

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calculate the size of the exterior and interior angles of all the different polygon.

Answer:

-14/3 or -4.67

Step-by-step explanation:

division.

Answer:

No, the lines are not parallel

Step-by-step explanation:

They are not parallel because the slopes of the lines are not equal.

Answer:

93%

Step-by-step explanation:

651/700

Answer: 93%

Step-by-step explanation:= (

(651 × 100/700) × 1/100 = 93/100

The rate of change of the distance with respect to time that the box submarine traveled is 11 feet per second

A rate of change describes how one quantity changes in relation to another quantity.

Mathematically, it is defined as the change in one quantity divided by the change in the other quantity.

In this case, we have:

rate of change = change in distance / change in time

Use the data in the table:

rate of change = 545-380/15-0

rate of change = 165/15 = 11

Note: You can pick any 2 data points for the calculation

Therefore, 11 feeet per second is the rate of change of the distance in feet below sea level with respect to time that the box submarine traveled

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The value of the angles of the given quadrilateral are;

8) ∠X = 124° = ∠W

∠Y = 56° = ∠Z

9) ∠J = 44° = ∠K

∠L = 136° = ∠M

The sum of angles of a quadrilateral is equal to 180 degrees. Now, in the quadrilateral given, the two angles on the slant side always equal 180 degrees. Thus;

8) From the given trapezium, we can use the definition above to say that;

∠X + ∠Y = 180°

Thus;

(13x - 7)° + (8x - 2)° = 180°

21x - 9 = 180

21x = 189

x = 189/21

x = 9

Thus;

∠X = (13(9) - 7)°

∠X = 124° = ∠W

∠Y = 180° - 124°

∠Y = 56° = ∠Z

9) From the above, we can apply the same to this quadrilateral to get;

7x + 2 + 25x - 14 = 180

32x - 12 = 180

32x = 180 + 12

32x = 192

x = 192/32

x = 6

∠J = (7(6) + 2)

∠J = 44° = ∠K

∠L = 180 - 44

∠L = 136° = ∠M

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Step-by-step explanation:

2X-Y=4 ---------(1)

x=4-y---------(2)

since x = 4 – y just substitute for eqn 1

2(4–y) – y = 4

8 – 2y –y=4

8 –3y = 4

–3y=4–8

–3y=–4

y=–4/–3

y= 4/3

since y = 4/3 just substitute for y in eqn (2)

x=4–4/3

multiply both sides by 3

3x=12–4

3x=8

x=8/3 or 2 2/3

The constant of proportionality of y and x in the graph is given as follows:

k = 3/4.

In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:

k = y/x.

A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.

The marked point on the graph has the coordinates given as follows:

(4,3).

Meaning that the constant of proportionality of y and x in the graph is calculated as follows:

k = y/x = 3/4.

(division of the value of the y-coordinate by the value of the x-coordinate).

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The figure is neither a rhombus nor a rectangle since the sides are of varied lengths and are not at right angles. "None of the other" applies.

Given that,

Consider parallelogram ABCD with vertices A(-6,6), B(0,10), C(2,4) and D(-4,0).

We have to find the parallelogram is square, rectangle, rhombus and none of the above.

We know that,

In the attached figure, which shows the number of grid squares for each side, we can see that one side is the diagonal of a 23 rectangle and the other side is the diagonal of a 13 rectangle. This reveals two things to you: The sides are not at perfect angles to one another and are of varied lengths. The slopes of the segments would be opposing reciprocals (if the sides were perpendicular).

Therefore, The figure is neither a rhombus nor a rectangle since the sides are of varied lengths and are not at right angles. "None of the other" applies.

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Answer:

76 ft^3

Step-by-step explanation:

A volume of small box = 12 ft^

A volume of large box = 4×4×4= 64 ft^

the sum of volume = 12+64=76 ft^3

Step-by-step explanation:

we need to bring them to the same denominator. in this case : 10

so, 1/10 of everything are red.

1/5 = 2/2 × 1/5 = 2/10 of everything are blue.

so, we now just add these two :

1/10 + 2/10 = 3/10

so, 3/10 are red and blue (rather red or blue, because none are red and blue)..

Answer:

c is your answer

Step-by-step explanation:

x = 1 +_ √61/6

Answer:

No.

Step-by-step explanation:

No.

In a proportional relationship, every minute has the same charge.

The kind of sequence shown 2, -1, -4, -7, -10, is definitely an arithmetic sequence.

In mathematics, a sequence is a collection of numbers or items that have been organised in a certain order in accordance with a set of rules. These sequences, which might be endless or finite, are useful for simulating a variety of real-world processes. In addition to its practical uses, sequences are an essential mathematical notion that allows us to analyse patterns and relationships between numbers. We may edit and examine sequences to better understand their characteristics and behaviour by applying mathematical operations. Sequences are frequently used to investigate patterns and relationships between numbers, as well as to solve problems in a variety of mathematical disciplines such as algebra, calculus, and geometry. Arithmetic sequences, geometric sequences, recursive sequence are a few examples of frequent sequence types.

How to solve?

In an arithmetic sequence, the difference between any two consecutive terms is constant.

In the given sequence, the difference between any two consecutive terms is -3. i.e.,

d = -10 - (-7) = -7 -(-4) = -4 - (-1) = -1 - (2) = -3

Therefore, the sequence is an arithmetic sequence.

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Answer: To calculate the volume of the concrete required to make the drain, we need to find the volume of the cylinder formed by the outside diameter of the drain and subtract the volume of the cylinder formed by the inside diameter of the drain.

The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

The radius of the base of the outside cylinder is 0.5m (the diameter of 1m divided by 2) and the height is 10m. The radius of the base of the inside cylinder is 0.4m (the diameter of 0.8m divided by 2) and the height is also 10m.

So the volume of the outside cylinder is:

V = π * 0.5^2 * 10 = 15.7 m^3

and the volume of the inside cylinder is:

V = π * 0.4^2 * 10 = 12.6 m^3

To find the volume of the concrete required to make the drain, we subtract the volume of the inside cylinder from the volume of the outside cylinder:

15.7 m^3 - 12.6 m^3 = 3.1 m^3

So the volume of concrete required to make the drain is approximately 3.1 cubic metres. To the nearest tenth of a cubic metre, this is 3.1 m^3.

The size of the letters appear on the retina is 0.00289 cm

Given data:

To determine the size of the letters on the retina, use the concept of angular size and the relationship between object size, distance, and angular size.

Angular size is the measure of the angle subtended by an object as seen from a particular point, in this case, the eye.

Angular size = Object size / Distance

Object size = 1.0 cm

Distance = 6 meters

Angular size = 1.0 cm / 6 meters

To convert the distance to centimeters, multiply by 100:

Angular size = 1.0 cm / (6 meters * 100 cm/meter)

Angular size = 1.0 cm / 600 cm

Angular size = 0.0017 radians

The angular size of the letters is 0.0017 radians.

Now, to determine the size of the letters on the retina, calculate the linear size on the retina using the angular size and the distance from the lens to the retina.

Linear size on retina = Angular size * Distance from lens to retina

Angular size = 0.0017 radians

Distance from lens to retina = 1.7 cm

Linear size on retina = 0.0017 radians * 1.7 cm

Linear size on retina ≈ 0.00289 cm

Hence, the letters appear to be approximately 0.00289 cm in size on the retina.

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Answer:

AGDB

Step-by-step explanation:

Pair 1: Alternate interior

Pair 2: Alternate exterior

Pair 3: Same-side interior

Pair 4: Same-side exterior