Find the distance between each pair of parallel lines with the given equations y=3x, y=3x+10

Answer:

3.7 x  10^-2

Step-by-step explanation: I know all...sike i dont...thats correct tho

Given that, a = 5i + j, b = i - 5jTo find, a + b Using the given vectors, we get; a + b = (5i + j) + (i - 5j)= 6i - 4jHence, a + b = 6i - 4jTo find, a - b Using the given vectors, we get; a - b = (5i + j) - (i - 5j)= 4i + 6j Hence, a - b = 4i + 6jTo find, |a|Using the given vector, a = 5i + j

We know that, |a| = √(a₁² + a₂²)where a₁, a₂ are components of vector a.Using the above formula,we get;|a| = √(5² + 1²)= √(25 + 1)= √26Hence, |a| = √26To find, |a - b|Using the given vectors, a = 5i + j, b = i - 5jWe know that, |a - b| = √(a₁ - b₁)² + (a₂ - b₂)²where a₁, a₂, b₁, b₂ are components of vector a and b.Using the above formula,we get;|a - b| = √[(5 - 1)² + (1 + 5)²]= √(4² + 6²)= √(16 + 36)= √52= √(4 × 13)= 2√13Hence, |a - b| = 2√13 To find, 4a + 2bUsing the given vectors,we get; 4a + 2b = 4(5i + j) + 2(i - 5j)= 20i + 4j + 2i - 10j= 22i - 6jHence, 4a + 2b = 22i - 6jTo find, |a + b - 2(a - b)|Using the given vectors, a = 5i + j, b = i - 5j

We know that, |a + b - 2(a - b)| = √[(a + b - 2(a - b))₁² + (a + b - 2(a - b))₂²]where a₁, a₂, b₁, b₂ are components of vector a and b.Using the above formula,we get;|a + b - 2(a - b)| = √[(6i - 4j - 2(4i + 6j))₁² + (6i - 4j - 2(4i + 6j))₂²]= √[(6i - 4j - 8i - 12j)² + (6i - 4j - 8i - 12j)²]= √[(-2i - 16j)² + (-2i - 16j)²]= √[(2² + 16²)(i² + j²)]= √260= √(4 × 65)= 2√65Hence, |a + b - 2(a - b)| = 2√65Therefore, the values of a + b, a - b, |a|, |a - b|, 4a + 2b, and |a + b - 2(a - b)| are 6i - 4j, 4i + 6j, √26, 2√13, 22i - 6j, and 2√65 respectively.

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The values of the vectors are:

a + b, a - b, |a|, |a - b|, 4a + 2b, and |a + b - 2(a - b)| are 6i - 4j, 4i + 6j, √26, 2√13, 22i - 6j, and 2√65 respectively.

Here, we have,

Given that,

a = 5i + j,

b = i - 5j

To find, a + b

Using the given vectors, we get;

a + b = (5i + j) + (i - 5j)= 6i - 4j

Hence, a + b = 6i - 4j

To find, a - b

Using the given vectors, we get;

a - b = (5i + j) - (i - 5j)= 4i + 6j

Hence, a - b = 4i + 6j

To find, |a|

Using the given vector, a = 5i + j

We know that, |a| = √(a₁² + a₂²)

where a₁, a₂ are components of vector a.

Using the above formula, we get;

|a| = √(5² + 1²)= √(25 + 1)= √26

Hence, |a| = √26

To find, |a - b|

Using the given vectors, a = 5i + j, b = i - 5j

We know that, |a - b| = √(a₁ - b₁)² + (a₂ - b₂)²

where a₁, a₂, b₁, b₂ are components of vector a and b.

Using the above formula, we get;

|a - b| = √[(5 - 1)² + (1 + 5)²]

= √(4² + 6²)

= √(16 + 36)

= √52

= √(4 × 13)

= 2√13

Hence, |a - b| = 2√13

To find, 4a + 2b

Using the given vectors, we get;

4a + 2b

= 4(5i + j) + 2(i - 5j)

= 20i + 4j + 2i - 10j

= 22i - 6j

Hence, 4a + 2b = 22i - 6j

To find, |a + b - 2(a - b)|

Using the given vectors, a = 5i + j, b = i - 5j

We know that,

|a + b - 2(a - b)| = √[(a + b - 2(a - b))₁² + (a + b - 2(a - b))₂²]

where a₁, a₂, b₁, b₂ are components of vector a and b.

Using the above formula, we get;

|a + b - 2(a - b)|

= √[(6i - 4j - 2(4i + 6j))₁² + (6i - 4j - 2(4i + 6j))₂²]

= √[(6i - 4j - 8i - 12j)² + (6i - 4j - 8i - 12j)²]

= √[(-2i - 16j)² + (-2i - 16j)²]

= √[(2² + 16²)(i² + j²)]

= √260= √(4 × 65)

= 2√65

Hence, |a + b - 2(a - b)| = 2√65

Therefore, the values of a + b, a - b, |a|, |a - b|, 4a + 2b, and |a + b - 2(a - b)| are 6i - 4j, 4i + 6j, √26, 2√13, 22i - 6j, and 2√65 respectively.

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The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

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Answer: 8.49 inches

Step-by-step explanation:

16.4-7.91=8.49 inches

To increase the injection rate q, we can increase the injection well pressure (piw), decrease the production well pressure (ppw), or decrease the distance between the injection and production well (d) any changes in these variables should be carefully evaluated and monitored to avoid any adverse effects on the reservoir performance.

How injection rate varies with different scenario?

The dimensionless productivity index for the well in the given equation can be calculated by dividing the flow rate (q) by the pressure difference (Pw-Ppw) and the distance between the wells (d).
The dimensionless productivity index = q / (Pw-Ppw)d

In order to increase the injection rate q, we can change the three controllable variables piw, ppw and d.

To increase the injection rate q, we can increase the injection well pressure (piw), decrease the production well pressure (ppw), or decrease the distance between the injection and production well (d).

However, there may be some restrictions on varying these variables freely. For example, increasing the injection well pressure beyond a certain limit may cause formation damage or fracture the reservoir rock. Similarly, decreasing the production well pressure too much may result in water coning or gas breakthrough.

Moreover, decreasing the distance between the wells may not be feasible due to the geological or physical constraints of the reservoir.

Therefore, any changes in these variables should be carefully evaluated and monitored to avoid any adverse effects on the reservoir performance.

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The trip there take if the return trip took eight hours is 5hrs.

What is Distance?

Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered.

What is Rate?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

We are given ;

A container ship made a trip to Madagascar and back

On the trip there it traveled 16 km/h.

the return trip it went 10 km/h.

if the return trip took eight hours;

then,

16x = 10 * 8

16x = 80

x = 80/16

x = 5

Therefore,  he trip there take if the return trip took eight hours is 5hrs.

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Answer:

3

Step-by-step explanation:

1.2/0.4=3, isolate the y to get the answer. Please mark brainliest!

The value οf x is 3

A variety οf issues are resοlved by algebraic calculatiοns that treat variables like explicit integers in a single cοmputatiοn. The quadratic fοrmula, fοr instance, can be used tο sοlve any quadratic equatiοn by exchanging the variables in the quadratic fοrmula fοr the numerical values οf the cοefficients in the equatiοn.

A variable in mathematical lοgic is either a symbοl fοr an undefined term οf the theοry (a meta-variable), οr it is a fundamental οbject οf the theοry that is changed withοut cοnsidering any pοtential intuitive meaning.

Given

8x+17 = 41

Sοlving fοr variable 'x'

Add '-17' tο each side.

17 + -17 + 8x = 41 + -17

Or, 8x=24

Divide each side by '8'

Or, x=3

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x - 3y = -11
-x + 2y = 7

We minus these equations : x - 3y - (-x + 2y) = -18

= x - 3y + x - 2y = -18
2x - 5y = -18

Now, we add these equations :

x - 3y = -11
-x + 2y = 7
-> x - 3y - x + 2y = -4
-y = -4
y = 4

Replace it in 2x - 5y = -18

2x - 20 = -18

2x = -18 + 20 = 2
x = 1

Recheck : 1 - 3 x 4 = -11

-1 + 8 = 7.

Answer:

A mathematical model represented by a quadratic equation such as Y = aX2 + bX + c, or by a system of quadratic equations. The relationship between the variables in a quadratic equation is a parabola when plotted on a graph.

Step-by-step explanation:

a) The horizontal distance between the fighter jet and the point of impact of the missile is 100 units.

b) The graph of the equation is a downward-opening parabola passing through the points (50, 22500), (100, 0), and (0, 0).

c) The instantaneous rate of change when the missile has half of the horizontal journey left is 0, indicating no change in height with respect to the horizontal distance at that point.

To find the horizontal distance between the fighter jet and the point of impact of the missile, we need to determine the x-coordinate when the missile hits the ground. This can be done by finding the x-intercepts of the equation -x² + 100x + 20000, which represents the path of the missile.

To find the x-intercepts, we set the equation equal to zero:

-x² + 100x + 20000 = 0

Using the quadratic formula, where a = -1, b = 100, and c = 20000, we can calculate the x-coordinate:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (-100 ± √(100² - 4(-1)(20000))) / (2(-1))

Simplifying further:

x = (-100 ± √(10000 + 80000)) / (-2)

x = (-100 ± √90000) / (-2)

x = (-100 ± 300) / (-2)

x = (200 or -100) / 2

Since negative values are not meaningful in this context, we take the positive value, which is x = 100. Therefore, the horizontal distance between the fighter jet and the point of impact of the missile is 100 units.

To graph the equation, we plot the points on a coordinate system. The equation -x² + 100x + 20000 represents a downward-opening parabola. The highest point of the parabola is at (50, 22500) because the x-coordinate represents the midpoint of the parabolic path, and the maximum height is reached when x = 50. The two ends of the parabolic path are located at the x-intercepts we calculated earlier, which are (100, 0) and (0, 0).

The graph of the equation would show a downward-opening parabola passing through the points (50, 22500), (100, 0), and (0, 0).

The instantaneous rate of change represents the derivative of the equation with respect to x at a given point. To find the instantaneous rate of change when the missile has half of the horizontal journey left, we need to find the derivative of the equation and evaluate it at that point.

Taking the derivative of -x² + 100x + 20000 with respect to x, we get -2x + 100. Evaluating this derivative at x = 50 (when the missile has half of the horizontal journey left), we have:

-2(50) + 100 = -100 + 100 = 0

Therefore, the instantaneous rate of change when the missile has half of the horizontal journey left is 0. This indicates that at that point, the height of the missile is not changing with respect to the horizontal distance.

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Answer:

0.15

Step-by-step explanation:

A shelving company shipped 2,483 shelving units to each of 417 warehouses 1035411 shelving units did the company ship in all.

Total shelving to one = 2483

Total shelving to 417 warehouse = 417 x 2483 = 1035411

A flexible display system that can be moved and altered to meet various product dimensions is a shelving unit. A gondola is an open-sided island shelving unit. Overstocks are kept on the riser, the top shelf atop a shelving unit.

Pallet racks are used for products placed onto pallets, whereas used shelving is often used for single things or boxes. The styles of used shelving include enclosed, nut and bolt, modular, wire, clip, and record storage, among others.

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Answer:

0

Step-by-step explanation:

7 + 5 - 15 -(-3)

=> 12 - 15 + 3

=> 12 - 12

=> 0

Answer:

5x-18=4x+7 ( vertical opposite angle)

5x-4x=7+18

x=25

Answer:

Yes, the perimeter and side length of a square are proportional. This is because a square has four equal sides, so if you increase the length of one side by a certain factor, the perimeter (which is the sum of all four sides) will also increase by the same factor. In other words, if you double the length of a side of a square, you will also double its perimeter. Similarly, if you reduce the length of a side by a certain factor, the perimeter will also be reduced by the same factor. This relationship holds true for all squares, regardless of their size or orientation.

Answer:

d=36m

Step-by-step explanation:

d=2r=2·18=36m

Answer:

Your in luck! I'm actually learning this right now!

Step-by-step explanation:

d = 2r so basically your diameter is your radius times 2! So 18 x 2 = 36 so the answer should be 36 hope this helps!

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.

It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

The complete question is,

Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].

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Answer:

FD ≈ 252.8 feet

Step-by-step explanation:

By applying tangent rule in the given right triangle,

tan(20°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(20°) = \(\frac{EF}{FD}\)

0.36397 = \(\frac{92}{FD}\)

FD = \(\frac{92}{0.36397}\)

FD = 252.77

FD ≈ 252.8 feet

Answer:

67.75

Step-by-step explanation:

\(84.95 - 2.15 \cdot (3.91 - 1.91)^3\)

\(3.91-1.91=2\)

\(2^3=8\)

\(2.15\cdot8=17.2\)

\(84.95 -17.2=67.75\)

So, the final answer is 67.75

2 I believe, there are 6 possibilities on a die, 1-2-3-4-5-6. 4 is one of those numbers. Any of the sides could be rolled so each has a probability of 1 out of 6. 1/6 is your answer.

Answer:

When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

Step-by-step explanation:

The Least Common Multiple ( LCM )

The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.

For example:

LCM(20,8)=40

LCM(35,18)=630

Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.

Find the LCM of 4,10,12. Follow this procedure:

List prime factorization of all the numbers:

4 = 2*2

10 = 2*5

12 = 2*2*3

Multiply all the factors the greatest times they occur:

LCM=2*2*3*5=60

Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

Since each triangle is a right triangle we can apply trigonometric functions:

Sin a = opposite side / hypotenuse

Where;

a = angle = 60° ( we are looking at the bottom left one)

Opposite side = 30 cm

Hypotenuse = AB

Replace:

Sin60 = 30 / AB

Solve for AB

AB = 30 / sin 60

AB = 34.64 cm

Answer : B

Step-by-step explanation:

Ape

The statement which is true is  KM = 2 .JM, the correct option is C.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

AJKL is an equilateral triangle

Now,

Using these properties, we can eliminate some of the options.

Option A is false because JK and KM are not equal. JK is half of JL, which is one side of the equilateral triangle AJKL, while KM is a perpendicular bisector of JL.

Option B is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 90 degrees.

Option D is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 45 degrees.

Option C must be true because KM bisects JL into two equal parts JM and ML. Since JL is one side of the equilateral triangle AJKL, we have JL = AK = AL. Therefore, JM = ML = JL/2 = AK/2 = AL/2. By Pythagoras’ theorem, we have:

KM^2 = AK^2 - AM^2

KM^2 = (AK/2)^2 - (AL/4)^2

KM^2 = (AK/4)^2 + (AL/4)^2

KM^2 = ((AK + AL)/4)^2

Since AK + AL = 2 * JL,

KM^2 = (JL/4)^2 * 4

KM^2 = (JL/4)^2 * 4

KM = JL/4 * 2

KM = JL/2

Therefore, the answer of the triangle will be KM = 2 * JM.

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Answer:because that’s what the answer is

Step-by-step explanation:

Answer:

Y=1/2x-3

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

(2 + x) (10) = 36 + 8x

20 + 10x = 36 + 8x

10x - 8x = 36 - 20

2x = 16

x = 8

Answer:

1. I know the number of seeds that there are I am trying to find out how many seeds you will be able to plant in each row, I also need to know how much the seeds will weigh.

2. The quantites in the problem are related because they are other how much they will weigh, or the number of seeds.

Step-by-step explanation:

3.

Answer:

y = 3.2x - 9   Hope this helps!

Answer:

1/8

Step-by-step explanation:

P(nectarine) = number of nectarines / total

                       =2/16

                        = 1/8