which two line are parallel? how do you know A.2x-y=5 B.2x+y=3 C.y=2x+3

a)  The direction in which you should walk to descend fastest is: (-12, -16)

b) The slope of your path is: -88

c) The direction of the greatest increase in temperature at the point (−2, 2) is: (-4, 4)

The maximum rate of change is: 4√2

d) The direction of the greatest decrease is: (4, -4).

The most negative rate of change is: 4√2

(a) The equation on the surface is:

z = 15 - (3x² + 2y²)

The gradient of this surface will be the partial derivatives of the equation. Thus:

Gradient of the surface z:

∇z = (-6x, -4y)

Since you are standing above the point (2,4), then the direction to descend fastest is:

∇z(2,4) = (-6(2), -4(4))

∇z(2,4) = (-12, -16)

That gives us the direction to descend fastest is in the direction.

(b) If you start to move in the direction (-12, -16) above, then slope of your path (rate of descent) is given by the dot product expressed as:

Slope = ∇z(2,4) · (-12, -16)

= (2)(-12) + (4)(-16)

= -24 - 64

= -88

(c) We want to find the direction of the greatest increase in temperature at the point (−2,2).

Thus, the gradient of T(x,y) is given by:

∇T = (2x, 2y).

The direction is:

∇T(-2, 2) = (2(-2), 2(2))

∇T(-2,2) = (-4, 4)

The maximum rate of change is:

∇T(-2,2) = √((-4)² + 4²)

= √(16 + 16)

= √(32)

= 4√2

(d) The direction of the greatest decrease is:

(-∇T(-2, 2)) = (-(-4), -4)

= (4, -4).

The most negative rate of change is:

∇T(-2, 2) = √(4² + (-4)²)

= √(16 + 16)

= √(32)

= 4√2

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Answer:

5x

Step-by-step explanation:

Answer/Step-by-step explanation:

The circle by your left:

(4x + 3y) + (2x - y)

Distribute +1

4x + 3y + 2x - y

Add like terms together

6x + 2y

The rectangle by at the bottom right:

(4x + 5y) - (x + 4y)

Distribute -1

4x + 5y - x - 4y

Group like terms

4x - x + 5y - 4y

3x + y

The circle at the bottom middle:

(2x - y) + (3x + y)

Distribute +1

2x - y + 3x + y

Group like terms

2x + 3x - y + y

5x

Given,Three possible risk scenarios X, Y and Z. The initial assessment found that X is twice as likely as Z and Y is three times as likely as Z.

Probability of X is p(X) = 2p(Z)
Probability of Y is p(Y) = 3p(Z)
Probability of Z is p(Z)Let the probability of Z be p. So, the probability of X and Y can be written as:
p(X) = 2p(Z)p(Y) = 3p(Z). And, Total probability, p(X) + p(Y) + p(Z) = 1. Given that, p(X) + p(Y) + p(Z) = 12p(Z) + 3p(Z) + p(Z) = 1(6p(Z) = 1)p(Z) = 1/6. Therefore, p(X) = 2p(Z) = 2(1/6) = 1/3p(Y) = 3p(Z) = 3(1/6) = 1/2. Hence, the probability of X, Y, and Z are p(X) = 1/3, p(Y) = 1/2, and p(Z) = 1/6 respectively.

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Answer:

3 packages of basil

Step-by-step explanation:

27/9 = 3 --> each package costs $3

9/3 = 3 --> amount of packages you can buy with $9

Can you please show the triangle?

The series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent.

To determine whether the series ∑[n=1 to ∞] \(8e^n\) / (3n(n+1)) is convergent or divergent, we can apply the ratio test.

Using the ratio test, we calculate the limit as n approaches infinity of the absolute value of the ratio of the (n+1)-th term to the n-th term:

lim(n→∞) |\((8e^(^n^+^1^) / (3(n+1)(n+2))) / (8e^n / (3n(n+1)))\)|

Simplifying the expression:

lim(n→∞) |\((8e^(^n^+^1^) * 3n(n+1)) / (8e^n * 3(n+1)(n+2))\)|

The common factors cancel out:

lim(n→∞) |e * n / (n+2)|

As n approaches infinity, the ratio tends to e, which is a finite non-zero value.

Since the ratio is a constant (e), which is less than 1, the series is convergent by the ratio test.

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The equation of the parabola is given as follows:

y = -16/33124(x - 182)² + 26.

The distance from the center at which the height is 16 feet is given as follows:

38.12 ft and 325.88 ft.

The equation of a parabola of vertex (h,k) is given by the equation presented as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

It has a span of 364 feet, hence the x-coordinate of the vertex is given as follows:

x = 364/2

x = 182.

It has a maximum height of 26 feet, hence the y-coordinate of the vertex is obtained as follows:

y = 26.

Considering that h = 182 and k = 26, the equation is:

y = a(x - 182)² + 26.

When x = 0, y = 0, hence the leading coefficient a is obtained as follows:

33124a + 26 = 0

a = -26/33124

Hence:

y = -16/33124(x - 182)² + 26.

For a height of 16 feet, we have that

y = 16

16/33124(x - 182)² = 10

(x - 182)² = 33124 x 10/16

(x - 182)² = 20702.5.

Hence the heights are:

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Answer:

\(21 in^{2}\)

Step-by-step explanation:

The square in the middle has a length and width of 3, so multiply. 9.

All of the triangles have a base of 3 and a height of 2. The area equation for triangles is

\(A=bh\frac{1}{2}\)

So base*height is 6. Divide that by 2 or multiply by 1/2.

You get 3. There are 4 triangles, so multiply that by 4. 12.

Add 12 and 9 together, and you get:

\(21 in^{2}\)

I hope this helps!

Answer:

The difference between 18 and seven times a number:    18 - 7x

Step-by-step explanation:

(ii)  One more than the difference between 18 and seven times a number:

Add 1 to the expression from step (i) and get

1 + (18 - 7x)

(iii)  One more than the difference between 18 and seven times a number is -9:

Set expression from step (ii) equal to -9 and get

1 + (18 - 7x) = -9

You can simplify and solve for x.

To make the definition more accurate, we should change it to: "An angle is formed by two non-collinear rays with a common endpoint."

Part A:
The given definition of an angle is incorrect, as it states that an angle is two collinear rays with a common endpoint. In reality, an angle is formed by two non-collinear rays with a common endpoint. An example that contradicts the given definition would be two rays that are collinear, which means they lie on the same line. In this case, no angle would be formed.


Part B:
An example of an undefined term in geometry is a "point." A point is a basic building block of geometric concepts and does not have a specific definition but is used to define other terms. It pertains to angles because angles are formed by two rays with a common endpoint, which is a point. The concept of a point helps us understand and visualize the formation of angles.

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Answer:

2.996

Step-by-step explanation:

14.98 * 0.20 = 2.996

Hope this helps!

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.

Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.

Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.

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Answer:

  2

Step-by-step explanation:

If the number must be even, the units digit must be 8. That leaves 2 choices for the tens digit. The possible numbers are ...

  78

  98

There are 2 of them.

Answer: Only two: 78 and 98

Step-by-step explanation: 8 is the only even number available to put in the units place where even or odd is determined. With no repetition allowed, the only possibilities left are to switch positions of the 7 and 9 in the tens place.

The value for the missing mean  which would result in no main effect for Factor as calculated from the given data ,  A is 2

Given ,

             B1             B2

A1            6               8          

B1            12               ?

Let X = missing mean

mean of A1,

( 6 + 8 ) / 2 = 14 / 2 = 7  

mean of A2

(12 + x ) / 2 = 7

x + 12 = 14\x = 14 -12 = 2

Therefore the value for the missing mean would result in no main effect for Factor A is 2

In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

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Answer: 210

Explanation:

Recall that the perimeter is the distance around the figure. It's the amount of fencing needed to enclose such a shape.

Add up all three sides and set the sum equal to the perimeter 70. Then solve for x.

side1+side2+side3 = perimeter

(3x)+(3x-1)+(4x+1) = 70

10x = 70

x = 70/10

x = 7

We can then calculate each side

Notice how 21+20+29 = 70 to confirm we have the correct side lengths.

Once we know the horizontal and vertical leg (aka base and height), we can find the area.

Area = 0.5*base*height

Area = 0.5*21*20

Area = 210 square cm

Step-by-step explanation:

first you have to find x . Then you can add them and equal them with triangle area.

A prime number is a number which has exactly two factors its self and on not prime.  

The orange divisor above are the prime factors of the number 663 if we put all of it together we have the factors 3*13*17=663. it can also be written in exponential form as 3^1 * 13^1 * 17^1.

Answer:

3 x 13 x 17

Step-by-step explanation:

The value of the variables on the equation:

x - 2y = 6 and 2x - 4y = 10 is 0.

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.

The equation is illustrated thus:

x - 2y = 6 ..... i

2x - 4y = 10 ... . ii

Equation ii can be reduced to x - 2y = 5

The equation will be:

x - 2y = 6

x - 2y = 5

Subtract the equations

In this case, the equations will give 0. It can't be solved further than this.

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Answer:

[C] 4x - 19 < 318

Step-by-step explanation:

For [C] I think you meant: [C] 4x - 19 < 318

Since, x = -8

then we can plug it in to each answer choice to find the answer:

[A] -3x - 2 = 24

⇒ -3(-8) - 2 = 24

-3(-8) = 24

24 -2 = 22 not 24

False.

[B]  12 + 2x > 9

⇒  12 + 2(-8) > 9

 12 -16 > 9

-4 > 9

False.

[C] 4x -19 < 318

⇒ 4(-8) -19= 318

-51 < 318

True.

[D] 17 + x>10​

⇒ 17 + (-8) >10​

-25 > 10

False.

Hence, the answer is [C] 4x - 19 < 318

Kavinsky

The simple interest on 5000 for 219 days at 4% per annum would be $120.

The formula for simple interest is -

A = P(1 + rt)

Given is a to find simple interest on $5000 for 219 days at 4% per annum.

We can write the interest as -

I = P x R x T

I = 5000 x 0.04 x 0.6

I = 120

Therefore, the simple interest on 5000 for 219 days at 4% per annum would be $120.

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Answer:

A line that is perpendicular to y=2/5x-5 must have a slope of -5/2, but a line parallel to line y=5/2x+6 must have a slope of 5/2, and these slopes do not match up.

Explanation:

In order for a line to be parallel to another line, they must have the same slope. In order for a line to be perpendicular to another line, their slopes must be opposite reciprocals (meaning that when they are multiplied, the product is -1). From here you can find what slope the line must have to perpendicular or parallel to another line, and then you can see that the answers to not match up to be the same line!

Hope this helped :)

Answer:

10+1=11 but the 55 so it is now 11:55+15min so it makes it 12:10

Answer:

Hello! The answer to your question is 12:10.

Step-by-step explanation:

1 hour after 10:55 is equivalent to 11:55. Now, we have 15 minutes remaining. We can add in increments of 5 to get to 15 in terms of time:

11:55 + 5 minutes

= 12:00 + 5 minutes

= 12:05 + 5 minutes

= 12:10

5 + 5 + 5 = 15, so we reached 15.

The teacher collected the answer scripts at 12:10.

The volume of the prism shown is equal to 145.89 cubic inches.

In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:

Volume of triangular prism, V = 1/2 × b × h.

Where:

By substituting the given dimensions (side lengths) into the formula for the volume of a triangular prism, we have;

Volume of triangular prism, V =  1/2 × 5.27 × 8.13 × 6.81

Volume of triangular prism, V = 291.775131/2

Volume of triangular prism, V = 145.89 cubic inches.

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The volume of the prism is 145.89 cubic inches.

To find the volume of a prism, multiply the area of the base by the height of the prism.

We know the formula for the volume of a triangular prism is:

\(V = \frac{1}{2}\times b \times h\)

Where:

b represent the base area of a triangular prism.

h represent the height of a triangular prism.

Therefore, we can calculate the volume of the prism by cubing the length of one of its sides:

\(V = \frac{1}{2}\times 5.27\times 8.13 \times 6.81\)

\(V= \frac{291.775131}{2}\)

\(V = 145.89\) cubic inches.

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The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".

This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,

collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.

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Answer:

V = 53.7 m/s ∠-21.41°

Step-by-step explanation:

Since the stone's initial vertical velocity, u is 0m/s(since it is thrown horizontally), we find the stone's final vertical velocity, v from v = u - gt  where u and v have the meanings as given above, g = acceleration due to gravity = 9.8 m/s² and t = time = 2 s

So, v = u - gt

v = 0 m/s - 9.8 m/s² × 2 s

v = 0 m/s - 19.6 m/s

v =  - 19.6 m/s

Since the stone's horizontal velocity is u' = 50 m/s, we find the resultant magnitude of velocity V from V = √(u'² + v²)

So, V = √((50 m/s)² + (-19.6 m/s)²)

V = √(2500 m²/s² + 384.16 m²/s²)

V = √(2884.16 m²/s²)

V = 53.7 m/s

Its direction Ф = tan⁻¹(v/u')

Ф = tan⁻¹(-19.6 m/s/50 m/s)

Ф = tan⁻¹(-0.392)

Ф = -21.41°

So it velocity V = 53.7 m/s ∠ -21.41°

False, a binary (categorical) predictor should not be used along with nonbinary (numerical) predictors

It is important to note that binary and non-binary predictors can both be utilized.

Categorical variables with two possible outcomes, such as yes/no or true/false, are represented by binary predictors. On the other hand, nonbinary predictors indicate numerical variables that can have a variety of values.

It is feasible to capture the links between several sorts of variables and enhance the predictive ability of a model by using both types of predictors. Utilizing methods like logistic regression and

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