Determine the set of points at which the function is continuous. F(x, y) = ((xy)/(2+e^(x-y)))
A)F is continuous on the set of real numbers
B)D = {(x, y) | (x, y) ≠ (1, 1)}
C)D = {(x, y) | (x, y) ≠ (0, 0)} - know this isn't correct
D)D = {(x, y) | y ≠ 0}
E)D = {(x, y) | x ≠ 2} - know this isn't correct
Please help me!

Answer:

x=-14

Step-by-step explanation:

first you add 5 to both sides, to get x/2=-7 then multiply each side by two to get x=-14 that is your answer :D

unless, it is \(\frac{x}{2-5}\)=-12 if so than the answer would be 36

Given:

The figure of a right angle triangle with hypotenuse=19, leg=x and opposite angle is 40°.

To find:

The trigonometric function that is used to solve for x.

Solution:

In a right angle triangle,

\(\sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

In can be written as:

\(\sin \theta=\dfrac{Opposite}{Hypotenuse}\)

Using this ratio for the given triangle, we get

\(\sin 40^\circ =\dfrac{x}{19}\)

Therefore, the correct option is C.

Answer:

45

Step-by-step explanation:

These work problems are always done in terms of fractions ie if both (Kevin & Eric) took 30mins to mow and Kevin took 1.5hrs (90mins) alone then we can make an equation like below

1/time took for both = 1/time took for Kevin + 1/time took for Eric

1/30 = 1/90+1/x    ==> calling time took for Kevin x

solving the above 1/x = 1/30-1/90

1/x=2/90

x=45

Given that Kevin takes 1.5 hours to mow the lawn alone and together

with Eric it takes 30 minutes The time it takes Eric alone is 45 minutes.

The time it takes Kevin to mow the lawn, K = 1.5 hours

The time it takes Kevin and Eric to mow the lawn, B = 30 minutes = 0.5 hours

Required:

The time it takes Eric to mow the lawn alone.

Solution:

Let K represent the time it takes Kevin to mow the lawn alone and let E

represent the time it takes Eric to mow the lawn alone, we have;

\(\mathbf{\dfrac{1}{K} + \dfrac{1}{E} }= \dfrac{1}{T}\)

Which gives;

\(\dfrac{1}{1.5} + \dfrac{1}{E} = \dfrac{1}{0.5}\)

Which gives;

\(\dfrac{1}{E} = \dfrac{1}{0.5} - \dfrac{1}{1.5} =\dfrac{4}{3}\)

Therefore;

\(E = \dfrac{1}{\dfrac{4}{3} } = \dfrac{3}{4} = \mathbf{ 0.75}\)

The time it takes Eric to mow the lawn alone, E = 0.75 hours

0.75 hours = 0.75 × 60 minutes = 45 minutes

The time it takes Eric to mow the lawn alone, E = 45 minutes

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Answer:

u + 15

Step-by-step explanation:

Since we don't know the value of u, we have to put the equation like this.

Hope I helped :)

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Answer:

<     (less than)

Step-by-step explanation:

4.7*0.001 ___ 4

0.0047___4

0.0047 < 4

Answer:

(0, -12)

Step-by-step explanation:

Using the slope-intercept form, the y-intercept is 12.

Answer:

distance = independant; time = dependant

Step-by-step explanation:

You are able to change the distance you travel, making it the independant. As you go farther, the time increases, so it is dependant on the distance traveled, therefore it is the dependant.

Answer:

  7. shifted right 8 units

  8. shifted left 4 and up 12 units

  9. shifted up 8 units

Step-by-step explanation:

You want to compare the given functions with p(x) = a(x -h)² +k and tell the value and effect of a, h, and k on the vertex.

In the equation for p(x) above, the value 'a' represents a vertical scale factor. It expands the graph vertically by the factor 'a'. If a < 0, the graph is reflected across the x-axis.

The values 'h' and 'k' in the equation for p(x) represent a right shift of the graph by 'h' units and a shift up by 'k' units. That is, the graph is translated by (h, k).

We have h = 8. The graph is shifted right 8 units.

We have (h, k) = (-4, 12). The graph is shifted left 4 units and up 12 units.

The values of the transformation parameters are a = -1/2 and k = 8. The vertical compression and reflection do not affect the vertex. The vertex is shifted up 8 units.

The maximum temperature allowed for receiving a shipment of yogurt is 41°F (5°C)

(Option C).

The maximum temperature allowed for receiving a shipment of yogurt will be determined based on common guidelines for food safety and the most appropriate temperature is 41°F (5°C)

This temperature is often considered the upper limit for receiving perishable food items like yogurt to ensure their freshness and prevent bacterial growth.

Thus, we can conclude based on the given options the maximum temperature allowed for receiving a shipment of yogurt is 41°F (5°C), which is considered upper limit for receiving perishable food.

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There are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

For the number to be divisible by 5, its units digit must be either 0 or 5. Since we cannot repeat digits, we have two cases to consider:

Case 1: The units digit is 0.

In this case, we have 5 choices for the units digit (0, 1, 2, 3, or 4). For the remaining four digits, we can choose them in 4! ways (i.e., 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit).

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 0 is:

5 × 4! = 120

Case 2: The units digit is 5.

In this case, we have only one choice for the units digit, which is 5. For the remaining four digits, we can choose them in 4! ways as before.

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 5 is:

1 × 4! = 24

The total number of ways to form a five-digit number that is divisible by 5 without repeating digits is the sum of the numbers from both cases:

120 + 24 = 144

Therefore, there are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

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Answer:

265

Step-by-step explanation:

First, find 8^3. 8^3 is equivalent to 8*8*8=64*8=512

Now you have 9+512/2

Divide 512 by 2, which is 256.

9+256=265

Length of line XY is 12cm

We apply the mid-segment of trapezoid theorem:

Length of line XY is 12cm

Answer:

Hello!!

32 to the power of 5 is

33554432

Hope this helps!!

32 to the power of 5 is 33554432

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.

Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know  the formula  for :

volume = x*y*z, as  here it is a square base, so the volume will be

volume =  x²*y, where x and y are the dimension of the base and height

So for the  given reason,  

=>x²*y =  500

=> y = 500/x²

Again, the surface area formula  will be

S=x²+4xy, substituting the value of  y in this question

=>S=x²+4x(500/x²)

=>S=x²+2000/x

Differentiating the above formula with respect to x, we get

=>2x-2000/x²=0

=>2x³= 2000

=>x³= 1000

=>x =10

so the substituting the x values of x in  the equation y , we get

y = 500/x²

=>y = 5

so the dimensions are x= 10 and y=5

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Answer:

x=0

Explanation:

Add 7 to -7 ( 0 )

Bring down 9x

then divide

x= 0

The approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent is 4.7%

The percentage of light remaining is calculated from the percentage of light remaining after a depth of one foot each.

Percentage of light remaining after 1 feet = 100 - 40% = 60%.

Percentage of light remaining after 6 feet = 60% × 60% × 60% × 60% × 60% × 60% = 4.7%

Therefore, the approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent is 4.7%.

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The solutions to the differential equations: (a) dy/dx - 1/xy = xy^2, This equation can be rewritten as: y^2 dy - x = xy^3 dx.

We can factor out $y^2$ from the left-hand side, and $x$ from the right-hand side, to get:

y^2 (dy - x/y^2) = x (y^3 dx)

This equation is separable, so we can write it as:

y^2 dy/y^3 = x dx/x

We can then integrate both sides of the equation to get:

1/y = ln(x) + C

where $C$ is an arbitrary constant.

(b)

dy/dx + y/x = y^2

This equation can be rewritten as:

(y^2 - y) dy/dx = y^2

We can factor out $y^2$ from the left-hand side, to get:

y^2 (dy/dx - 1) = y^2

This equation is separable, so we can write it as:

dy/dx - 1 = 1

We can then integrate both sides of the equation to get:

y = x + C

where $C$ is an arbitrary constant.

(c)

dy/dx + 2xy = −x 2 cos(x)y 2

This equation can be rewritten as:

dy/dx + xy = −x^2 cos(x) y

We can factor out $y$ from the right-hand side, to get:

dy/dx + xy = -x^2 cos(x) y/y

We can then write this equation as:

dy/dx + y = -x^2 cos(x)

This equation is separable, so we can write it as:

dy/y = -x^2 cos(x) dx

We can then integrate both sides of the equation to get:

ln(y) = -x^2 sin(x) + C

where $C$ is an arbitrary constant.

(d)

2 dy/dx + tan(x)y = (4x+5)2 cosx y 3

This equation can be rewritten as:

2 dy/dx + y tan(x) = y^3 (4x + 5)^2 cos(x)

We can factor out $y^3$ from the right-hand side, to get:

2 dy/dx + y tan(x) = y^3 (4x + 5)^2 cos(x)/y^3

We can then write this equation as:

2 dy/dx + y tan(x) = 4x + 5)^2 cos(x)

This equation is separable, so we can write it as:

2 dy/y = (4x + 5)^2 cos(x) dx

We can then integrate both sides of the equation to get:

2 ln(y) = (4x + 5)^2 sin(x) + C

where $C$ is an arbitrary constant.

(e)

x dy/dx + y = y 2x 2 lnx

This equation can be rewritten as:

dy/dx = y - x y^2 lnx

We can factor out $y$ from the right-hand side, to get:

dy/dx = y (1 - x y lnx)

We can then write this equation as:

dy/y = 1 - x y lnx

This equation is separable, so we can write it as:

dy/y = 1 - x lnx dx

We can then integrate both sides of the equation to get:

ln(y) = x lnx - x + c

where $C$ is an arbitrary constant

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Answer:

6 hours and 25 minutes

Step-by-step explanation:

10:15 to 4:40 = 6 hours and 25 minutes

the answer I think is he saved $2.9

Answer:

$2.9

Step-by-step explanation:

The Expression is:

14.5 − 0.8(14.5)

The Answer is:

$2.9

Answer:

New eq: 11x + 1. The line will become steeper.

Step-by-step explanation:

Slope is rise over run. In the original equation, y increased 4 times everytime x increased by one. In the new equation, y increased 11 times everytime x increased by one making it steeper.

Answer:

the answer is 12.2 :)

Step-by-step explanation:

The probability that the student chosen will walk to school is 0.5156. 

Out of the 64 understudies (students) overviewed, let x be the number of understudies overviewed in Year 9.

At that point, we know that x = 1.3*20 = 26.

Out of the 20 understudies (students) studied in Year 7, 75% strolled to school, so 15 understudies in Year 7 strolled to school.

In Year 9, 8 more understudies strolled to a school than did not walk. Let w be the number of understudies in Year 9 who strolled to school.

At that point, the number of understudies in Year 9 who did not walk to school is x - w. So we have:

w + (x - w) = 26 (since x is the entire number of understudies overviewed in Year 9)

w - (x - w) = 8 (since 8 more understudies strolled to a school than did not walk)

Understanding this framework of conditions, we get w = 17 and x - w = 9

Out of the remaining understudies studied, which are in Year 11, we know that more strolled to a school than in Year 9.

In this manner, the likelihood that an understudy chosen at irregular strolls to school is:

P(walk to school) = (15 + 17 + x/4)/64

where x/4 is the number of understudies overviewed in Year 11 who strolled to school. We do not know the esteem of x/4, but we do know that it is more prominent than 9, since more understudies strolled to school in Year 11 than in Year 9.

In this manner, ready to say that:

P(walk to school) > (15 + 17 + 9)/64 = 0.5156

So the likelihood that a student chooses irregular walks to school is more noteworthy than 0.5156. 

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Answer:

$475

Step-by-step explanation:

The percentage of discount of the item is 72 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage of discount in the price be = A

The marked price of an item at the supermarket = $ 3.42

The original price of an item at the supermarket = $ 4.75

Now , the equation will be

The percentage decrease = ( marked price of an item at the supermarket / original price of an item at the supermarket ) x 100

Substituting the values in the equation , we get

The percentage decrease A = ( 3.42 / 4.75 ) x 100

The percentage decrease A = 0.72 x 100

The percentage decrease A = 72 %

Therefore , the value of A is 72 % and the percentage of discount is 72 %

Hence , The percentage of discount of the item is 72 %

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Answer:

B

Step-by-step explanation:

reduction is \(\frac{4}{5}\) per plant , that is

\(\frac{4}{5}\) × $6 = 0.8 × $6 = $4.80 per plant

total cost = 5 × $4.80 = $24.00

Answer:

(-8, 8)

Step-by-step explanation:

Plug in the y from the top equation into the y of the bottom equation

x² + (x + 16)² = 128

x² + x² + 32x + 256 = 128

Subtract 128 from both sides to make it equal to zero

2x² + 32x + 256 = 128

                 - 128    - 128

2x² + 32x + 128 = 0

Divide both sides by 2

(2x² + 32x + 128)2 = 0/2

x² + 16x + 64 = 0

Factor the equation

(x + 8)(x + 8) = 0

We see that x will have to be -8 for it to equal zero

so x = -8

Plug the new x into one of the original equations; let's use the top one

y = -8 + 16

y = 8

Answer:

Step-by-step explanation:

To convert this mixed numbers;  mixed numbers are converted by multiplying the denominator with the whole number and add answer gotten to the numerator.  you then place final answer over the denominator.

1.  21 /3  x  9 2/3  = 21/3 x 29/ 3

7 x 9.67  = 67.66

2.  5 3/7 x 2 2/5  =  38 / 3   x   12 /5  =

                             12.67   x  2.4 =  30.43

3.  2 6/13  x  2 1/4  =  32 / 14   x  9 /4

                                     2.28  x  2.25  = 9.13

4.  2 11/12 x 3 7/9   =  35 / 12  x  34 /9

                                  2.916  x 3.77   =  11.016

5.  5 3/5 x 5 1/7  =  28/5  x 31 / 7

                              5.6   x 4.428  = 24.8

6.   2 2/3 x 2 11/14   =  8/3  x  39/14

                                    2.66      x  2.78 =  7.413

7.   7 1/4  x 2 1/2  = 29/4   x  5 /2

                              7.25   x 2.5   = 18.125

8.  1 12/3  x 2 2/3 =  15 /3   x  8/3

                               5  x 2.66   =  13.33

9. 2 3/4  x 1 1/6 =   11/4  x 7/6

                                2.75 x  1.166  = 3.20

10.  10 1/3  x 2 1/5 =  31/3 x 11/5

                                  10.33  x  2.2  =  22.726

Answer: 3

Step-by-step explanation:

Basically all you have to do is subtract 6 from both sides so you will get:

3 = v

Answer:

B/a

Step-by-step explanation:

Because 1/a is still the same as a to power negative one and so 1/b. 1/a divided by 1/b is b/a