What is the simplified form of the expression?
(3x^2+5x-8)+(5x^2-13x-5)

To find the point on the given surface that has a positive x-coordinate and at which the tangent plane is parallel to the given plane, we use the following steps:Step 1: First, we rewrite the equation of the given surface, x2 + 9y2 + 2z2 = 6768, in terms of z,  so we get:z = ± sqrt [(6768 - x2 - 9y2)/2]

Step 2: We then compute the partial derivatives of z with respect to x and y.Using the chain rule, we get the following: z_x =

(-x)/sqrt[2(6768 - x2 - 9y2)]and z_y = (-9y)/sqrt[2(6768 - x2 - 9y2)]

Step 3: Next, we find the normal vector of the given plane, which is given by: n = (18, 108, 12)Step 4: We then find the gradient vector of the surface, which is given by: grad f(x, y, z) = (2x, 18y, 4z)Step 5: We now need to find the point (x, y, z) on the surface such that the tangent plane at this point is parallel to the given plane. This means that the normal vector of the tangent plane must be parallel to the normal vector of the given plane. We have:n x grad f(x, y, z) =

(18, 108, 12)x(2x, 18y, 4z) = (-216z, 36z, 324x + 2,916y)

We then equate this to the normal vector of the given plane and solve for x, y, and z.

(18, 108, 12)x(2x, 18y, 4z) = (18, 108, 12)x(1, 6, 0) ⇒ (-216z, 36z, 324x + 2,916y) = (-648, 108, 0) ⇒ 216z/648 = -36/(108) = -1/3 ⇒ z = -2/3

Step 6: We substitute z = -2/3 into the equation of the surface and solve for y and x. We have:

x2 + 9y2 + 2(-2/3)2 = 6768 ⇒ x2 + 9y2 = 484 ⇒ y2 = (484 - x2)/9

We now differentiate the equation y2 = (484 - x2)/9 with respect to x to find the critical points, and we get:dy/dx = (-2x)/9y ⇒ dy/dx = 0 when x = 0Thus, the critical points are (0, ± 22), and we can check that both these points satisfy the condition that the tangent plane is parallel to the given plane (the normal vector of the tangent plane is given by the gradient vector of the surface evaluated at these points).Thus, the points on the surface that have a positive x-coordinate and at which the tangent plane is parallel to the given plane are (0, 22, -2/3) and (0, -22, -2/3).

The points on the surface that have a positive x-coordinate and at which the tangent plane is parallel to the given plane are (0, 22, -2/3) and (0, -22, -2/3).

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Answer:

Step-by-step explanation:

Given:

Area formula:

Substitute values and solve for w:

The width is 6 in, find the length:

width be x

Now

On solving we will get

Now

Length=2(6)=3=15in

Answer:

9/6

Step-by-step explanation:

I think this is what you're looking for...

Answer:1.

5

x

−

2

y

=

4

; (−1, 1)

2.

3

x

−

4

y

=

10

; (2, −1)

3.

−

3

x

+

y

=

−

6

; (4, 6)

4.

−

8

x

−

y

=

24

; (−2, −3)

5.

−

x

+

y

=

−

7

; (5, −2)

6.

9

x

−

3

y

=

6

; (0, −2)

7.

1

2

x

+

1

3

y

=

−

1

6

; (1, −2)

8.

3

4

x

−

1

2

y

=

−

1

; (2, 1)

9.

4

x

−

3

y

=

1

;

(

1

2

,

1

3

)

10.

−

10

x

+

2

y

=

−

9

5

;

(

1

5

,

1

10

)

11.

y

=

1

3

x

+

3

; (6, 3)

12.

y

=

−

4

x

+

1

; (−2, 9)

13.

y

=

2

3

x

−

3

; (0, −3)

14.

y

=

−

5

8

x

+

1

; (8, −5)

15.

y

=

−

1

2

x

+

3

4

;

(

−

1

2

,

1

)

16.

y

=

−

1

3

x

−

1

2

;

(

1

2

,

−

2

3

)

17.

y

=

2

; (−3, 2)

18.

y

=

4

; (4, −4)

19.

x

=

3

; (3, −3)

20.

x

=

0

; (1, 0)

Find the ordered pair solutions given the set of x-values.

21.

y

=

−

2

x

+

4

; {−2, 0, 2}

22.

y

=

1

2

x

−

3

; {−4, 0, 4}

23.

y

=

−

3

4

x

+

1

2

; {−2, 0, 2}

24.

y

=

−

3

x

+

1

; {−1/2, 0, 1/2}

25.

y

=

−

4

; {−3, 0, 3}

26.

y

=

1

2

x

+

3

4

; {−1/4, 0, 1/4}

27.

2

x

−

3

y

=

1

; {0, 1, 2}

28.

3

x

−

5

y

=

−

15

; {−5, 0, 5}

29.

–

x

+

y

=

3

; {−5, −1, 0}

30.

1

2

x

−

1

3

y

=

−

4

; {−4, −2, 0}

31.

3

5

x

+

1

10

y

=

2

; {−15, −10, −5}

32.

x

−

y

=

0

; {10, 20, 30}

Find the ordered pair solutions, given the set of y-values.

33.

y

=

1

2

x

−

1

; {−5, 0, 5}

34.

y

=

−

3

4

x

+

2

; {0, 2, 4}

35.

3

x

−

2

y

=

6

; {−3, −1, 0}

36.

−

x

+

3

y

=

4

; {−4, −2, 0}

37.

1

3

x

−

1

2

y

=

−

4

; {−1, 0, 1}

38.

3

5

x

+

1

10

y

=

2

; {−20, −10, −5}

Part B: Graphing Lines

Given the set of x-values {−2, −1, 0, 1, 2}, find the corresponding y-values and graph them.

39.

y

=

x

+

1

40.

y

=

−

x

+

1

41.

y

=

2

x

−

1

42.

y

=

−

3

x

+

2

43.

y

=

5

x

−

10

44.

5

x

+

y

=

15

45.

3

x

−

y

=

9

46.

6

x

−

3

y

=

9

47.

y

=

−

5

48.

y

=

3

Find at least five ordered pair solutions and graph.

49.

y

=

2

x

−

1

50.

y

=

−

5

x

+

3

51.

y

=

−

4

x

+

2

52.

y

=

10

x

−

20

53.

y

=

−

1

2

x

+

2

54.

y

=

1

3

x

−

1

55.

y

=

2

3

x

−

6

56.

y

=

−

2

3

x

+

2

57.

y

=

x

58.

y

=

−

x

59.

−

2

x

+

5

y

=

−

15

60.

x

+

5

y

=

5

61.

6

x

−

y

=

2

62.

4

x

+

y

=

12

63.

−

x

+

5

y

=

0

64.

x

+

2

y

=

0

65.

1

10

x

−

y

=

3

66.

3

2

x

+

5

y

=

30

Part C: Horizontal and Vertical Lines

Find at least five ordered pair solutions and graph them.

67.

y

=

4

68.

y

=

−

10

69.

x

=

4

70.

x

=

−

1

71.

y

=

0

72.

x

=

0

73.

y

=

3

4

74.

x

=

−

5

4

75. Graph the lines

y

=

−

4

and

x

=

2

on the same set of axes. Where do they intersect?

76. Graph the lines

y

=

5

and

x

=

−

5

on the same set of axes. Where do they intersect?

77. What is the equation that describes the x-axis?

78. What is the equation that describes the y-axis?

Part D: Mixed Practice

Graph by plotting points.

79.

y

=

−

3

5

x

+

6

80.

y

=

3

5

x

−

3

81.

y

=

−

3

82.

x

=

−

5

83.

3

x

−

2

y

=

6

84.

−

2

x

+

3

y

=

−

12

Step-by-step explanation:

The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

y = 2x + 56       ....1

y = 9x               ....2

From equations 1 and 2, then we have

9x = 2x + 56

7x = 56

 x = 8

Then the value of the variable 'y' is given as,

y = 9(8)

y = 72

The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

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Answer:

Step-by-step explanation:

scale factor=3/2

(8,6)

(12,6)

(12,10)

use formula

(x,y)=(kx,ky)  (k means scale factor)

(8,6)=(3/2*8 , 3/*6)

=(24/2 , 18/2)

=(12 , 9)

(12,6)=(3/2*12 , 3/2*6)

=(36/2 , 18/2)

=(18 , 9)

(12,10)=(3/2*12 , 3/2*10)

=(36/2 , 30/2)

=(18 , 15)

Answer:

18 ,15

Step-by-step explanation:

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The quadrilateral that is described with the given properties is known as; Rhombus

A quadrilateral is defined as a closed shape and a type of polygon that has four sides, four vertices and four angles.

Now, we are told that at least  at least two pairs of consecutive sides are congruent, diagonals are perpendicular to one another.

The only quadrilaterals that fit into thus definition are square and rhombus.

Now, we are told that the quadrilateral cannot be inscribed in a circle. A square can be inscribed in a circle but not a rhombus and as such we can say that the quadrilateral with the given properties is a rhombus,

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Answer:

12.85

Step-by-step explanation:

Answer:

n = 12.85

Step-by-step explanation:

n - 9.01 = 3.84 --> add 9.01 to both sides

n = 12.85

Answer:

-71

Step-by-step explanation:

(M+3)/4=-17

M+3=-17*4

M+3=-68

M=-68-3

M=-71

Answer:

946 milliliter can

Step-by-step explanation:

She should consider how much is in it. Which one will last longer and is better. The bigger can has more in it so that one should be bought.

Hope this helps!

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

What is serious opera called?

What is Wagnerian leitmotif?

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Answer:

x = -2/3  x=1

Step-by-step explanation:

We cant solve by substitution with just one equation

-3x^2 + x +2=0

Factor out a negative

-(3x^2 -x-2) = 0

Divide by negative 1

(3x^2 -x-2) = 0

Factor

(3x +2) (x-1)=0

Using the zero product property

3x+2 =0   x-1 =0

3x= -2   x=1

x = -2/3  x=1

Answer:

\(x = \frac{2}{3} \\ x = - 1\)

Step-by-step explanation:

\(x - 3 {x}^{2} + 2 = 0 \\ - 3 {x}^{2} + x + 2 = 0 \\ - 3 {x}^{2} - 3x + 2x + 2 = 0 \\ - 3x(x + 1) + 2(x + 1) = 0 \\ ( - 3x + 2)(x + 1) = 0\)

\( - 3x + 2 = 0 \\ - 3x = - 2 \\ \frac{ - 3x}{ - 3} = \frac{ - 2}{ - 3} \\ x = \frac{2}{3} \)

\(x + 1 = 0 \\ x = - 1\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

a. direct

Step-by-step explanation:

direct variation is y = kx and y = -2/5x is written in direct variation.

Answer:

S=2t

or

T=1/2 S

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

There are a total of four components in a time series model.

Trend, Seasonal, Cyclical, and Error.

Seasonal Component is a wavelike pattern that is repeated throughout a time series and has a recurrence period of at most one year.

Cyclical Component is a wavelike pattern within the time series that repeats itself throughout the time series and has a recurrence period of more than one year.

Error Term represents the changes in time series data that are unpredictable and can't be associated with a seasonal , cyclical component.

Trend Component is the long-term increase or decrease in a variable being measured over time.

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

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Answer:

  p - q = 5

Step-by-step explanation:

You have p+q = 12 and p²-q² = 60. You want the value of p-q.

The difference of squares is factored as ...

  p² -q² = (p +q)(p -q)

Substituting given values, this becomes ...

  60 = 12(p -q)

Dividing by 12 gives the difference of interest:

  5 = p -q

Answer:

9

Step-by-step explanation:

can fit in 9 times

Answer:

3

Step-by-step explanation:

count the unit boxes on the top of figure B which is 9 and the boxes on top of figure A is 3, the unit boxes on the bottom have the same scale factor of both figure A and B.

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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Answer:

it's c

y < x

y < 2

Step-by-step explanation:

Hope this helps have a nice day!!!

:)

Considering that the amount deposited is the total deposited subtracted by the cash received, it is found that the amount that Kay deposit in cash and coins is given by:

d. $284. 50.

It is given by the total deposited subtracted by the cash received.

In this problem, we have that:

Hence, the deposit is of:

D = 498.01 - 213.51 = 284.5.

Hence option D is correct.

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Answer:

C!!!!!!!!! NOT D

Step-by-step explanation:

(2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.

Annabella can express her average cost per gallon of gasoline as 2.25 × 2.15(x + 5)/(2x + 5)²

The meaning of the parts of this rational expression in the context of the situation are as follows: 2.25 and 2.15 are the cost per gallon of gas at the two different gas stations.

x represents the number of gallons of gas bought at the first station.

5 is the number of miles driven between the first and second gas stations. And 2x + 5 is the total number of gallons of gas used in the entire trip (from the first gas station to the second).

Therefore, (x + 5) is the amount of gasoline bought from the second gas station, and 2x is the amount of gasoline bought from the first gas station.

The expression (x + 5)/(2x + 5) represents the weighted average of the cost per gallon of gas at the two gas stations.

Finally, (2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

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Answer:

40/5 = 8

So Karen worked 8 hours yesterday.

Step-by-step explanation:

There are 6 possible permutations of the given 3 items.

The given permutation is P 12 13.

A permutation is a way of arranging objects in a specific order.

A permutation of n objects is a way of arranging n objects into a specific order.

We use the notation P (n, r) or n P r to denote the number of permutations of n objects taken r at a time.

To compute the permutation P(n, r) or n P r, we can use the following formula:

P(n, r) = n!/(n - r)!

The given permutation is P 12 13. It means we have 3 items (12, 1, 3) and we need to place them in a specific order.

Since there are only three items, we can simply list out all the possible permutations:

P 12 13, P 13 12, P 21 13, P 23 11, P 31 12, P 32 11

Hence, there are 6 possible permutations of the given 3 items.

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Answer:

A

C

D

Step-by-step explanation: Every other answer is wrong

Answer:

A, C,

Step-by-step explanation:

Answer:

Step-by-step explanation:

(1/2)(1/2)=1/4

Answer:

2.-2y=x

Step-by-step explanation:-2y=x

y=kx  for constant k

The  Commutative property Associative property Identity property  property of addition states that the way addends are grouped does not affect their sum.

The commutative property of addition states that the sum is unaffected by the order of the addends. 2+3=3+3

Changing the order of the addends has no effect on the sum, according to the associative property of addition.

(2+3)+4=2+(3+4)

Identity of addition property: Any number is equal to the sum of 0 00 and that number. For instance 0+5=5

According to the commutative property of addition, altering the order of addends has no impact on the sum. 2+3 = 3+2

as 3 rules are there only

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