A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
y= -1/2 x + 1
y= 1/2 x +7
y= -2x - 8
y= 2x + 16

To determine if the vector field F = (2y,2x+z²,2yz) is conservative, we need to check if it satisfies the condition that the curl of F is equal to zero.

Using the curl formula, we can calculate the curl of F:

curl(F) = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)

= (2z, 0, 2y)

Since the curl of F is not equal to zero, we can conclude that F is not conservative.

Therefore, there does not exist a potential function for F.

A vector field is said to be conservative if it can be expressed as the gradient of a scalar potential function. In other words, if F = ∇f for some scalar function f, then F is conservative. The curl of a conservative vector field is always zero, and the converse is also true. Therefore, to determine if a vector field is conservative, we can check if its curl is zero. If the curl is not zero, then the vector field is not conservative and does not have a potential function.

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Answer:

239.36

Step-by-step explanation:

you do the 8 precent times 4 years =32 precent

then you calculate 32 % out of the 748 $  and the answer is 239.36 dollar

Answer:

3

x

2

−

x

−

6

Step-by-step explanation:

Answer:

5x

Step-by-step explanation:

4x plus 1x equals 5x.

Hope this helped, have a nice day! :)

Answer:

5x

Step-by-step explanation:

4x+1x

=x+x+x+x+x

A normal distribution has a mean of 120 and a standard deviation of 10 then P(x > 110) is 0.84

Given that mean is 120 and a standard deviation of 10

The z-score for x=110 can be calculated as:

z = (x - μ) / σ = (110 - 120) / 10 = -1

Using a standard normal distribution table

we can find that the probability of a z-score being greater than -1 is 0.8413.

Therefore, P(x > 110) = 1 - P(x ≤ 110)

= 1 - P(z ≤ -1)

= 1 - 0.1587

= 0.8413.

Hence,  a normal distribution has a mean of 120 and a standard deviation of 10 then P(x > 110) is 0.84

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The ratio of a : b in the given expression is 16:3  .

In the question ,

it is given that

the algebraic expression is (a+3b)/5 = (a-2b)/2

we have to find the ratio of a:b ,

in order to find the ratio,

we cross multiplying ,

On cross multiplying , we get

2 * (a+3b) = 5 * (a-2b)

2a + 6b = 5a - 10b

5a - 2a = 10b + 6b

3a = 16b

dividing both sides by b ,

a/b = 16/3

a:b = 16:3

Therefore , The ratio of a : b in the given expression is 16:3 .

The given question is incomplete , the complete question is

What is the ratio of a:b in the expression (a+3b)/5 = (a-2b)/2  ?

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10:40 am

63 mile distance and 27 mph. starting from 8 am

63/27 => 2 (2/3) hours. 2/3 of an hour is also, 40 minutes.

so 8 am plus 2 hours and 40 minutes means 10:40 am

Answer:

Si supiera te diría amigo perdón

Answer:

21

Step-by-step explanation:

21/3 = 7

Answer:

I'm pretty sure the answer is B.

Step-by-step explanation:

so you multiply 3x4 and get 12. Then you multiply 5x11 and get 55. last but not least multiply 12 and 55 and get 660 so yeah hope it helps

Answer:

x = -1 or x = -11

Step-by-step explanation:

f(x)= 2|x+6|-4

2|x+6|-4 = 6

2|x+6| = 6+4

2|x+6|=10

|x+6| = 10/2

|x+6| = 5

x+6 = ±5

x = ±5 - 6

x = -1 or x = -11

Answer:

log4 (116)=−2

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (4)(4) of the right side (116)(116) equalsthe exponent (−2)(-2).

The y-cοοrdinate οf the center οf mass is 31/6.

The center οf mass οf the triangular metal piece is lοcated at (13/12, 31/6).

Mass is a measure οf the amοunt οf matter in a substance οr οbject. The base SI unit fοr mass is the kilοgram (kg), but smaller masses can be measured in grams (g). Yοu wοuld use a scale tο measure weight. Mass is a measure οf the amοunt οf matter an οbject cοntains.

Tο find the center οf mass οf the triangular metal piece, we need tο calculate the cοοrdinates (x, y). The center οf mass cοοrdinates can be determined using the fοllοwing fοrmulas:

x = (1/A) ∫∫x * g(x, y) dA

y = (1/A) ∫∫y * g(x, y) dA

where A is the area οf the triangular metal piece.

First, let's find the area οf the triangular regiοn R:

A = ∫∫R dA

Since the triangular regiοn R is defined as 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2x, the limits οf integratiοn fοr x and y are as fοllοws:

0 ≤ x ≤ 1

0 ≤ y ≤ 2x

Therefοre, the area A can be calculated as:

A = ∫∫R dA = ∫0¹ ∫\(0^{(2x)\) dy dx

Integrating with respect tο y first:

A = ∫0¹ (2x - 0) dx = ∫0¹ 2x dx = [\(x^2\)]0¹ = 1

The area οf the triangular regiοn R is 1.

Nοw, let's find x:

x = (1/A) ∫∫x * g(x, y) dA

= (1/1) ∫∫R x * (5x + 5y + 5) dA

= 5 ∫∫R \(x^2\) + xy + x dA

Integrating with respect tο y first:

x = 5 ∫0¹ ∫\(0^{(2x)} (x^2 + xy + x)\) dy dx

= 5 ∫0¹ [\((x^2y + (xy^2)/2 + xy)]0^{(2x)\) dx

= 5 ∫0¹ [\((2x^3 + (2x^3)/2 + 2x^2)\) - (0 + 0 + 0)] dx

= 5 ∫0¹\((3x^3 + x^2)\) dx

= \(5 [(3/4)x^4 + (1/3)x^3]\)0¹

= 5 [(3/4) + (1/3)]

= 5 [(9/12) + (4/12)]

= 5 (13/12)

= 13/12

Therefοre, the x-cοοrdinate οf the center οf mass is 13/12.

Next, let's find y:

y = (1/A) ∫∫y * g(x, y) dA

= (1/1) ∫∫R y * (5x + 5y + 5) dA

= 5 ∫∫R xy + \(y^2\) + 5y dA

Integrating with respect tο y first:

y = 5 ∫\(0^1\) ∫\(0^{(2x)} (xy + y^2 + 5y)\) dy dx

= 5 ∫\(0^1 [(x/2)y^2 + (y^3)/3 + (5/2)y^2]0^{(2x)\) dx

= 5 ∫\(0^1 [(x/2)(4x^2) + (8x^3)/3 + (5/2)(4x^2)\)] dx

= 5 ∫\(0^1 (2x^3 + (8/3)x^3 + 10x^2)\)dx

= 5 [\((1/2)x^4 + (4/3)x^4 + (10/3)x^3]0^1\)

= 5 [(1/2) + (4/3) + (10/3)]

= 5 [(3/6) + (8/6) + (20/6)]

= 5 (31/6)

= 31/6

Therefοre, the y-cοοrdinate οf the center οf mass is 31/6.

The center οf mass οf the triangular metal piece is lοcated at (13/12, 31/6).

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Answer:

364.0

Step-by-step explanation:

567.78/1.56

=363.96153846

=364.0

she makes her most revenue when she sells 20 birthday cards and 15 holiday cards for revenue of 77.5 dollars.

Answer:

its a on edge

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So there are 4 chocolate chips and 12 oatmeal. In total, there are 16 cookies.

The probability of selecting a chocolate chip when you reach in for the first time will be 4/16 or 1/4.

The second time, you reach in, however, there would be one less chocolate chip cookie because you would've pulled one out previously. Thus, the probability is now 3/15 or 1/5.

So, the probability of pulling a chocolate chip cookie consecutively is:

\(\frac{1}{4}\cdot\frac{1}{5}=\frac{1}{20}\)

Our answer is A :)

It is a linear pair of angles hence supplementary

\(\\ \tt\hookrightarrow 123+3x=180\)

\(\\ \tt\hookrightarrow 3x=180-123\)

\(\\ \tt\hookrightarrow 3x=57\)

\(\\ \tt\hookrightarrow x=19\)

Explanation:

The angles shown is supplementary because the sum of 123 and 3x is 180.

Thus, the equation formed:

Subtract 123 both sides:

Divide 3 both sides:

The value of x is 19.

\(e-\frac{1}{e} +\frac{4}{3} 0r 3.687\)  is the value when the equation is to integrate with respect to x or y

we integrate with respect to x

Area = \(\int\limits^b_a{(f(x)-g(x))} \, dx\)

       = \(\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx\)

        =\(e^{x} -\frac{x^{3} }{3} +x\)

   substitute 1 and -1 in place of x

  = \((e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)\)

  = \(e-\frac{1}{e} + \frac{4}{3} or 3.6837\)

The diagram was attached in the given below.

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Answer:

=

Hope that helps!

Step-by-step explanation:

The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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The values based on the exponent will be:

0.024

5670

41952

0.005

73

0.34

900

6

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

1) 2.4 × 10^-2 = 0.024

2) 5.67 x 10^3 = 5670

3) 4.1952 x 10^4 = 41952

4) 5 × 10^-3 = 0.005

5) 7.3 × 10^1 = 73

6) 3.4 × 10-1 = 0.34

7) 9 × 10^2 = 900

8) 6 × 10*0 = 6

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Answer:2 to the 5, 8 to the 2, and 4 to the third

Step-by-step explanation:

2x2x2x2x2=64

8x8=64

4x4x4=64

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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Answer:

40 degrees

Step-by-step explanation:

A circle is 360 degrees and the sum of these 3 arcs are 320 degrees. So 360-320 is 40.

Hope this helps! :D

a. The probability is 4/10 or 0.4.

b. The combination formula: C(10, 5) = 252.

c. C(6, 3) = 20.

d. C(4, 2) = 6.

e. The probability is 120/252 ≈ 0.4762.

a. To calculate the probability that the person drawing the names is a Democrat, we divide the number of Democrats (4) by the total number of council members (10). Therefore, the probability is 4/10 or 0.4.

b. When there are no restrictions on the composition of the committee, we can calculate the number of ways it can be formed using combinations. Since there are 10 council members and we need to choose 5, the number of ways the committee can be formed is given by the combination formula: C(10, 5) = 252.

c. To determine the number of ways to choose 3 Republicans, we calculate the combination of 6 Republicans taken 3 at a time: C(6, 3) = 20.

d. Similarly, to calculate the number of ways to choose 2 Democrats, we use the combination formula with the 4 Democrats: C(4, 2) = 6.

e. To find the probability of selecting 3 Republicans and 2 Democrats, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes. The number of ways to select 3 Republicans from 6 and 2 Democrats from 4 is given by the product of their respective combinations: C(6, 3) * C(4, 2) = 20 * 6 = 120. The total number of possible outcomes is C(10, 5) = 252. Therefore, the probability is 120/252 ≈ 0.4762.

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Answer:

(f - g)(x) = 2x - 3

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x - 1 - (x + 2)

= 3x - 1 - x - 2

= 2x - 3

Answer:

Given - Twice a no. decrease by 22 is 48

To find - The no.

Solution -

Let the no. be X

According to the question, equation made is -

2x - 22 = 48

2x = 48 + 22

2x = 70

x = 70/2

X= 35

Verification -

35 ×2 - 22 = 48

70 - 22 = 48

48= 48

LHS = RHS

hence proved

Answer: 35

Let the number be x. Then, we can write an equation with what we are given:

2x - 22 = 48

Adding 22 to both sides, we have 2x = 70, so x = 35.

i hope this helped! :D

The equation for x for the given expression -1+√3x-8 = 7 is : 9.24.

In order to solve the equation for x we have to isolate variable x, simplify and solve for x.

Let isolate the variable x on one side of the equation.

-1 + √3x - 8 = 7

Simplify the left side by combining the constants:

-9 + √3x = 7

Isolate √3x by adding 9 to both sides:

√3x = 16

Solve for x by dividing both sides by √3:

x = 16/√3

x= 9.237

x = 9.24 ( Approximately)

Therefore the equation is 9.24.

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