simplest form 3/56 ​

9514 1404 393

Answer:

  11/20

Step-by-step explanation:

It is appropriate to "invert and multiply".

  [tex]\dfrac{5}{20}\div\dfrac{5}{11}=\dfrac{5}{20}\times\dfrac{11}{5}=\dfrac{5\times11}{5\times20}=\boxed{\dfrac{11}{20}}[/tex]

Answer:

x = 5 ± i √ 11 /6

Step-by-step explanation:

The roots (zeros) are the  x  values where the graph intersects the x-axis. To find the roots (zeros), replace  y  with  0  and solve for  x .

Answer:

The solution for given system of equation is: [tex]x=\frac{1}{5}\:and\:y=\frac{-9}{5}[/tex] and ordered pair is: [tex]\mathbf{(\frac{1}{5},\frac{-9}{5})}[/tex]

So, (1,3) is not solution to the given system of equations.

Step-by-step explanation:

we can solve the system of equations to find the value of x and y and then verify if (1,3) is a solution or not.

The system of equation given is:

[tex]y=6x-3\\y=x-2[/tex]

Solving:

Let:

[tex]y=6x-3--eq(1)\\y=x-2--eq(2)[/tex]

Put value of y from equation 2 into equation 1

[tex]y=6x-3\\Put\:y=x-2\\x-2=6x-3\\x-6x=-3+2\\-5x=-1\\x=\frac{-1}{-5}\\x=\frac{1}{5}[/tex]

Now, put value of x in equation 2 to find value of y

[tex]y=x-2\\Put\:x=\frac{1}{5} \\y=\frac{1}{5} -2\\y=\frac{1-2*5}{5} \\y=\frac{1-10}{5}\\ y=\frac{-9}{5}[/tex]

So, the solution for given system of equation is: [tex]x=\frac{1}{5}\:and\:y=\frac{-9}{5}[/tex] and ordered pair is: [tex]\mathbf{(\frac{1}{5},\frac{-9}{5})}[/tex]

So, (1,3) is not solution to the given system of equations.

Answer:

29

Step-by-step explanation:

2x - 14 = x + 15

2x - x = 15 + 14

x = 29

check

44 = 44

Answer:

pretty sure it's 29

Step-by-step explanation:

equation: 2x-14=x+15

how to solve: add 14 to both side, and subtract x from both sides. The equation will then be x=29.

I might be wrong tho.

Answer:

-3/4

Step-by-step explanation:

-5/4 + 2/4 = -3/4

Hope this helps :)

Answer: a = 10

Step-by-step explanation:

3/5 = a + 5/25

Multiply both sides by 25 to get rid of it:

3/5 * 25 = 25(a + 5) /25

15 = a + 5

a = 15 - 5

a = 10

Answer:

Yes i think its -96,

if thats what your asking

Answer:

[tex]\dfrac{-8^3}{6}[/tex]

Step-by-step explanation:

According to the divergence theorem;

The flux through the surface S is given by the formula:

[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]

where the vector field is:

F = [tex]\langle y,z-y,x \rangle[/tex]

Then the divergence of the vector field is:

[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]

= 0 - 1 + 0

= -1

Thus, the flux through the surface of the tetrahedron is:

[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]

To determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus;

[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]

[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]

[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]

i.e.

[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]

[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]

[tex]= \dfrac{-8^3}{6}[/tex]

This question is based on the Gauss Divergence theorem. Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

Given:

F(x, y, z) = y i + (z − y) j + x k S in outward orientation.

Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).

We have to evaluate the surface integral  [tex]\int\limits {F.dS}[/tex] .

According to the Gauss divergence theorem ,

The flux through the surface S is given by the formula:

[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]

Where the vector field is:

F  = ( y, z-y, x )

Therefore,  the divergence of the vector field is:

[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]

Thus, the flux through the surface of the tetrahedron is:

[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]

Now, determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus,

[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]

Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

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9514 1404 393

Answer:

  (x, y) = (10, 2)

Step-by-step explanation:

The upper angle marked with an expression in x and y is supplementary to the angle marked 70°. The lower angle marked with an expression in x and y is an alternate interior angle with respect to the one marked 70°, is equal to that. This gives the two equations in x and y:

  6x +10y +30 = 110

  4x +10y +10 = 70

Subtracting the second equation from the first gives ...

  2x +20 = 40

  x +10 = 20 . . . . . divide by 2

  x = 10 . . . . . . . . . subtract 10

Substituting into the second equation gives ...

  4(10) +10y +10 = 70

  4 + y + 1 = 7 . . . . . . . . divide by 10

  y = 2 . . . . . . . . . . . . . . subtract 5

The values of x and y are 10 and 2, respectively.

Answer:

9514 1404 393

Step-by-step explanation:

Answer:

Option B is correct

For  , the function for the given sequence is defined as;  

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.

An explicit formula for this arithmetic sequence given by;

where a represents first term

Since, the given sequences; 7 , 10 , 13 , 16 and 19

⇒ common difference(d) = 3 and a = 7

Since.

10 -7 = 3

13- 10 = 3  ....

The function which defined this sequence is;

using distributive property:

therefore, the function for the given sequence for all integers  is;  

Answer:

The perimeter of a rectangle is the sum of both lengths and both widths, which is equal to 54 meters. Let's call Length L and Width W.

The question is saying this: L = 3 meters + 3(W). We have 2 variables, which means we need at least 2 equations to solve. So far we have one, our second equation is from the perimeter.

2 lengths + 2 Widths = 54. Now, it's just a plug and chug.

2(3 + 3W) + 2W = 54.

6 + 6W + 2W = 54

8W = 48

W=6

L = 3 + 3(6) = 21

To double check: 2(21) + 2(6) = 42 + 12 = 54

The Width is 6 meters, and the Length is 21 meters.

Answer:

Answer:

A cuz x+6 is double x-3 so divide them and equate it to 2 you'd get x+6 = 2x-6

12=2x-x

Answer:

the right half

Step-by-step explanation:

We know that cosine is a pair function.

This means that:

Cos(a) = Cos( -a)

We also know that:

Cos(pi) = 0

then:

Cos(-pi) = 0

pi and -pi are located in the y-axis, so from this we can know that the cosine function will be always positive on the right side, or in the left side, we can discard the other two options.

Now, we also know that cos(0) = 1.

And:

-pi < 0 < pi

So the two zeros are at the y-axis, and we know that cos(0) is positive (the angle 0 would be on the positive side of the x-axis, at the right), then all the right side must be positive.

Then the correct option is:

the right half

Answer:

C - The right half

Step-by-step explanation:

Just took the quiz on edge

Answer: 20

Step-by-step explanation:

Answer:

Each metal sheet costs 18 dolares per square foot

Step-by-step explanation:

7.6x−2.3x= $95.40

simplify

5.3x = $95.40

/5.3

x = 18

Answer:

n = 1.42857

Step-by-step explanation:

if a2 is -140 then somewhere between is -100.  3/7 is equal to 0.42857142857 in which it is 3/7 from -70 to -140 in a number range of 1 to 2.  1.42857142857 is your best bet as your answer.

Answer:

B

Step-by-step explanation:

-3/4y - 1/5y = 380 can be simplified to -19/20y = 380.

In order for the student to incorrectly get 361, they likely just multiplied the 380 by 19/20 rather than multiplying by the reciprocal (which would be -20/19).

This means the best answer should be B.

Answer:

[tex]\displaystyle y=2\sqrt{6}[/tex]

[tex]\displaystyle x=2\sqrt{2}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

[tex]\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}[/tex]

Solving for y:

[tex]y=4\sqrt{2}\cos 30^\circ[/tex]

Since:

[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]

[tex]\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}[/tex]

Simplifying:

[tex]\displaystyle y=2\sqrt{6}[/tex]

Now we use the sine ratio:

[tex]\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}[/tex]

Solving for x:

[tex]x=4\sqrt{2}\sin 30^\circ[/tex]

Since:

[tex]\sin 30^\circ=\frac{1}{2}:[/tex]

[tex]\displaystyle x=4\sqrt{2}\frac{1}{2}[/tex]

Simplifying:

[tex]\displaystyle x=2\sqrt{2}[/tex]

The choices are not clear, but it seems like the correct answer is C.

[tex]\boxed{\displaystyle y=2\sqrt{6}}[/tex]

[tex]\boxed{\displaystyle x=2\sqrt{2}}[/tex]

Answer:

3.125

Step-by-step explanation:

Answer:

25/8 in a decimal form is

Step-by-step explanation:

3.125

Answer:

It is 31:5

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

B. rate of water flow.

Step-by-step explanation:

Given that in a research study the explanatory variable is a form of a variable that is independent and it is used by the researcher to make predictions or analyze variations in other variables known as response variables.

Hence, in this case, the Explanatory variable is the "rate of water flow" because it is the variable researcher wishes to utilize in predicting the amount of soil washed away.

From the linear equation, the option that describes the graph of the two corresponding lines is C. The lines are parallel.

Based on the complete information, it should be noted that the lines are not coinciding and they don't intersect at only one point.

Rather, it can be deduced that the graph of the two corresponding lines in the xy-plane are parallel.

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Answer:

D?

Step-by-step explanation:

Answer:

The exponential form of expression is 4⁵.

To grow at an ever-increasing rate is referred to as exponential growth. On the other hand, it is a mathematical expression with one or more exponents in mathematics. As a result, we call it an exponential form.

We can say that something might grow at an exponential rate if it grows faster and faster as the thing being discussed gets bigger.

Given expression

4.4.4.4.4

Writing a number as the product of its prime factors is the very first step in expressing it in exponential form.

number is in factors

4 x 4 x 4 x 4 x 4

a numerical term that has been increased to certain powers of its prime factors

= 4⁵

where 5 is exponent.

Hence the  exponential form is 4⁵.

Learn more about  exponential form;

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#SPJ2

Explanation:

The probability of rolling a "2" is 1/6

The probability of rolling a "4" is also 1/6

Multiplying those fractions leads to (1/6)*(1/6) = 1/36. We can multiply the probabilities because the events are independent. Each dice roll does not affect any others.

The probability of rolling a 2 the first time and a 4 the second time is 1/36

There are 6 faces on a die.

Of these 6 faces, one of them is 2 and one of them is 4

So, the probabilities of rolling a 2 and a 4 are:

P(2) = 1/6

P(4) = 1/6

The probability of rolling a 2 the first time and a 4 the second time is calculated as follows:

[tex]\mathbf{Pr = P(2) \times P(4)}[/tex]

This gives

[tex]\mathbf{Pr = \frac 16 \times \frac 16}[/tex]

Multiply

[tex]\mathbf{Pr = \frac 1{36}}[/tex]

Hence, the probability of rolling a 2 the first time and a 4 the second time is 1/36

Read more about probabilities at:

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Answer:

let jolene's dvd be x

2x+x+3x= total dvds = 6x

2x/6x=1/3

Salena has 1/3 of the total dvds

Answer:

[tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]

Step-by-step explanation:

From the question we are told that

Temperature is given [tex]T ( x, y, z) = x + yz.[/tex]\

A fly is at (1,2,1)

Generally the direction of fly is given by

      [tex]\triangleT(x,y,z) =(1,z,y)\\[/tex]

       [tex]v= \triangleT(1,2,1)\\v=(1,1,2)[/tex]

Mathematically solving for the vector direction

       [tex]|v|=\sqrt{1^2+1^2+2^2}[/tex]

       [tex]|v|=\sqrt{6}[/tex]

       [tex]u=- \frac{v}{|v|}[/tex]

       [tex]u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}[/tex]

Therefore this the direction which should be taken to cool down soonest