What is 1/4 as a decimal and as a representation fraction?

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.

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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 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:

D?

Step-by-step explanation:

Answer:

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:

$450

Step-by-step explanation:

First, find an equation that represents the proportional relationship between number of months (x) and amount spent (y).

A proportional equation can be represented in the form, y = kx, where,

k = constant of proportionality = y/x

Using a point on the line, (1, 50),

k = 50/1 = 50.

Substitute k = 50 into y = kx

The equation would be:

y = 50x

After 9 months (x), they would pay the following:

Substitute x = 9 into y = 50x

Thus:

y = 50(9)

y = 450

Answer:

3.125

Step-by-step explanation:

Answer:

25/8 in a decimal form is

Step-by-step explanation:

3.125

Answer:

30in²

Step-by-step explanation:

A=1/2(4)(5+10)

A=2x15

A=30in²

Answer:

x=59

Step-by-step explanation:

3x+3=180

3x=177

x=59

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

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

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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:

[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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Answer:

y = 0

Step-by-step explanation:

Given (-5, 0) and (0, 0),

Find the slope (m):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 0}{0 - (-5)} = \frac{0}{5} = 0 [/tex]

Slope (m) = 0.

Find the y-intercept (b):

y-intercept (b) = 0. This is the value of y, when x = 0.

To write the equation of the line, substitute m = 0, and b = 0 into y = mx + b

y = (0)(x) + 0

y = 0 + 0

y = 0

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]

The line perpendicular to the line y = 2/3x + 4 is 4) y = -3/2x + 4.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

The given equation of a line in slope-intercept form is y = (2/3)x + 4.

Now, We know lines perpendicular to each other have slopes that are negative reciprocal to each other.

If one line has a slope of 'm' the line perpendicular to it will have slope

(-1/m).

Therefore, From the given options the line y = -(3/2)x + 4 is the line perpendicular to the line y = (2/3)x + 4.

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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:

-3/4

Step-by-step explanation:

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

Hope this helps :)

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]

The axis of symmetry is x = -1 and the vertex is (-1,0). Therefore, option D is the correct answer.

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The given quadratic equation is y=x²+2x+1.

From the graph axis of symmetry is x=-1

Rewrite in vertex form and use this form to find the vertex (h,k).

(-1, 0)

Therefore, option D is the correct answer.

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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:

They have a y-value of 0.

They are in Quadrant I.

They are not above or below the origin.

Step-by-step explanation:

i hope this helps:)

Answer:

4 stones is the answer use basic mathematics

Answer:

The slope of the line is [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The Slope of a Line

Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

It's given the points (1,3) and (-2,2). Let's calculate the slope:

[tex]\displaystyle m=\frac{2-3}{-2-1}[/tex]

Calculating:

[tex]\displaystyle m=\frac{-1}{-3}[/tex]

[tex]\displaystyle m=\frac{1}{3}[/tex]

The slope of the line is [tex]\frac{1}{3}[/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 price was reduced from $60 to $45 - So the price was reduced by $15. $15 is what percent of the original price of $60? Percentages can be expressed as fractions or decimals. For example, 30% is the same as 0.30 or 30/100.

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:

x = 35°

y = 55°

Step-by-step explanation:

60° + 50° + 2x = 180° (Sum of angles on a straight line is 180°)

2x = 180° - 110°

x = 70°/2 = 35°

2x + 2y = 180°( Sum of interior angles of a triangle is 180°)

2× 35° + 2y = 180°

70° + 2y = 180°

2y = 180° - 70°

y = 110°/2

y = 55°