Write and equation for a line that has a slope of 2/5 and passes through the point (0,-4)

Usando un sistema de ecuaciones, se encuentra que

Para el sistema, hay que:

$845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial, o sea:

\(3x + 5y + 3z = 845\)

$580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial, o sea:

\(4x + 2y + z = 580\)

$605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial, o sea:

\(x + 3y + 3z = 605\)

Reemplazando la segunda equación en las otras duas:

\(z = 580 - 4x - 2y\)

\(3x + 5y + 3z = 845\)

\(3x + 5y + 3(580 - 4x - 2y) = 845\)

\(-9x - y = -895\)

\(9x + y = 895\)

\(y = 895 - 9x\)

\(x + 3y + 3z = 605\)

\(x + 3y + 3(580 - 4x - 2y) = 605\)

\(-11x - 3y = -1135\)

\(11x + 3y = 1135\)

\(y = 895 - 9x\), por eso:

\(11x + 3(895 - 9x) = 1135\)

\(-16x = -1550\)

\(x = \frac{1150}{16}\)

\(x = 96.875\)

\(y = 895 - 9x = 895 - 9(96.875) = 23.125\)

\(z = 580 - 4(96.875) - 2(23.125) = 146.25\)

Un problema similar, que también envuelve un sistema de ecuaciones, es dado en https://brainly.com/question/24646137

The dimensions of each enclosure should be 300 ft by 300 ft to maximize the total area.

Let's call the length of each enclosure L and the width of each enclosure W. Since the two enclosures share a side, we can think of them as being attached along that side. Thus, the total length of the fence used for the enclosures will be:

L + 2W + L = 2L + 2W

Since the farmer has 1200 ft of fence, we know that:

2L + 2W = 1200

or

L + W = 600

To maximize the area, we need to write it in terms of just one variable. The area of each enclosure is given by:

A = LW

Since the two enclosures are identical, the total area will be:

2A = 2LW

We can use the equation L + W = 600 to solve for one variable in terms of the other. For example, we could solve for L:

L = 600 - W

Now we can substitute this expression for L into the formula for the total area:

2A = 2LW = 2(600 - W)W = 1200W - 2W^2

To find the maximum area, we need to find the value of W that maximizes this expression. We can do this by taking the derivative of 2A with respect to W and setting it equal to zero:

d/dW (1200W - 2W^2) = 1200 - 4W = 0

Solving for W gives:

W = 300

Plugging this value of W back into the equation L + W = 600 gives:

L = 300

So the dimensions of each enclosure should be 300 ft by 300 ft to maximize the total area.

To learn more about dimensions visit:

https://brainly.com/question/15586512

#SPJ11

\(4x + 3 = 3x + 12\)

Both sides minus 3

\(4x = 3x + 12 - 3\)

\(4x = 3x + 9\)

Both sides minus 3x

\(4x - 3x = 9\)

\(x = 9\)

So :

TVU = 3(9)+12 ----¢ TVU = 27 + 12

TVU = 39°

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer: x = 2, y = 4/2

Step-by-step explanation:

Solve the System of Equations

x + 3y = 6 6x − 6y = 4

Subtract 3y from both sides of the equation.

x = 6 − 3y 6x − 6y = 4

Replace all occurrences of x with 6 − 3y in each e quation.

Replace all occurrences of x in 6x − 6y = 4 with 6 − 3y.

6 (6 − 3y) − 6y = 4

x = 6 − 3y

Simplify 6 (6 − 3y) − 6y.

36 − 24y = 4

x = 6 − 3y

Solve for y in the first equation.

Move all terms not containing y to the right side of the equation.

−24y = −32

x = 6 − 3y

Divide each term by −24 and simplify.

y = 4/3

x = 6 − 3y

Replace all occurrences of y with 4/3 in each equation.

Replace all occurrences of y in x = 6 − 3y with 4/3

x = 6 − 3 ( 3 )

y= 4/3

Simplify 6 − 3 ( 4 )

x = 2  

y = 4/3

The solution to the system is the complete set of ordered pairs that are valid solutions.

(2, 4 /3 )

The result can be shown in multiple forms.

Point Form:  2, 4 /3

Equation Form:  x = 2, y = 3

The surface area of the triangular prism is 27.4 ft².

The diagram above is a triangular base prism. Therefore, the surface area of the prism can be found as follows:

surface area of the prism = 2(area of the triangle) + 3(area of the rectangular face)

Therefore,

area of the rectangular face = 2 × 4

area of the rectangular face = 8 ft²

area of the triangular face = 1.7 ft²

Hence,

surface area of the prism = 2(1.7) + 3(8)

surface area of the prism = 3.4 + 24

surface area of the prism = 27.4 ft²

learn more on surface area here: https://brainly.com/question/2835293

#SPJ1

Answer:

9/20 or 0.45

Step-by-step explanation:

The least common multiple of 12, 20 and 6 is 60. Reducing the fractions to the denominator 60 we have:

\( \bold{ \dfrac{7}{12} + \dfrac{4}{20} - \dfrac{2}{6} = \dfrac{35}{60} + \dfrac{12}{60} - \dfrac{20}{60} } \\ \\ \bold{= \frac{35 + 12 - 20}{60} = \frac{27}{60} = \frac{9}{20} }\)

If any addend is an integer, an I is placed as denominator and the same operation is done.

Answer:

20 units²

Step-by-step explanation:

I have included the answer as well as an explanation and formula above. Note that the formula is only for area of trapeziums/trapezoids

The correct statement about the solution of system of inequalities is:

Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

Given inequality:

y > 3x + 1

y < 3x – 3

Now the equation of the given inequalities are:

y = 3x + 1

y = 3x - 3

Now from the points through which lines are passing,

Line 1: (-2,-5) and (0,1) .

Line 2 : (0,-3) and (1,0) .

Form the intersecting region of the two lines .

Thus the values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

Know more about inequalities in lines,

https://brainly.com/question/31511107

#SPJ1

The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

answer to the question is that all real numbers or (−∞,∞)

To know more about Range visit:
https://brainly.com/question/12789483

#SPJ4

Answer:

I think it is 2/3x + 50/3

Step-by-step explanation:

So to find the first step, you go to the points that are on the actual corners and that's 2/3 slope. Then looking from the bottom of the graph it goes by tens, so it will help with the second part of the equation, and then you go over 3 so it would be 50/3. I could be very much wrong though

Answer:

94 marbles

Step-by-step explanation:

4512/48 = 94

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

a. The radius of circle P is 5 inches.

b. The side length of the large square is 25 cm.

c. The side length of the large equilateral triangle is 26 feet.

a. The area of circle N is π\(r^2\) = π(\(3^2\)) = 9π square inches.

The area of circle O is π\(r^2\) = π(\(4^2\)) = 16π square inches.

The area of circle P is the sum of the areas of circles N and O, so it is 9π + 16π = 25π square inches.

The formula for the area of a circle is A = π\(r^2\), so we can rearrange it to find the radius:

r = √(A/π)

Plugging in the area of circle P, we get:

r = √(25π/π) = √25 = 5

b. The area of the small square is \(7^2 = 49\) square cm.

The area of the medium square is \(24^2 = 576\) square cm.

The area of the large square is the sum of the areas of the small and medium squares, so it is 49 + 576 = 625 square cm.

The formula for the area of a square is A =\(s^2\), so we can rearrange it to find the side length:

s = √A

Plugging in the area of the large square, we get:

s = √625 = 25

c. The area of the small equilateral triangle is \((\sqrt{3} )/4)\times 10^2 = 25\sqrt{3}\)square feet.

The area of the medium equilateral triangle is \((\sqrt{3} /4)\times 24^2 = 144\sqrt{3}\)square feet.

The area of the large equilateral triangle is the sum of the areas of the small and medium equilateral triangles, so it is \(25\sqrt{3} + 144\sqrt{3} = 169\sqrt{3}\) square feet.

The formula for the area of an equilateral triangle is\(A = (\sqrt{3} /4)\times s^2\), so we can rearrange it to find the side length:

\(s = \sqrt{(4A/\sqrt{3} )}\)

Plugging in the area of the large equilateral triangle, we get:

\(s = \sqrt{(4(169\sqrt{3} )/\sqrt{3} )} = \sqrt{676} = 26\)

for such more question on equilateral triangle

https://brainly.com/question/28004852

#SPJ11

Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence, if 9 is the greater side:

8 + x > 9

x > 1.

If 8 and 9 are the smaller sides:

x < 8 + 9

x < 17.

Hence the range of possible lengths is:

(1, 17).

More can be learned about triangles at https://brainly.com/question/25401493

#SPJ1

Answer:

i think this is what u are,asking

The investment of each brother is $21,000, $14,000, and $14,000 if they are in the ratio 3 : 2 : 2 and they all are investing a total of $49,000.

As the brother invest in the ratio of 3 : 2 : 2 then,

Let the investment of the first brother be 3x

the investment of the second brother be 2x

the investment of the third brother be 2x

Total investment = 3x + 2x + 2x

= 7x

Thus, the fraction of investment of the first brother = \(\frac{3x}{7x}\)

The fraction of the investment of the second brother = \(\frac{2x}{7x}\)

The fraction of the investment of the third brother = \(\frac{2x}{7x}\)

Hence, the investment of the first brother = \(\frac{3x}{7x}\) * 49000 = $21,000

The investment of the second brother = \(\frac{2x}{7x}\) * 49000 = $14,000

The investment of the third brother = \(\frac{2x}{7x}\) * 49000 = $14,000

Learn more about Ratio:

https://brainly.com/question/2914376

#SPJ4

Answer:

12

Step-by-step explanation:

1 - 1/4 = 3/4 (remaining animals which are cats and ferrets)

1 - 8/9 = 1/9 (means 1/9 of the remaining animals are ferrets)

1/9 x 3/4 = 1/12 (means 1/12 of the animals are ferrets)

1/12 x 144 = 12 ferrets

Answer: We can start by finding the width of the rectangular field using the formula for area of a rectangle:

Area = length x width

80 = 20 x width

width = 4 meters

Now we can use the formula for perimeter of a rectangle:

Perimeter = 2 x length + 2 x width

Perimeter = 2 x 20 + 2 x 4

Perimeter = 40 + 8

Perimeter = 48 meters

So, you would have traveled 48 meters if you walked the whole way around the field.

Step-by-step explanation:

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

Learn more about Perimeter of a rectangle at

https://brainly.com/question/29595517

#SPJ4

Answer: 16.7901

Step-by-step explanation: when dividing decimals, you need to make the divisor a whole number.
So, in this case you move the decimal point on 0.081 until it is a whole number.
then it would be 81 after moving the point 3 times to the right.

Now to make it even, you need to move the decimal point on 1.36: 3 times. You will then get: 1,360 divided by 81

And add back the decimal point once you divide.

Answer:

1: 6 5/6

Step-by-step explanation:

Answer:

113m²

Step-by-step explanation:

The large square without the missing part has an area of 169m² becuase length times width 13x13. Now we find the area of the missing part, 7x8=56 so we subtract 56 from 169 and that is 113m².

Answer:

the sale price would be $48

Step-by-step explanation:

To get the sale price you would have to find the decimal form of 40 which is 0.40. Then you multiply 0.40 by 120. And that is 48.00. So than the $48.00 becomes the sale price.

Hope that helps :)

The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

\(H_{o} :p=0.20\), null hypothesis

\(H_{1} :p\neq 0.20\), alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

\(Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }\)

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

\(Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }\)

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

To learn more about claims and hypothesis test; click here:

https://brainly.com/question/17134633

#SPJ4

Answer:

d

Step-by-step explanation:

This occurs when x = π/6 or x = 5π/6, since these are the angles in [0, 2) whose sine is 1/2.So the exact solutions on [0, 2) are: x = 0, π/6, 5π/6.

To find all exact solutions on [0, 2) of the equation tan(x) − 2 sin(x) tan(x) = 0, we can factor out tan(x) from both terms on the left side, then use the fact that tan(x) = sin(x) / cos(x).Here's the

So we solve the equations: tan(x) = 0 ==> x = kπ for integer k, since tan(x) is zero at integer multiples of π. Since the interval [0, 2) includes zero, we have one solution in this interval: x = 0.The other factor 1 - 2sin(x) = 0 if sin(x) = 1/2, since 1/2 is the only value of sin that makes this equation true.

This occurs when x = π/6 or x = 5π/6, since these are the angles in [0, 2) whose sine is 1/2.So the exact solutions on [0, 2) are: x = 0, π/6, 5π/6.

To know more about Angles  visit :

https://brainly.com/question/31818999

#SPJ11

Answer:

Explanation:

Using the following:

For the first triangle with angles 45 degrees

The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

The statement is given as:

Divide 24x2y + 8xy2 + 8xy by -4xy

The quotient is represented as:

Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)

Factor out -4xy

Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)

Evaluate the quotient

Quotient = -6x - 2y - 2

Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

Read more about quotient at:

https://brainly.com/question/8952483

#SPJ1

Answer:

four billion two hundred fifty-eight million one hundred forty-five thousand three hundred ninety-seven

Step-by-step explanation:

Answer:

Word form-

four billion, two hundred fifty-eight million, one hundred forty-five thousand, three hundred ninety-seven.

Step-by-step explanation:

Answer:

The pentagon MNPQR has a perimeter of 22 units.

Step-by-step explanation:

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

\(p = MN + NP + PQ + QR + RM\) (1)

\(p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}\) (1b)

If we know that \(M(x,y) = (2,4)\), \(N(x,y) = (5,8)\), \(P(x,y) = (8,4)\), \(Q(x,y) = (8,1)\) and \(R(x,y) = (2,1)\), then the perimeter of the pentagon MNPQR is:

\(p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}\)\(p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}\)

\(p = 22\)

The pentagon MNPQR has a perimeter of 22 units.

The pentagon MNPQR has a perimeter of 22 units.

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

p = MN + NP + PQ + QR + RMp=MN+NP+PQ+QR+RM (1)

p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}p=

MN

∙

MN

+

NP

∙

NP

+

PQ

∙

PQ

+

QR

∙

QR

+

RM

∙

RM

(1b)

If we know that M(x,y) = (2,4)M(x,y)=(2,4) , N(x,y) = (5,8)N(x,y)=(5,8) , P(x,y) = (8,4)P(x,y)=(8,4) , Q(x,y) = (8,1)Q(x,y)=(8,1) and R(x,y) = (2,1)R(x,y)=(2,1) , then the perimeter of the pentagon MNPQR is:

p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}p=

(5−2)

2

+(8−4)

2

+

(8−5)

2

+(4−8)

2

+

(8−8)

2

+(1−4)

2

+

(2−8)

2

+(1−1)

2

+

(2−2)

2

+(4−1)

2

p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}p=

3

2

+4

2

+

3

2

+(−4)

2

+

0

2

+(−3)

2

+

(−6)

2

+0

2

+

0

2

+3

2

p = 22p=22

The pentagon MNPQR has a perimeter of 22 units.