Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3

Answer:

[tex]1\frac{1}{4}\ hours[/tex]

Step-by-step explanation:

we know that

using proportion

[tex]\frac{(1/4)}{(1/5)}\frac{hour}{paper}=\frac{x}{1}\frac{hour}{paper} \\ \\x=5/4\ hours[/tex]

covert to mixed number

[tex]5/4\ hours=1\frac{1}{4}\ hours[/tex]

Answer:

Brenda

Step-by-step explanation:

You can divide the number of pages by the number of minutes to find the amount of minutes it takes to read 1 page. For Arnold, 3 pages / 7 minutes = 1 page per approximately 0.43 minutes. For Brenda, 8 pages / 14 minutes = 1 page per approximately 0.57 minutes. Brenda reads slightly faster since 0.57 > 0.43

➷ cos38 = 79/x

x = 79/cos38

x = 100.2524

The correct option would be 100.25

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

100.25

Step-by-step explanation:

Using the cosine ration in the right triangle, then

cos38° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{79}{x}[/tex]

Multiply both sides by x

x × cos38° = 79 ( divide both sides by cos38° )

x = [tex]\frac{79}{cos38}[/tex] ≈ 100.25

First you need to rewrite the equation in the form y = mx +b:

2y = x-4

Divide all terms by 2:

2y / 2 = x/2 - 4/2

Simplify:

y = 1/2x - 2

The slope of the line is 1/2.

A perpendicular line has a slope of the negative reciprocal, which would be -2.

Now using the point slope method:

y - y1 = m(x-x1)

Using the given point of (8,-4) and m = -2

you get:

y +4 = -2(x-8)

Simplify:

y +4 = -2x +16

Now subtract 4 from both sides to get the final equation:

y = -2x +12

Answer:

b: [tex] x= 8 \sqrt7 y= 4 \sqrt{21} [/tex]

Step-by-step explanation:

Euclid 1st theorem:

[tex] x^2 = 16 * (16+12); y^2 = 12*(12+16) [/tex]

Calculation is trivial

Answer:

  3 ft by 7 ft

Step-by-step explanation:

Try the solutions and find the one that works.

  3.5 × 6 — area OK, perimeter = 19 ft

  4 × 6 — area = 24 ft², perimeter OK

  3 × 7 — area OK, perimeter OK

  3.5 × 7 — area 24.5 ft², perimeter 21 ft

___

The perimeter is the sum of the four side lengths; the area is the product of two adjacent side lengths.

Answer:

The answer is A. 48 divided by 3 equals 16. Therefore, if you earn $48 for 3 hours, then you are earning $16 per hour.

Step-by-step explanation:

Hey there!

The correct answer is A. $48 for 3 hours

I figured this out by multiplying 16 by 3 which equals 48

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

1/8 chance since there are 8 numbers from 5 to 12 and 1 is only one number so 1/8

Answer:

0.05% means 0.05 per every 100.

Step-by-step explanation:

We find it useful to convert 0.05% to decimal, because if you need to find 0.05% of any number, you can simply multiply that number with 0.0005.

hope this helps!!!!!

The value of 0.05% written as a decimal is 0.0005.

To write 0.05% as a decimal, you need to divide the percentage value by 100.

A decimal number is a number that uses the base-10 numbering system. It is a way of representing numbers using the digits 0-9 and a decimal point. Each digit in a decimal number represents a specific place value, which is a power of 10.

The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts or decimal fractions.

0.05% divided by 100 is equal to 0.0005.

Therefore, 0.05% written as a decimal is 0.0005.

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Moving the decimal point left or right works in the metric systems because; The metric system is based on powers of 10.

It follows from the task content that the reason for moving the decimal point left or right in metric system conversions be identified.

It follows from metric system conversions that;

Based on the aforementioned, it can be concluded that the measurements conversion in the metric system is such that the decimal point is moved left or right.

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The volume of the cylinder is 25295.26 cubic meters.

To find the volume of a cylinder, we can use the formula V = π * r^2 * h, where r is the radius and h is the height. Given that the diameter is 34 m, the radius is half of that, which is 17 m. The height is given as 27 m.

Plugging in the values into the formula, we get V = 3.14 * (17^2) * 27. Evaluating this expression, we find that the volume of the cylinder is 25295.26 cubic meters.

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The volume of a cylinder is 25295.26 cubic meters.

To find the volume of a cylinder, use the formula V = πr^2h, where V represents the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, the diameter of the cylinder is given as 34 m, so the radius is half of the diameter, or 17 m.

The height of the cylinder is given as 27 m. Substitute these values into the formula to calculate the volume.

V = 3.14 × (17^2) × 27

= 25295.26 cubic meters.

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Answer:

3100ft

Step-by-step explanation:

There are 2 sides to the prism that have an area of 50ft * 10ft or 500ft. The total of those will be 500ft * 2 or 1000ft. There are 2 more sides to the prism that have an area of 30ft * 10ft or 300ft. The total would be 300ft * 2 or 600ft. Then the last two sides to the prism have an area of 50ft * 30ft or 1500ft. Since we're imagining this prism to be a house, you can't paint the floor (well, I guess you could but I think they want us to leave that part out because you can't pick the house up to paint the bottom that would be ridiculous). So the surface area is each area added, or 1000ft + 600ft + 1500ft = 3100ft.

Answer:

3,100 ft^2

Step-by-step explanation:

choice D is the correct solution

PARALLEL slopes always have the same slope no matter what because they are parallel

The equation of the line that is parallel to y = 5x-4 and passes through the point (3, 4) is y = 5x - 11 because it has the same slope, 5, as the given line depicting parallelism and it passes through the specified point.

In Mathematics, two lines are parallel if their slopes are equal. In this case, the given line is y = 5x - 4, and its slope is 5. To find an equation of a line that is parallel to this line and passes through a specific point, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes.

Replace m with 5 (the slope of the given line), and (x1, y1) with (3, 4) (the point through which the line passes), and we have y - 4 = 5(x - 3). Distributing and simplifying, we get y = 5x - 15 + 4 = 5x -11. Therefore, the equation of the line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

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3x+4y-5z=8

1x+0y+2z=-3

4x-3y+0z=6

|`3 4 (-5)`||`x`| |`8`|

| 1 0 2 | |y |=|-3 |

|.4 (-3) 0 .||.z.| |.6.|

Answer:

The number of goats in the farm is [tex]74[/tex]

The number of sheep in the farm is [tex]63[/tex]

Step-by-step explanation:

Let

x----> the number of goats in the farm

y----> the number of sheep    

we know that

[tex]x+y=137[/tex] ----> equation A

[tex]x=y+11[/tex] -----> equation B

substitute the equation B in equation A and solve for y

[tex](y+11)+y=137[/tex]

[tex]2y=137-11[/tex]

[tex]2y=126[/tex]

[tex]y=126/2=63[/tex]

Find the value of x

[tex]x=63+11=74[/tex]

therefore

The number of goats in the farm is [tex]74[/tex]

The number of sheep in the farm is [tex]63[/tex]

Answer:

option a

[tex]log\frac{x^{5} }{(x-8)^{6} }[/tex]

Step-by-step explanation:

Given in the question an expression

5logx - 6log(x-6)

To solve this question we will apply two of the logarithm property

1) power rule

alogx = log[tex]x^{n}[/tex]

log[tex]x^{5}[/tex] - log[tex](x-8)^{6}[/tex]

2) substraction rule

The log of a quotient is the difference of the logs

loga (x/y) = loga x - loga y

[tex]logx^{5}- log(x-8)^{6}[/tex]

log[tex]\frac{x^{5} }{(x-8)^{6} }[/tex]

Answer:

a edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.3. x + 18.3

The data for tree 1 is an illustration of a linear equation.

The linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

From the complete question, we have the following points

[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]

[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]

First, we calculate the slope (m)

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

So, we have:

[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]

[tex]\mathbf{m = \frac{0.6}{2}}[/tex]

[tex]\mathbf{m = 0.3}[/tex]

The equation is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]

[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]

[tex]\mathbf{y = 0.3x + 18.3}[/tex]

Hence, the linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

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Answer:

sqrt(sqrt(x))

Step-by-step explanation:

A quartic root of is written mathematically as . THe quartic root of 16 is 2 since 2*2*2*2 = 16. However, a quartic root can also be defined as the square root of a square root. For example the √16 = 4 and the √4 = 2. This is the same response as taking the quartic root. This means you can write it as the sqrt(sqrt(x)). In the example, it would be sqrt(sqrt(16)) = sqrt(4) = 2.

The quartic root of a variable x can be calculated using the expression Math.sqrt(Math.sqrt(x)), which calls the square root function twice. This computes the square root of x, then computes the square root of the result, yielding the quartic root.

In order to compute the quartic root of a variable x, we call the Math.sqrt() method twice in a nested manner. The quartic root is essentially the square root of a square root, hence the need for the double call. The appropriate expression in this case would be:

Math.sqrt(Math.sqrt(x))

This expression first computes the square root of x and then computes the square root of the result, which gives us the quartic root of x. As a result, if x is 16.0, the result of this expression would be 2.0, and if x is 81.0, the result would be 3.0.

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Answer:

5 cm by 5 cm

Step-by-step explanation:

The perimeter of this rectangle is 20 cm, and the relevant formula is

P = 20 cm = 2W + 2L.  Then W + L = 10 cm, or W = (10 cm) - L.

The area of the rectangle is A = L·W, and is to be maximized.  Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²

Note that this is the equation of a parabola that opens down.  With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is

x = -b / (2a).  Subbing 10 for b and -1 for a, we get:

x = -[10] / [2·(-1)] = 10/2, or 5.

This tells us that one dimension of the rectangle is 5 cm.

Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:

20 cm = 2(5 cm) + 2W, or

10 cm = W + 5 cm, or W = 5 cm.

Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.

The dimensions that give the maximum area is 5 cm by 5 cm.

Given:

The perimeter of this rectangle is 20 cm, and formula for perimeter is

P= 2(W+L)

P = 20 cm = 2W + 2L.  

Then W + L = 10 cm,

or W = (10 cm) - L.

The area of the rectangle is A = L·W, and is to be maximized.  

On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²

Note that this is the equation of a parabola that opens down.  With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is

x = -b / (2a).  Subbing 10 for b and -1 for a, we get:

x = -[10] / [2·(-1)] = 10/2, or 5.

This tells us that one dimension of the rectangle is 5 cm.

Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:

20 cm = 2(5 cm) + 2W, or

10 cm = W + 5 cm, or W = 5 cm.

Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.

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Answer:

8x³ + 125

Step-by-step explanation:

Cubes:  look for the exponent 3 and for perfect cubes such as 1, 8, 27, ...

8x^3 + 125 is a sum, and 8 is a perfect cube (the cube of 2), and x^3 is a cube, and 125 is a cube.

Thus, the correct answer is 8x^3 + 125 (which is equivalent to

(2x)³ + 5³).

Answer:

Graphic attached

Step-by-step explanation:

The oblique asymptote of the function has the shape of a line of the form

[tex]y = mx + b[/tex]

We need to find the slope m and the intercept b.

The oblique asymptote is found by these two limits:

[tex]m = \lim_{x \to \infty}\frac{f(x)}{x}\\\\b = \lim_{x \to \infty}[f(x) - mx][/tex]

If [tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex] then:

[tex]m = \lim_{x \to \infty} \frac{\frac{(2x+3)(x-6)}{(x+2)(x-1)}}{x}\\\\m = \lim_{x \to \infty} \frac{2x^2-9x-18}{x^3 +x^2 -2x}\\\\m = 0[/tex]

The slope is 0. Therefore the function has no oblique asymptote.

Horizontal asymptote:

[tex]y = 2[/tex]

Vertical asymptote

[tex]x = -2\\x = 1[/tex]

Answer:

246.

Step-by-step explanation:

Let the number be 2xy, then

2 + x + y = 2y    and y must be even because the whole number is even.

y = 2 + x .

Now x must be even because y is even.

The only 2 numbers which fit are x = 4 and y = 6 so the number is 246.

Checking: 2+4+6 = 12 and 12 = 2*6.

Answer: second option.

Step-by-step explanation:

By definition, you know that:

[tex]b^0=1[/tex]

You can see in the graph that the interception with the y-axis is at -1.

Therefore, in that point: x=0 and y=-2

Substitute into the function and solve for a:

[tex]-1=a(b)^0\\-1=a(1)\\a=-1[/tex]

Now, choose any point of the function and substitute this point and the value of a into the function and solve for b. Then you obtain:

Point (2,-4)

[tex]-4=-1(b)^2\\\frac{-4}{-1}=b^2\\b=\sqrt{4}\\b=2[/tex]

Answer:

Its B

Step-by-step explanation:

Because it is

On edge

[tex]\widehat{DPR}=\frac{1}{2}(\stackrel\frown{ET}-\stackrel\frown{DR}) = \frac{1}{2} (118 - 26) = \frac{92}{2} = 46°[/tex]

Answer:

10

Step-by-step explanation:

We'll note the numbers as [tex]x_{n}, x_{n+1} ...[/tex]

[tex]x_1 + x_2 + x_3 + x_4 = 20\\Avg = 5\\\frac{x_1 + x_2 + x_3 + x_4 + x_5 }{5} = 6 = \frac{20 + x_5}{5}\\ 4 + \frac{x_5}{5} = 6\\\\frac{x_5}{5} = 2\\\x_5 = 10[/tex]

Answer:

10.

Step-by-step explanation:

The average of the 5 numbers =

(20 + x) / 5 = 6  where x is the 5th number.

20 + x = 30

x = 10

The fifth number is 10.

We want to find all [tex]f(x)[/tex] such that

[tex](D^2-12D-45)[f(x)]=0[/tex]

We have

[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]

so that either

[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]

or

[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]

These solutions are linearly independent; we confirm this by computing the Wronskian:

[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]

We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:

[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]

[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]

The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.

The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.

To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.

The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.

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23.5 hours is the anser yeteressdfdsfsjufrhhmrgijfjfxkjvnrtjeigrjiegre

Answer:

49.6 square meters

Step-by-step explanation:

first, circumference is 2*pi*r, so we want to find r.  so we take 2*pi*r=24.8 and solve for r which is 4.

Now, area is pi*r^2 so pi*4^2 = pi*16 = 49.6