how do i prove 2 lines are parallel

Answer:

4 and 5

Step-by-step explanation:

√20 is between 4 and 5 because 20 is between \(\sf 2^4\) and \(\sf 2^5\):

\(\sf 2^4=16\)  and  \(\sf 2^5=32\)

Answer:

It falls in between 4 and 5

Step-by-step explanation:

Hello!

We can find the perfect squares that are before and after 20.

Perfect squares are numbers that are made by multiplying a number by itself. Numbers that are multiplied by itself 3 times are called perfect triples.

To find the square root of a number is to find out what number multiplied by itself gives us the number.

The perfect square before 20 is 16, as it is 4², or 4 x 4

The perfect square after 20 is 25, as it is 5², or 5 x 5

Therefore, the square root of 20 will fall between 4 and 5.

Answer: 36

12 out of 15 people play in the school band. In the class, 36 do not play.

12:15 is equal to a ration of 36:45.

So, it is the answer. 36 out of 45 people in the class play in the band.

Hope this helps!

Answer:

9 I think

Step-by-step explanation:

I wanted to simplify 12 out of 15 and I did by dividing 3 out of both of them which would now equal 4 out of 5. I know that 4 out of 5 is 80%. so, I did 80 % of 45 which equals 36 which means 36 people were in band. So now you minus 36 from 45 which is 9

9 people did not play in band

It is possible to multiply or divide an equation by the same number on each side of the equation without changing the answer, according to the "multiplication property" of the equation.

How can you use the properties of operations to multiply linear expressions?

According to the equation's "multiplication property," it is possible to multiply or divide an equation by the same number on each side of the equation without changing the equation's outcome. The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same sign will be positive. If a and b are positive integers and x is a variable, then (xa * xb) = x(m + n). The identity, commutative, associative, and distributive properties of multiplications are four properties that can facilitate the process. They offer guidelines for solving multiplication problems quickly using properties that always hold true for particular equations.

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Answer:

251 miles

Step-by-step explanation:

To answer this, we first must subtract the total Bill ended up paying by the base fee:

222.77 - 16.95 = 205.82

Now, we divide this total by 82 cents:

205.82 / 0.82 = 251

So, Bill drove the truck 251 miles

Hope this helps :)

Answer:

49.0197m

Step-by-step explanation:

The formula is d = c / π, allow d to be diameter and c to be circumference

Answer:

To solve a system of equations by substitution, we can use one equation to solve for one variable in terms of the other variable, and then substitute that expression into the other equation.

Given the system of equations:

10x + 2y = 4

.-9x + 3y = 18

We can start by isolating y in one of the equations. For example, we can use the first equation:

10x + 2y = 4

To solve for y, we can divide both sides by 2:

y = -5x + 2

Now we can substitute this expression for y into the second equation:

-9x + 3(-5x + 2) = 18

-9x - 15x + 6 = 18

-24x + 6 = 18

-24x = 12

x = -0.5

Now that we know x = -0.5, we can substitute this value back into the original expression we found for y:

y = -5(-0.5) + 2

y = 2.5

So the solution of the system of equations is (x, y) = (-0.5, 2.5).

Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

The interval of convergence of the given power series is I=[0, 2/9] and the radius of convergence of power series is R=1

The disk of convergence is the set of all places whose distance to an is strictly less than the radius of convergence.

Given, the power series is,

\(\sum_{k=1}^{\infty }\) 1/(k²+k)\((9x-1)^{k}\)

Let \(u_{k}\)=1/(k²+k)

The radius of the convergence is,

R=\(\lim_{k \to \infty}\)| \(u_{k}\)/\(u_{k+1}\)|

=\(\lim_{k \to \infty}\) ((k+1)²+(k+1))/(k²+k)

=\(\lim_{k \to \infty}\) (k²+3k+2)/(k²+k)

=\(\lim_{k \to \infty}\) ((1+(3/k)+(2/k²))/(1+(1/k))=1

The interval of convergence is:

|9x-1|<1

Or, -1<9x-1<1

Or, 0<9x<2

Or, 0<x<2/9

Given the power series is converges in the interval (0, 2/9)

If x=0, then the power series becomes as shown,

\(\sum_{k=1}^{\infty }\)(1/(k²+k)(\(-1^{k}\))

Let \(a_{k}\)=(\(-1^{k}\))(1/(k²+k)

\(\lim_{k \to \infty}\)  \(a_{k}\)=0 and { \(a_{k}\)} sequence is monotone decreasing

Hence by Leibnitz's test,

\(\sum_{k=1}^{\infty }\)(1/(k²+k)(\(-1^{k}\)) is convergent

If x=2/9 then the power series becomes \(\sum_{k=1}^{\infty }\)(1/(k²+k)

Let  \(a_{k}\)=(1/(k²+k)and let \(b_{k}\)=1/k²

Then \(\sum_{k=1}^{\infty }\)  \(a_{k}\)/ \(b_{k}\)

\(\sum_{k=1}^{\infty }\) k²/(k²+k)=1 (≠0)

By comparison test, we know that ∑ \(a_{k}\) and ∑ \(b_{k}\) converge or diverge together.

As  ∑ \(b_{k}\)= ∑1/k² converges this implies that  ∑ \(a_{k}\)=(1/(k²+k) converges

Hence the interval of convergence of the given power series is,

I=[0, 2/9]

Therefore, the interval is I=[0, 2/9] and the radius of convergence in the power series is R=1.

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The volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

We are given that the radius of the cylinder is 1.2 cm and the height is 4 cm.

So,

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π * \((1.2)^{2}\) * 4

⇒ Volume = 3.14 * 5.76

⇒ Volume = 18.0864 cubic cm

Similarly,

⇒ Total surface area = 2πrh + 2π\(r^{2}\)

⇒ Total surface area = 2π * 1.2 * 4 + 2π\((1.2)^{2}\)

⇒ Total surface area = 2π * 4.8 + 2π * 1.44

⇒ Total surface area = 2π * (4.8 + 1.44)

⇒ Total surface area = 2 * 3.14 * 6.24

⇒ Total surface area = 39.1872 square cm

Hence, the  volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

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The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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the function value f(14) = 4.8.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function if one were mapped to a single value instead. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(1)= 10

f(21)= 2

Let the function f(x) = ax+b

f(1)= 10 = a+b

f(21)= 2 = 21a +b

20a = -8

a=-8/20

b = 208/20

f(14) = 14*(-8/20)+208/20 = 4.8

Hence the function value f(14) = 4.8.

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For a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.

This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.

The normal distribution is characterized by its bell-shaped curve, which is symmetric around the mean. The mean is also the midpoint of the curve, and the curve approaches but never touches the horizontal axis. The standard deviation of the distribution controls the spread of the curve.

In a normal distribution, the probability of a value being between a positive z-value and its population mean is indeed the same as that of a value being between a negative z-value and its population mean.

This is due to the symmetric nature of the normal distribution curve, where probabilities are mirrored around the mean.

This means that if we have a normal distribution with a mean of μ and a standard deviation of σ, the probability of a value falling between μ+zσ and μ is the same as the probability of a value falling between μ-zσ and μ.

This property of the normal distribution makes it easy to compute probabilities for any range of values, by transforming them into standard units using the z-score formula.

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0.76282051282 in decimal form.

38141025641

___________

50000000000

Above it it in fraction from

Answer:

\(96\ \text{inches}\)

Step-by-step explanation:

Fabric used for one curtain = 24 inches = \(\dfrac{24}{12}=2\ \text{feet}\)

Number of curtains Jane's company wants to make is 48.

So, total feet of fabric used by Jane's company will be the product of the fabric used for one curtain and the number of curtains.

Total fabric needed = \(48\times 2=96\ \text{inches}\)

Hence, Jane will need \(96\ \text{inches}\) of fabric.

Answer:

1:2

2:4

4:8

8:16

16:32

Answer:

y = -x

Step-by-step explanation:

(0, 0) and ( -100, 100)

m= (y2-y1)/(x2-x1)

m=(100-0)/( -100 -0)

m = 100/ -100

m = -1

y - y1 = m(x - x1)

y - 0 = -1(x - 0)

y - 0 = -x + 0

y = -x

The coordinates of the vertices of the resulting image A'B'C'D'E' is A'(-2,2), B'(-4, 2), C'(-6,4), D'(-4,6) and E' (-2,6) when ABCDE

is rotated 90° counterclockwise about the origin.

When point M (h, k) is rotated through 90 degrees in a clockwise direction around the origin O, the rotation of the point occurs. M' will represent the updated location of point M (h, k) will become M'(k, -h).

In 90° counterclockwise rotation,

(x, y) becomes (-y, x)

A(2, 2) becomes A (-2, 2)

B (2, 4) becomes B' (-4,2)

C(4,6) becomes C (-6, 4)

D (6,4) becomes D' (-4,6)

E (6, 2) becomes E' (-2, 6)

Answers:

A'(-2,2)

B'(-4, 2)

C'(-6,4)

D'(-4,6)

E' (-2,6)

Hence there are the answers for the given question.

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The money which is expected to spend on new word processors during this year is

The probability distribution is

x:          0            1             2            3

f(x)         \(\frac{1}{10}\)           \(\frac{3}{10}\)           \(\frac{2}{5}\)              \(\frac{1}{5}\)

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is \(1200x-50x^2\)          

Then the equation of expenses will be

\(\text{Expenses}=E(1200x-50x^2)\)

We can rewrite it as

\(\text{Expenses}=E(1200x)-E(50x^2)\)  

  \(\text{Expenses}=1200E(x)-50E(x^2)\)   -----------------(1)

Now the mean of the probability distribution is ,

\(E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7\)      

The variance of the function is

\(E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)\)

        \(=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})\)

        \(=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}\)

        \(=\frac{37}{10}\)

        \(=3.7\)

On substituting the values in equation (1)

\(\text{Expenses}=1200E(x)-50E(x^2)\)

              \(=1200(1.7)-50(3.7)^2\)

              \(=2040-684\)

              \(=1855\)

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9514 1404 393

Answer:

  x = 12

Step-by-step explanation:

The two marked angles are a linear pair, so are supplementary.

  (8x -20)° +(8x +8)° = 180°

  16x -12 = 180 . . . . . . . . . . . divide by °, collect terms

  16x = 192 . . . . . . . . . . . add 12

  x = 12 . . . . . . . . . . . divide by 16

Points A, B, and C are collinear and the lengths of AB, BC, and AC are:

AB = 14, BC = 19, AC = 33.

Since points A, B, and C are collinear, we can use the segment addition postulate to relate their lengths. According to the postulate, the sum of the lengths of smaller segments equals the length of the whole segment.

Given: AB = x + 4, BC = 2x - 1, and AC = 4x - 7.

We know that AB + BC = AC.

Substituting the given values, we have:

(x + 4) + (2x - 1) = 4x - 7.

Now, let's solve this equation to find the value of x:

x + 4 + 2x - 1 = 4x - 7.

Combining like terms:

3x + 3 = 4x - 7.

Moving all terms containing x to one side and constants to the other side:

3x - 4x = -7 - 3.

-x = -10.

Dividing both sides by -1 (which is the same as multiplying by -1):

x = 10.

Now that we know the value of x, we can substitute it back into the given expressions to find the lengths of AB, BC, and AC.

AB = x + 4 = 10 + 4 = 14.

BC = 2x - 1 = 2(10) - 1 = 19.

AC = 4x - 7 = 4(10) - 7 = 33.

Therefore, the lengths of AB, BC, and AC are:

AB = 14,

BC = 19,

AC = 33.

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Answer:

no solution

Step-by-step explanation:

Given

2(x - 3) = 2x + 5 ← distribute parenthesis on left side

2x - 6 = 2x + 5 ( add 6 to both sides )

2x = 2x + 11 ( subtract 2x from both sides )

0 = 11 ← not possible

This indicates the equation has no solution

The number that must be added to both sides of the equation y = x² + 6x to complete the square is 9. Adding 9 allows us to rewrite the equation in the form of (x + 3)², which is a perfect square trinomial. Option D.

To complete the square in the equation y = x² + 6x, we need to add a specific number to both sides of the equation. The goal is to manipulate the equation into a perfect square trinomial form.

To determine the number that needs to be added, we take half of the coefficient of the x term and square it. In this case, the coefficient of the x term is 6. Half of 6 is 3, and squaring 3 gives us 9.

So, to complete the square, we add 9 to both sides of the equation:

y + 9 = x² + 6x + 9

Now, let's rewrite the right side of the equation as a perfect square trinomial:

y + 9 = (x + 3)²

By adding 9 to both sides, we have successfully completed the square. The right side is now in the form of a perfect square trinomial, (x + 3)². option D is correct.

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Step-by-step explanation:

multiple 2× 4

then your answer. would be 8

Answer:

(5²)⁴ =5²×5⁴  =5⁸

Step-by-step explanation:

No, multiplying by 10x10x10 is not the same as multiplying by 10 factors of 3.

Multiplying by 10x10x10 is not equivalent to multiplying by 10 factors of 3. When you multiply a number by 10, you're essentially adding a zero to the end of it, shifting all the digits one place to the left. So, multiplying by 10 three times (10x10x10) adds three zeros to the original number. However, when you multiply by 10 factors of 3, you are essentially multiplying the number by 3 ten times consecutively. This results in a different outcome.

For instance, if you start with the number 5 and multiply by 10x10x10, you would get 5,000. On the other hand, multiplying by 10 factors of 3 would yield a much larger number, 59,049, because each multiplication by 3 amplifies the result. Therefore, the two operations are not equivalent.

Therefore, multiplying by 10x10x10 and multiplying by 10 factors of 3 yield different outcomes. The former adds three zeros to the original number, while the latter multiplies the number by 3 repeatedly, resulting in a much larger value. It's crucial to understand the distinction between these operations to avoid confusion and accurately calculate mathematical expressions.

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Answer:

y=7x−5

Explanation:

We have; y=x4+2x2−x

First we differentiate wrt x;y=x4+2x2−x

∴dydx=4x3+4x-1

We now find the vale of the derivative at (1,2) (and it always worth a quick check to see that y=2 when x=1) we have dydx=4+4−1=7

So at the tangent passes through the coordinate (1,2) and has gradient m=7

We now use y−y1=m(x−x1) to get the equation of the tangent:

∴y−2=7(x−1)

∴y−2=7x−7

∴y=7x−5

There are no free variables, the vectors are linearly independent.

To either show that the following sets of vectors are linearly independent or find a linear relation between them, we can follow these steps:

. Form a matrix using the given vectors as columns.
. Calculate the determinant of the matrix (if it's a square matrix) or row reduce to echelon form.
. If the determinant is non-zero or the matrix has no free variables, the vectors are linearly independent. If the determinant is zero or the matrix has free variables, the vectors are linearly dependent, and we can find a linear relation.

(a) Create the matrix A using the given vectors:
A = | 1 0 1 |
     | 1 1 0 |
     | 0 1 1 |
The determinant of A is:
det(A) = 1(1(1) - 1(0)) - 0(1(1) - 1(0)) + 1(1(0) - 1(1)) = 1 - 1 = 0
Since the determinant is zero, the vectors are linearly dependent.

(b) Create the matrix B using the given vectors:
B = | 2  0 -1 |
     | 1  1  2 |
     | 0  0  0 |
Row reduce B to echelon form:
B = | 1  1  2 |
     | 0  1 -4 |
     | 0  0  0 |

Since there are no free variables, the vectors are linearly independent.

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Answer:

The answer are

\(m < 1 = 27 \\ m < 2 = 27 \\ m < 3 = 90 \\ m < 4 = 27 \\ m < 5 = 63 \\ m < 6 = 63\)

Answer:

Step-by-step explanation:

A. $268,10 B. $14155 c. $255.54 b. $11400. fociaral and state governmenta? ... record payroll tax expense and pay to the federal and state governments :.

1 answer

·

Top answer:

Amount of state and federal unemployment tax that the employer must record payroll tax expense and pay to the federal and state governments : According ...

Missing:255.54