Express 21 as a product of prime
factors

Answer: 227 is a rational number because it can be expressed as the quotient of two integers: 227 ÷ 1.

Step-by-step explanation:

An advantage of a weighted moving average (WMA) is that recent actual results can be given more importance than what occurred a while ago is a "true" statement because "Weighted moving averages could be adjusted to emphasize more recent data in forecasting."

Moving averages are popular tools for measuring momentum among active traders. The formula used to calculate the average is the primary distinction between a simple moving average, a weighted moving average, and an exponential moving average.

Some key features regarding the weighted moving average are-

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An equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5) is [tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]

Find the line [tex]$y=m x+b$[/tex] passing through [tex]$(-4,-1),(8,-5)$[/tex]

Compute the slope [tex]$(-4,-1),(8,-5): \quad m=-\frac{1}{3}$[/tex]

Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=-\frac{7}{3}$[/tex]

Construct the line equation [tex]$y=m x+b$[/tex] where [tex]$m=-\frac{1}{3}$[/tex] and [tex]$b=-\frac{7}{3}$[/tex]

[tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]

A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil.

Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90° angle.

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Answer:

7√3

Step-by-step explanation:

Answer:

[tex]x = \frac r{s + t}[/tex]

Step-by-step explanation:

Hello!

Solve by isolating the variable.

The solution for x is [tex]x = \frac r{s + t}[/tex].

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If there is only one equation with more than one parameter, then the number of the solution will be infinite.

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

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Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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Step-by-step explanation:

[tex] - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23[/tex]

Answer: x=6.5

Step-by-step explanation:

3(2x - 4) = 8 + 2x + 6

6x-12=14+2x

4x-12=14

4x=26

x=26/4

x=6.5

The y values from:

1. ₋6

2. ₋3

3. 0

4. 3

Given the x values and y value as y = 3x

1. when x = ₋2 then y = 3x

y = 3(₋2)

y = ₋6

2. when x = ₋1 then y = 3x

y = 3(₋1)

y = ₋3

3. when x = 0 then y = 3x

y = 3(0)

y = 0

4. when x = 1 then y = 3x

y = 3(1)

y = 3

therefore we get the points as (₋2 , ₋6) (₋1 , ₋3) (0,0) (1 , 3).The graph is pltted and attached.

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The pyramid's volume will increase by 11.79%.

A Pyramid's volume is calculated as:

[tex]V=\frac{B h}{3}[/tex]

Where:

When the height increases from 458 to 512, the initial and final volumes are as follows:

[tex]\begin{aligned}&V_1=\frac{458}{3} b \\&V_2=\frac{512}{3} b\end{aligned}[/tex]

The percentage difference is then calculated as follows:

[tex]\% \text { Change }=\frac{V_2-V_1}{V_1} \times 100 \%[/tex]

We obtain:

[tex]\% \text { Change }=\frac{512 b / 3-458 b / 3}{4586 / 3} \times 100 \%\\\% \text { Change }=\frac{54 b / 3}{4586 / 3} \times 100 \%\\\% \text { Change }=0.1179 \times 100 \%\\\% \text { Change }=11.79 \%[/tex]

Therefore, the pyramid's volume will increase by 11.79%.

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The correct question is given below;
If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase

The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting.

If we divide two numbers by each other then the upper word is called the numerator, a lower word is called the denominator, and the representation is known as the fraction.

Given that,

Maritza bought 1.5 liters of blue paint.

The given painting is going to be used 1/2 fraction of the total liters of blue paint.

1/2 of the blue paint ⇒

(1/2)1.5

⇒ (1/2)15/10

⇒ (1/2)3/2

⇒ 3/4 liters of blue paint.

Hence "The fraction of 1/2 of the number of liters of blue paint is 3/4 therefore 3/4 liters of blue paint must be used to draw that painting".

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The given question is in another language the translation in English is as follows;

Maritza bought 1.5 liters of blue paint. if I use 1/2 of the contents of that can to paint a mural

How many liters of blue paint do I use on this?

Answer:

The zeros are x =5, -7/2

Step-by-step explanation:

To find the zeros, set the expression equal to zero

(x-5)(2x+7) =0

Using the zero product property

(x-5)=0     (2x+7)=0

Solve each equation

x=5               2x = -7

x=5                  x = -7/2

The zeros are x =5, -7/2

Answer:

5, -7/2

Step-by-step explanation:

[tex]x - 5 = 0 = 5\\\\2x + 7 = 0\\2x + -7 = 0\\\frac{2x}{2} = \frac{-7}{2}\\ x = \frac{-7}{2}\\x = -\frac{7}{2}[/tex]

Thus,

x = 5

x = -7/2

Answer:

y-20=0.75(x-4)

Step-by-step explanation:

First, use slope formula to find the slope.

The points I will use are (4, 20) and (8, 23).

Formula:

y2-y1/x2-x1

23-20/8-4=

=3/4

The slope in decimal form is 0.75.

Now you put the linear equation in point-slope form.

m=0.75

Use the point (4, 20).

y-y1=m(x-x1)

y-20=0.75(x-4)

The linear equation is point-slope form is y-20=0.75(x-4).

Hope this helps!

Please mark as brainliest if correct!

The points Y and Z after transition are (-4,-2) and (-2,4)

In this case, we are required to find x' and y' to find the direction of transition

x' =x coordinate of point 2 - x coordinate of point 1

   = 0-2 = -2

y'= y coordinate of point 2 - y coordinate of point 1

   =4-2 = 2

Now we are required to  subtract these transition from the points given,

Transition of point Y = (-2-2 ,0-2)  =(-4,-2)

Transition of point Z =(0-2,6-2)  = (-2,4)

Hence the points after transition are  Y as(-4,-2) and Z as (-2,4)

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Answer:

The distance between both points is 5 units

Step-by-step explanation:

The distance formula is: d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}

Answer:

0.02

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

x=-3

g(x)=4(-4(-3)-8)

g(x)=4(4)

g(x)=16

the correct option is:

"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."

Miguel wants to do the product below:

-0.6*(5/6)

And he know that to do it, he should convert both numbers to the same form, only that he does not know if he should transform the decimal number into a fraction or the fraction into a decimal.

It is always easier to work with fractions, so the blind answer is to go with the fraction, but let's see why this is the best option.

5/6 written as a decimal will give:

5/6 = 0.833....

It is a repeating decimal number, so taking the exact product would be impossible to do by hand if we used both numbers in decimal form.

While -0.6 written as a fraction is really trivial, just multiply it and divide it by 10, it becomes:

-0.6  = -6/10

Then the product is:

(-6/10)*(5/6) = -5/10 = -1/2

Then the correct option is:

"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."

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Answer:

1/2

Step-by-step explanation:

simply divide 3/10 to get 0.3 and then divide 3/5 to get 0.6 then just divide 0.3 to 0.6 to get 0.5 or 1/2

Answer:

Rs 984

Step-by-step explanation:

Principal (P) = Rs 9,600

Time (T) = 2 years

Rate (R) = 5%

Simple Interest (SI) = [tex]\frac{PTR}{100}[/tex]

SI = [tex]\frac{9600*2*5}{100}[/tex]

SI = [tex]\frac{9600}{10} = Rs 960[/tex]

Compound Interest (CI) = 9600 * [tex]\frac{41}{100} = 24*41 = Rs 984[/tex]

Answer: 1

Step-by-step explanation:

How big is the table? 1 table can fit all 17 people if the table is big enough.

The cinnamon-scented jar candle brunt faster.

Relativity means observing some action with different perspective.

Suppose you are moving in a bus at 100 km/hr and you are reading a book.To an observer which you are passing by you and the book he observes moving at a speed of 100 km/hr.But for you the book is not moving at all because both you and the book is moving at a speed of 100 km per hour.

According to the given question Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours.

From the given data of burning hours we can observe that berry-scented pillar candle that burned for 888888 hours which is more that of Andrei had cinnamon-scented jar candle that brunt for 303030 hours because

30303030 < 888888.

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Answer:

1 : 4 1/2 :: 8 1/5 : x            proportion

x = (4 1/2)(8 1/5)                product of means/extremes

x = (9/2)(41/5)                   change improper fraction

x = 369/10                         multiply

x = 36.9                              change to decimal