Find the Greatest Common Factor and Least Common Multiple for 20 and 8. GCF is LCM​

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer:

y=3x-3

Step-by-step explanation:

Answer:

y = (1/2)x - (15/2)

Step-by-step explanation:

goal: to rearrange the expression such that it is in the form

y = f(x); where f(x) is an expression in terms of x

given:

x - 2y = 15      (subtract x from both sides)

-2y = 15 - x    (multiply both sides by -1 to make left side positive)

2y = -15 + x   (divide both sides by 2 and rearrange)

y = (1/2)x - (15/2)

Explanation

We are required to determine the pros and cons of using the factorial function on the calculator.

Hence, the answers are:

- Pros

• It makes calculation easier.

• It makes calculations to be done in an efficient manner.

• It helps students to solve complicated questions seamlessly.

- Cons

• It cannot help with large numbers as the calculator has limited space for answer preview.

• It does not help to understand better how the calculation is done.

Answer:

C. 7°F

Step-by-step explanation:

Answer: 10 (D)

Step-by-step explanation: 90,000 x 10 = 900,000

Answer:

10

Step-by-step explanation:

Answer:

x = -6 and x = 12 are parallel

Step-by-step explanation:

they are both vertical lines, one crosses the x-axis at -6, the other at 12

Answers:

The options that describe the climate effect on a constant rate of weathering are cold climates favor mechanical weathering, lower precipitation levels lead to more chemical reactions, and the chemical reaction rates of minerals are not impacted by temperature.

Carry on Learning!

Step-by-step explanation:

cold climates favor mechanical weathering

Answer:

The 4 interior angles in the square are each 90 degrees. The four angles formed by the intersection of the 2 diagonal lines are each 90 degrees. The rest of the angles <PQT, <RQT, etc. Are all 45 degrees.

Answer:

The following angles are 45 degrees: SPT, QPT, PQT, RQT, QRT, SRT, RST, PST.

The following angles are 90 degrees: STP, PTQ, QTR, RTS

Step-by-step explanation:

Notice that it is a square. Since it is a square, any diagonal line drawn from a corner to the opposite corner will bisect the angle at both corners. Since in a square each angle at each corner is 90 degrees, we know that the angles listed above are 45 degrees.

There are multiple ways to arrive at the conclusion that angles STP, PTQ, QTR, RTS are all 90 degrees. The easiest way to arrive at that answer is looking at each triangle. Notice how the square is divided into 4 triangles. Each triangle contains two 45 degree angles. Since the internal angles of each triangle must sum to 180 degrees, this means the last angle is 90 degrees.

Answer:

182=9=3×3 Hence we have two 3's as prime factors. The prime factorization for 72 is 2×2×2×3×3 .

Step-by-step explanation:

Answer:

in day 15

Step-by-step explanation:

3, 6, 9, 12, (15)

5, 10, (15)

After solving by the LCM method, both teams have games on the same day, which will be the 15th day.

The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers. It can also be computed for several different numbers.

As per the given information in the question,

Number of days after which both the teams will have the game on the same day again

Take the LCM of both numbers,

= LCM (3, 5)

= 15 days.

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The line passes through the point (-10,1) and has a slope of 3/20 has the equation as: y - 1 = 3/2 (x + 10)

The general form of a linear equation is y - y₁ = m (x - x₁).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept)

The point slope formula is given by y - y₁ = m (x - x₁), where:

y = output value

y₁= the given y coordinate point

m = slope

x = input value

x₁ = the given x coordinate

substituting the point (-10,1) and slope 3/2

y - y₁ = m (x - x₁)

y - 1 = 3/2 (x + 10)

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Answer Bike trail

Step-by-step explanation:

Answer:

Bike trail

Step-by-step explanation:

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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The diameter of a circle is the twic of the radius.

The given diameter = 16mm

So, Radius = 16mm/2

Radius = 8mm

Circumference of the circle is express as :

Substitute the values and simplify

The circumference = 50.24mm

Answer: 50.24mm

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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The population reached in the year 2079 is 1,65,400 and the total population in the year 2081 would be 1,80,623.

To find the population reached in the year 2079, we need to consider the initial population and the growth rate, as well as the number of people who migrated.

The initial population in 2078 was 1,20,000. The population growth rate is 4.5%, which means the population will increase by 4.5% each year.

To calculate the population in 2079, we first need to calculate the increase in population due to the growth rate:

Population increase due to growth rate = 1,20,000 * (4.5/100) = 5,400

Then we add the number of people who migrated:

Total population in 2079 = Initial population + Population increase due to growth rate + Number of migrants

= 1,20,000 + 5,400 + 20,000

= 1,45,400 + 20,000

= 1,65,400

To calculate the total population in the year 2081, we need to consider the growth rate and the population in 2080.

The population in 2080 would be the population in 2079 plus the population increase due to the growth rate:

Population increase due to growth rate in 2080 = 1,65,400 * (4.5/100) = 7,444

Total population in 2080 = 1,65,400 + 7,444

= 1,72,844

To calculate the total population in 2081, we need to consider the growth rate and the population in 2080:

Population increase due to growth rate in 2081 = 1,72,844 * (4.5/100) = 7,779

Total population in 2081 = Population in 2080 + Population increase due to growth rate in 2081

= 1,72,844 + 7,779

= 1,80,623

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The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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9514 1404 393

Answer:

  g(x) = f(x -2) -1

Step-by-step explanation:

The transformation g(x) = f(x -h) +k causes the graph of function f(x) to be translated h units to the right and k units up. Here, g is translated 2 units right and 1 unit down, so (h, k) = (2, -1). The translated function is ...

  g(x) = f(x -2) -1

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

7.84

Step-by-step explanation:

your answer is wrong

mods can you delete it, this was a mistake. thanks.

Answer:

40 shirts.

Step-by-step explanation:

The budget is $170.
There's a one time fee of $10.
A T-shirt costs $4.
Put that in an equation with x, where x is the amount of t-shirts that can be made, to solve for it.
170 - (4x + 10) = 0
170 = 4x + 10
-10
160 = 4x
/4
40 = x
So, 40 shirts can be made at most.

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

D (point Y, ray YZ, angle XYZ)

Step-by-step explanation:

--> a point is just one letter, it cannot be more than one because more than one indicates a connection between 2+ points.

--> a ray is only 2 points/letters, unless the letters are all on one line. the ray is 2 points because it indicates a connection between point Y and point Z.

--> an angle should be 3 letters, and the letter in the middle (in XYZ it's Y) is the point where the angle "occurs" or closed at

Hope this helps!

Answer:

0.46

Step-by-step explanation:

Answer:

0.4667

Step-by-step explanation:

First off, we'll interpret the fraction bar to mean "divided by." This means that 7/15 is the same as 7 divided by 15.

Second, you have requested to see 3 decimal places in your answer, so we'll write the 7 as 7.000 instead (a 7 with 3 zeros after the decimal point).

Now, we'll just do what the fraction bar says: divide 7.000 by 15:

And that's about it! 7/15 written as a decimal to 3 decimal places is 0.467

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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