What is the GCF of the following terms 20n3 and 15n2 ?

Answer:

Step-by-step explanation:

\( \underline{ \boxed {\sf \color{cyan}{x = \frac{129}{2}}}}\)

\(\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

\(\: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{2x- 17 =51 +61}\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{2x- 17= 112}\)

\(\: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{2x- 17 + 17 = 112 + 17}\)

\(\: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{2x = 129}\)

\(\: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{\frac{ \cancel2x}{ \cancel2}=\frac{129}{2}}\)

\(\: \: \: \: \: \: \: \: \: \: \: \: \)

\(\Longrightarrow\sf{x = \frac{129}{2}}\)

\(\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

\({\pink{\boxed{\blue{2x - 17 = 51 + 61}}}}\)

2x - 17 = 51 + 61

\({\blue{\boxed{{Take -17 \: \: to \: \: the \: \: other \: \: side \: \: and }}}}\)

\({\blue{\boxed{{its \: \: sign \: \: will \: \: change \: \: \: into \: \: + }}}}\)

2x = 112 + 17

2x = 129

\({\blue{x = {\pink{ \frac{129}{2} }}}}\)

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

-37

Step-by-step explanation:

The answer is -37

Hope this is the answer u needed have a great rest of ur day

Answer:

the answer is -37

Step-by-step explanation:

hope this helps have a good rest of your night :)❤

- We have 52 cards in a deck of cards.

- We have 4 cards of the same number (4 jack, 4 aces...).

Probability of drawing a jack = 4/52

Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592

We have a series: 2 1/2, 3 3/4, ...

We can consider this is a arithmetic series, so it has a common difference. This difference can be calculated as:

We then can consider that each term adds 1 1/4 to the previous term.

We can calculate the third and fourth term of the series as:

Answer: the third term is 5 and the fourth term is 6 1/4.

The given function  x^2 - 12x+36 can be written in vertex form as

y=(x-6)^2 .

What is Quadratic Equation?

Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where a,,b,c are constants.

Given,

to find the vertex form for each function,

Given function x^2 - 12x+36

(x^2 - 12x ) can be written as the (x-6)^2-36

so , let

y = x^2-12x+36 .

y =  (x-6)^2-36 + 36

y = (x-6) ^2+0

y-0 = (x-6)^2 .

So, in this way the completing the square method works.

Hence, The given function  x^2 - 12x+36 can be written in vertex form as

y=(x-6)^2 .

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The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

Greater than because the answer would be 7,180

Step-by-step explanation:

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Answer:

26. $46.75

27. $4.80

28. $32.00

29. $3.60

Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.

Step-by-step explanation:

Answer:

Step-by-step explanation:

divide by R

Answer:

224 cubic centimeters

Step-by-step explanation:

Use the formula to find the volume of the pyramid, which is (length * width * height)/3.

7 * 8 * 12 = 672

Divide 672 by 3.

672 ÷ 3 = 224

When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.

What is a graph?

We use the term graph to describe the presentation of data by the use of cartesian coordinates. The coordinates are usually the x and the y coordinates and the data that is plotted is the dependent and the independent variable.

Now when we have a variable whose value lies so much apart from the rest of the values, we call this an outlier. When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

The correct option is Option D: Yes, the graph passes the vertical line test.

The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.

The vertical line test states that

If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.

So here in this function shown in the graph.

If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.

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Answer:

r = 6 cm

Step-by-step explanation:

C = 2πr

12π = 2πr

12π/2π = 2πr/2π

(The mistake is in the next step when calculating the division.

12π/2π = 6, same way 2πr/2π = r and NOT πr)

6 = r

r = 6 cm

Answer:

In which step did the student make an error?

Step

✔ 4

.

Solving for r, the length of the radius should be

✔ 6

cm.

Step-by-step explanation:

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer:

2/6 or 1/3

Step-by-step explanation:

To find probability, we have to look at the favorable outcome (the outcome we're looking for - in this case, rolling greater than a 4) divided by the total outcomes (the total possible outcomes - in this case, 6).

There are 6 sides on a dice, as laid out in the question. How many numbers on a dice are greater than 4? Well, 5 and 6, of course. These are only two sides of the dice, so our probability would be 2/6, or simplified, 1/3, and that's our answer.

If you'd like a more in-depth explanation, please let me know and I'd be happy to help. :)

Answer:

B

Step-by-step explanation:

The inequality says "t is greater than -196".

We can assume 't' means temperature.

With water, the gas state is warmer than the other states. (Steam is hotter than liquid water or water frozen solid.)

I took basic chemistry and I can tell you it is the same for other substances. - The gas state is the warmest.

So we can assume that Nitrogen is a gas at the warmer temperature.

Thus, we are looking for the statement that says Nitrogen is a gas when its temperature is greater than -196° Celsius.

B is the only one that matches.

Answer:

1) When r = 2, M = 20.

2) When M  = 540, r = 6.

Step-by-step explanation:

M is a directly proportional to r cubed

This means that the equation for M has the following format:

\(M = ar^3\)

In which a is a multiplier.

When r=4 M=160.

We use this to find a. So

\(M = ar^3\)

\(160 = a(4^3)\)

\(64a = 160\)

\(a = \frac{160}{64}\)

\(a = 2.5\)

So

\(M = 2.5r^3\)

1) work out the value of M when r=2

\(M = 2.5*2^3 = 2.5*8 = 20\)

When r = 2, M = 20.

2) work out the value of r when M=540

\(M = 2.5r^3\)

\(540 = 2.5r^3\)

\(r^3 = \frac{540}{2.5}\)

\(r^3 = 216\)

\(r = \sqrt[3]{216}\)

\(r = 6\)

When M  = 540, r = 6.

The length of the wing is, 12 inches.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The scale is,

⇒ 1 inch = 2 feet

And, Wing of airplane is 24 feet.

Now, We have;

The scale is,

⇒ 1 inch = 2 feet

Hence, The length of wing is,

⇒ 24 / 2 inches

⇒ 12 inches

Thus, The length of the wing is, 12 inches.

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Answer:

12,200

Step-by-step explanation:

hope this helps!!!

Answer:

12,200%

Step-by-step explanation:

Let p= the percent and translate.

To solve for p, we can now divide each side by 121 and simplify.

14,762 =121p

p=122.0

Since the problem asks us to find percent, we should convert p to a percent. To convert p to a percent, multiply by 100.

p=122.0

=12,200%

It follows that 14,762 is 12,200% of 121.

Answer:

We will turn the 1/5 into 1/10, then 1/10 into 2/10 because of the 10%. Then, we will have 8/10 left.

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

\( \sqrt{4 \times 5 + \sqrt{4 \times 9} } \)

Given:

Number of choices offered, n = 15

Number of toppings (sample), r = 4

Let's find the number of possible 4-topping pizzas possible.

To solve this exercise, we are to use combination.

Combination involves the arrangement of objects without any repitition of orders of arrangement.

Apply the formula:

Thus, we have:

Solving further:

Therefore, there are 1365 possible 4-topping pizzas.

ANSWER:

1365