which expression is equivalent to 6a + 12

6(a+6)
3(3a+9)
6(a+9)
2(3a+6)

Answer:

The sum of the infinite geometric sequence is given by:

[tex]S_{\infty} = \frac{a_1}{1-r}[/tex]          ....[1]

where,

[tex]a_1[/tex] is the first term

r is the common ratio.

As per the statement:

Given that [tex]a_1 = 0.3[/tex] and r = 0.55

To find the sum of this infinite geometric series.

Substitute the given values in [1] we have;

[tex]S_{\infty} = \frac{0.3}{1-0.55}[/tex]

⇒[tex]S_{\infty} = \frac{0.3}{0.45}[/tex]

Simplify:

[tex]S_{\infty} \approx 0.67[/tex]

Therefore,  the sum of this infinite geometric series approximate is, 0.67

The x value is ( z - 2 ) / 3z.

Given,

3x+y/z=2

We need to solve for x.

We have,

3x+y/z=2

Subtracting y/z on both sides.

we get,

3x + y/z - y/z = 2 - y/z

3x = 2 - y/x

Dividing 3 into both sides.

we get,

x = ( 2 - y/z ) / 3

We can simplify further.

x = [( z - 2 ) / z ] / 3

x = ( z - 2 ) / 3z

Thus the x value is ( z - 2 ) / 3z.

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Answer:

A) Median, 1.5

Step-by-step explanation:

Since we have given that the collected data as follows:

|  2  |  14  |  1  |  2  |  0  |  1  |  0  |  2  |

As we know that there are three measures of central tendency.

1) Mean is given by

2) Media of 0, 0, 1, 1, 2, 2, 2, 14 is given by

3) Mode of 0,0,1,1,2,2,2,14 = 2as 2 is occurring most of the times, but we know that median is the best measure to find the center. Hence, Median is the best measure and its value is 1.5.

To solve this problem, we are given the formulas for our new x and y. To use this formula, we must first establish our points 1 and 2. Since the problem specifically directed the point E which partitions the line segment “from J to K”, therefore

point 1 = point J                = (x1, y1)

point 2 = point K = (x2, y2)

The variables m and n indicates the portion of partition segment JE and EK that takes up from the original segment. Since the ratio is 1:4, then:

JE = m = 1

EK = n = 4

Therefore calculating for x and y using the given formulas:

x = [1 / (1 + 4)] (25 – (-15)) + (-15)

x = -7

y = [1 / (1 + 4)] (15 – (-5)) + (-5)

y = -1

Therefore the coordinates of point E is (-7, -1)

The x- and y- coordinates of point E (-7,-1)

In the coordinates of the two-dimensional plane (xy) there is a position vector.

Two dimensions because the coordinates are only x and y, three dimensions if the coordinates are x, y, and z.

If there is a point P then

You can write P as:

P = xi + yi

where i denotes the unit vector in the x and y directions

While the size of the vector:

[tex]\displaystyle P = \sqrt{x^2+y^2}[/tex]

and its direction

[tex]\displaystyle \theta=arc\:tan\:\frac{y}{x}[/tex]

If a point C divides the line segment AB by the ratio m: n, then the coordinates of point C can be formulated:

[tex]\displaystyle \vec{C}=\frac{m\vec{b}+n\vec{a}}{m+n}[/tex]

Coordinate x :

[tex]\displaystyle x=\frac{m.x_2+n.x_1}{m+n}[/tex]

Coordinate y :

[tex]\displaystyle y=\frac{m.y_2+n.y_1}{m+n}[/tex]

line segment from J to K into a ratio of 1:4, then m = 1 and n = 4

(x1,y1) from point  J= (-15,-5)

(x2,y2) from point  K= (25,15)

So coordinates of point E :

Coordinate x :

[tex]\displaystyle x=\frac{1.25+4.-15}{5}[/tex]

x = -7

Coordinate y :

[tex]\displaystyle y=\frac{1.15+4.-5}{5}[/tex]

y = -1

Which vector should be negative

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the statements that describe a vector

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the resultant vector

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Keywords: line segment, vector, two-dimensional coordinates , x,y, partitions

The answer is 1249.69

To write the expression using all six trigonometric function, we need to understand about trigonometric function relation.

The trigonometric expression are as follows,

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times \sin(x) + \sec(x)\times \cos(x) + \tan(x)\times \cot (x) - 1[/tex]

Given:

The trigonometric function are as follows,

[tex]\sin, \cos, \tan, \csc, \sec \:\rm and \:\cot.[/tex]

Write the relationship between [tex]\sin[/tex] and [tex]\cos[/tex].

[tex]\sin^2 (x) + \cos^2 (x) = 1[/tex]

Write the relationship between [tex]\tan[/tex] and [tex]\cot[/tex].

[tex]\tan(x)\times \cot(x) = 1[/tex]

Write the relationship between [tex]\csc[/tex] and [tex]\sin[/tex].

[tex]\csc(x)\times \sin(x) = 1[/tex]

Write the relationship between [tex]\sec[/tex] and [tex]\cos[/tex].

[tex]\sec(x)*\cos(x) = 1[/tex]

Now combine all the above relationship

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times sin(x) + \sec(x)\times \cos(x) +\tan(x)\times \cot(x) - 1 = 3[/tex]

Now solve further,

[tex]1+1+1+1-1=3\\3=3[/tex]

Thus, the trigonometric expression are as follows,

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times \sin(x) + \sec(x)\times \cos(x) + \tan(x)\times \cot (x) - 1[/tex]

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Answer:

x = 1

Step-by-step explanation:

Answer:

You should place 4 red beads and 10 yellow beads into the container

Step-by-step explanation:

There are 57 sides does the polygon have.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The sum of the interior angles of a polygon is,

⇒ 9900 degrees

Since, We know that;

The formula is,

⇒  (n - 2) × 180

Hence, We get;

⇒ 9900 = (n - 2) × 180

⇒ n - 2 = 9900 / 180

⇒ n - 2 = 55

⇒ n = 55 + 2

⇒ n = 57

Thus, There are 57 sides does the polygon have.

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Final answer:

Aaron's plane flew 225 centimeters further than Noah's plane after converting their flight distances from meters to centimeters and finding the difference.

Explanation:

Aaron's plane flew 4.5 meters, and Noah's plane flew half the distance. To find out how much further Aaron's plane flew than Noah's, we need to calculate Noah's distance first:

Half of 4.5 meters is 2.25 meters.

Now, let's find the difference in their flight distances in centimeters. Since 1 meter is equal to 100 centimeters, we'll convert both distances to centimeters:

Aaron's plane: 4.5 meters x 100 cm/meter = 450 centimeters

Noah's plane: 2.25 meters x 100 cm/meter = 225 centimeters

Next, we calculate the difference:

450 centimeters - 225 centimeters = 225 centimeters

So, Aaron's plane flew 225 centimeters further than Noah's plane.

Final answer:

Aaron's plane flew 4.5 meters, which is equal to 450 centimeters. Noah's plane flew half the distance, which is 225 centimeters. Therefore, Aaron's plane flew 225 centimeters further than Noah's plane.

Explanation:

Aaron's plane flew 4.5 meters. Noah's plane flew half the distance, which is 4.5 / 2 = 2.25 meters. To find out how many centimeters further Aaron's plane flew, we need to convert the distances to centimeters. Since 1 meter is equal to 100 centimeters, Aaron's plane flew 4.5 x 100 = 450 centimeters. Noah's plane flew 2.25 x 100 = 225 centimeters.

To calculate the difference, we subtract the distance Noah's plane flew from the distance Aaron's plane flew: 450 - 225 = 225 centimeters.

Therefore, Aaron's plane flew  225 centimeters further than Noah's plane.

To find the number of fluid ounces of butter, use the given conversion factor and the mass of the butter in grams.

To determine the number of fluid ounces of butter she will use, we need to know the mass of the butter in grams. Since the relationship 1 oz = 28.349 g, we can convert the mass in grams to ounces using the conversion factor. Let's say the mass of the butter is 125 grams. We can use the equation X oz = 125 g * unit conversion factor to find the number of fluid ounces of butter.

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James buy 7 yard of ribbon

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

James= 10 pieces of ribbon

Each of length= 2.1 feet

So, length of 10 ribbons

=2.1*10

=21 feet

Now, 1 yard=  3 feet

So, 21 feet= 21/3= 7 yard

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volume = l x w x h

36 = 2 x 6 x ?

36=12 x ?

? =36/12 =3

 the closet is 3 feet wide

The width of the closet is 3 feet, which is obtained by rearranging the formula for the volume of a rectangular prism and substituting the given dimensions.

To find the width of the closet, we use the formula for the volume of a rectangular prism, which is volume = length  times width times height. The problem gives us the volume (36 cubic feet), the length (2 feet), and the height (6 feet). The width can be found by rearranging the formula to width = volume / (length times height).

Next, we substitute the given values into the rearranged formula:

width = 36 cubic feet / (2 feet times 6 feet) = 36 cubic feet / 12 square feet = 3 feet

Therefore, the width of the closet is 3 feet.

slope = m

 slope equation = y=mx+b so the first number is the slope

-1/2