Each group of tables in the cafeteria is set up in 3 rows with 3 in each row. Mr. Grant needs 27 tables for the open house. How many groups of tables does he need to set up?

Answer:

x²+6x +8 ≥ 195

Step-by-step explanation:

The age of C is represented by  c=  x .

Building B was built two years before building C.

Age of Building B   b = x+ 2

Building D was built two years before building B

Age of Building d= x+4

The product of the building B’s age and building D’s age is at least 195.

b*d ≥ 195

≥ means product is greater than or equal to 195 at least 195

Putting the values of b and d

(x+ 2) (x+4) ≥ 195

It can be further solved

x²+6x +8 ≥ 195

Answer:

x^2+6x+8>195

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given relations can be used to write three equations for the angle values.

  t + y + z = 180 . . . . . sum of all angle measures

  y + z = 5t . . . . . . . . second and third total 5 times the first

  y + 30 = z . . . . . . third angle is 30 more than the second.

__

Using the third equation to substitute for z in the first two equations gives ...

  t + y + (y +30) = 180   ⇒   t +2y +30 = 180

  y + (y +30) = 5t   ⇒   2y +30 = 5t

Using the second of these equations to substitute for (2y+30) in the first, we have ...

  t +5t = 180

  t = 180/6 = 30 . . . . . . divide by the coefficient of t

Using this value in our equation for 5t gives ...

  2y +30 = 5(30)

  2y = 120

  y = 60

Then the value of angle z is ...

  y +30 = z = 60 +30

  z = 90

The first, second, and third angles are 30°, 60°, and 90°, respectively.

Answer:

A

Step-by-step explanation:

Its A, 7/12 - 19/60 is 4/15

Answer:

i beleive its A

Step-by-step explanation:

i say its A due to the phrase "no more" is accurate to showing that the 200 is truly "More than or equal too"

The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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True, The coefficient of xkyn-k in the expansion of (x+y)n equals (n/k) .

What does a math expression mean?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

                                 This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The rth term in a binomial expansion is defined as

 r th term  = ⁿCr xⁿ⁻ˣ yr

   Let the coefficient of \(x^{k} y^{n - k }\) be A. The power of x is k and the power of y is n-k. It means

         k = n - r

        n - r = t

The coefficient of x^{k} y^{n - k } is

  \(C^{n} _{n - r} =\) ( n n - k )

Using the property of combination,

   \(C^{n} _{n - r} = C^{n}_{r}\)

\(C^{n} _{n - k} = C^{n} _{k} ( ^{n} _{k} )\)

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The complete question is -

The coefficient of xkyn-k in the expansion of (x+y)n equals (n/k) true or false

Answer:

Step-by-step explanation:

Let the polynomial be y.

(3x-1)(x+6) +5 = y

3x^2+18x-x-6=y

y=3x^2+17x-6

Answer: I can’t read it

Step-by-step explanation:

In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

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Answer:

F (5,-8)

Step-by-step explanation:

By rearranging,

y= 4x-28

Substitute each of the x values of the answers, eventually you will get to F and discover that when x = 5, y= -8

y= 4(5) - 28

y= -8

So, when x= 5, y= -8,

Point F is  (5,-8)

hello to solve this question, we can take the two triangles apart and then solve the individual missing part

let's solve for triangle a

to solve for x, let's use pythagorean theorem

let's solve for right-angle triangle b

from the calculation above, the value of x and y is 10.30 and 5.83 respectively

Answer:

9758

Step-by-step explanation:

697 x 14 = 9758

The slant height of the cone is calculated as: 13.00 feet

The surface area of a cone is calculated using the formula:

SA = πr(s + r) square units, where:

SA = surface area

r = radius of the cone

s = slant height of the cone

Given the following parameters of the cone as follows:

Surface area (SA) = 439.6 square feet

Slant height (s) = ?

Radius (r) = 7 ft

π = 3.14

Plug in the values:

439.6 = 3.14 * 7(s + 7)

439.6 = 21.98s + 153.86

439.6 - 153.86 = 21.98s

285.74 = 21.98s

285.74/21.98 = s

13 = s

s = 13.00 feet

Therefore, the cone in the image above that has a surface area of 439.6 square units will have a slant height of 13.00 feet.

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Answer:

Step-by-step explanation:

32.5

Answer:

The cost of the mug is of $6.50.

Step-by-step explanation:

The cost of the mug and r refills is given by the following equation:

\(C(r) = 2.3r + 6.5\)

Cost of the mug:

The cost of the mug is found when no refills are bought, that is, C when \(r = 0\), which is \(C(0)\)

\(C(0) = 2.3*0 + 6.5 = 6.5\)

The cost of the mug is of $6.50.

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The value of the expression Illustrated as (2a⁴)²/a^0a^5 is C. -500

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number

From the information (2a⁴)²/a^0a^5

We know ( xy) ^z = x^z y^z

(2a^4)^2 = 2^2 a^4^2

and x^y^z =x^(y*z)  so a^4^2 = a^(4*2) = a^8

(2a^4)^2 = 4 a^8

We know that a^0 = 1

4 a^8/1 a^5

We know x^y / x^z = x^ ( y-z)

4 a^( 8-5)

4 a^3

Let a = -5

4 ( -5) ^3

4 ( -125)

= -500

The correct option is C.

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The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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Answer:

−  2x^ 3  +  8 x ^2

Step-by-step explanation:

Hope this helps:)

Answer:

Answer:

answer can be either 5 square root 2 or 7.01

Step-by-step explanation:

you can cancel out 2 (outside of brackets) with 2( denominator of the fraction)

Answer:

\(5\sqrt{2}\)

Step-by-step explanation:

The 2 in the denominator and outside the parenthesis both cancels out, which just leaves with the most simplified answer.

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answering the questiοn, we may state that Thus, the aquarium's area fοundatiοn has a 5760 cm² surface area.

An area is a measure οf a regiοn's size οn a surface. The term "surface area" refers tο the area οf an οpen surface οr the perimeter οf a three-dimensiοnal οbject, whereas "planar regiοn" οr "planar regiοn" refers tο the area οf a fοrm οr planar layer. The area οf an item is the entire vοlume οccupied by its planar (2-D) surface οr fοrm. On a sheet οf paper, make a square using a pencil. a twο-dimensiοnal character. On paper, a shape's area is the amοunt οf space it οccupies. Cοnsider that the square is made up οf smaller unit squares.  

Multiplying the aquarium's length by its breadth yields the area οf the base.

Area is equal tο length times breadth.

Given that the length in this instance is 96 cm and the breadth is 60 cm, we have:

= 96 x 60 cm in size.

Size = 5760 cm²

Thus, the aquarium's fοundatiοn has a 5760 cm² surface area.

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The area of the base of the aquarium is 5760 square cm.

What is a dimension?

Dimension refers to the measurement of the size, length, width, height, or depth of an object or space. In geometry, dimension can also refer to the number of coordinates required to locate a point in a space.

To find the area of the base of the aquarium, we need to multiply its length by its width.

Given that Marco measured the length and width of the aquarium to be 96 cm and 60 cm respectively, the area of the base of the aquarium is:

Area = length x width

= 96 cm x 60 cm

= 5760 square cm

Therefore, the area of the base of the aquarium is 5760 square cm.

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