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3 years ago

The sum of three consecutive number is 114. what is the smallest of the three numbers?

Mathematics

2 answers:

solong [7]3 years ago

7 0

Answer: the smallest of the three numbers is 37

Step-by-step explanation:

Let x represent the smallest number.

Since the three numbers are consecutive, it means that the next number would be x + 1

Also, the last and also the largest number would be x + 2

If the sum of the three consecutive numbers is 114, it means that

x + x + 1 + x + 2 = 114

3x + 3 = 114

Subtracting 3 from the Left hand side and the right hand side of the equation, it becomes

3x + 3 - 3 = 114 - 3

3x = 111

Dividing the Left hand side and the right hand side of the equation by 3, it becomes

3x/3 = 111/3

x = 37

velikii [3]3 years ago

6 0

Answer:

Step-by-step explanation:

37+38+39

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Which correctly describes a cross section of the cube below? Check all that apply.

yarga [219]

A cross section parallel to the base is a square measuring 4 cm by 4 cm 

Step-by-step explanation:

Here we have to select the correct statement regarding a cross section of the cube :

A cross section parallel to the base is a square measuring 4 cm by 4 cm :

Since , every side of a cube is same . Any cross section of a cube must be parallel to a square base . Hence, correct statement .

A cross section parallel to the base is a rectangle measuring 4 cm by greater than 4 cm :

Since , every side of a cube is same . Any cross section of a cube must be parallel to a square base . Here, base is rectangle . We don't have a rectangle base in cube . Not correct statement.

A cross section perpendicular to the base through the midpoints of opposite sides is a rectangle measuring 2 cm by 4 cm:

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3 years ago

Which of the following is a solution of x^2+8x= -32

juin [17]

Answer:

X1=-4+4i

X2=-4-4i

Step-by-step explanation:

X^2+8x+32=0

Δ=b^2-4ac=8^2-4(32)=-64<0

X1=(-b-i√Δ) /2a=(-8-8i)/2=-4-4i

X2=(-b+i√Δ) /2a=(-8+8i)/2=-4+4i

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3 years ago

I have no clue how to do this please help

mel-nik [20]

Answer:

Max = (6,0); min = (-2, 4)

Step-by-step explanation:

1. Summarize the constraints

$\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}$

2. Optimization equation

z = 5x + 2y

3. Graph the constraints to identify the feasible region

See the figure below.

The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.

The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.

5. Determine the points of intersection among the constraints

(i) Constraints (a) and (b)

$\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\$

The lines intersect at (3,-6).

(ii) Constraints (a) and (c)

$\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}$

The lines intersect at (6,0).

(iii) Constraints (b) and (c)

$\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}$

The lines intersect at (-2,4).

6. Determine the x- and y-intercepts of the feasible region

The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.

Each vertex is a possible maximum or minimum of z.

7. Calculate the maxima and minima

Calculate z at each of the vertices.

(i) At (-2,4)

z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2

(ii) At (3,-6)

z = 5(3) + 2(-6) = 15 - 12 = 3

(iii) At (6,0)

z = 5(6)+ 2(0) = 30 + 0 = 30

The maximum of z occurs at (6,0).

The minimum of z occurs at (-2, 4).

7 0

3 years ago

Simplify (y x y^1/3)^3/2

jok3333 [9.3K]

Answer:

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Step-by-step explanation:

(y x y^1/3)^3/2 would be clearer if written as

(y*y^(1/3))^(3/2).

Because y^a*y^b = y^(a + b), the quantity inside the first set of parentheses becomes

y^(4/3)

and if we apply the power (3/2) to this result, we get:

4 3

(y^(4/3))^(3/2) = y^{ ----- * ----- ) = y^2

3 2

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stiks02 [169]

Answer:

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Step-by-step explanation:

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3 years ago

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