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Cerrena [4.2K]
3 years ago
5

Can anyone help me with these?

Mathematics
1 answer:
katrin2010 [14]3 years ago
6 0

Answer:

Step-by-step explanation:

Distributive property: a*(b + c)  = ab + ac

16)5x²(7 - x²) = 5x²*7 - 5x²*x²

                   =35x² - 5x⁴

17)

10x(4 - 3x) = 10x*4 - 10x*3x

                  = 40x - 30x²

18) 9( y +4) = 9*y + 9*4

                 = 9y + 36

19) 3(4 - x) - 3(2 - x) = 3*4 - 3*x -3*2 - x*(-3)

                                = 12 - 3x - 6  + 3x  {add/subtract like terms}

                                = 12 - 6 - 3x + 3x

                                = 6

20) 6y + 6(y - 4) = 6y + 6*y - 6*4

                          = 6y + 6y - 24

                          = 12y - 24

                         

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What graph represents −3x+1≤10
nalin [4]

The solution of the inequality is x ≥ -3 and the graph is shown below

<h3>Graph of inequalities </h3>

From the question, we are to determine the graph that represents the given inequality

The given inequality is

−3x + 1 ≤ 10

First, we will solve the inequality

−3x + 1 ≤ 10

Subtract 1 from both sides

−3x +1 -1 ≤ 10 - 1

−3x ≤ 9

Divide both sides by -3 and<u> flip the sign</u>

x ≥ -3

The graph of the inequality is shown below

Learn more on Graphing inequalities here: brainly.com/question/13053003

#SPJ1

6 0
2 years ago
Algebra 2, how do you solve these questions?
adelina 88 [10]
#13:

s² = 144
√(s²) = √144
|s| = 12

s = -12 OR s = 12

--------------------

#15 (not sure what letter you used so I went with 'g')

(g-6)² = 25
√[(g-6)²] = √25
|g-6| = 5

g - 6 = -5 OR g - 6 = 5

g = 1 OR g = 11
3 0
3 years ago
I need help with this question plzzz <br><br> Geometry
KATRIN_1 [288]

Answer:

  • If the perimeter of a square measures 32 cm, each side measures 32/4= 8 cm, because all sides are equal.
  • The diagonal that passes through the center of the square divides the square into two triangles. The triangles are formed by a <u>hypotenuse </u>(the diagonal, which is k in this case), <u>and two sides,</u> that measure 8 cm each, in this case.
  • Because of Pythagoras' theorem, we know that the <u>lenght of the hypotenuse</u> (in this case the hypotenuse is k) equals the squared root of the sum of the squared sides, which in this case can be expressed as k=\sqrt{8^2+8^2} =\sqrt{64+64}=\sqrt{128}=11.31.
  • Then, k=11.31 cm.

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3 years ago
What is the slope of a line between the points (-4,-3) and (4, -2)?<br> Nour answer
Rufina [12.5K]

Answer:

1/8

Step-by-step explanation:

The slope of a line given two points is found by

m = (y2-y1)/ (x2-x1)

   = (-2 - -3)/(4 - -4)

   = (-2 +3)/(4+4)

    1/8

4 0
3 years ago
Read 2 more answers
Use Lagrange multipliers to find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Enter the dimens
Dima020 [189]

Answer:

(x,y,z) = (12,12,12) cm

Step-by-step explanation:

The box is assumed to be a closed box.

The surface area of a box of dimension x, y and z is given by

S = 2xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = 1728

The constraint can be rewritten as

xyz - 1728 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 2xy + 2xz + 2yz - λ(xyz - 1728)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 2y + 2z - λyz = 0

λ = (2y + 2z)/yz = (2/z) + (2/y)

(∂L/∂y) = 2x + 2z - λxz = 0

λ = (2x + 2z)/xz = (2/z) + (2/x)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x)

(∂L/∂λ) = xyz - 1728 = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(2/z) + (2/y) = (2/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(2/z) + (2/x) = (2/y) + (2/x)

(2/z) = (2/y)

z = y

Hence, at the point where the box has minimal area,

x = y = z

Putting these into the constraint equation or the solution of the fourth partial derivative,

xyz - 1728 = 0

x³ = 1728

x = 12 cm

x = y = z = 12 cm.

7 0
2 years ago
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