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3 years ago

Which ordered pair will be solution for the function y = 12 - x?

Mathematics

2 answers:

fenix001 [56]3 years ago

5 0

Answer:

(6, 6)

Step-by-step explanation:

ordered pair (6, 6) will be solution for the function y = 12 - x.

When x = 6

y = 12 - 6

y = 6

(x, y) = (6, 6)

LekaFEV [45]3 years ago

5 0

Answer:

6,6

Step-by-step explanation:

You might be interested in

1. What is the length of XU? X U Y 36 in V Z W 23 in

mixer [17]

Answer: 49 in

Step-by-step explanation:

[23 + XU]/2 = 36 [trapezoid midsegment theorem]
23 + XU = 72 [multiply both sides by 2]
XU = 49 [subtract 23 from both sides]

7 0

2 years ago

The perimeter of a rectangle is 96 inches. If the

WINSTONCH [101]

Answer:

The width of the rectangle=21 inches

Step-by-step explanation:

Step 1: Determine the dimensions of the rectangle

Width=w

Length=l

But;

triple width=length+36

3×w=l+36

3 w=l+36

The length can be expressed as;

l=3 w-36

width=w

length=3 w-36

Step 2: Determine the perimeter of the rectangle

P=2(L+W)

where;

P=perimeter

L=length

W=width

In our case;

P=96 inches

W=w

L=3 w-36

replacing;

2(w+3 w-36)=96

2(4 w-36)=96

8 w-72=96

8 w=96+72=168

8 w=168

w=168/8=21

The width of the rectangle=21 inches

7 0

4 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

Zarrin [17]

Answer:

The volume of the box is maximized when x = 0.53 cm

Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³

Step-by-step explanation:

Please refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denotes the length of the sides of the square as shown in the diagram.

The width of shaded region is given by

$Width = 3 - 2x \\\\$

The length of shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

Take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15)\\\\18x^2 -38x + 15 = 0\\\\$

We may solve the quadratic equation using the quadratic formula.

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

The values of coefficients a, b, c are

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

Substituting the values into quadratic formula yields,

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of box when x = 1.59:

$V = \frac{1}{2} (5 - 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of box when x = 0.53:

$V = \frac{1}{2} (5 - 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

As you can see, the volume of the box is maximized when x = 0.53 cm

Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³

8 0

3 years ago

Factorise fully 24x+16

ZanzabumX [31]

Answer:

8(3x + 2)

Step-by-step explanation:

→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.

→The GCF is 8:

8(3x + 2)

6 0

3 years ago

Read 2 more answers

The heights of a group of boys and girls at a local middle school are shown on the dot plots below.

netineya [11]

Answer:

The most appropriate answer option is D) The girls are generally taller than the boys.

Step-by-step explanation:

A) The shortest boy is taller than the shortest girl:

The shortest guy is not taller than the girl so its false.