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anyanavicka [17]
2 years ago
5

PLS ANSWER!! 14.975 ➗ 9.5

Mathematics
1 answer:
Dafna1 [17]2 years ago
5 0

Answer:

14.975÷9.5=1.57631578947

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When f(x) = 2x 2 + 3, find f(-3).<br> -15<br> 21<br> 39
notsponge [240]

Answer:

21

Step-by-step explanation:

f(x) = 2x^2 + 3

f(-3) = 2(-3)^2 + 3

f(-3) = 2(9) + 3

f(-3) = 18 + 3

f(-3) = 21

6 0
3 years ago
A rectangular image of length 5 cm and width 7 cm is magnified in a studio. On magnification, 1 cm of the image represents 15cm.
Andre45 [30]

Answer:

238 cm

Step-by-step explanation:

so we have a scale factor   of  17: 1

originally we had the dimensions:   3cm by 4m

now we have    3*17  by 4*17  = 51 cm by 68 cm

Perimeter = 2*51 + 2*68 = 238 cm

8 0
1 year ago
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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
kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

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

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

The width of the shaded region is given by

Width = 3 - 2x \\\\

The length of the 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) \\\\

In order to maximize the volume enclosed by the box, 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 are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

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

Where

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

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 the box at 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 the box at x= 0.53:

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

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

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0
3 years ago
Identify the index in the radical below.<br> A. 1<br> B. 2<br> C. 3<br> D. 4
marysya [2.9K]

Answer:

It is four/4 I believe D.4

Step-by-step explanation:

3 0
3 years ago
The three sides of a triangle are n, 3n+3, and 2n+11. If the perimeter of the triangle is 50 inches, what is the length of each
mylen [45]

Answer:

6, 21, and 23 inches

Step-by-step explanation:

The perimeter of a triangle is equal to the sum of all side lengths in that triangle. We're given the perimeter as 50 inches, and the side lengths as n, 3n + 3, and 2n + 11.

  • This means that we can algebraically solve the equation n + 3n + 3 + 2n + 11 = 50

Step 1: Combine like terms.

  • (n+3n+2n) + (3+11) = 50
  • 6n + 14 = 50

Step 2: Subtract 14 from both sides.

  • 6n + 14 - 14 = 50 - 14
  • 6n = 36

Step 3: Divide both sides by 6.

  • 6n/6 = 36/6
  • n = 6

Step 4: Plug in the value of n as 6 in each side.

  • (6) + (3(6) + 3) + (2(6)+11) = 50
  • (6) + (18+3) + (12+11) = 50
  • (6) + (21) + (23) = 50  

Therefore, the side lengths are 6, 21, and 23 inches.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

6 0
2 years ago
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