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Eddi Din [679]
3 years ago
6

Twelve less than seven times a number is 16

Mathematics
1 answer:
Murljashka [212]3 years ago
7 0
Are you asking a question? Or would you like this question checked for you?
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If f(x)=x^2-11, for what values of z is f(x) < 25?
GuDViN [60]

Answer:

D

Step-by-step explanation:

f(x) < 25

x² - 11 < 25

x² < 36

-6 < x < 6

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3 years ago
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The answer is C that can be the x-intercepts of the parabola
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2 years ago
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Find 90% of 0.4<br>No equation needed. ​
myrzilka [38]

90% = 0.9

0.9 * 0.4

= 0.36

8 0
3 years ago
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A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru
Viktor [21]

Answer:

1) S = 2\cdot w\cdot l - 8\cdot x^{2}, 2) The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l, 3) S = 176\,in^{2}, 4) x \approx 4.528\,in, 5) S = 164.830\,in^{2}

Step-by-step explanation:

1) The function of the box is:

S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)

S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w

S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x

S = 2\cdot w\cdot l - 8\cdot x^{2}

2) The maximum cutout is:

2\cdot w \cdot l - 8\cdot x^{2} = 0

w\cdot l - 4\cdot x^{2} = 0

4\cdot x^{2} = w\cdot l

x = \frac{\sqrt{w\cdot l}}{2}

The domain of S is 0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}. The range of S is 0 \leq S \leq 2\cdot w \cdot l

3) The surface area when a 1'' x 1'' square is cut out is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}

S = 176\,in^{2}

4) The size is found by solving the following second-order polynomial:

20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}

20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}

8\cdot x^{2} - 164\,in^{2} = 0

x \approx 4.528\,in

5) The equation of the box volume is:

V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x

V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x

V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}

V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}

V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}

The first derivative of the function is:

V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}

The critical points are determined by equalizing the derivative to zero:

12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0

x_{1} \approx 4.952\,in

x_{2}\approx 1.548\,in

The second derivative is found afterwards:

V'' = 24\cdot x - 78\,in

After evaluating each critical point, it follows that x_{1} is an absolute minimum and x_{2} is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

x \approx 1.548\,in

The surface area of the box is:

S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}

S = 164.830\,in^{2}

4 0
3 years ago
A student was required to multiply a number by 4 and add 6 to it. Instead he added 6 to it first and then multiplied by 4. What
GalinKa [24]

Answer:

The correct answer is 18

the correct expression is (4n+6)

Step-by-step explanation:

let the number be n

therefore  if he is required to multiply n by 4 and added to 6 we have

(4n+6)= 0-----1

given that he did otherwise by adding 6 to n and multiply by 4 we have

(n+6)4= 36------2

Firstly we need to solve for n in equation 2

4n+24= 36\\4n= 36-24\\4n= 12\\

Dividing both sides by 4 we have

n= \frac{12}{4\\}\\n= 3

In order to solve for the correct answer let us input n=3 in equation 1 we have

=(4n+6)= 0-------1\\=(4*3+6)= 0\\=(12+6)=0\\= 18

7 0
3 years ago
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