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3 years ago

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-9x-(x+7)<33

e=" - 9x - (x + 7) \leqslant 33" alt=" - 9x - (x + 7) \leqslant 33" align="absmiddle" class="latex-formula">

1 answer:

alina1380 [7]3 years ago

7 0

your answer will be: x<-4

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What is the next term In the sequence? 1, 4, 9, 16, __

Pachacha [2.7K]

Answer:

25

Step-by-step explanation:

Everytime, you add a value number 2 greater than the previous.

1+3=4

4+5=9

9+7=16

16+9=25

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4 years ago

Read 2 more answers

Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metalli

Veseljchak [2.6K]

Answer:

Kwame's team will save = 7.8 $\times$ $0.24 = $1.87

Step-by-step explanation:

i.) Let the side of the equilateral triangle base be a

ii.) the area of the base = 3.9 square feet

iii.) the area of equilateral triangle is = $\frac{\sqrt{3} }{4} a^{2}$ = 3.9

iv.) Base area = 3.9 square feet

v.) The area that is not covered is the base.

vi.) The total area that is not covered = 3.9 $\times$ 2 since there are two pyramids

therefore the total area not covered = 7.8 square feet

vii.) therefore Kwame's team will save = 7.8 $\times$ $0.24 = $1.87

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4 years ago

Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second

Marrrta [24]

Answer:

$a) x=0, x=\frac{12}{11}, x=2 \:$ b) The 2nd Derivative test shows us the change of sign and concavity at some point. c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

Step-by-step explanation:

a) To find the critical numbers, or critical points of:

$f(x)=x^{6}(x-2)^{5}$

1) The procedure is to calculate the 1st derivative of this function. Notice that in this case, we'll apply the <em>Product Rule</em> since there is a product of two functions.

$f(x)=x^{6}(x-2)^{5}\Rightarrow f'(x)=(f*g)'(x)\\=f'g+fg'\Rightarrow (fg)'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4} \Rightarrow 6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}=0\\f'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}$

2) After that, set this an equation then find the values for x.

$x^{5}(x-2)^{4}[6(x-2)+5x]=0\Rightarrow x^{5}(x-2)^{4}[11x-12]=0\Rightarrow x_{1}=0\\(x-2)^{4}=0\Rightarrow \sqrt[4]{(x-2)}=\sqrt[4]{0}\Rightarrow x-2=0\Rightarrow x_{2}=2\\(11x-12)=0\Rightarrow x_{3}=\frac{12}{11}$

$x=0\:(smallest\:value)\:x_{3}=\frac{12}{11}\:x=2 (largest value)$

b) The Second Derivative Test helps us to check the sign of given critical numbers.

Rewriting f'(x) factorizing:

$f'(x)=(11x-12)(x-2)^4x^{5}$

Applying product Rule to find the 2nd Derivative, similarly to 1st derivative:

$f''(x)>0 \Rightarrow Concavity\: Up\\\\f''(x)$

$f''(x)=11\left(x-2\right)^4x^5+4\left(x-2\right)^3x^5\left(11x-12\right)+5\left(x-2\right)^4x^4\left(11x-12\right)\\f''(x)=10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)$

1) Setting this to zero, as an equation:

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\\\$

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\(x-2)^{3}=0 \Rightarrow x_1=2\\x^{4}=0 \therefore x_2=0\\11x^{2}-24x+12=0 \Rightarrow x_3=\frac{12+2\sqrt{3}}{11}\:,x_4=\frac{12-2\sqrt{3}}{11}\cong 0.78$

2) Now, let's define which is the inflection point, the domain is as a polynomial function:

$D=(-\infty$

Looking at the graph.

Plugging these inflection points in the original equation $f(x)=x^{6}(x-2)^{5}$ to get y coordinate:

We have as Inflection Points and their respective y coordinates (Converting to approximate decimal numbers)

$(1.09,-1.05)$ Inflection Point and Local Minimum

$(2,0)$ Inflection Point and Saddle Point

$(0,0)$ Inflection Point Local Maximum

(Check the graph)

c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

At

$x=\frac{12}{11}\cong1.09$ Local Minimum

$At\:x=0,\:Local \:Maximum$

$At\:x=2, \:neither\:a\:minimum\:nor\:a\:maximum$ (Saddle Point)

5 0

3 years ago

Help please fast!!!!!!!!!!!

Oduvanchick [21]

Answer:

Step-by-step explanation:

32 tubes of yellow paint is needed

3 0

2 years ago

What is the point-slope form if it's through (1,4) and the slope is 3

Ratling [72]

For this case we have that by definition, the equation of the line of the point-slope form is given by:

$y-y_ {0} = m (x-x_ {0})$

Where:

m: It's the slope

$(x_ {0}, y_ {0}):$ It is a point through which the line passes

According to the given statement we have:

$(x_ {0}, y_ {0}) :( 1,4)\\m = 3$

Substituting we have:

$y-4 = 3 (x-1)$

Finally, the equation is:

$y-4 = 3 (x-1)$

Answer:

$y-4 = 3 (x-1)$

8 0

3 years ago