HELPWITH THIS QUESTION

Please help. find the measure of all missing angles.<br>

Shtirlitz [24]

Answer:

M1= 62 M2= 45 M3= 24

Step-by-step explanation:

For angle 1:

180-118 = 62

Angle 2:

180- (73+62)

Angle 3:

part 1

180-73= 107

part 2

180-(107+49)= 24

7 0

3 years ago

Read 2 more answers

Bangladesh has 2596 persons per square mile, while the united states has 780 persons per square mile and canada has 9 persons pe

8_murik_8 [283]

These statistics compare the population density of these countries.

6 0

4 years ago

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What is the equation of the axis of symmetry of the graph of y+3x-6=-3(x-2)2+4

eimsori [14]

A graph shows the vertex to be at (1.5, 4.75).

The equation of the axis of symmetry is x=1.5.

_____
If you want to find it analytically, you can put the equation in standard form.
y = -3(x -2)² +4 -(3x -6)
y = -3x^2 +9x -2
This is of the form y = ax² +bx +c with a=-3 and b=9. The axis of symmetry is given by ...
x = -b/(2a) = -9/(2×(-3)) = 3/2 . . . . . same as above

6 0

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

Order these numbers from least to greatest.<br> 2.5, 2.304, 3.21, 2.34

AysviL [449]

Answer:

2.304, 2.34, 2.5, 3.21

Step-by-step explanation:

1. Look at the digit in the ones place. See how they are all 2s except for one 3? Well, now we know the one with the 3 must be the greatest, since 3>2.

2. Next, look at the digit in the tenths place. We have a 3, 3, and a 5. Since 5 > 3, we know thar 2.5 is the second greatest.

3. Last, look at the hundreths place. We have a 0 and a 4. Since 4 > 0, that means 2.34 is the third greatest.

4. Since this is from least to greatest, put 2.304 first and the others as follows in the answer. Hope this helps.

6 0

3 years ago