For what values of a are the following expressions true?

| a-5 | = 5-a

Answer:

39/2, 39/2 give a maximum product.

Step-by-step explanation:

Let 1 number be x then the other is 39-x.

Product P = x(39 - x)

= 39x - x^2.

Finding the derivative:

dP/dx = 39 - 2x

When P is a maximum or minimum dP/dx = 0, so

39 - 2x = 0

x = 39/2.

The 2 numbers are both 39/2.

There are four basic properties of logarithms. The solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex].

There are four basic properties of logarithms:

[tex]\rm log_aU+ log_aV = log_a(UV)\\\\\rm log_aU - log_aV = log_a(\dfrac{U}{V})\\\\\rm log_aU^n = n\ log_aU\\\\\rm log_ab = \dfrac{log_xb}{log_xa}[/tex]

The given logarithmic problem can be solved in the following manner,

[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex]

By using the division law of logarithm, [tex]\rm log_a(\dfrac{x}{y}) = log_ax - log_ay[/tex]

[tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5} = log_{12}\ {x^4\sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]

By addition law of Logarithm, [tex]\rm log_a(xy)= log_ax+ log_ay[/tex]

[tex]\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}[/tex]

Using the logarithmic Property, [tex]\rm log\ a^m =mlog\ a[/tex]

[tex]=\rm log_{12}\ x^4+ log_{12} \sqrt{x^3-2}}-log_{12}{(x+1)^5}\\\\=log_{12}\ x^4+ log_{12} (x^3-2)^{\frac12}-log_{12}{(x+1)^5\\\\[/tex]

[tex]=4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]

Hence, the solution of the logarithmic problem [tex]\rm log_{12}\dfrac{x^4\sqrt{x^3-2}}{(x+1)^5}\\\\[/tex] is [tex]\rm 4log_{12}\ x+\dfrac12 log_{12} (x^3-2)-5log_{12}{(x+1)[/tex]

Learn more about Logarithms:

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Answers:  he markup price is $9.6

You will be paying 120% which is 1.20 as a decimal

So you multiply. 8(1.20) which gives you $9.6

Step-by-step explanation: thank you for letting me answer this question hope it's helpful

Answer:

40 14/25 years

Step-by-step explanation:

Well, this certainly is fun.

First, to find the fraction of the doctor's life which 13 years represents, subtract the fractions from 1 (and in this case l stands for lifetime):

[tex]13 = (1 - (\frac{1}{13} + \frac{4}{39} + \frac{1}{2}))(l)[/tex]

[tex]13 = (\frac{25}{78})(l)[/tex]

So, multiply this equation by the reciprocal of 25/78 to isolate one of l:

[tex]13(\frac{78}{25}) = l[/tex]

[tex]l = 40\frac{14}{25}[/tex] years

Answer:

6:5

Step-by-step explanation:

c = number of cats

d = number of dogs

d = c+6

Set up a ratio:

4/3 = d/c

Then replace d with c+6, so your equation only has one variable.

[tex]\frac{4}{3} = \frac{c+6}{c}[/tex]

Cross multiply

4c = 3(c+6)

Multiply everything in the parentheses by 3.

4c = 3c + 18

Subtract 3c from both sides

4c - 3c = 18

c = 18

d = c + 6 = 18 + 6 = 24

If 2 more cats join, then you will have 20 cats and 24 dogs, so the ratio of dogs to cats will now be 24:20.  Divide each side by 4 for a ratio of 6:5.

Answer:

steps 4 and 5

Step-by-step explanation:

i think

Answer:

idrk

Step-by-step explanation:

Answer:

It will represent the slope of the graph

Step-by-step explanation:

Here, we are interested in getting what the cost per mile driven represent

From the information, we can represent the cost as;

C = 15d + 39

In this case we have a representation of the cost using the fixed daily cost(y-intercept) and the cost depending on the number of miles driven which will change based on the number of miles.

Since it is changing, it represents the slope of the function for cost

Answer:

m = - 6.9

Step-by-step explanation:

3 × (m + 2) = - 3 × 4.9

3m + 6 = - 14.7

3m = - 20.7

m = - 6.9

Answer:

1.79m^2

Step-by-step explanation:

(0.1×1)+2(0.5×0.8×0.1)+(1×0.8)+(1×0.81)

=1.79

Answer:

17.5m

Step-by-step explanation:

You gotta do this:

0.81 x 1 = Top area

((0.8 x 0.1) ÷ 2) x 2 = left side and right side area

1 x 0.1 + Back Area

0.8 x 1 = Bottom

Add them all together and remember that the final answer has to be in metres, you get - 17.5m

Answer:

2 x 20^2

Step-by-step explanation:

I did it on paper and looked it up to make sure

Explanation:

Multiply the outer term 7 by each term inside the parenthesis.

We then add up those results, combining like terms if possible.

That's how we get to 7t + 28

Answer:

7t+28

Step-by-step explanation:

multiply each term in the parentheses by 7

7t+7×4

multiply the numbers

7t+28

Answer:

Step-by-step explanation:

[tex]4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3[/tex]

Answer:

a4 = -12

Step-by-step explanation:

Answer:

m(∠AOF) = 148°

Step-by-step explanation:

From the figure attached,

CD intersects line EF at a point O.

Line CD is perpendicular to the line EF.

m(∠AOE) = 32°

m(∠COE) = 90°

Since m(∠COE) = m(∠AOE) + m(∠AOC) = 90°

32° + m(∠AOC) = 90°

m(∠AOC) = 90° - 32° = 58°

m(∠AOF) = m(∠AOC) + m(∠COF)

               = 58° + 90°

               = 148°

Therefore, m(∠AOF) = 148° will be the answer.

Answer: x

2

=

81

can be written as

x

2

−

81

=

0

by property ,

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

The expression becomes

x

2

−

(

9

)

2

=

0

(

x

−

9

)

(

x

+

9

)

=

0

equating each of the terms with zero we obtain the solution

x

−

9

=

0

and

x

+

9

=

0

the solutions are

x

=

9

or

x

=

−

9

Step-by-step explanation:

Answer:

A) Take the square root of both sides to solve

E) x = ±9

Step-by-step explanation:

Answer:

[tex]\tt x=5[/tex]

Step-by-step explanation:

[tex]\tt 18x-5=13x+4x+1-11[/tex]

[tex]\tt 18x-17x=15-10[/tex]

[tex]\tt x=5[/tex]

~

Answer:

7.27 is the irrational number

Step-by-step explanation:

7.27 can not turn into a fraction because it keeps on repeating

There are no Irrational numbers in the list.

We have a set of numbers - 7.27, 5, 9215, 2196.

We have to circle out the Irrational ones.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction - p/q where p and q are integers.

According to the question, we have -

7.27, 5, 9215, 2196

Now -

7.27 =  [tex]$\frac{727}{100}[/tex]  → It is Rational.

5 = [tex]$\frac{5}{1}[/tex] → It is Rational.

9215 = [tex]$\frac{9215}{1}[/tex] → It is Rational.

9215 = [tex]$\frac{2196}{1}[/tex] → It is Rational.

All the numbers are Rational as they can be expressed in the form of p/q.

Hence, there are no Irrational numbers in the list.

To solve more questions on Rational and Irrational numbers, visit the link below-

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Answer:

[tex]y=0,\:x=3[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}y=\frac{2}{3}x-2\\ y=-x+3\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-x+3[/tex]

[tex]\begin{bmatrix}-x+3=\frac{2}{3}x-2\end{bmatrix}[/tex]

Isolate x for -x+3=2/3x-2: x=3

[tex]\mathrm{For\:}y=-x+3[/tex]

[tex]\mathrm{Substitute\:}x=3[/tex]

[tex]y=-3+3[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]y=0[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]y=0,\:x=3[/tex]

Answer:

○ [tex]\displaystyle None\:of\:these[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(2x - \frac{\pi}{2})} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle \boxed{y = 2sin\:2x} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:2x,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(2x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-2\frac{1}{4}\pi, -2],[/tex]from there to [tex]\displaystyle [-1\frac{1}{4}\pi, -2],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer: $36.80 and the difference is $9.20

Step-by-step explanation:

Answer:

1. BS = 4

2. RS = 2√5

3. ST = 4√5

Step-by-step explanation:

Use the right triangle altitude theorem.

Then use the Pythagorean Theorem.

1.

BT/BS = BS/BR

8/BS = BS/2

(BS)² = 16

BS = 4

2.

2² + 4² = (RS)²

RS = √(20)

RS = 2√5

3.

4² + 8² = (ST)²

ST = √(80)

ST = 4√5

Answer:

No Clue

Step-by-step explanation:

Answer:

a9=20

Step-by-step explanation:

an=3n-7

a1=3(1)-7

  =3-7

  =-4

a2=3(2)-7

   =6-7

   =-1

a3=3(3)-7

   =9-7

   =2

a=-4....a2=-1....a3=2

d=a2-a1

 =3

a9=a+(n-1)d

   =-4+(9-1)3

   =-4+8(3)

   =-4+24

   =20..

Answer:

C. -16.25 inches

Step-by-step explanation:

First, we need to find out the total rainfall in the three days

0.75 + 0.75 + 0.75 = 2.25

Now, we need to subtract this number from 18.5

18.5 - 2.25 is 16.25

So, your answer is -16.25

I really hope this is right and I really hope this helps!

Answer:

2/3

Step-by-step explanation:

Divide 1/2 by 3/4 to get 1/2 x 4/3 = 2/3 mph

Answer:

22 is the median

the minimum is 16

idrk for number 3 or 5

the maximum is 28

idrk for 6 or 7

Step-by-step explanation:

i wrote some of the answers, all you have to do is use the box plot

Answer:

b. 1.97

Step-by-step explanation:

1cm≈0.032feet

60/0.032≈1.97feet