Given the function:
[tex]h(x)=2log\left(x-3\right)[/tex]To find its inverse:
[tex]\begin{gathered} y=2log\left(x-3\right) \\ x=2log\left(y-3\right) \end{gathered}[/tex]solving for y:
[tex]\frac{x}{2}=log(y-3)[/tex][tex]\begin{gathered} 10^{\frac{x}{2}}=y-3 \\ \\ 10^{\frac{x}{2}}+3=y \end{gathered}[/tex]ANSWER
[tex]h^^{-1}(x)=10^{\frac{x}{2}}+3[/tex]If f(x) = 2x^3 + 10x^2 + 18x + 10 and x + 1 is a factor of f(x), then find all of the zeros of f(x) algebraically
Given the polynomial:
[tex]f(x)=2x^3+10x^2+18x+10[/tex]We know that (x + 1) is a factor of f(x). We divide f(x) by (x + 1):
Then:
[tex]f(x)=(x+1)(2x^2+8x+10)=2(x+1)(x^2+4x+5)[/tex]For the quadratic term, we solve the following equation:
[tex]x^2+4x+5=0[/tex]Using the general solution for quadratic equations:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt{4^2-4\cdot1\cdot5}}{2\cdot1}=\frac{-4\pm\sqrt{16-20}}{2}=\frac{-4\pm\sqrt{4}}{2} \\ \\ \therefore x=-2\pm i \end{gathered}[/tex]The zeros of f(x) are:
[tex]\begin{gathered} x_1=-1 \\ \\ x_2=-2-i \\ \\ x_3=-2+i \end{gathered}[/tex]A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5 questions if you guess randomly on each question?A. 0.9936B. 0.2C. 0.0264D. 0.0003
If there are 10 questions with 5 answer choices, then first we need to find out the probability of getting the first questions randomly correct.
Therefore, that is:
[tex]\begin{gathered} Probability\text{ of getting 1 answer correct= }\frac{1}{5} \\ \\ Then\text{ if we need to get the second question correct it is:} \\ \frac{1}{5}(first\text{ question\rparen x }\frac{1}{5}=\text{ \lparen}\frac{1}{5})^2 \\ \\ And\text{ for the other questions applies the same. Therefore, if we need 5 correct answers, then:} \\ \frac{1}{5}\text{ x }\frac{1}{5}x\frac{1}{5\frac{}{}}x\frac{1}{5}x\text{ }\frac{1}{5}=\text{ \lparen}\frac{1}{5})^5\text{ = }\frac{1}{3125}=\text{ 0.0003} \end{gathered}[/tex]The answer is D. 0.0003
The total number of photos on Hannah's camera is a linear function of how long she was in Rome. She already had 44 photos on her camera when she arrived in Rome. Then she took 24 photos each day for 6 days. What is the initial value of the linear function that represents this situation? 24 photos 44 photos 6 days o days per day
she already had 44 photos
She took 24 photos each day for 6 days.
The function is:
y= 44+24x
where y is the total number of photos and x is the number of days.
The initial value is when x=0
y= 44+24(0) =44
The initial value is 44.
Latoya cut a circle into & equal sections and arranged the pieces to form a shape resembling a parallelogram. So in of
Based on the diagram, the base length of the new shape is half the circumference of the circle as indicated by 1/2C.
A farmer has 36 ft of fencing and wants to enclose the maximum rectangular area for his llamas. Find the dimensions of three possible areas he could enclose. What do you think the maximum area is? Why?
The farmer would like to eclose a rectangle
First we know that the perimeter of the rectangle is
[tex]P=2x+2y[/tex]We also know that we have 36 ft of fence, that is we only can enclose a rectangle of 36 ft of perimeter. Then
[tex]36=2x+2y[/tex]From this we can find y
[tex]\begin{gathered} 36=2x+2y \\ 36-2x=2y \\ y=\frac{36-2x}{2} \\ y=18-x \end{gathered}[/tex]The area of the rectangle is
[tex]A=xy[/tex]But we know the value of y, plugging this value into the last equation we have that
[tex]A=x(18-x)[/tex]To find three possible values for the area we only have to give values to x. This values have to be positive (since we can't have a negative lenght). We also notice that the value can't exceed 18 since that would mean a zero area. With those point in consideration we choose three values between zero and 18.
If x=3, then the area is
[tex]\begin{gathered} A=3(18-3) \\ =3(15) \\ =45 \end{gathered}[/tex]If x=9, then the area is
[tex]\begin{gathered} A=9(18-9) \\ =9(9) \\ =81 \end{gathered}[/tex]if x=15, then the area is
[tex]\begin{gathered} A=15(18-15) \\ =15(3) \\ =45 \end{gathered}[/tex]Then we have three possible areas for the rectangle.
The maximum value for the area is 81, and we see that because the equation for the area is a parabola that opens down with vertex in the point (9,81)
Find the exact value of s in the given interval that has the given circular function value.
Recall that:
[tex]\tan x=\frac{\sin x}{\cos x}\text{.}[/tex]Therefore:
[tex]\tan s=1\Leftrightarrow\frac{\sin s}{\cos s}=1.[/tex]Then:
[tex]\sin s=\cos s\text{.}[/tex]Now, notice that:
[tex]\sin s-\cos s=-\sqrt{2}\cos (s+\frac{\pi}{4}).[/tex]Then:
[tex]-\sqrt[]{2}\cos (s+\frac{\pi}{4})=0.[/tex]Therefore:
[tex]\cos (s+\frac{\pi}{4})=0.[/tex]Then:
[tex]\begin{gathered} s+\frac{\pi}{4}=\frac{\pi}{2}+n\pi, \\ s+\frac{\pi}{4}=\frac{3\pi}{2}+n\pi\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} s=\frac{\pi}{4}+n\pi, \\ s=\frac{5\pi}{4}+n\pi\text{.} \end{gathered}[/tex]Since:
[tex]s\in\lbrack\pi,\frac{3\pi}{2}\rbrack^{},[/tex]we get that:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]Answer:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]Which of the following equations does the graph below represent?
A. -3x - 6y = 36
B. -3x + 6y = 36
C. x + 6y = 36
D. 3x + 6y = 36
The equation of the line which represents the given graph is -3x + 6y = 36
We can infer from the graph that the equation of the line passes through the points (0,6) and (-12,0).
Therefore the slope of the line passing through these two points is given by:
m = (0-6)/(-12-0)
or, m = 1 / 2
Now we can use the general equation of the line to get the required equation.
y-6 = 1/2 (x-0)
or, 2y - x = 12
Now we will multiply throughout by 3 we get:
6y - 3x = 36
or, -3x + 6y = 36
The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.
There are numerous ways to express the equation of a straight line, such as slope-intercept form, point-slope form, standard form, general form, etc.
Hence the required equation is -3x + 6y = 36 .
To learn more about equation visit:
https://brainly.com/question/2564656
#SPJ1
witch is an equation in point slope form the given point and slope point (1, 9) point 5
The formula for equation of line pasing through point (x_1,y_1) with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Substitute point and slope in the equation to obtain the equation of line.
[tex]\begin{gathered} y-9=5(x-1) \\ y-9=5x-5 \\ y=5x+4 \end{gathered}[/tex]So equation of line is y=5x+4.
How is the series 7 + 13 + 19+...+ 139 represented in summation notation?
Each term is 6 greater than the previous term.
First term is "7".
So,
a = 7
d = 6
Let's find the formula for the series,
[tex]\begin{gathered} a+(n-1)d \\ 7+(n-1)(6) \\ 7+6n-6 \\ 6n+1 \end{gathered}[/tex]We can immediately eliminate the firsst and third choice.
The variable is "t", so the general formula will be:
[tex]6t+1[/tex]How many terms are there?
The series starts from t = 1,
since 6(1) + 1 = 6 + 1 = 7
and 6(2) + 1 = 12 + 1 = 13
The terms match!
So, 2nd answer choice is correct!!
Answer[tex]\sum ^{23}_{t\mathop=1}(6t+1)[/tex]What is the surface area of a right square pyramid with height of 3 centimeters and a base that measures 8 centimeters by 8 centimeters?
Okay, here we have this:
Considering the provided measures, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will use the following formula:
A = a(a + √(a^2 + 4h^2))
A = 8 cm(8cm + √((8 cm)^2 + 4(3 cm)^2))
A = 8 cm(8cm + √(64 cm^2 + 4*9 cm^2))
A = 8 cm(8cm + √(64 cm^2 + 36 cm^2))
A = 8 cm(8cm + √(100 cm^2))
A = 8 cm(8cm + 10 cm)
A = 8 cm(18 cm)
total surface areaA = 144 m^2
Finally we obtain that the total surface area is equal to 144 m^2
please help me Solve for a6=a/4+2-6+x/4=-59x-7=-70=4+n/5-4=r/20-52(n+5)=-2-9x+1=-80144=-12(x+5)10-6v=-104
6=a/4+2
Subtract 2 from both sides of the equation:
6-2 = a/4+2-2
4 = a/4
Multiply both sides by 4
4 (4) = a/4 (4)
16 = a
a= 16
A) 9- (-22) - 13B) 9 - (-22) = -13A football team gained 9yards on one play andthen lost 22 yards on thenext. Write a sum ofintegers to find theoverall change in fieldposition-9- (-22) = -13D) None of the above
The sum of integers should be written like:
9 + (-22) = -13
because the are asking in fact for a SUM of integers
The two integers are 9 and -22
when added you get:
9 + (-22) = 9 - 22 = -13
Greetings, i need help with this math problem. Thank you
The numerator of the left hand side can be rewritten as:
[tex]x^2+6x+9=(x+3)^2[/tex]Then, the given equation can be written as:
[tex]\frac{(x+3)^2}{x+3}=0[/tex]Since
[tex](x+3)^2=(x+3)(x+3)[/tex]we have
[tex]\frac{(x+3)(x+3)}{x+3}=0[/tex]We can to can cancel out one term x+3 and get
[tex]x+3=0[/tex]which gives
[tex]x=-3[/tex]Finally, in order to check that this value corresponds to a real answer, we need to subsitute this value into the equation and compute the limit when x approaches to -3, that is,
[tex]lim_{x\rightarrow-3}\frac{x^2+6x+9}{x+3}[/tex]which gives
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{x^{2}+6x+9}{x+3}=\frac{0}{0}[/tex]Since the limit has the form 0/0 we can to apply L'Hopital rule, that is,
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{\frac{d}{dx}(x^2+6x+9)}{\frac{d}{dx}(x+3)}[/tex]which gives
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{\frac{d}{dx}(x^{2}+6x+9)}{\frac{d}{dx}(x+3)}=l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{2x+6}{1}=\frac{0}{1}=0[/tex]Since the limit exists and is equal to zero then the solution of the equation is: x= -3
Question 4 of 10Select the correct product of the exponential expression.35A. 5.5.5B. 3.5C. 15D. 3.3.3.3.3SUBMIT
You have the following expression:
[tex]3^5[/tex]it means that the number 3 is multipled by itself five times (because of the exponent), then, the previous expression can be written as follow:
[tex]3^5=3\cdot3\cdot3\cdot3\cdot3[/tex]The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
y
Convert the following units as indicated.2,250 watts to horsepower (Round answer to the nearest thousandth.)
The question given is to convert
[tex]2250\text{ watts to horse power}[/tex]From a conversion calculator,
[tex]1\text{ horse power = }745.699872\text{Watt}[/tex]Therefore,
[tex]1\text{ watts = }\frac{1}{745.699872}\text{horse power}[/tex]Therefore,
2250 watts will be
[tex]\begin{gathered} =2250\times\frac{1}{745.699872} \\ =\frac{2250}{745.699872}\text{horse power} \\ =3.0172997\text{ horse power} \\ \approx to\text{ the nearest thousandth} \\ =3.017\text{ horsepower} \end{gathered}[/tex]Hence,
The final answer = 3.017 horse power
8. Select the equation that has no real solution.12x + 15 = 12x - 157x +21= 21-5x-25 = 5x + 2512x+ 15 = 3(4x+5)
We will have that the equation with no real solution is:
[tex]12x+15=12x-15[/tex]Because:
[tex]12x-12x=-15-15\Rightarrow0\ne-30[/tex]And each diagram below, right, the 2 number on the sides of the acts that are multiplied together to get the top number of the x, but added together to get the bottom number of the x.
-34 = x*y
15 = x +y
17 and -2
__________________________
_____________
9 = x*y
6 = x +y
_
We use absolute value to find distances in the real world. Suppose you travel 10 miles north to the grocerystore, then 6 miles south to the post office. From there, you travel 8 miles north to the nearest bank. What isthe total distance you have traveled?A. 4 milesB. 8 milesC.12 milesD. 24 milesPlease select the best answer from the choices providedOAOBOCOD
Given:
Thesis about question is given
Required:
To select which option is correct
Explanation:
assumption S1 is the distance to the grocery store
assumption S2 is the distance to the south post office
assumption S3 is the distance to the north bank
assumption S is the total distance
according to the question
S1= 10 miles S2=6 miles S3=8 miles
S=S1+S2+S3=10+6+8=24 miles
Required answer:
option D
There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the collection is Rupees 8.50, how many of each are there?
We will have the following:
*First:
**We stablish that x will represent the number of 20 paise coins.
**We stablish that y will represent the number of 25 paise coins.
Second: From this we will then have:
[tex]x+y=38[/tex]&
[tex]20x+25y=850[/tex][This 850 is due to the fact that 8.50 Rupees are equal to 850 paise].
*Third: We solve for either x or y in the first equation:
[tex]x=38-y[/tex]Now, we replace this in the second equation and solve for y:
[tex]20(38-y)+25y=850\Rightarrow760-20y+25y=850[/tex][tex]\Rightarrow5y=90\Rightarrow y=18[/tex]So, we have that there are 18 25 paise coins.
Now, using this we solve for x in the first equation:
[tex]x+18=38\Rightarrow x=20[/tex]So, we have that there are 20 20 pais coins.
make an equation to find the area of rectangle. move number and symbols to the line
We know that the multiplication of both sides of the rectangle is the area of it.
In this case
Area: 6 x 8 = 48A survey asked "Do you think the president is doing a great job?" Of the 1200 Americans surveyed, 800 responded yes. For a 95% level of confidence find the sample proportion and the margin of error associated with the poll.
We have here working with estimating a population proportion.
We have the following information from the question:
• The sample size, n, is equal to 1200 (n = 1200).
,• We have that the fraction that responded "Yes" is 800.
,• We need to find a 95% level of confidence for the margin error associated with the poll.
Now, we have the sample proportion for the sample size, n = 1200 is as follows:
Sample Proportion[tex]\begin{gathered} \hat{p}=\frac{800}{1200}=\frac{2}{3}\approx0.666666666667\approx0.67 \\ \\ \hat{p}=\frac{800}{1200}\approx0.67 \end{gathered}[/tex]Therefore, the sample proportion for the sample size is 800/1200, which is, approximately, 0.67.
The margin of error associated with the pollThe margin of error, in this case, is given by the next formula:
[tex]E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]Where:
[tex]\begin{gathered} Z_c\text{ is the critical value for a 95\% level of confidence} \\ \\ n\text{ is the sample size \lparen n = 1200\rparen} \\ \\ \hat{p}\text{ is the sample proportion \lparen800/1200\rparen} \\ \end{gathered}[/tex]Now, we have that, for a level of confidence of 95%, the critical value is equal to z = 1.96:
Now, using all of the values at our disposal, we can use the formula to find the margin of error as follows:
[tex]\begin{gathered} E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ E=1.96\sqrt{\frac{\frac{8}{12}(1-\frac{8}{12})}{1200}} \\ \\ E=0.0266722216436\approx0.027 \end{gathered}[/tex][tex]\begin{gathered} E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ E=1.96\sqrt{\frac{\frac{8}{12}(1-\frac{8}{12})}{1200}} \\ \\ E=0.0266722216436\approx0.027 \end{gathered}[/tex]Therefore, in summary, we have that:
1. The sample proportion is:
[tex]\hat{p}=\frac{800}{1,200}\approx0.67[/tex]2. The margin of error associated with the poll is:
[tex]E=0.0266722216436\approx0.027[/tex]Find the area of a rectangle that is 3 3 over 4 inches long by 2 1 fourth inches wide. ANS.( Use mixed number) _______. in squared
Let's begin by listing out the given information:
[tex]\begin{gathered} Length(l)=3\frac{3}{4} \\ Width(w)=2\frac{1}{4} \\ Area=l\cdot w \\ Area=3\frac{3}{4}\cdot2\frac{1}{4} \\ Area=\frac{15}{4}\cdot\frac{9}{4}=\frac{15\cdot9}{4\cdot4} \\ Area=\frac{135}{16}=8\frac{7}{16} \\ Area=8\frac{7}{16}in^2 \\ \\ \therefore Area=8\frac{7}{16}in^2 \end{gathered}[/tex]a rectangle with a base of 6 and height of 4 has been scaled with a scale factor of 3. what is the area of the scaled copy?
We have a rectangle of base 6 and height 4. We have a rectangle like this:
Now, we have a scale factor of 3. We need to multiply each side by 3:
Now the rectangle has a height of 12 and a base of 18.
The area of a rectangle is h*b. Then, the area of the scaled copy is:
[tex]A=12\cdot18\Rightarrow A=216[/tex]Therefore, the scaled copy has an area of 216 square units.
The expression to represent the decrease in temperature then the explanation and it’s meaning
The expression would be:
[tex]\frac{10}{1000}\cdot x[/tex]Where x are the meters climbed.
For 2,000 m we'll have:
[tex]\frac{10}{1000}\cdot2000\rightarrow20[/tex]A 20°C decrease in temperature.
2705 is compound annually at a rate of 8% for 1 year
The formula of compound interest is,
[tex]\begin{gathered} A=P(1+i)^n \\ \text{Here, A=2075, i=8\%, n=1 year} \\ 2075=P(1+\frac{8}{100})^1 \\ P=1921.3 \end{gathered}[/tex]ANYONE HELP ME WITH THE AREA OF THE FLOOR PLAN FOR THE OFFICE
NEED CLEAR EXPLAINATION AND ANSWER.
The area of the floor plan for the office is 2200 m².
We are given a diagram. The diagram shows the floor plan of an office. The height of the office is 50 meters. The length of the floor of the office is 55 meters. The width of the floor of the office is 40 meters. We need to find the area of the floor of the office.
The shape of the floor of the office is a rectangle. The area of a rectangle is calculated as the product of its length and width. Let the area of the floor of the office be represented by the variable "A".
A = 55*40
A = 2200
Hence, the area of the floor of the office is 2200 m².
To learn more about area, visit :
https://brainly.com/question/27683633
#SPJ1
Consider a die rolling game that costs $15 per play. Rolling a 6 wins you $40, rolling a 5 gets you$25, and rolling anything else gets you nothing. Find the expected value and determine if the gameis fair.
Explanation
We need to present the information given in a table as follows:
The second column shows the probability of obtaining each event. Since they are equiprobable events, their probability are 1/6.
The next column determine the cost of obtaining each event; keeping in mid that each play costs $15.
The last column shows the expected value.
We know that If the value of the game is zero i.e. there is no loss or gain for any player, then the game is fair.
According to the table, there is a loss of 25/6, hence, the game is not fair.
taxes :2.69 * 10 ^ 5 square miles Rhode Island:1.21 * 10 ^ 3 square miles Determine the differences in square miles between the area Texas and the area Rhode Island. write your answer in scientific notation
Explanation:
The difference is:
[tex]2.69\cdot10^5-1.21\cdot10^3[/tex]To solve this we need the exponent of 10 be the same for both terms of the substraction. It is better is we change the exponent of the area of Texas, by moving the decimal point two places to the right:
[tex]2.69\cdot10^5-1.21\cdot10^3=269\cdot10^3-1.21\cdot10^3[/tex]Now we can substract the numbers and leave the 10³ out:
[tex]269\cdot10^3-1.21\cdot10^3=(269-1.21)\cdot10^3=267.79\cdot10^3[/tex]Scientific notation has always only one place with a number before the decimal point. Therefore 267.79x10³ is not in scientific notation, we have to move the decimal point two places to the left and add 2 to the exponent of 10:
Answer:
The difference is 2.6779 x 10⁵ square miles
Ivanna is on her way home in her car. Her drive is 12 miles long. She has finished one-fourth of the drive so far. How far has she driven?miles
Fractions
Ivanna has to drive 12 miles. She has already driven 1/4 so far.
The distance she has driven is:
[tex]\frac{1}{4}\cdot12=\frac{12}{4}=3[/tex]Ivanna has driven 3 miles so far