find the domain of the following equationsfor the domain I got [tex]x \ \textgreater \ 0[/tex]and x cannot be equal to one but it said my answers were wrong
![Find The Domain Of The Following Equationsfor The Domain I Got [tex]x \ \textgreater \ 0[/tex]and X Cannot](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/zy5eFTpCBPy7F1XNqJGj2zM4oEKaepPB.jpeg)
Answers
To find the domain of a function, look for the restrictions over the functions involved in it.
[tex]\text{Let }f(x)=\log _3(\sqrt[]{x}+1)[/tex]The log functions are defined whenever their argument is greater than 0. This means:
[tex]\sqrt[]{x}+1>0[/tex]Since 1>0 and the square root of x is always greater than or equal to 0, then this does not restrict the domain of the function.
Nevertheless, the square root of x requires that:
[tex]x\ge0[/tex]This is the only restriction over the variable x.
Therefore, the domain of the function, is:
[tex]0\leq x[/tex]Next, solve the equation:
[tex]\log _3(\sqrt[]{x}+1)=1[/tex]Notice that given this equation, then 3 to the power of each side of the equation should be equal:
[tex]3^{\log _3(\sqrt[]{x}+1)}=3^1[/tex]Use the fact that:
[tex]3^{\log _3(a)}=a[/tex]to simplify the equation:
[tex]\begin{gathered} 3^{\log _3(\sqrt[]{x}+1)}=3^1 \\ \Rightarrow \\ \sqrt[]{x}+1=3^1 \end{gathered}[/tex]Simplify the power 3^1:
[tex]\sqrt[]{x}+1=3[/tex]Substract 1 from both sides of the equation:
[tex]\sqrt[]{x}=2[/tex]Square both sides of the equation:
[tex](\sqrt[]{x})^2=2^2[/tex]Simplify the powers:
[tex]x=4[/tex]Check the answer by plugging in x=4 into the equation:
[tex]\begin{gathered} \log _3(\sqrt[]{x}+1)=1 \\ \Rightarrow \\ \log _3(\sqrt[]{4}+1)=1 \\ \Rightarrow \\ \log _3(2+1)=1 \\ \Rightarrow \\ \log _3(3)=1 \\ \Rightarrow \\ 1=1 \end{gathered}[/tex]Since we got an identity, the answer x=4 is correct.
Related Questions
3 8. A toy box is shaped like a cylinder. The diameter is 4 feet and the height of the container is 2 feet. Which measurement is closest to the volume of the toy box in cubic feet? A. 153.5 B. 12.22 C. 10.49 D. 38.37
Answers
Step 1
Write out the formula for volume of cylinder
[tex]\begin{gathered} \text{Volume of cylinder = }\pi r^2h \\ \end{gathered}[/tex]r = radius
h = height
pi = 3.142
Step 2
write out the parameters
diameter = 4 feet
radius = diameter/2 = 4/2 = 2 feet
height = 2 feet
Step 3
input values in the foemula
[tex]\begin{gathered} \text{Volume of a cylinder = }\pi r^2h \\ =\text{ 3.142 }\times2^2\text{ }\times\text{ 2} \\ =\text{ 3.142 x 4 x 2} \\ =\text{ 25.136} \end{gathered}[/tex]Haseem was given the following enlargement. A triangle has a side with length 22.5 centimeters.What is the perimeter, in centimeters, of the enlarged triangle?
Answers
First, let's calculate the perimeter of the smaller triangle:
[tex]P=3+5+6=14\text{ cm}[/tex]Now, let's calculate the ratio between the corresponding sides of the triangles:
[tex]r=\frac{22.5}{5}=4.5[/tex]Then, to find the perimeter of the bigger triangle, we can multiply the perimeter of the smaller triangle by the ratio:
[tex]\begin{gathered} P=14\cdot4.5\\ \\ P=63\text{ cm} \end{gathered}[/tex]Therefore the correct option is the fourth one.
Problem P14-11, p. 638: Stock dividend: Investor Sarah Warren currently holds 400 shares of Nutri-Foods. The firm has 40,000 shares outstanding. The firm most recently had earnings available for common stockholders of $80,000, and its stock has been selling for $22 per share. The firm intends to retain its earnings and pay a 10% stock dividend. d. At what market price would you expect the stock to sell after the stock dividend?
Answers
First, consider there are 40,000 shares with a proce $22 each.
The price of all shares is:
22 x 40,000 = 880,000
Next, consider that stock dividend of %10 is payed:
880,000 - 0.1x880,000 = 792,000
THe price per share is:
792,000/40,000 = 19.8
Hence, the market price would be $19.8
find the equation with enfpoints
Answers
the radius is the distance from the centre to either of the 2 given points
Let (x1, y1) = (-4,1) and (x2,y2) = (4,-5) (the given points)
then:
[tex]r\text{ = d = }\sqrt[]{(4-(-4))^2+(-5-1)^2}\text{ = }\sqrt[]{(8)^2+(-6)^2\text{ = }}\text{ 10}[/tex]then, take the equation of the circle is:
[tex](x-0)^2+(y+2)^2\text{ = 10}[/tex]that is:
[tex](x)^2+(y+2)^2\text{ = 10}[/tex]Given that angle 3 equals 3x and angle 6 equals 6x, determine the value for x
Answers
When two lines are crossed by another line (like in this case), the angles matching corners are called corresponding angles:
Now, since angle 3 and angle 6 are consecutive interior angles, we have the following:
[tex]\begin{gathered} 3x+6x=180 \\ \Rightarrow9x=180 \\ \Rightarrow x=\frac{180}{9}=20 \\ x=20 \end{gathered}[/tex]Therefore, x=20
Malorie earned $240 in 6 hours. How much will she earn if she works for 8 hours at the same rateA.246B.280C.320D.380
Answers
Using proportion,
let x be the amount she earn in 8 hours
$240 = 6 hours
x = 8 hours
cross - multiply
6x = 240(8)
6x = 1920
Divide both -side by 6
x = $320
What is the volume of this container? 2 in. 648 in3 6 in. 504 in3 6 in. 72 in 8 in. 3 576 in 12 in.
Answers
ok
Volume of the container = 12 x 8 x 6
= 576 in^3
Volume of the hole = 6 x 6 x 2
= 72 in^3
Real volume = 576 - 72
= 504 in^3
A jar contains 2 green marbles, 4 blue marbles, and 3 yellow marbles. A marble is chosen at random from the jar and replaced. Find the possibility that the first marble is green and the second is yellow.
Answers
Answer:
2/27
Explanation:
• Number of green marbles = 2
,• Number of blue marbles = 4
,• Number of yellow marbles = 3
Total = 2+4+3 =9
• Probability of choosing a green marble = 2/9
,• Probability of choosing a yellow marble = 3/9
Therefore, the possibility that the first marble is green and the second is yellow is:
[tex]\begin{gathered} =\frac{2}{9}\times\frac{3}{9} \\ =\frac{2}{27} \end{gathered}[/tex]solve each system of the equation by elimination method. -4x+5y=122x+5y=-6
Answers
(-3,0)
1) Let's solve that system, using this method. We need to pick one variable first.
-4x+5y=12
2x+5y=-6
2) Let's eliminate x, multiplying the 2nd equation by 2
-4x+5y=12
4x+10y=-12 Adding both equations simultaneously
---------------------------
15y =0
y= 0
3) Plug y=0 into one of those equations, usually the simplest.
2x+5y=-6
2x+5(0)=-6
2x = -6 Dividing both sides by 2
x= -3
Hence, the answer is (-3,0)
Which one of the following statements is false?Bias can be reduced by taking a larger sample.O A statistic is used to estimate a parameter.Response errors cannot be completely eliminated, even if a census is taken.O As the sample size increases, the margin of error decreases.O If several high school students are surveyed about their favorite sport, the individuals would be the students.
Answers
Bias can be reduced by taking a larger sample is false because an increase in sample tends to reduce the sampling error but a large sample size cannot correct for the methodological problems (undercover, nonresponse bias, etc.) that produce survey bias.
19/27 what is equivalent to this
Answers
The decimal form of 19/27 is a repeating decimal where the digits 703 keeps repeating indefinitely.
the product of two and the difference between eleven and a number
Answers
I need to know the answer to this on a graph
Answers
Graph the linear equation using the slope and y-intercept:
[tex]y=2x+3[/tex]Using a desmos graph to show the equation
Simplify(x^10)/(x^5)
Answers
racheal recorded the flight of a red bird and a blue bird the red bird flew to 2km less than four times as far as the blue bird and the difference between their flight 298 km how far did the red bird fly
Answers
racheal recorded the flight of a red bird and a blue bird
The red bird flew to 2km less than four times as far as the blue bird
Distance travel by Red Bird - 2 = 4(Distance travel by Blue Bird )
Let the distance travel by blue bird is x
Then distance travel by red bird is :
Distance travel by Red Bird = 4(Distance travel by Blue Bird ) + 2
Distance travel by Red Bird = 4x + 2
The difference between their flight 298
Distance travel by Blue Bird - Distance travel by Red Bird = 298
4x + 2 - x = 298
3x + 2 = 298
3x = 298 - 2
3x = 296
x = 296/3
x = 98.66 km
Since, x express the distance travel by blue bird flight
Distance travel by Blue bird flight is 98.66 km
Distance travel y red bird flight = 4x + 2
Substitute the value of x = 98.66
Distance travel y red bird flight = 4x + 2
Distance travel y red bird flight = 4(98.66) + 2
Distance travel y red bird flight = 396.64 km
So, Red Bird flight cover the distance of 396.64 km
Answer : Red Bird flight cover the distance of 396.64 km
Evaluate the expression 2bc2 for b = 1.5 and c = 5. 0 O 225 O 75 O 30 O O 15
Answers
b= 1.5
c= 5
To evaluate 2bc^2
we substitute b = 1.5 and c = 5 into the equation
[tex]\begin{gathered} 2bc^2 \\ \Rightarrow2x1.5x5^2 \\ \Rightarrow\text{ 2 x 1.5 x 25} \\ \Rightarrow75 \end{gathered}[/tex]The answer = 75
For which values in the domain is the value of f(x) shown on the graph? select all the apply.A). -1.5B). -2 C). 8D). -21E). 14F). 6
Answers
The graph shows all the values of x from -10 to 10. Then the values that apply are:
-1.5, -2, 8 and 6.
Therefore the answer is A, B, C and F.
Find the equation of the line tangent to the graph of the function f(x)=2(x+1)^2 at the point (-2, 2).
Answers
SOLUTION
Write out the function
[tex]f(x)=2(x+1)^2[/tex]
To find the equation of the line tangent of this function, we different the function to obtain the slope.
Expanding the function we have
[tex]\begin{gathered} f(x)=2(x+1)^2 \\ \text{expand the function } \\ f(x)=2\lbrack(x+1)(x+1)\rbrack \\ f(x)=2(x^2+2x+1) \\ \text{Hence} \\ f(x)=2x^2+4x+2 \end{gathered}[/tex]Apply the differebtiation rule, we have
[tex]\begin{gathered} f(x)=x^n,f^1(x)=nx^{n-1} \\ f(x)=2x^2+4x+2 \\ f^1(x)=4x+4 \\ \text{ Recall the derivative of a constant is zero} \end{gathered}[/tex]hence, at the point (-2,2), the slope will be
[tex]\begin{gathered} f^1(x)=4x+4 \\ \text{substitute x=-2} \\ \text{slope,m}=4(-2)+4=-8+4=-4 \\ \text{Hence} \\ \text{slope,m}=-4 \end{gathered}[/tex]Then
Apply the Point- slope form for the equation of a line at point (-2,2)
[tex]\begin{gathered} \text{The point slope form is given by } \\ y-y_1=m(x-x_1) \\ \text{Where } \\ m=-4,x_1=-2,y_1=2 \end{gathered}[/tex]
Substituting the value, we have
[tex]\begin{gathered} y-2=-4(x-(-2)) \\ y-2=-4(x+2) \\ \\ \end{gathered}[/tex]Exapand the paranthesis, and write the equation
[tex]\begin{gathered} y-2=-4x-8 \\ \text{Add 2 to both sides } \\ y-2+2=-4x-8+2 \\ y=-4x-6 \end{gathered}[/tex]Hence
The equation of the line of tangent to the function is
y=4x-6 or y+4x= -6
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking. Last week: walked 18 miles in 16 hours This week: d= 2,5h Which statement must be true?
Answers
answer: Last week Rosemary walked at a faster pace.
This because her speed last week was 3 miles per hour and this week was 2.5 miles per hour.
3-2x - 3y = 18у10-10Slope-intercept form:10х-10)
Answers
Answer
The equation in the slope-intercept form is
y = (-2x/3) - 6
Comopa
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, we just need to simplify the equation given in the form we want
-2x - 3y = 18
-3y = 2x + 18
We can then divide through by -3
(-3y/-3) = (2x/-3) + (18/-3)
y = (-2x/3) - 6
Hope this Helps!!!
8-23. Cooper Toy Company has designed a new toy that oscillates up and down and its position can be modeled by a sinusoidal curve. At time t = 5 seconds, the toy is at its maximum height, 18 cm above the ground. Four seconds later, the toy is at its minimum height, 6 cm above the ground. Write an equation to model the height, in centimeters of the toy at any time t, in seconds.
Answers
Given data:
The maximum height of the toy at t=5 seconds is M= 18 cm.
The minimum height of the toy at t=9 seconds is m=6 cm.
The expression for the amplitude is,
[tex]\begin{gathered} A=\frac{M-m}{2} \\ =\frac{18-6}{2} \\ =6 \end{gathered}[/tex]The expression for the mean value is,
[tex]\begin{gathered} x=\frac{18+6}{2} \\ =12 \end{gathered}[/tex]The period of the given curve is,
[tex]\begin{gathered} P=\frac{2\pi}{10} \\ =\frac{\pi}{5} \end{gathered}[/tex]The equation for the given curve is,
[tex]y=6\cos (\frac{\pi}{5}(t-4))+12[/tex]Thus, equation of the given curve is y=6 cos(π(t-4)/5)+12.
A line passes through the point (-3, 2) and has aslope of 1/3. Which of the following points also lieson this line?
Answers
ANSWER :
EXPLANATION :
5. Name the following parts of the expression. 6x2 – 2x + 11A. exponentB. coefficientC. constant
Answers
we have
6x^2-2x+11
The constant is 11
In 6x^2 and -2x ------> 6 and -2 are coefficient
in 6x^2 ------> 2 is a exponent
Which equation, when graphed with the given equation will form a system that has an infinite number of solutions?1. y+ 1 - 3x 2. y=-3x+13. y-3x+14. y-3X=-3
Answers
An equation system has an infinite amount of solution when all the equations that conform it correspond to the same line.
The line shown in the graph has the equation y = 3x - 1
The equation that is equal to the graphed one will be the one that forms a system with an infinite number of solutions.
What you have to do is express each option in slope-intercept form and compare it to the given one:
1.
[tex]\begin{gathered} y+1-3x=0 \\ y+1-1+3x=-1 \\ y+3x-3x=-1-3x \\ y=-3x-1 \end{gathered}[/tex]This option does not form a system with infinite solutions with the given equation.
2.
[tex]y=-3x+1[/tex]This equation has a different slope and y-intercept than the given line, so it does not form a system with infinite solutions with it.
3.
[tex]\begin{gathered} y-3x+1=0 \\ y-3x+3x+1=3x \\ y+1-1=3x-1 \\ y=3x-1 \end{gathered}[/tex]This equation is exactly the same as the one given in the graph, so it will form a system with infinite solutions with it.
4.
[tex]\begin{gathered} y-3x=-3 \\ y-3x+3x=3x-3 \\ y=3x-3 \end{gathered}[/tex]This equation has the same slope but a different y-intercept than the given equation, which means that they are parallel. A system formed between this option and the given line would have no solutions since both lines are parallel.
The only equation which will form a system with infinite equations with the one shown in the graph is number 3. y-3x+1=0
Is this function f(x)=ײ linear, exponential, or neither?
Answers
We will investigate the three different types of functions.
Linear:-
A linear function expresses a relationship between two variables in a straight line fashion. It develops a relation between two variables linearly. It is also categorized as a polynomial off highest order 1. The general form of a linear function is given below:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ Slope / Gradient} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]Hi I need to subtract two fractions or improper fractions I’m not sure I need to subtract 9/14 -3/7
Answers
In order to calculate this subtraction, first we need to put both fractions in the same denominator.
To do so, we need to find the least common multiple (LCM) between 14 and 7.
Since 14 is a multiple of 7, the LCM between 14 and 7 is 14.
So we can calculate the subtraction by doing the following steps:
[tex]\begin{gathered} \frac{9}{14}-\frac{3}{7}\\ \\ =\frac{9}{14}-\frac{3}{7}\cdot\frac{2}{2}\\ \\ =\frac{9}{14}-\frac{6}{14}\\ \\ =\frac{9-6}{14}\\ \\ =\frac{3}{14} \end{gathered}[/tex]Therefore the result is 3/14.
Calculate the constant of proportionality for this table.A. 5/4B. 4/5C. 5 D. 5/2 Write the equation that represents the relationship in the table. Use y and x as variables in your equation.
Answers
The constant of proportionality is the constant value of the ratio of y and x. It is usually denoted as k.
k = y/x
OR
y = kx
From the information given, the value of k is derived as;
[tex]\begin{gathered} k=2\frac{1}{2}\text{ / }\frac{1}{2} \\ k=\frac{5}{2}\times\frac{2}{1} \\ k=5 \end{gathered}[/tex]Where y = kx, then
[tex]y=5x[/tex]That means, the value of y can always be derived by multiplying x by the constant of proportionality
Solve for x.My choice is 1. -1/4=1 or 2. -3/4x =1 or 3. 7=1/4 x or 4. 7=3/4x-1/2x+3=4-1/4x.
Answers
The equation is
[tex]\begin{gathered} -\frac{1}{2}x+3=4-\frac{1}{4}x \\ -\frac{x}{2}+\frac{x}{4}=4-3 \\ \frac{-2x+x}{4}=1 \\ -x=4 \\ x=-4 \end{gathered}[/tex]So x= -4 is the correct answer.
how do you do ratios
Answers
A ratio is how much of one object is there related to the other object. It is a division.
For example:
The ratio between an object A and an object B is:
A/B
The ratio between an object B and an object A is:
B/A
Real example:
Last NFL season
Buffalo Bills 10 wins
New York Jets 7 wins
Ratio between the Bills wins and Jets wins
10/7
Ratio between the Jets wins and Bills wins
7/10
How do you find the area and how much tile he needs ?
Answers
SOLUTION
Let us sketch the composite figure of the floor plan
We are have now divided the floor plan into two sections which consist of two rectangles.
Let us now solve for the area of the floor-plan
The formula for the area of a rectangle is,
[tex]\text{Area}=\text{length}\times width[/tex]Therefore, the area of section A is,
Given
[tex]\begin{gathered} \text{length}=40ft \\ \text{width}=8ft \end{gathered}[/tex]Hence,
[tex]A=40\times8=320ft^2[/tex]Also, the area of section B is
Given
[tex]\begin{gathered} \text{length}=30ft \\ \text{width}=12ft \end{gathered}[/tex]Hence,
[tex]B=30\times12=360ft^2[/tex]Therefore, the amount of the tile needed to cover the floor is the sum of the area of section A and the area section B is
[tex]320ft^2+360ft^2=680ft^2[/tex]Hence, the answer is 680ft² (OPTION A).