Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.
What is a domain?The dependent variable and the independent variable are the two types of variables used to define a function.
The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.
Despite x=0, the domain of g(x)=1/x can contain any real number.
The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:
Domain → Function → Range
We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.
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The expression 81√ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
Using perfect squares to solve the expression √81-√100 the distance between home plate and first base is 1 feet
Which numbers are perfect square?The perfect square is the number which can be written as the square of some integer.
A number x is a perfect square if x=y² for some y. or y =√x
Given:
The number of feet between home plate and first base = |√81-√100|
|x| absolute function is put because number of feet need to be a positive number
81 is a perfect square ∵ 81 = 9×9 = 9²
As 81 = 9²
⇒ √81 = √9² = 9
100 is also a perfect square ∵ 100= 10×10 =10²
As 100=10²
⇒ √100= √10² = 10
The expression √81-√100 = 9-10 = -1
The distance between home plate and first base = Number of feet between home plate and first base = |√81-√100| = |-1| = 1 feet
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The complete question is given below:
The expression √81-√100 represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
If f(x)=x²+5 and g(x)=3x, find
a. (f+ g)(x)
b. (f -g)(x)
c. (f . g)(x)
d. (f/g)(x)
a. (f + g)(x)= _____
(Simplify your answer.)
The value of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/(3x)
How to Solve Functions?If we are given an expression of functions, we need to plug in each of the given functions into the equation and solve as you would simplify an algebraic expression.
We have the functions:
f(x) = x² + 5
g(x) = 3x
a. (f + g)(x) means we are going to add the functions f(x) and g(x):
(f + g)(x) = x² + 5 + 3x = x² + 3x + 5
b. (f - g)(x) means we are going to find the difference of the functions f(x) and g(x):
(f - g)(x) = x² + 5 - 3x = x² - 3x + 5
c. (f * g)(x) means we are to find the product of the two functions f(x) and g(x):
(f * g)(x) = (x² + 5)(3x) = 3x³ + 15x
d. (f/g)(x) means we are to find the quotient of the two functions f(x) and g(x):
(f/g)(x) = (x² + 5)/(3x)
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a rectangle solid measures 8cm long by 2cm wide by 2cm high. what is the surface-to-area-to-volume ratio?
The ratio of surface to area to volume of the given rectangle is 5 : 4 : 8
Length of the rectangle , l = 8 cm
Breadth of the rectangle , b = 2 cm
Height of the rectangle , h = 2 cm
Perimeter of the rectangle is
P = 2 (l +b)
= 2(8 + 2)
= 2 (10)
= 20 cm
Therefore , the perimeter of the rectangle is 20 cm
Area of the rectangle is
A = l x b
A = 8 x 2
A = 16 cm²
Therefore , area of the rectangle is 16 cm²
Volume of the rectangle is
V = l x b x h
V = 8 x 2 x 2
V = 8 x 4
V = 32 cm³
Therefore, volume of the rectangle is 32 cm³
Ratio of surface to area to volume = 20 : 16 : 32
= 5 : 4 : 8
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Use the properties of determinants to find the value of the second determinant, given the value of the first.
According to the sum property, we have:
[tex]\begin{gathered} det\begin{bmatrix}{32-s} & {16-t} & {64-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=det\begin{bmatrix}{32} & {16} & {64} \\ {0} & {0} & {0} \\ {0} & {0} & {0}\end{bmatrix}+det\begin{bmatrix}{-s} & {-t} & {-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix} \\ det\begin{bmatrix}{32} & {16} & {64} \\ {0} & {0} & {0} \\ {0} & {0} & {0}\end{bmatrix}=0 \\ det\begin{bmatrix}{-s} & {-t} & {-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-det\begin{bmatrix}{s} & {t} & {u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-3 \\ \therefore det\begin{bmatrix}32{-s} & {16-t} & {64-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-3 \end{gathered}[/tex]In which quadrant does -336 lie?A. IVOB.IOC. IID. IIIReset Selection
Recall that an angle Θ:
1) Lies in quadrant 1 if Θ is coterminal to an angle between 0 and 90 degrees.
2) Lies in quadrant 2 if Θ is coterminal to an angle between 90 and 180 degrees.
3) Lies in quadrant 3 if Θ is coterminal to an angle between 180 and 270 degrees.
4) Lies in quadrant 4 if Θ is coterminal to an angle between 270 degrees and 360 degrees.
Now, recall that Θ and Θ+360 degrees are coterminal angles.
Notice that:
[tex]-336^{\circ}+360^{\circ}=24^{\circ}.[/tex]Since:
[tex]0^{\circ}<24^{\circ}<90^{\circ},[/tex]and -336 degrees is coterminal to 24 degrees, then -336 degrees lies on quadrant I.
Answer: Option B.
1. Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: -foot, -foot, and foot. Andre stacks two-foot blocks, two-foot blocks, and two-foot blocks to create a tower. What will the height of the tower be in foot? Explain or show how you know.
Height of the tower = 1.75 ft
Explanations:The thickness of the blocks are 1/2 ft, 1/4 ft, and 1/8 ft
Two 1/2 ft blocks will have a thickness of:
2 x 1/2 = 1 ft
Two 1/4 ft blocks will have a thickness of:
2 x 1/4 = 1/2 ft
Two 1/8 ft blocks will have a thickness of:
2 x 1/8 = 1/4 ft
The height of the tower = 1 + 1/2 + 1/4
The height of the tower = (4 + 2 + 1) / 4
The height of the tower = 7/4 = 1.75 ft
Question 5
Use technology to find the line of best fit for the following data.
(1,4), (2, 3), (3,5), (4,4), (5,5)
When the equation of the line is in the form y=mx+b, what is the value of **m**?
Enter your answer as a decimal rounded to the nearest tenths place, like this: 42.5
Click on the following link to use the GeoGebra graphing calculator .
The value of b is equal to 0 in slope-intercept form equation .
What is slope-intercept form?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form.The data points are:
(1,4), (2, 3), (3,5), (4,4), (5,5)
The equation of best fit line in the form of and then find the value of b.
The general form of best fit line is
y = mx + c ...(i)
Where, m is the slope of best fit line and b is the y-intercept of the line.
Using the graphing calculator, we get the equation for the best fit line and the equation is
y = x ...(ii)
On comparing (i) and (ii), we get
c = 0
Therefore, the value of m is equal to 0
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the position from its starting point of a small plane preparing for takeoff is given by x(t)=1.64t^2 meters…
Given:
The position of the small plane is given by,
[tex]x(t)=1.64t^2[/tex]Explanation:
The accelration of plane can be obtained by double derivative of the position function.
Determine the double derivative of the position function.
[tex]\begin{gathered} \frac{d^2}{dt^2}x(t)=\frac{d^2}{dt^2}(1.64t^2) \\ a(t)=1.64\cdot\frac{d}{dt}(2t) \\ =3.28\cdot1 \\ =3.28 \end{gathered}[/tex]So acceleration of the small plane is 3.28 m/s^2
Answer: 3.28
Find the exact value of cos 4pi/3 in simplest form with a rational denominator?
The given expression is
[tex]cos\frac{4\pi}{3}[/tex]Since the angle is greater than pi, then it lies in the 3rd quadrant
Since in the 3rd quadrant the value of cosine is negative, then we will use the expression
[tex]cos\frac{4\pi}{3}=cos(\pi+\frac{\pi}{3})=-cos\frac{\pi}{3}[/tex]Since the value of cos(pi/3) = 1/2, then
[tex]\begin{gathered} cos\frac{\pi}{3}=\frac{1}{2} \\ \\ cos\frac{4\pi}{3}=-cos\frac{\pi}{3}=-\frac{1}{2} \end{gathered}[/tex]The answer is -1/2
sales tax is caculated as a percantage of the sales price . if sales tax 5% what is the sales tax on clothing that cost 170
The school is having a bake sale and the pep squad is selling cookies. On one ticket they sold two chocolate chip cookies and five oatmeal cookies for $23. On another ticket they sold three chocolate chip cookies and three oatmeal cookies for $21.
Which system of equations below can be used to determine the price of a chocolate chip cookie and the price of an oatmeal cookie?
Let x represent the cost of a chocolate chip cookie, and let y represent the cost of an oatmeal cookie.
A.
2x + 3y = 23
5x + 3y = 21
B.
2x + 3x = 20
5y + 3y = 24
C.
5x + 8y = 44
5x - 8y = 44
D.
2x + 5y = 23
3x + 3y = 21
Answer:
[tex]\begin{aligned}\textsf{D.}\quad 2x + 5y &= 23\\3x + 3y &= 21\end{aligned}[/tex]
Step-by-step explanation:
Definition of variables:
Let x represent the cost of a chocolate chip cookieLet y represent the cost of an oatmeal cookie.Given information:
2 chocolate chip cookies and 5 oatmeal cookies = $23. 3 chocolate chip cookies and 3 oatmeal cookies = $21.Therefore, the system of equations that can be used to determine the price of a chocolate chip cookie and the price of an oatmeal cookie is:
[tex]\large\boxed{\begin{aligned}2x + 5y &= 23\\3x + 3y&= 21\end{aligned}}[/tex]
What is the length of a rectangle with width 10 in. and area 97 in.²?
Answer:
9.7
Step-by-step explanation:
97/10= 9.7
formula for rectangle= length x width
area divided by width= 97/10
97/10=9.7
length=9.7
9.7x10=97
Michael has 2 1/2 cups of orange juice in a jar he pours the juice into glasses that each hold 3/4 cups how many glasses can he fill?
Number of glasses Michael can fill is [tex]3\frac{1}{3}[/tex] or 3.33 cups
How to find amount of 1 when amount of many are given ?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. Of course, in order to be fair, you should always pay each person the same amount.
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Given: Number of cups Michael have = 2 1/2 cups = 2 + 0.5 = 2.5 cups
To find : How many glasses he can fill .
So since each glass holds 3/4 cups = 0.75
Thus number of glasses which can be filled = 2.5 / 0.75
= 3.33 or [tex]3\frac{1}{3}[/tex]
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Evaluate the expression3y if x = 4 and y = -2
Answer:
[tex]-6[/tex]
Step-by-step explanation:
[tex]3y=3(-2)=-6[/tex]
Using a trigonometric ratio to find an angle measure in a right
ANSWER :
x = 33.6 degrees
EXPLANATION :
Recall that the cosine function is :
[tex]\cos\theta=\frac{\text{ adjacent}}{\text{ hypotenuse}}[/tex]From the problem, the adjacent to the angle x is 15 and the hypotenuse is 18.
Using the formula above :
[tex]\begin{gathered} \cos x=\frac{15}{18} \\ \\ \text{ take the arccos :} \\ x=\arccos(\frac{15}{18}) \\ \\ x=33.56\sim33.6 \end{gathered}[/tex]is [tex]1.2345 \: repeating \: \times \sqrt{4} [/tex]irrational or rational?
If we can write this expression as a fraction, then this will be rational. Otherwise, irrational.
First, let's write the repeating decimal as fraction. Excluding the 1 point to the left of the decimal.
We have:
0.234523452345...
We can write it as:
[tex]\frac{2345}{9999}[/tex]Tagging along the "1", we have:
[tex]1\frac{2345}{9999}[/tex]Then, we have square root of 4, which is "2".
If we multiply the fraction shown above by 2, we will definitely have a fraction.
That will be a rational number.
Please help. Need help bad don’t know what to do
The combination that gives the most profit exists 12nVIP rings and 12 SST rings (900 day).
What is meant by linear programming?When a linear function is exposed to various constraints, it is maximized or reduced using the mathematical modeling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
R = 40 V + 35 S
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
Amount of rings (less or equal than 24 a day):
V + S ≤ 24
Amount of man-hours (up to 60 man-hours per day):
3 V + 2 S ≤ 60
The number of rings of each type is a positive integer:
V, S ≥ 0
This restrictions can be graphed and then limit the feasible region. The graph is attached.
In which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V = 0 and S = 24
R = 40 V + 35 S = 40 × 0+35 × 24 = 0 + 840
R = 840
Point 2: V = 12 and S = 12
R = 40 V + 35 S = 40 × 12 + 35 × 12 = 480 + 420
R = 900
Point 3: V = 20 and S = 0
R = 40 V + 35 S = 40 × 20+35 × 0 = 800 + 0
R = 800
The combination that gives the most profit is 12nVIP rings and 12 SST rings (900 day).
The complete question is:
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
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2.85-6.2 divided by 2 square
Answer:
142.5 i think that answer
If you save $750 monthly for the next 30 years, how much would your retirement fund be worth, assuming that you can earn 3%, compounded monthly?
The amount compounded monthly is 1092.63.
The expression for calculating the amount compounded monthly is given by the formula
CI = P[tex](1 + (\frac{r}{12} ) )^{12t}[/tex] - P
where P is the principal amount, r is the interest rate in decimal form, and t is the time.
The Data and information which are provided in the question are,
The principle amount, P = 750
The rate of interest, R = 3%, so 3÷100 = 0.03
The period, t = 30.
By substituting the data in the equation, the equation becomes
CI = 750×[tex](\frac{1+0.03}{12}) ^{360}[/tex] - 750.
By solving the above equation, the result is obtained as CI = 1092.63
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Which is not an example of U.S. foreign policy?
President Taft turning away from military intimidation and toward monetary incentives with other nations
President Franklin Roosevelt establishing the Lend-Lease program to aid Britain during World War II
President Lyndon Johnson asking Congress to pass the Civil Rights Act of 1964
President Theodore Roosevelt sending U.S. warships to Asia to display their power
Answer:
The correct answer is D. President Lyndon Johnson asking Congress to pass the Civil Rights Act of 1964
Step-by-step explanation:
For the following function, determine whether the function is one-to-one.{(4,9), (3,6), ( - 8,11), (1, -17)}Is the function a one-to-oneYES OR NO
Answer
The function is one-to-one.
Check Explanation.
Explanation
Like the name suggests, one-to-one functions have each input variable having exactly one unique output. That is, multiple inputs never give the same output.
Also noting that the data in the function are written as
(x, y) OR (Input, Output)
For this question, we see that all of the input variables are different and all have unique output variables.
Hence, this function is a one-to-one function.
Hope this Helps!!!
*GEOMETRY*please help me find the surface area of the solid along with the volume of it step by step!
Surface area of the solid = 7.1781 in²
Volume of the solid = 0.804 in³
Explanation:
Surface area of the solid = surface area of the square prism - 2(base of the cylinder) + lateral surface of cylinder
surface area of a square prism = 2(lw + lh + wh)
l = length = 1 in
w = length = 1 in
h = height = 1 in
[tex]\begin{gathered} \text{Surface area = 2(1}\times1\text{ + 1}\times1\text{ + 1}\times1) \\ \text{Surface area = 2(1 + 1 + 1) = 2(3)} \\ \text{Surface area = 6 in }^2 \end{gathered}[/tex]using the value π as it is on the calculator
Base area of a cylinder = πr²
2(Base area of cylinder) = 2πr² = 2π(0.25)² = 0.3927
Lateral surface area = 2πrh = 2π(0.25)(1) = 1.5708
Surface area of the solid = 6 - 0.3927 + 1.5708
Surface area of the solid = 7.178 in²
Volume of the solid = Volume of the square prism - volume of the cylinder
Volume of square prism = length × width × height
length = 1 in, width = 1 in, height = 1 in
Volume of the solid = 1 in × 1 in × 1 in = 1 in³
Volume of a cylinder = πr²h
Volume of the cylinder = π × 0.25 × 0.25 × 1 = 0.196
Volume of the solid = 1 - 0.196
Volume of the solid = 0.804 in³
Aidan buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.
What is the probability that Aidan reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Write your answer as a percent. Round to the nearest tenth of a percent.
Answer- 62%
Step-by-step explanation
5+5+8+8= 26 There are 8 peanut butter cookies,so 8/26 is the chance we will get a peanut butter cookie. In percentage form that is 0.307692308 or 30% chance that a peanut butter cookie will be selected. This also means that since there are 8 oatmeal there is a 30% percent chance for those as well.5/26 is 0.192307692, which is almost 20 percent. 30 +30 +20+20 is 100 percent. Now that we know there is a 30 percent for both peanut butter and oatmeal, we would have to have the percent of 8+8/26. 16/26 is 0.615384615. This means that the chance of picking a peanut butter then oatmeal cookie, back-to-back would be around 62%
Hope this helps good luck.
at a shoe store shoes are one third of their original price the sale price of a pair of gym shoes is $ 15.50 write and solve an equation that could be used to find the original cost of the shoes
We will write an equation to find the original cost as follows:
[tex]15.50=\frac{x}{3}[/tex]And the general equation will be:
[tex]y=\frac{x}{3}[/tex]Here y is the price after discount and x the price without discount.
****
Since we have that the price is a third of the original, then the discounted price is found by multiplying the original value of the shoe times 1/3. After this operation takes place, the value we will obtain is the discounted prices [1/3 their original value].
Skill BuildeWatch the video and then solve the problem given below.Click here to watch the videoMargaret drove to a business appointment at 40 mph. Her average speed on the return trip was 30 mph. The return trip took 1/3 hour longer because of heavy traffic. How far did she travel to theappointment?She traveled milesEnter your answer in the answer box and then click Check Answer.All parts showing
Let's call the distance to the appointment 'd', and the time of the first travel (going to the appointment) 't'.
Now, we need to use the formula for the distance:
[tex]\text{distance}=\text{average speed }\cdot\text{ time}[/tex]For the first part of the trip, we have the distance 'd', the average speed is 40 mph and the time is 't':
[tex]d=40\cdot t[/tex]Then, for the second part of the trip (return trip), the distance is also 'd', the average speed is 30 mph, and the time is 't + 1/3', because she took 1/3 hour longer than the first trip.
So we have that:
[tex]d=30\cdot(t+\frac{1}{3})=30t+10[/tex]Now, we just need to equate both 'd':
[tex]\begin{gathered} 40t=30t+10 \\ 10t=10 \\ t=1 \end{gathered}[/tex]So the time 't' is 1 hour. Now we can use that to find the distance 'd':
[tex]d=40t=40\cdot1=40[/tex]So the distance to the appointment is 40 miles.
Ten members of the Science Club went to a history muesum. It cost $7.25 for each member of the club. If 90 members went to the muesum, how much would the total cost?
Answer: $652.5
Step-by-step explanation:
If it costs $7.25 for each member of the club, we can multiply this unit value ($7.25) by 90 to find the total cost.
$7.25 * 90 = $652.5
GIVEN: AD is angle bisector of
Given:
AD is angle bisector of angle BAC.
AB = AC.
The objective is to prove BD = DC.
Step 1:
Statement: AD is angle bisector of angle BAC.
Reason: Given.
Step 2:
Statement:
[tex]\angle BAD=\angle\text{DAC}[/tex]Reason: Definition of angle bisector.
Step 3:
Statement:
[tex]AB\cong AC[/tex]Reason: Given
Step 4:
Statement: AD = AD.
Reason: Reflexive.
Step 5:
Statement:
[tex]\Delta BAD\text{ }\cong\text{ }\Delta CAD[/tex]Reason: By SAS criteria.
Step 6:
Statement:
[tex]BD\cong DC[/tex]Reason: By Corresponding parts of congruent triangles (CPCT).
Hence, the required results are obtained.
function c gives the cost,in dollars, of buying n apples. what does each expression or equation represent in this stiuation1.C(5)=4.502C(2)
1)
From the function given, the cost of 5 apples is $4.50
5 apples cost $4.50
A model of a dinosaur was created using a scale factor of 1:20. The model is 3.75 feet long. How long is the actual dinosaur in feet?
ANSWER
75 feet
EXPLANATION
The scale factor means that the ratio of the model to the actual size of the dinosaur is 1 : 20.
The model is 3.75 feet long.
Let the actual length of the dinosaur be x.
So, it means that:
[tex]\begin{gathered} \frac{1}{20}\text{ = }\frac{3.75}{x} \\ \text{Cross}-\text{ multiply:} \\ 1\cdot\text{ x = 20 }\cdot\text{ 3.75} \\ x\text{ = 75 feet} \end{gathered}[/tex]The actual length of the dinosaur is 75 feet.
Please help!! Will give brainliest
f(x)=3/[tex]4\sqrt{x}[/tex] evaluate function f ' (3) = [tex]-1/4.3 root 1/4[/tex]
f(x)=3/[tex]4\sqrt{x}[/tex] evaluate function f ' (7)= [tex]-3/4.7root5/4[/tex]
How is a function evaluated?
Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function. Simply swap out all instances of x with the value of x to do this. For instance, x has been given the value 4 if we are asked to evaluate f(4).
root function illustration
F(x)=x f (x) = x is the square root function. The formula for the cube root is f(x)=3xf(x)=x3. A function that is defined by a radical expression is known as a radical function.
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