Since functions are frequently composed of two smaller functions to create new functions, this definition of function is sometimes used.
What is the domain and range of f/x )= 3x 2?The graph of the function will be a straight line with no discontinuities when the equation f(x) = 3x - 2 is used.
The domain of this expression is all real integers.
The expression f(x) = 3x - 2 has as its domain "x | x is a real number," which can be written as (-,","") for any x > R.
F (x) = 3 x f (x) = 3 x f (x) = 3 x is the given function.
The domain of f f f is R mathbbR R since 3 x 3x 3x is defined for any x R x in mathbbR xR (where R mathbbR R is the set of all real numbers).
Consider the function y = f(x),
which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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Claire drew a model of five tenths explain how Claire could change her model to show how many hundredths are in five tenths
Let x be the number of hundredths in 5/10. Then 100 times x gives 5/10.
[tex]100x=\frac{5}{10}[/tex]Solve for x.
[tex]\begin{gathered} x=\frac{\frac{5}{10}}{100} \\ =0.005 \end{gathered}[/tex]So, there are 0.005 hundredths in 5/10.
Angie is working on solving an exponential equation 23^x=6; however, she’s not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation using the change of base formula.
we have the equation
[tex]23^x=6[/tex]Remember the definition of logarithm
[tex]\begin{gathered} If \\ a^x=b \\ then \\ x=\log_ab \end{gathered}[/tex]Applying the definition of a logarithm to this problem
we have that
[tex]x=\log_{23}6[/tex]Apply change of base formula
Remember that
[tex]\log_bM=\frac{\log_{10}M}{\log_{10}b}=\frac{logM}{logb}[/tex]so
[tex]\log_{23}6=\frac{log6}{log23}[/tex]therefore
The answer is
[tex]x=\frac{log6}{log23}[/tex]Use Sine to find the value of C. B #1-2 39° C a w A А 6 in. C Show your work for full credit.
Tell whether the data represents a linear, an exponential, or a quadratic function. Then, write the function. Picture is attached. I need help!
SOLUTION:
Case: Equations
Method:
The table:
Plotting the points
Studying the points, could either be quadratic or exponential.
We will proceed to test the points but because the increase of the y values as x increases from left to right is not a fine pattern, it will most likely not be exponential.
Next, we test a quadratic model on the graph
[tex]y=ax^2+bx+c[/tex]Final answer:
Quadratic function
[tex]y=x^2+4x-12[/tex]To be linear, you'd need a fixed increase in the y-values for a constant increase in the x-values. As x increases by 1 in each new point, your y-values increase by 1, 3, 5, and 7 respectively. That is not the same increase each time. This is not linear.
To be exponential, you need a fixed percent increase in the y-values between the points. From (-2,-16) to (-1,-15), your increase is 1/16 or 6.25%. From (-1,-15) to (0,-12), your increase is 3/15 or 20%. That is not a constant percent increase.
The only option left is quadratic.
To find the function, start with c = -12, based on the point (0,-12).
This gives you f(x) = ax^2 + bx -12
Next plug in (2,0) into f(x): 0 = 4a + 2b - 12
And plug in (1,-7) into f(x): -7 = a + b -12
You now have two equations with two unknowns.
Solve equation 2 for a:
5-b = a
Substitute that into equation 1
0 = 4(5-b) + 2b - 12
0 = 20 -4b + 2b - 12
-8 = -2b
4 = b
Substitute that b-value into 5-b=a
5 - 4 = a
1 = a
You have your three values and have your function:
f(x) = 1x^2 + 4x - 12 or f(x) = x^2 + 4x - 12
You can confirm that the other points also fit with this function.
4.An object of mass 480 kg is in free fall in a vacuum where there is no air resistance. Determine the acceleration of the object.
The only force is free fall. Mass is not relevant and there is no air resistance
It takes bbb minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 333 same-size bathtubs?
Write your answer as an expression.
Time taken to fill 3 same-size bathtubs is 3b minutes.
Its given in the question that it takes b minutes to fill Sylvia's bathtub with water.
Time taken to fill same-size bathtub as an expression = 3*b
= 3b minutes.
Hence, time takes to fill 3 bathtubs of the same size as of Sylvia's bathtub to fill with water is 3b minutes.
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which is more 95 fluid ounces or 3 quarts
95 fluid ounces or 3 quarts.
To solve htis problem, convert the ounces to quarts and compare the results.
1 ounce ----------------------- 0.03125 quart
95 ounces ------------------- x
x = (95 x 0.03125) / 1
x = 2.97 quarts
2.97 ounces < 3 quarts
Three quarts is more
express in simplest form: sec 0 • cot 0 • sin 0
Note that;
secθ = 1/cosθ cotθ= cosθ/sinθ
substitute into into the expression
[tex]\sec \theta.\cot \theta.\sin \theta=\frac{1}{\cos\theta}.\frac{\cos \theta}{\sin \theta}\text{. sin}\theta[/tex]cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator
[tex]=1[/tex]Sarah has 3 candy bars. She wants to share the candy bars with her friends that everyone gets a serving that is equivalent to 2/5 of a candy bar. To determine how many servings Sarah can make, she dividends 3 divided by 2/5 and get gets 7 1/2
Sarah is unsure this is correct. Use the diagram below and the dropdown menus to help explain if Sarah is correct or not.
For the polynomial f(x) = 2x3 – 9x2 +117 - 20 as x → -0,f(x) > 0 O A. True O B. False
Given the function;
[tex]\begin{gathered} f(x)=2x^3-9x^2+11x-20 \\ \end{gathered}[/tex]The leading exponent is odd and the leading coeeficient is positive, so as x tends to positive infinity, f(x) also tends to positive infinity and as x tends to negative infinity, f(x) also tends to negative infinity.
Thus, the correct answer is FALSE.
the product of two consecutive integers is 90 find the two integers then check your answer?
Let n be the integer. Then, we can write the following equation
[tex]n(n+1)=90[/tex]which is equal to
[tex]n^2+n-90=0[/tex]We can solve this quadratic function by applying the quadratic formula:
[tex]n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where in our case a=1, b=1 and c= -90. By substituting these values into the last formula, we get
[tex]n=\frac{-1\pm\sqrt[]{1^2-4(1)(-90)}}{2(1)}[/tex]then, we have
[tex]\begin{gathered} n=\frac{-1\pm\sqrt[]{1+360}}{2} \\ n=\frac{-1\pm\sqrt[]{361}}{2} \\ n=\frac{-1\pm19}{2} \end{gathered}[/tex]Then, the first solution is
[tex]\begin{gathered} n=\frac{-1+19}{2} \\ n=\frac{18}{2} \\ n=9 \end{gathered}[/tex]and the second solution is
[tex]\begin{gathered} n=\frac{-1-19}{2} \\ n=-\frac{20}{2} \\ n=-10 \end{gathered}[/tex]Then, we have the following solutions:
- Negative integer: n= - 10
- Positive integer: n=9
I need to solve this to get zero can you help?
sin 0 = 26/30
sin 0 = 0.87
0 = 60°
Result 0 = 60°
Can someone help me, please and thanks!
Answer:
wait do you need all the answers to it
A restaurant bill for four people is 122 route leave the $8018 tip what percentage tip is that A restaurant beer for four people is 120 the group me is a tip of $18 what percent of tip is that
The total tip for a four-person meal at a restaurant is $122, people $8018. The percentage of the tip is 22%.
Given that,
The total tip for a four-person meal at a restaurant is $122, people $8018. What proportion of a tip is that? Four restaurant beers cost 120 each, and the group tip is $180.
We have to calculate the how much percentage of a tip is there.
In a variety of situations, such as restaurants, hotels, salons, and other establishments in the service sector, leaving a tip is common. Knowing how to compute a tip and knowing how much to tip is crucial for a variety of reasons, including the fact that many service sector personnel, like waiters, rely heavily on gratuities for the majority of their income. This means that these experts might not be able to support themselves and their families without tips.
Percentage= tip/amount
Percentage= $180/$8018
Percentage= 22%
Therefore, the percentage of the tip is 22%
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How does the graph of the transformed function g(x) = log7(3x-9) compare to the graph of its parent function f(x) = log7x
The correct option is A
The graph has been horizontally stretched, 9 units to the right.
Explanation:Given the function:
[tex]f(x)=\log _7x[/tex]The function:
[tex]f(x)=\log _7(3x-9)[/tex]is a horizontally stretched transformation, 9 units to the right.
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.
How much would the painting company charge to paint a house that needs 20 hours of labor? A house that needs 50 hours?
Draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. Label the two points from the earlier question on your graph.
Answers:
20hr=100$
50hr=2500$
Step-by-step explanation:
1. Do you recommend this person open a credit card account? Why or why not?
2. If they do open the new credit card account, what's one thing this individual should monitor or use caution?
Crystal-
Took time off after high school and during the first year, worked full-time and moved out of her parents house
Is responsible for her own expenses
Took out a large car loan which she quickly fell behind on in payments
Overdrew her checking account numerous times, spending money she didn't have to live a fun, carefree lifestyle
In year two, traded in the car for a much cheaper one, settled her outstanding debt on the car loan, and put herself on a much stricter budget
Now moved back in with her parents and enrolled in community college
Considering applying for her first credit card
1. Crystal can open a new credit card account.
2. If Crystal opens a credit card account, she should keep track of her spending and pay monthly bills on time.
Since Crystal has paid off her debts from the car loan, moved to her parent's home, and enrolled in community college, the chances of her getting into debt are quite low, so she can get a credit card to take care of her expenses as long as she works full time and keeps track of her monthly bills.
If Crystal opens a credit card account, she should keep a spending track and pay her monthly bills on time. She should work full-time and make sure that she pays it off.
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A quadrilateral has two angles that measure 210° and 82º. The other two angles are in aratio of 7:10. What are the measures of those two angles?o andSubmit
Solution
The interior angles of a quadrilateral measure to 360 degrees
Two of them are known and are 210 and 82. They add to 292 degrees.
The other two angles must sum to (360-292)=68 degrees.
They are in a ratio of 7:10
The sum of these two numbers is 17
[tex]\frac{68}{17}=4[/tex][tex]\begin{gathered} 7\times4=28^0 \\ 10\times4=40^0 \end{gathered}[/tex]The other two angles are 28 and 40 degrees respectively.
The sum of all 4 angles is 360 degrees.
The final answer
The other two angles are 28 and 40 degrees respectively.
you are standing on a cliff that is 400 feet tall. You throw your Geometry book off the cliff and it lands 300 feet from the base of the cliff. What is the angle of depression that you are looking down at your book (round to the nearest tenth)
From the question,
Let H be the height of the Cliff
Let Y be the distance of the geometry book from the base of the cliff.
[tex]\begin{gathered} \text{The Height of the Cliff, H=400} \\ \text{The distance at the base, Y = 300} \\ \emptyset\text{ = The angle of depression} \end{gathered}[/tex]Note that the angle of depression is alternate to the angle of elevation'
[tex]undefined[/tex]You are mixing up a recipe that requires 7:3:2:1 flour, water, sugar, butter. When you are done, you should have 39 cups of batter. How many cups of each ingredient do you need?¶ Please show your work. Hint: this is really a total proportion problem and you will want to set up 3 to 4 proportions to find the result. 1 Flour = Water = Sugar = Butter= cups. cups. cups. cups.
The proportion of flour, water, sugar and butter required in the batter are 21, 9, 6 and 3 cups respectively
What is RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this given question, we can find the value of each ingredient;
The cups of flour required is
[tex]7:3:2:1 = 7 + 3 + 2 + 1 = 13\\\frac{7}{13} * 39 = 21 cups[/tex]
The cups of water required is
[tex]\frac{3}{13}*39 = 9 cups[/tex]
The cups of sugar required is
[tex]\frac{2}{13}* 39 = 6 cups\\[/tex]
The cups of butter required is
[tex]\frac{1}{13}*39 = 3 cups[/tex]
The number of cups of flour, water, sugar and butter required are 21, 9, 6 and 3 cups respectively.
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Write an integer for this situation.12°C above zero
12°C above zero -----> means
0°C+12°C=12°C
answer is
the integer is +12If u(x) = −2x² +3 and v(x)=1/x, what is the range of (uv)(x)?
Given:
[tex]\begin{gathered} u(x)=-2x^2+3 \\ v(x)=\frac{1}{x} \end{gathered}[/tex]Required:
To find the range of the function (uv)(x).
Explanation:
We know that
[tex]\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u(\frac{1}{x}) \\ \\ =-2(\frac{1}{x^2})+3 \\ \\ =-\frac{2}{x^2}+3 \end{gathered}[/tex]The horizontal asymptote of this function is at y=3.
So, the range of this function is from
[tex](-\infty,3)[/tex]Final Answer:
The range of (uv)(x) is
[tex](-\infty,3)[/tex]Apply the Pythagorean theorem to find the distance between two points in a coordinator system
Using pythagoras theorem to find the distance between two points in a coordinate:
[tex]\begin{gathered} A=(-5,5) \\ B=(-1,1) \end{gathered}[/tex][tex]\begin{gathered} A=(-5,5)\longrightarrow x_1=-5,y_1=5 \\ B=(-1,1)\longrightarrow x_2=-1,y_2=1 \\ \text{vertical line = opposite =5-1=4} \\ \text{horizontal line = adjacent = -5--1=-5+1=-4} \end{gathered}[/tex]To calculate the distance between the points AB = hypotenuse
[tex]\begin{gathered} \text{Hypotenuse}^2=opposite^2+adjacent^2 \\ AB^2=4^2+(-4)^2 \\ AB^2=16+16 \\ AB^2=32 \\ AB=\sqrt[]{32} \\ AB=4\sqrt[]{2} \end{gathered}[/tex]Therefore the distance between the points in the coordinate system = 4√2
Find the scale factor that was used to changethe Original (O) to the Scaled Image (S).o10"S
QUESTION
Find the scale factor that was used to change (o) to the scale image (s)
[o]10 [s] 4
solution
To find the scale factor, you will simply use the formula:
Scale factor = scaled image / original
Scale factor = 4/10 = 0.4
Answer:
Find the scale factor that was used to change the Original (O) to the Scaled Image (S).o'10"S
The basic formula that is used for calculating the scale factor is, Scale factor = Dimension of the new shape ÷ Dimension of the original shape. In case, if the original figure is scaled up, the formula is written as, Scale factor = Larger figure dimensions ÷ Smaller figure dimensions.
Step-by-step explanation:
Help me pleaseeeeeeeeee
The side lengths of the right triangle in exact form are z = (15√3)/2, x = 15/2, y = (15√3)/4, a = 15/4 and b = 45/4.
How determine the sides of a right triangle using trigonometric ratios?Three out of the six functions used in trigonometry is expressed as;
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
From diagram, we solve for side z of the right triangle.
cosθ = adjacent / hypotenuse
cos( 30° ) = z / 15
Solve for z
z = cos( 30° ) × 15
z = (√3)/2 × 15
z = (15√3)/2
Next solve for side x
sinθ = opposite / hypotenuse
sin( 30° ) = x / 15
x = sin( 30° ) × 15
x = 15/2
Solve for side y
sinθ = opposite / hypotenuse
sin( 60° ) = y / 15/2
y = sin( 60° ) × 15/2
y = (15√3)/4
Solve for side a
cosθ = adjacent / hypotenuse
cos( 60° ) = a / 15/2
a = cos( 60° ) × 15/2
a = 15/4
Solve for side b
b = 15 - a
b = 15 - 15/4
b = 45/4
Therefore the length of side of b is 45/4
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a regular octagon (a polygon with 8 equal sid3s) is inscribed in a circle of radius 19.9cm. find the perimeter of the octagon
Perimeter of an octagon
radius R = 19.9 cm
then To find perimeter
Multiply 8 times lenghts of octagon
with height=
internal angle is= 360/8 = 45°
Now apply rule of Sines
then sin 45/ lside = sin ( 180-45)/2/ radius
Therefore
Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm
Now multiply 8 times this lenght side to find perimeter
8x 15.23 = 121.84 cm
Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scaleA. x=1.86feet, y=4.41 feet and z=65 degreeB.x=4.41 feet, y=1.69 feet, and z=155 degreeC. x=8.58 feet, y=9.46 feet and z=65 degreeD.x=9.46 feet, y=8.58 feet and z=155 degree
Since the triangle is a right-angled triangle, we can use SohCahToa to find x
Using the ratio
[tex]Tan25=\frac{\text{opposite}}{\text{adjacent}}[/tex]Opposite = 4ft
adjacent = x
Substituting these values yield
[tex]\begin{gathered} \text{Tan 25 =}\frac{4}{x} \\ x\text{ =}\frac{4}{\tan 25} \\ x\text{ =8.57}8ft \\ x\approx8.58ft \end{gathered}[/tex]To find Z we use the fact that the sum of angles in a triangle is 180 degrees
so that in triangle XYZ
90 + 25 +Z = 180
Z = 180 - 115
Z= 65 degrees
We will now use Pythagoras theorem to find y
[tex]\begin{gathered} \text{For that} \\ y^2=x^2+4^2 \\ \text{but x = 8.58ft} \\ y^2=8.58^2+4^2 \\ y=\sqrt[]{73.6164\text{ +16}} \\ y\text{ =9.46 ft} \end{gathered}[/tex]
Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C
Essential Question How can you write an algebraic expression?
Answer:
Step-by-step explanation:
In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.
...
Use a ⋅ or × sign if you see words like double, per, or product.
Twice 16 → 2 ⋅ 16.
Five per day → 5 ⋅ d or 5d. ...
The product of 8 and 20 → 8 ⋅ 20.
The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013? Round to the nearest whole number, Show all work for full credit.
We have a initial population P(0) of 3800.
We know that the population is decreasing by 1.4% each year, so the population at year 1 (2009) we will have a population of:
[tex]\begin{gathered} P(1)=P(0)-0.014\cdot P(0) \\ P(1)=(1-0.014)\cdot P(0) \\ P(1)=0.986\cdot P(0) \end{gathered}[/tex]We can generalize this for P(n), where n is the number of years from 2008.
[tex]\begin{gathered} P(2)=0.986\cdot P(1)=0.986\cdot(0.986\cdot P(0))=0.986^2\cdot P(0) \\ \Rightarrow \\ P(n)=0.986^n\cdot P(0)=0.986^n\cdot3800=3800\cdot0.986^n \end{gathered}[/tex]From 2008 to 2013 we have 2013-2008=5 years, so for the year 2013, the value of n is n=5.
Then, the population for 2013 will be P(5) and can be calculated as:
[tex]P(5)=3800\cdot0.986^5\approx3800\cdot0.932\approx3541[/tex]Answer: the predicted population for the year 2013 is 3541.
HELP PLEASEEEEEEEEE!!!!!!!!
Answer:
n∧4 basically its n to the power of 14
Step-by-step explanation:
your work is in the pic below check it out sorry if incorrect have a wonderful day:)
