Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it. (10 points)
f(x) h(x)
f(x) = −4(x − 8)^2 + 3 graph of negative 1 times the quantity of x minus 3 squared, plus 2
I have attached a picture of the graph below.
Please do not answer if you don't know or are not sure. Thank you.
Answers
Answer:
x = 8 for f(x) and x = 3 for h(x)
Step-by-step explanation:
the axis of symmetry is a vertical line which passes through the vertex of the graph with equation
x = c ( c is the value of the x- coordinate of the vertex )
the equation of a parabola in vertex form is
f(x) = a(x - h )² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = - 4(x - 8)² + 3 ← is in vertex form
with vertex (h, k ) = (8, 3 )
equation of axis of symmetry of f(x) is x = 8
given the graph of h(x) with vertex = (3, 2 ) , then
equation of axis of symmetry of h(x) is x = 3
Related Questions
Find the total surface area of this cone.
Leave your answer in terms of T.
25m
ما
8m
TT
Hint: Surface Area of a Cone = Tre + B
Where l = slant height, and B = area of the base
Enter
Answers
Given
[tex]\begin{gathered} r=8m \\ l=25 \end{gathered}[/tex]The given formula
[tex]\begin{gathered} Surface\text{ area of a cone =}\pi rl+B \\ where\text{ l is slant height} \\ and\text{ B is the area base} \end{gathered}[/tex]The base is circle
[tex]\begin{gathered} Area\text{ of a circle=}\pi r^2 \\ Area\text{ of a circle=}\pi8^2 \\ Area\text{ of a circle =64}\pi \end{gathered}[/tex]Now back to the given formula
[tex]\begin{gathered} Surface\text{ of area of cone=}\pi rl+B \\ B=64\pi \\ l=25 \\ r=8 \\ \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ of area of cone =}\pi\times8\times25+64\pi \\ Surface\text{ofareaofcone=200}\pi\text{+64\pi} \\ Surface\text{ofareaofcone=264\pi} \end{gathered}[/tex]The final answer
[tex]264\pi m^2[/tex]
Playing basketball carries a met value of 8 and you weigh 130lbs or roughly 59kg, approximately how many calories per minute would you burn?.
Answers
The average person burns 575-775 calories per hour in a game of basketball. If they are shooting baskets, they will burn 325-450 calories per hour.
What is Calories?
Calories are a measure of energy. Two main definitions of "calorie" are frequently used due to historical factors. The amount of heat required to increase the temperature of one kilogramme of water by one degree Celsius was the original definition of the large calorie, food calorie, as well as kilogramme calorie (or one kelvin). The amount of heat required to produce the same increase in one gramme of water was known as the small calorie or gramme calorie. As a result, 1000 small calories are equal to 1 large calorie.
How many calories do basketball players burn?
Calories expended per minute equal (MET x body weight in kg x 3.5) / 200
"MET" is a unit of measurement for the energy expended during a given period of physical exercise. The chart above shows the MET for each activity.The energy required to perform a task with a MET of 1 is roughly equivalent to what it would take to sit stationary at room temperature without actively digesting food.When compared to a task with a MET of 1, one with a MET of 2 requires twice as much energy. Ten times as much energy is expended on a work with a MET of 10 as on one with a MET of 1.Hence, the average person burns 575-775 calories per hour in a game of basketball. If they are shooting baskets, they will burn 325-450 calories per hour.
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HELP QUICKLY PLSSSSS
Answers
Answer:
5, 6, 7, 8
Step-by-step explanation:
substitute the values of x from the table into f(x)
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
the values of f(x) are 5, 6, 7, 8
Give the information asked for to each problems Ax Styles Tags Assignments Calendar In each of the following state the Start Value Growth Value 1. C-5f + 32 Calts FE 2. Y= 4000 - 250x 3 х -3 0 6 у -9 3 -1 -5 3 4. x -4 4 8 Olo у 3 15 21 5. A financial account begins with $5900. Each week $300 is deducted. 6. Also point to the start value Apps Hus Type here to search
Answers
Explanation:
1) C = 5/9 f + 32
The start value is the constant = 32.
The start value = 32
Growth value = rate of change
Growth value = 5/9
2) y = 4000 - 250x
The start value is the constant = 4000
The start value = 4000
Help the question is attached
Answers
The correct option will be A that is t=(A-P)/Pr by the simplification of equation, "an equation is a mathematical statement that shows that two mathematical expressions are equal ".
What is equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Some examples of important equations are:
Linear equationsQuadratic equationsCubic equationQuadratic equationsDifferential equationsParametric equationsHere,
A=P+Prt
A-P=Prt
t=(A-P)/Pr
The answer is A, which is t=(A-P)/Pr using the equation's simplified form. An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.
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12 eggs for 3$ how much is the cost of each egg
Answers
Answer:
0.25
Step-by-step explanation:
3 / 12 = 0.25
Answer: 0.60
Step-by-step explanation:
how can I rewrite 0.000000417 in appropiate scientific notation?
Answers
We have the following:
the number of 0 represents the number of the exponent
as is the are zeros to the right, the exponent is negative
[tex]0.000000417=4.17\cdot10^{-7}[/tex]Therefore, the answer is:
[tex]4.17\cdot10^{-7}[/tex]what is seven and fifteen hundredths as a decimal
Answers
Seven hundredths is:
[tex]0.07[/tex]Fifteen hundredths is:
[tex]0.15[/tex]Write the explicit formula for the given arithmetic sequence in explicit form: a(n)=a(1)+d(n-1)
Answers
The daily cost of production in a factory is calculated using f(x)= 400+ 13x where x is thenumber of products made. Which set of numbers best defines the domain of f(x)?A) IntegersB) Positive real numbersC) Positive rational numbersD) Whole numbers
Answers
Recall that the domain of a function is the set of numbers to which the function is defined. That is, if you replace the value of the independant variable (normally represented as x), then the function will give another number as a result.
In this case, we are given the function 400+13x. Since x is the independant variable, to determine the domain we must think on what possible values the variable x can take. Since in this case x represents the number of products made, it is impossible that it takes negative values, since in real life you can't produce negative amounts of products.
So far, we know that x should be greater or equal to zero. Once again, in this context, it doesn't make sense that, for example, x=7.8, since this would mean that 7.8 number of products were made. Since x represents the number of products made, it can only take values as x=0,x=1, x=2, x=3 and so on.
This set receives the name of whole numbers.
Lauren walks 400 m in 125 seconds what is her speed
Answers
Answer:
3.2 m/s
Step-by-step explanation:
If we use the equation distance/time=speed, we can find this pretty quickly.
Our distance is 400 m.
Our time is 125 s.
400/125=
3.2 m/s
Select the correct image.
Which image shows triangle A dilated by a scale factor of 2 with a center at the origin?
Answers
The triangle ABC undergoes a dilation of scale factor 2 centered at the origin.
Dilation About the Origin
Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).
If we are given the dilated point, then we can find the original point by dividing by the scale factor.
Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).
The coordinates of triangle ABC are:
A=(-4/2,4/2) = (-2,2)
B=(-4/2,6/2) = (-2,3)
C=(2/2,4/2) = (1,2)
The coordinates of ABC are respectively (-2,2), (-2,3), and (1,2).
Hence the answer is the triangle ABC undergoes a dilation of scale factor 2 centered at the origin.
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Answer:i'm pretty sure it's the one to the right of the example
Step-by-step explanation:
a homeowner estimates that it will take him 16 days to roof his house. a professional roofer estimates that he could roof the house in 3 days. how long will it take if the homeowner helps the roofer?
Answers
If the homeowner helps the professional roofer they will do the job in 2.53 days
How to determine how long it takes to do the roofing jobLet the number of days to complete the job be x
The rate at which the homeowner will roof is x / 16
The rate at which the professional roofer will roof is x / 3
Adding the rates together gives
x / 16 + x / 3
19x / 48
The rate it will take them both to finish the job is
= 48 / 19
= 2.53 days
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Which point shown on the grid is located at (-3,6)
Answers
If the coordinates of the points are (x, y), then the point lies in the 1st quadrant
If the coordinates of the point are (-x, y), then the point lies in the 2nd quadrant
If the coordinates of the point are (-x, -y), then the point lies in the 3rd quadrant
If the coordinates of the point are (x, -y), then it lies in the 4th quadrant
Since the given point is (-3, 6), then it should be in the 2nd quadrant
Since point B is in the 2nd quadrant, then
The answer is B the third answer
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The domain for f(x) and g(x) is the set of all real numbers. let f(x)=3x+5 and g(x)=x^2. find f(x) +g(x)
Answers
1) In this question, we are dealing algebra of functions. So, let's add them up.
2)
[tex]\begin{gathered} f(x)=3x+5 \\ g(x)=x^2 \\ f(x)+g(x)=3x+5+x^2 \\ (f+g)(x)=x^2+3x+5 \end{gathered}[/tex]Note that we wrote it in the standard form.
2) Hence, the answer is:
[tex](f+g)(x)=x^{2}+3x+5[/tex]Consider the probability model with sample space (A,B,C} and P(A)=0.1, P(B)=0.1, P(C)=0.8.Then
Answers
The sum of all the possible events is 1, which means that all the events are independent of the others, in that case
P(A or C) = P(A)+P(C) = 0.1 + 0.8 = 0.9
P(B and C) = P(B)*P(C) = 0.1 * 0.8 = 0.08
(24x3 − 14x2 + 20x + 6) ÷ (4x2 − 3x + 5) = Q +
R
4x2 − 3x + 5
Q =
R =
Answers
Answer:
Step-by-step explanation:
Dividend = 24x³ - 14x² + 20x + 6
ctg 30° + 2 csc 60° - 3 cos 30°
Answers
The value of the expression ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6
The expression is calculated using trignometic values
ctg 30° + 2 csc 60° - 3 cos 30°
1/tan 30 + 2/sin 60 - 3 cos 30
1/(1/√3) + 2/(√3/2) - 3 (√3/2)
√3 + 4/√3 - 3√3/2
LCM is 2√3
(√3(2√3) + 2(4) - 3√3(√3) )/2√3
(6 + 8 - 9)/2√3
5/2√3
5√3/6
The value of the expression ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6
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Erika sells bags of fresh coffee beans at a local food co-op. She created the table below that shows her last four sales. Based on Erika's data, what was the cost per pound of coffee?
Answers
By using division of decimal numbers, it is obtained that cost of 1 pound of coffee is $8.99
What is decimal number and division?
Decimal numbers are those numbers which consist of an integer part and a fractional part.
Decimal are of two types-
Terminating decimals are those decimals which has finite number of figures after decimal point
Non terminating decimals are those decimals which has infinite number of figures after decimal point.
Division is the process by which value of single unit can be calculated from the value of multiple unit
The number which is divided is the dividend, the number by which dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula in division
Divisor x Quotient + Remainder = Dividend
Here, division of decimal will be used
Cost of 5 pounds of coffee = $44.95
Cost of 1 pound of coffee = $[tex]\frac{44.95}{5}\\[/tex]
= $8.99
Cost of 8 pounds of coffee = $71.92
Cost of 1 pound of coffee = $[tex]\frac{71.92}{8}\\[/tex]
= $8.99
Cost of 14 pounds of coffee = $125.86
Cost of 1 pound of coffee = $[tex]\frac{125.86}{14}\\[/tex]
= $8.99
Cost of 20 pounds of coffee = $179.80
Cost of 1 pound of coffee = $[tex]\frac{179.80}{20}\\[/tex]
= $8.99
So cost of 1 pound of coffee = 8.99
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If EG = 10 and EF = 4, thenFG = [?]
Answers
In the exercise we first formulate and then replace values to find an unknown;
It is important to first look at what data the exercise gives us and then place them in the correct way, it must coincide with what the graph shows us.
people with type o-negative blood are universal donors. that is, any patient can receive a transfusion of o-negative blood. only 7.2% of the american population have o-negative blood. if we choose 10 americans at random who gave blood, what is the probability that at least 1 of them is a universal donor?
Answers
The probability that any given person is a universal donor is 7.2%. This means that the probability that a person is not a universal donor is 92.8%.This indicates that there is a 0.65 percent chance that at least 1 out of every 10 randomly selected individuals is a universal donor.
Now, if we choose 10 people at random, we can use the binomial distribution to calculate the probability that at least 1 of them is a universal donor. The binomial distribution tells us that the probability of getting exactly k successes in n trials is:
P(k; n, p) = (n choose k) p^k (1-p)^(n-k)
where n is the number of trials, p is the probability of success on a single trial, and k is the number of successes.
plugging in our values, we get:
P(1; 10, 0.072) = (10 choose 1) (0.072)^1 (1-0.072)^9
P(1; 10, 0.072) = 10(0.072) (0.928)^9
P(1; 10, 0.072) = 0.65
This means that the probability that at least 1 out of 10 people chosen at random is a universal donor is 0.65.
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A contractor is pouring a rectangular concrete slab with dimensions of 16 feet by 30 feet. To ensure that the sides of the slab form 90° angles, how many feet should each diagonal measure?.
Answers
If each sides of the slab form 90° angles, The number of feet that
each diagonal measure is 34 feet.
How to find the diagonal feet?
Using Pythagoreans theorem formula to find the diagonal feet
D² =L² + W²
Where:
D = Diagonal
L= Length = 16 feet
W = Width = 30
Let plug in the formula
D² = 16² + 30²
D² = 256 + 900
D=√1156
D= 34 feet
Therefore the diagonal measure 34feet
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Justify [tex] \sqrt[3]{8} \times \sqrt[3]{8} = 16[/tex]using the properties of exponents in at least two different ways.
Answers
EXPLANATION
Given the cubic root:
[tex]\sqrt[3]{8}\cdot\sqrt[3]{8}[/tex]Rewriting 8 as 2^3:
[tex]=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}[/tex]Applying the property of roots:
[tex]\sqrt[3]{a^3}=a[/tex][tex]=2\cdot2=4[/tex][tex]\sqrt[3]{8}\cdot\sqrt[3]{8}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]can yall help me with this
Answers
Answer:
B
Step-by-step explanation:
If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.
I need help solving questions 28 and 34 by expanding and simplifying please
Answers
#28
The given expression is
[tex]\lbrack x+(y-2)\rbrack\lbrack x-(y-2)\rbrack[/tex]At first, we will simplify each square bracket
Note that, the + sign does not change the terms in the bracket but the - sign change the signs of the terms inside the bracket
[tex]\begin{gathered} \lbrack x+(y-2)\rbrack=\lbrack x+y-2\rbrack \\ \lbrack x-(y-2)\rbrack=\lbrack x-y+2\rbrack \end{gathered}[/tex]Now, we will multiply the 2 brackets
[tex]\begin{gathered} \lbrack x+y-2\rbrack\lbrack x-y+2\rbrack= \\ (x)(x)+(x)(-y)+(x)(2)+(y)(x)+(y)(-y)+(y)(2)+(-2)(x)+(-2)(-y)+(-2)(2)= \\ x^2-xy+2x+xy-y^2+2y-2x+2y-4 \end{gathered}[/tex]Now we will add the like terms
[tex]\begin{gathered} x^2+(-xy+xy)+(2x-2x)-y^2+(2y+2y)-4= \\ x^2-y^2+4y-4 \end{gathered}[/tex]1. Michelle used a standard deck of 52 cards and selected a card at random. Afterrecording the suit of the card she picked, she then replaced the card.SultOutcomeSpades 9Hearts11Clubs7Diamonds3Part A: Determine the empirical probability of selecting a heart.Part B: Determine the theoretical probability of selecting a heart.Part C: Determine the empirical probability of selecting a club or diamond.Part D: Determine the theoretical probability of selecting a club or diamond.
Answers
The card deck is a standard deck of 52 cards, with 13 cards in each suit.
For the experiment carried out by Michelle, we have the following information:
n(Spades) = 9
n(Hearts) = 11
n(Clubs) = 7
n(Diamonds) = 3
The total number of times she performed the experiment is
[tex]n(\text{Total) = 9+11+7+3 = 30}[/tex]The empirical probability will make use of the experimental results, while the theoretical probability will make use of the total possibilities.
PART A: Empirical Probability of selecting a heart.
Probability is calculated by
[tex]P(\text{outcome) = }\frac{n(outcome)}{n(total)}[/tex]Therefore, the probability is calculated as
[tex]P(\text{heart) = }\frac{11}{30}[/tex]PART B: Theoretical probability of selecting a heart.
This is calculated by
[tex]\begin{gathered} P(\text{heart) = }\frac{13}{52} \\ P(\text{heart) = }\frac{1}{4} \end{gathered}[/tex]PART C: Empirical probability of selecting a club or diamond.
To calculate the probability for two outcomes, A or B, the probability can be calculated by
[tex]P(A\text{ or B) = P(A) + P(B)}[/tex]Therefore, we will find the probability of getting a club and then a diamond.
[tex]P(\text{heart) = }\frac{11}{30}[/tex][tex]P(\text{diamond) = }\frac{3}{30}=\frac{1}{10}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{11}{30}+\frac{1}{10} \\ P(\text{heart or diamond) = }\frac{7}{15} \end{gathered}[/tex]PART D: Theoretical probability of selecting a club or a diamond
We will find the probability of getting a club and then a diamond.
[tex]P(\text{club) = }\frac{13}{52}=\frac{1}{4}[/tex][tex]P(\text{diamond) = }\frac{13}{52}=\frac{1}{4}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{1}{4}+\frac{1}{4} \\ P(\text{heart or diamond) = }\frac{1}{2} \end{gathered}[/tex]PLEASE HELP ME OUT What is x^2 - 4
Answers
Answer: (x-2)(x+2) is the solution
Step-by-step explanation:
Use the sum-product pattern
Common factor from the two pairs
Rewrite in factored form
Answer:
(x-2)(x+2)
Step-by-step explanation:
hello!! Can someone please explain and solve this problem for me? I’m having a hard time understanding.. I believe you start with terminal point and then initial.. but the rest i have no clue
Find the component form of vector v with initial point (-6,2) and terminal point (7,-3).
Answers
The component form of vector v with initial point (-6,2) and terminal point (7,-3) is (13,-5).
What is component form of vector?The component form of a vector is represented as x, y >, where x denotes the direction of travel (right or left) and y denotes the direction of travel (up or down) of the vector. Any two-dimensional vector may be conceived of as exerting influence in two separate directions. In other words, it can be considered to have two pieces. Components are the individual pieces that make up a two-dimensional vector. A vector's elements show how that vector will act in a specific direction.
Here,
initial point A=(-6,2)
terminal point B=(7,-3).
AB=(Bx-Ax, By-Ay)
=(7-(-6), -3-2)
= (13, -5)
The component form of the vector v with the starting points (-6, 2) and terminal points (7, -3) is (13,-5).
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Kehlani went into a movie theater and bought 6 bags of popcorn and 8 drinks, costing a total of $76. Madelyn went into the same movie theater and bought 7 bags of popcorn and 4 drinks, costing a total of $62. Determine the price of each bag of popcorn and the price of each drink.
Answers
The price of each bag of popcorn and the price of each drink are $6 and $5 respectively.
What is equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given:
The no of popcorn bags bought by Kehlani = 6,
The no of popcorn bags bought by Madelyn = 7,
The no of drinks bought by Kehlani = 8,
The no of drinks bought by Madelyn = 4,
The costing by Kehlani = $76,
The costing by Madelyn = $62,
Let the price of the popcorn bag is x and the price of the drink is y, then,
According to the question statement,
6x + 8y = 76 and 7x + 4y = 62,
Solve the equation by the elimination method,
x = 6 and y = 5
Therefore, the price of each bag of popcorn and the price of each drink are $6 and $5 respectively.
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An isosceles trapezoid has perimeter of 70. Each of the congruent nonparallel sides has length 13, and the height of the trapezoid is 12. How long is the longest side?
Answers
The length of the longest side is 27 units, in the isosceles trapezoid.
What is isosceles trapezoid?
A four-sided shape called a trapezoid has two parallel lines on each side (normally the top and bottom sides). A trapezoid that has equal-length non-parallel sides (the legs) is said to be isosceles. Considering everything mentioned before, we may start learning how to calculate an isosceles trapezoid's perimeter.
Given, the congruent nonparallel sides has length 13.
he height of the trapezoid is 12.
the extra length of the larger side will be 2*x, as it will be extra portion in both side.
So x² = 13²-12²
x² = 169-144 = 25
x = √25 = 5
So the lentgh of the larger side is 10 unit larger than smaller side.
The perimer of the isosceles trapezoid will be P = sum of all sides
P = 2*13 + L + L+10
⇒70 = 26+10 +2L
⇒2L = 70 - 36
⇒2L = 34
⇒L = 17
The length of the larger side will be 17+10 = 27 units.
Hence the length of the longest side is 27 units.
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