1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
10 points: Write the vertex form equation for g(x) below.
Answers
A graph of f(x) is shown in the image below.
A graph of f(x) is shown in the image below.
The vertex form equation for g(x) is g(x) = -x²
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;
f(x) = (x + 3)² - 2
g(x) = -[(x + 3 - 3)² - 2 + 2]
g(x) = -x²
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Related Questions
In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG = DH. Prove that quadrilateral EFGH is a square.
First to answer gets brainliest
Answers
Answer:proving that EFGH is a square: points E,F,G,H
separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then
AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square
HAE~EBF~FCG
An online television company is sending out surveys to rank 10 TV-show genres watched. What is the probability that you guess the top 3 genres correctly and in the correct order?
Write your answer as an exact fraction which is reduced as much as possible.
Answers
Answer:
The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:
1/10 * 1/9 * 1/8 = 1/720
So the exact probability is 1/720, which is already reduced to its simplest form.
How much more total interest will you earn when interest is calculated on the new yearly amount, rather than the original principal? (Compare the last row of the tables). In the next section, we will get to “see” the larger snowball, called compound interest.
Answers
The rate of interest with the given amount and compound interest is 5 percent.
Given that,
After 1 year: compound interest = $30 and total amount=$630.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Here, principal = 630-30=600
630=600(1+r/100)¹
630/600 = 1+r/100
1.05=1+r/100
1.05-1=r/100
0.05=r/100
r=5%
Therefore, the rate of interest with the given amount and compound interest is 5 percent.
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use the product to rewrite log16(256b)
Answers
Log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm is 2 + log₁₆(b)
We can use the product rule of logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the factors.
Therefore, we can write
log₁₆(256b) = log₁₆(256) + log₁₆(b)
We can simplify log₁₆(256) as follows:
log₁₆(256) = log₁₆(16^2) = 2
Therefore, we have:
log₁₆(256b) = log₁₆(256) + log₁₆(b)
= 2 + log₁₆(b)
So, we have rewritten log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm.
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Sophia wishes to retire at age 65
with $1,600,000
in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
compounded monthly. What is the monthly deposit that Sophia must make in order to reach her goal? Round your answer to the nearest cent, if necessary
Answers
Answer:
To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)
P = monthly deposit
r = annual interest rate (which is 9%)
n = number of times interest is compounded per year (which is 12 for monthly compounding)
t = number of years until retirement (which is 65 - 28 = 37)
Substituting the given values, we get:
1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)
Simplifying and solving for P, we get:
P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)
P ≈ $524.79
Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.
Step-by-step explanation:
Mona pays $1.00 for the first call of the day on her mobile phone plus $0.15 per minute of the call. She paid $2.95 for her first call today. Write an expression that you could use to calculate the length in minutes of the phone call.
Answers
The requreid Mona's phone call was 13 minutes long.
Let's let the variable "m" represent the length of the phone call in minutes.
We know that Mona pays $1.00 for the first call of the day plus $0.15 per minute of the call. So the total cost of the call can be represented by the expression:
$1.00 + $0.15m
We also know that Mona paid $2.95 for her first call today. So we can set the expression for the total cost of the call equal to $2.95:
$1.00 + $0.15m = $2.95
To solve for the length of the call in minutes, we can first subtract $1.00 from both sides of the equation:
$0.15m = $1.95
Then we can divide both sides by $0.15:
m = 13
Therefore, Mona's phone call was 13 minutes long.
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PLEASE PLEASE HELP DUE IN A FEW HOURS ILL GIVE U ANYTHING
What age represents the median of this data? (1 point)
4. What age(s) represent the mode? (1 point)
5. Beth is 63 years old. She loves to bike. She decides to look at other clubs to join. Why do you think she didn’t want to join this club? Explain your answer using the stem-and-leaf plot above. (1 point)
Are there any outliers in this data? If so, what age(s) are they? (Hint: you’ll need to find the quartiles first. Show your work.) (4 points)
Answers
Beth could not join the club because the highest age which is allowed here is only 55 years
We know that;
A statistical expression obtained from a list of data that refers an abnormal gap from other values.
And, The statistical rules that instruct us to divides the data or observation values into four parts.
After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.
the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.
hence, Beth did not join the club because her age was above the highest age that allowed in this club.
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Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Answers
The electricity cost for the Val's AC to run for a summer month of 30 days is $84.
Given that,
Val's whole-house central air conditioner uses 4,000 watts when running.
Val runs the AC 7 hours per summer day.
Electricity costs (10 cents)/(1 kilowatt-hour).
Total electricity used for the whole house = 4000 watts = 4 kilowatts
Number of hours that the AC runs = 7 hours
Cost of electricity = (10 cents)/(1 kilowatt-hour).
Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents
Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents
= $2.80
Cost of electricity for a summer month of 30 days = $2.80 × 30
= $84
Hence the total cost for the electricity is $84.
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PLEASE HELP ME PICK THE RIGHT ANSWER!!!!!
Answers
The meaning of the absolute value of -5.5 is given as follows:
The temperature decreases 5.5 degrees.
What is the absolute value of a number?The absolute value of a number is the number without the signal, for example:
|-2| = |2| = 2.
The number in this problem is given as follows:
-5.5.
Hence:
The negative sign means that the temperature decreased.The absolute value of 5.5 means that the temperature decreased by 5.5 degrees.Hence the second option is the correct option in the context of this problem.
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Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex] units. What is a simplified expression for the difference in the areas of Circle A and Circle B
Answers
The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²
Area of a Circle:The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.
We know that :
The formula of circle's circumference is = 2πr
We have :
Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units
and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]
Now, First we calculate the area of circle A is:
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
Area = πr² = (4/x+2)²π
Now, for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
Area =( 2/2x+2)²π
Simplified expression for the difference in the areas of Circle A and Circle B are:
(4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Answers
From the problem, we know that:
2(x + 1) + x^2 = 13
Simplifying and rearranging:
x^2 + 2x - 11 = 0
Using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(1)(-11))) / (2(1))
x = (-2 ± sqrt(48)) / 2
x = (-2 ± 4sqrt(3)) / 2
x = -1 ± 2sqrt(3)
Since the problem states that the numbers are positive, we can ignore the negative solution. Therefore, the smaller number is:
x = -1 + 2sqrt(3)
And the larger number is:
x + 1 = 2sqrt(3)
So the two numbers are -1 + 2sqrt(3) and 2sqrt(3).
what 7 coins make 82 cents
Answers
Answer:
1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
Step-by-step explanation:
One possible set of 7 coins that make 82 cents is:
1 quarter (25 cents)
2 dimes (10 cents each)
1 nickel (5 cents)
3 pennies (1 cent each)
Adding up the values of these coins:
25 + 10 + 10 + 5 + 1 + 1 + 1 = 82
Therefore, a set of 1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
The growth of a colony of bacteria is modeled by the function below, where t is the
is time in hours after the culture is begun and f(t) is the number of bacteria present.
After how many hours will there be 2000 bacteria in the colony? Round your answer
to the nearest hundredth (two decimal places).
f(t) = 500e^0.195t
Answers
namely, what is "t" when f(t) = 2000
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]
A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is an even number.
Answers
The probability that the sum of the numbers is even is,
⇒ P = 0.47
Since, We know that;
To have this kind of event you can have the following events, where
(d₁ ,d₂), d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:
(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)
And, the total number of events is 36 since every dice have 6 numbers.
The probability is:
P(Event)=P(sum is even)/Total number of events
P = 17/36
P = 0.47
Thus, The probability that the sum of the numbers is even is,
⇒ P = 0.47
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26=-9w-2w-18?????????????????
Answers
Answer:
w = -4
Step-by-step explanation:
Hope this helps
26= 11w -18
+18. +18
44 = 11w
11. 11
4 = W
Problem 5:
Find the missing side using
trigonometry:
52
18 H
AWO
Drag&Drop the correct trig function:
Cos
Tan
Rati
Circle which shortcut you use.
Multiply
Round your answer to the nearest tenth:
Give Feedback to Micrones
Sin
%
or
IN
Divide
Ans
Ans
Answers
The missing length is 11.0818 unit.
We have,
Angle = 52 degree
H = 18
Using Trigonometry
cos 52 = B/H
cos 52 = x / 18
0.615661 = x /18
x = 11.0818 unit
Thus, the missing length is 11.0818 unit.
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Triangles ABC and DEF are mathematically similar. 9 Cm B The area of triangle ABC is 34 cm. Calculate the area of triangle DEF. F 13.5 cm
Answers
Answer:
Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.
If the area of triangle ABC is 34 cm, then the area of triangle DEF is:
Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2
Therefore, the area of triangle DEF is 76.5 cm^2.
Step-by-step explanation:
find the compound interest on rs 6950 for 3 years if the interest is payable half yearly,the rate for the first two years being 6% p.a and for the third year 9% p.a
Answers
Answer:
Rs 2150.81.
Step-by-step explanation:
The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.
For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.
Hence, the total compound interest for three years would be Rs 2150.81.
Which of the following scatterplots shows a correlation affected by an influential point?
Answers
Answer:
The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.
Step-by-step explanation:
Please give the brainliest, really appreciated. Thank you
In the data set below, what is the upper quartile?
24 28
28 47 53 55 58 78 79
Submit
Answers
Answer:
68
Step-by-step explanation:
the median is the term in the middle (53) the upper quartile is the median of the terms above the median. Since there are an even number of terms, you need to average them (58+78)/2
Can someone help me pleasee
Answers
Answer:
The answer is 50% or 1/2
Step-by-step explanation:
There are four outcomes on that chart: 1,2,3,3
There are two threes which means 2/4=.5 or 1/2
Answer:
1/2 chance of landing on a 3.
Step-by-step explanation:
Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.
The data set is: 6, 2, 6, 3, 5, 6, 7, 9, 1 For this question, find the IQR
Answers
The IQR of the data set is 4.
First, let's arrange the data set in order from smallest to largest:
1, 2, 3, 5, 6, 6, 6, 7, 9
Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:
Q2 = 6
Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:
Q1 = (2 + 3) / 2 = 2.5
Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:
Q3 = (7 + 6) / 2 = 6.5
Now that we have Q1, Q2, and Q3, we can calculate the IQR as:
IQR = Q3 - Q1
IQR = 6.5 - 2.5
IQR = 4
Therefore, the IQR of the given data set is 5.5.
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Complete the sentences to compare the intervals for which each function is decreasing
Answers
The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)
Completing the sentences to compare the intervalsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
From the graph of the functions, we can see that
The function g(x) decreases all through because it is a linear function with a negative slopeThe function f(x) decreases at [0, ∝) because it a quadratic function with a maximum vertex at (0, 5)Read more about functions at
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10 points. please awnser
Answers
The angle measures for the triangles are given as follows:
m < G = 105º.m < H = 55º.m < I = 20º.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:
m < Z + 20 + 105 = 180
m < Z + 125 = 180
m < Z = 55º.
Hence the measures are given as follows:
m < G = 105º. -> equivalent to X.m < H = 55º. -> equivalent to Z.m < I = 20º. -> equivalent to I.More can be learned about similar triangles at brainly.com/question/14285697
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the graph of f(x)= 3 times 2x -3 is shown below. g(x) is a transformation of f(x).
Answers
The function of g(x) is 3 ([tex]2^x[/tex]) + 3.
We have,
f(x) = 3 ([tex]2^x[/tex]) -3
Now, the function f(x) have shifted by -3 unit to move 6 unit up.
This means that we have the shifting of
= -3 + 6
= +3 unit
Also, g(x) crosses the y-axis at about 5 or 6 when x=0.
Then, the function of g(x) is
= 3 ([tex]2^x[/tex]) + 3
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Hurry up please time limit
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range ?
Answers
Answer:No, X=-3, yly =-4,0,4
Step-by-step explanation:
Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
Answers
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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Given the vectors a and b. sketch the vector a+b
Answers
The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.
What is parallelogram law of vector addition?
Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.
For the given vector a, and vector, the resultant of the two vector is calculated as;
-----------> a and --------------->b = a + b
The diagram represents the addition of the two vectors, a and b;
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Determine the measures of the arcs and angles:
*It may help to find all central angle measures before answering the hotspots.
If you do any calculating, you can type that into the hotspot with your final answer.
m HE
m HD
m DG
m EG
m < DEG
m < HGE
Answers
The values of the arc length and angles are:
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
We have,
The central angle is equal to the intercepted arc length.
So,
62° = HE
And,
∠A = HD
∠A + 62 = 180
∠A = 180 - 62
∠A = 118
HD = 118
And,
DG = ∠M (say)
∠A + 118 = 180
∠M = 180 - 118
∠M = 62
DG = 62
And,
∠A is opposite to ∠N (say)
So,
∠A = ∠N = 118
∠A = EG
EG = 118
And,
From the definition of the exterior angle.
∠DEG + ∠HGE = 62 ______(1)
Also,
The sum of the three angles in AEG = 180
∠EAG + ∠DEG + ∠HGE = 180
∠EAG = 180 - 62 = 118
So,
∠DEG + ∠HGE = 180 - 118
∠DEG + ∠HGE = 62 _______(2)
Thus,
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
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Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
Answers
Answer: A
Step-by-step explanation: -87
