Subject: Maths
Level: High-school
Topic: transforming graphs
Points: 90
PLEASE HELP!
(i have the answer for part i, i just need hel with ii and iii)
Answers
Answer:
(-1, -5), (-1/2, -3), (-1, -9)Step-by-step explanation:
The function in vertex form is:
f (x) = a(x - h)² + k, where (h, k) is the vertexf(x) = (x - 1)² - 3i) y = f(x) - 2 = (x - 1)² - 3 - 2 = (x - 1)² - 5 ⇒ h = 1, k = -5
Minimum point:
(- 1, -5)ii) y = f(2x) = (2x - 1)² - 3 = 4(x - 1/2)² - 3 ⇒ h = 1/2, k = -3
Minimum point:
(-1/2, -3)iii) y = 3f(x) = 3((x - 1)² - 3) = 3(x - 1)² - 9 ⇒ h = 1, k = -9
Minimum point:
(-1, -9)
Related Questions
3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?
Answers
Answer
12
Step-by-step explanation:
click on square root
click on 144
then your answer will pop out below your equation
15 cm
19 cm
Work out the perimeter of this shape.
Answers
Answer:
102
Step-by-step explanation:
because you're finding the perimeter you already have 2 sides which is 15 and 19 so the other sides would of been 30 and 38 so 15 + 19+30+38=102 I really hope I am correct
A medical researcher needs 7 people to test the effectiveness of an experimental drug. If 15 people have volunteered for the test, in how many ways can 7people be selected?
Answers
Given:
A medical researcher needs 7 people to test.
15 people have volunteered for the test.
To find:
We need to find a number of ways to select 7 from 15 people.
Explanation:
The number of ways to select 7 from 15 people can be found by the given formula.
\(nC_r=\frac{n!}{r!(n-r)!}\)Substitute n=1`5 and r=7 in the formula.
\(15C_7=\frac{15!}{7!(15-7)!}\)\(15C_7=\frac{15\times14\times13\times12\times11\times10\times9\times8!}{7\times6\times5\times4\times3\times2\times(8)!}\)\(15C_7=15\times13\times11\times3\)\(15C_7=6435\)Final answer:
The number of ways = 6435 ways.
The table shows information about the
heights, in cm, of a group of Yr 11 girls.
height (cm)
least height
143
median
165
159
lower quartile
interquartile range
8
Complete the boxplot for this information.
range
33
i dont know where i am going wrong!
Answers
The value of the whisker on the left is 143.
The value of the first line on the box is 159.
The value of the line in the middle of the box is 165
The value of the third line in the box is 167.
The value of the whisker on the left is 176.
What are the values needed to complete the boxplot?A box plot is used to study the distribution and level of a set of scores. The box plot has two whiskers. The whisker on the left represents the minimum value and the whisker on the right represents the maximum value.
The first line on the box to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Maximum value = range + minimum value
143 + 33 = 176
Upper quartile = lower quartile + interquartile range
159 + 8 = 167
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What is the coefficient of the product experssion 6x? I NEED HELP SO PLS HURRYYYYY.
Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
please please help me!!!
Answers
the reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.005 seconds. what is the probability that a reaction requires more than 0.5 seconds?
Answers
Answer:0.02275
Normal distribution:
Which is symmetrical about mean.
Mean:
It is the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Complement rule:
When two disjoint sets are meant to occur then the sets are said to be complementary.
Given:
Mean= 0.4 seconds
Standard deviation= 0.005 seconds
Let, X be the reaction time for the driver to view stimulus.
So, distribution of X is given by:
X~ N( 0.4, 0.005)
Where σ= 0.05 and µ= 0.4
Solving this ques by using normal standard deviation and z score given as:
z=\frac{x-µ}{σ}
Applying formula:
P(X>0.5)= P{(x-µ/σ) > (0.5-µ/σ)} P {Z > (0.5-0.4/0.05)}
=P(Z > 2)
By using complement rule we get,
P(Z>2) = 1- P(Z<2)
Using normal standard table we have,
P(Z>2)=1- P(Z<2)
= 1- 0.97725
= 0.02275
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The probability that a reaction requires more than 0.5 seconds is 0.0227
Z-score standardization:
The amount of standard deviations the data point deviates from the mean is shown by the standardized z-score.
• If the z-score increases when it is higher than the mean (0).
• If the z-score is below the mean and takes a negative value (0).
Given that,
Mean = μ =0.4
Standard deviation = σ =0.005
The probability that a reaction requires more than 0.5 seconds is obtained by;
Let X denotes the reaction time of a driver which follows a normal distribution with a mean of 0.4 seconds and a standard deviation of 0.005 seconds.
P(X > 0.5) = 1 - P(X < 0.5)
= 1 - P(0.4 < X < 0.5) (0.5 - 0.4/0.005)
= 1 - P(25.06)
= 1 - P(252)
From the “standard normal table”, the area to the left of is 0.9773.
P(X > 0.5) = 1 - P(252)
= 1 - 0.9773
= 0.0227
Hence, the probability that a reaction requires more than 0.5 seconds is 0.0227
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selena created a scale model of an airplane where 1 centimeter on the model equals 6 meters on the airplane. the wingspan of the model is 10.7 centimeters. selena wants to make a new model where a scale of 1 centimeter on the model equals 3 meters on the airplane. which of the following best describes how the wingspan of the new model will compare to the wingspan of the first model?
Answers
The wingspan of the new model will be 2 times larger than the wingspan of the first model.
A scale model is a physical model of an object. Scale models are often used in engineering, architecture, and filmmaking, among other fields, to simulate the appearance or functionality of real-world objects.
According to the question, 1 cm of the scale model equals 6 meters of the airplane. Thus, to find the actual wingspan of the airplane, you can multiply the wingspan of the scale model by the ratio of the actual wingspan to the wingspan of the scale model, as shown below:
Wingspan of the airplane = Wingspan of the model × Ratio
To convert the scale model ratio from 1 cm = 6 meters to 1 cm = 3 meters, divide by 2. Since Selena's model has a wingspan of 10.7 cm, you can calculate the wingspan of the actual airplane using the equation above, as shown below:
Wingspan of the airplane = 10.7 × 6/1 = 64.2 m (for the first model)Wingspan of the airplane = 10.7 × 3/1 = 32.1 m (for the new model)
Now you can compare the wingspan of the two models to determine how the wingspan of the new model compares to the wingspan of the first model.
The wingspan of the new model will be 2 times larger than the wingspan of the first model, since 64.2 ÷ 32.1 = 2. Therefore, the correct answer is that the wingspan of the new model will be 2 times larger than the wingspan of the first model.
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all objects with mass have momentum. true or false
Answers
Answer:
False
Step-by-step explanation:
Even though I said that, an object that moves with a velocity has momentum but on the other way around as far the object is at rest the object will have a momentum of zero a.k.a no momentum.
The velocity of a particle moving along the x-axis is modeled by a differentiable function v, where the position is measured in meters, and the time I is measured in seconds. Selected values of (t) are given in the table below. The particle is at position x = 7 when I = 0 seconds. NC0 8 20 25 32 40 1 (seconds)t (v) t (meters per second) 3 5 -10 -8 -4 7 a) Estimate the acceleration of the particle at 1 = 36 seconds. Show the computations that lead to your answer. Indicate units of measure. b) Using correct units, explain the meaning of v(e)dt in the context of the problem. Use a trapezoidal sum with the three subintervals indicated by the data to approximate Sa(tdt. c) For OSIS 40, must the particle change direction in any of the subintervals indicated by the data in the table? If so, identify the subintervals and explain your reasoning. If not, explain why not. d) Suppose the acceleration of the particle is positive for O
Answers
The acceleration of the particle at t = 36 seconds is 11/8 meters/s2
Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt
using the second derivative of a and to find the time at 36 seconds is
a(36)=v'(36)=\(\frac{v(40)-v(32)}{40-32} \\\)
=7-(-4)÷8
a(36)=11/8 meters/s^2
The Trapezoidal Rule:
This is a rule that defines the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles.
The formula for the trapezoidal rule:
T n = 1 2 Δ x ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ⋯ + 2 f ( x n − 1 ) + f ( x n ) )
∫v(t) dt is the particle’s change in position in meters from time
t = 20 seconds to time 40 t = seconds.
\(\int\limits {v(t)} \, dx =\frac{v(20)+v(25)}{2}*5+\frac{v(25)+v(32)}{2} *7+\frac{v(32)+v(40)}{y} *8 \\\\=\frac{-18*5}{2} +\frac{-12*7}{2} +\frac{24}{2} \\\\=\frac{-90}{2} +\frac{-84}{2} +\frac{24}{2} \\\\=-45-42+12\\=-75\)
∫v(t) dt=-75meters.
For 0 ≤t≤40, must the particle change direction in any of the subintervals indicated by the data in the table
since v(t) is differentiable, v(t) is continuous.
Particle changes direction is v(t) changes sign.
The particle must change direction in (8,20) and (32,40)
v(8)=5>0 and v(20)=-10<0 for this v(t) changes sign for same C for8<C<20.
v(32)=-4<0 and v(4)=7>0 for this v(t) changes sign for some d for 32<d<40
the above is true due to the Intermediate Value theorem.
since v(t) changes sign in (8,20) and in (32,40)
The particle changes sign in (8,20) and in (32,40)
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Has this app helped u
Answers
Answer:
Discoveries and scientific and technical inventions do not influence the behavior of people, but their lives do
Step-by-step explanation: what app and ok
Which figure is a translation of Figure 1?
Figure A
Figure B
Figure C
None of the above
Answers
The diameter of a dime is 17.91 mm. The diameter of a strand of human hair is
6.0 x 10-2 mm. How many times greater is the diameter of a dime than the diameter of
the strand of human hair?
Answers
The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.
What is DiameterThe diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.
In this problem, the diameter tells us about the length of the each quantity.
The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.
Comparing both values
Dime = 17.91mm
Hair = 6.0*10^-2
Divide both quantity together.
17.91 / 6.0*10^-2 = 298.5≅299
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What is 223,692 divided by 42 using the standard algorithm and showing work?
Answers
The value of 223,692 divided by 42 using the standard algorithm and showing work is 5326.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
The value of 223,692 divided by 42 using the standard algorithm and showing work is given below:
Dividing the two values by 2, a common factor
223,692 / 42
= 111,846 / 21
Dividing the two values by 3, a common factor
111,846 / 21
= 37282 / 7
Dividing the two values by 7, a common factor
37282 / 7
= 5326 / 1
Hence, the value of the division is 5326.
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use a quadratic equation to find two real numbers with a sum of 31 and a product of 210. two real numbers with a sum of 31 and a product of 210 are and
Answers
Answer:
The numbers are 10 and 21.
Step-by-step explanation:
x + y = 31
xy = 210
x = 31 - y
(31 - y)y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21)(y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
The two real numbers are 10 and 21.
What is a quadratic equation?Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.
In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.
Given that, there are two real numbers with a sum of 31 and a product of 210.
We need to find their values using the concept of quadratic equation,
So, according to the question,
x + y = 31 (eq 1)
xy = 210 (eq 2)
x = 31 - y
(31 - y) y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21) (y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
Hence, the two real numbers are 10 and 21.
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the probability model for the number of heads observed when you flip a coin 4 times is below. what is the probability of observing less than 3 heads?
Answers
The probability of observing less than 3 heads is 0.6875 when you flip a coin four times.
Probability is a method that is used to find the number of events likely to occur. There are 3 types of probability which are Theoretical Probability, Experimental Probability, and Axiomatic Probability.
The formula used to find the probability is given as ;
P(E) = Number of Outcomes / Total Number of Outcomes.
We have to find the probability of observing less than 3 heads.
if the coin is tossed four times then the total number of outcomes is 16
Let X be the number of heads observed in 4 tosses of a coin, Then
the probability of getting x heads in 4 flips is P ( X = x )
The probability of observing less than 3 heads is expressed as,
P ( X < 3 ).
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= 1/16 + 4/16 + 6/16
= 11/16
= 0.6875
Therefore, the probability of observing less than 3 heads is 0.6875.
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9x+16
3
<7
solve each inequality
Answers
Step-by-step explanation:
9+16×+3
28×<7
35x it's answer can I help
Pls help me fast! Thank you! 10 points
Answers
Determine what type of model best fits the given situation:
The temperature of a cup of coffee decreases by 5 F every 20 minutes.
A. none of these
B. quadratic
C. exponential
D. linear
Answers
Answer:
T = -t / 4 + T0 where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature
This is a linear equation in T and t
(-1 / 4 represents -5 deg / 20 min = - 1 deg / 4min
The given situation is linear equation in T and t. so option D is correct option.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given situation:
The temperature of a cup of coffee decreases by 5 F every 20 minutes.
T = -t / 4 + T0
where t is the temperature in minutes elapsed.
T is the final temperature.
T0 is the initial temperature.
We need to find the type of model best fits the given situation.
(-1 / 4 represents -5 deg / 20 min = - 1 deg / 4min
Therefore, The given situation is linear equation in T and t. so option D is correct option.
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A pail that is 10 inches tall, has a base with a circumference of 6 inches,
and has an opening on top that is twice the diameter of the base.
Calculate how much sand will fit in the pail.(Find the volume)
Answers
The volume of the pale is 16.71 cubic inches.
The circumference of the base of the pail is 6 inches, so the diameter of the base is:
d = circumference / π = 6 / π ≈ 1.9099 inches
The diameter of the opening on top is twice the diameter of the base, so:
D = 2d ≈ 3.8197 inches
The height of the pail is 10 inches.
To find the volume of the pail, we can use the formula for the volume of a frustum of a cone:
V = (πh/3)(R² + r² + Rr)
where h is the frustum's height (10 inches in this instance), R is its top radius (D/2 = 1.9099 inches in this instance), and r is its bottom radius (d/2 = 0.9549 inches in this instance).
When we enter the values, we obtain:
V = (π(10)/3)((1.9099/2)² + (0.9549/2)² + (1.9099/2)(0.9549/2))
Simplifying and solving for V, we get:
V ≈ 16.71 cubic inches
Therefore, the pail can hold about 16.71 cubic inches of sand.
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How many and what type of solutions does 5x2−2x+6 have?
1 rational solution
2 rational solutions
2 irrational solutions
2 nonreal solutions
Answers
Answer:
2 nonreal solutions
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 (a ≠ 0 )
then the nature of the roots are determined by the discriminant
b² - 4ac
• if b² - 4ac > 0 then 2 real and irrational solutions
• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions
• if b² - 4ac = 0 then 2 real and equal solutions
• if b² - 4ac < 0 then no real solutions
5x² - 2x + 6 = 0 ← in standard form
with a = 5 , b = - 2 , c = 6
b² - 4ac
= (- 2)² - (4 × 5 × 6)
= 4 - 120
= - 116
since b² - 4ac < 0
then there are 2 nonreal solutions to the equation
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A bird was sitting 8 meters from the base of an oak tree. It then flew in a straight line 9 meters to reach the top of the tree.
How tall is the tree?
The tree is
meters tall.
Note: Round your answer to the nearest hundredth.
Answers
Answer:
wouldn't it be 17 meters?
=========================================================
Explanation:
Draw a right triangle. The horizontal leg is 8 meters. The hypotenuse is 9 meters. The vertical height is unknown, so we'll call it x.
Apply the pythagorean theorem to solve for x
\(a^2 + b^2 = c^2\\\\8^2 + x^2 = 9^2\\\\64 + x^2 = 81\\\\x^2 = 81-64\\\\x^2 = 17\\\\x = \sqrt{17}\\\\x \approx 4.1231056\\\\x \approx 4.12\\\\\)
The tree is approximately 4.12 meters tall
Check out the diagram below.
A binomial experiment with probability of success p=0.63 and n=11 trials is conducted. What is the probability that the experiment results in 10 or more successes? Do not round your intermediate computations, and round your answer to three decimal places (if necessary consulta list of formes.)
Answers
To find the probability of getting 10 or more successes in a binomial experiment with p = 0.63 and n = 11 trials, we can use the cumulative probability function.
P(X ≥ 10) = 1 - P(X < 10)
Using a binomial probability formula, we can calculate the probability of getting exactly k successes:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where C(n, k) represents the binomial coefficient.
Let's calculate the probability for each value from 0 to 9 and subtract it from 1 to get the probability of 10 or more successes:
P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)
P(X < 10) = Σ[C(11, k) * p^k * (1 - p)^(11 - k)] for k = 0 to 9
Using this formula, we can calculate the probability:
P(X < 10) ≈ 0.121
Therefore, the probability of getting 10 or more successes in the binomial experiment is:
P(X ≥ 10) ≈ 1 - P(X < 10) ≈ 1 - 0.121 ≈ 0.879
Rounding to three decimal places, the probability is approximately 0.879.
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Factor.
x^2 - 10xy+16y^2?
Answers
Answer:
x2−10xy+16y2
Step-by-step explanation:
Let's simplify step-by-step.
x2−10xy+16y2
There are no like terms.
help meeeeeeeeeeeeee
Answers
I'm pretty sure its c I dont really understand stand what its asking
Answer:
A
Step-by-step explanation:
Since all of the answer choices are non-terminating decimals, to find which is rational, we will have to see which is a repeating decimal. Repeating decimals have repeating sets of numbers, such as in the number:
0.33333333333333333333333333333333...
which can be written as the fraction 1/3.
All repeating decimals are rational because they can always be rewritten as a fraction.
From looking carefully at the answer choices, we can see that answer choice A is a repeating decimal, and therefore, is rational. Therefore, answer choice A is the correct answer.
I hope you find my answer and explanation to be helpful. Happy studying.
A clothing designer is interested in determining if there is a relationship between a person’s age and their preference for a particular style of dress. A survey is written and asks questions including questions about age and dress size. Should these questions be included in the survey?
A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
B. The questions should not be included because people may not want to answer questions about age and dress size.
C. The questions can be included but there should be an option where the participant can choose not to respond to the questions.
D. The questions should not be included because surveys should never ask for personal information.
Answers
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
What is the age in math?Age is any person time he live till time calculated. Use age we solve different math problems.
Like calculate the age of a person or what was his age 5 year ago.
If the age is given in the form of a ratio, for example, a:g, then the age shall be considered as g h and a h. If you are assuming the current age to be h, then n times the current age will be (h × n) years. If you are assuming the current age to be h, then 1/n of the age shall be equal to ( h / n) years.
Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship between age and preferred dress style.
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The researcher is investigating the association between age and favourite dress style, thus the questions are appropriate. The assertion is true.
What exactly is my age?Days are calculated as the difference between both the current day and the person's birth day. Age is calculated as follows: aged = (years x 365) + (months x 31) + days. The person's age is expressed in days. For the age in years, divide the figure by 365.
How do you determine age manually?Age is determined by comparing a person's birthdate to the day on which age must be determined. The age of a person is determined by subtracting the provided date from the individual's birthdate. Provided date minus birthdate equals age of a person.
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Mr. Maynard's class is taking a field trip to a science museum. They will be at the museum for 3 hours, and they want to divide their time evenly among the 10 exhibits.
How much time should they spend at each exhibit?
Answers
The even distribution of time to be spent on each exhibit by Mr. Maynard's class is 18 minutes.
Firstly let us convert the time to minutes for better clarity on amount of time to be spent on each exhibit. So, we know 1 hour has 60 minutes. Thus, 3 hours will be = 3 × 60
Amount of time in 3 hours = 180 minutes
Now, amount of time to be spent on 10 exhibits = 180 minutes
The amount of time to be spent on 1 exhibit = 180/10
Cancelling zero on Right Hand Side of the equation
The class students should spend amount of time = 18 minutes
Therefore, the spent on each exhibit should be 18 minutes.
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5 - 2y + 1/3 + y^3 - 10y for y = 4
I solved this equation but I'm not sure if I got the answer correct and if I messed up somewhere when I was solving it then I got my answer wrong. So if someone could please help me that would be very much appreciated!!!!!
Answers
Answer:
4
Step-by-step explanation:
i think i am correct but if im not sorry
A jar of olives had a circumference of 11. 99 cm. What was the approximate diameter of the jar?
Answers
If the jar of olives had a circumference of 11. 99 cm, the approximate diameter of the jar is 3.82 cm
The circumference of a circle is given by the formula C = 2πr, where C is the circumference, π is the constant pi (approximately equal to 3.14), and r is the radius. The diameter is twice the radius, so we can also write the formula as C = πd, where d is the diameter.
In this case, the circumference is 11.99 cm, so we can set up the equation
11.99 = πd
To solve for d, we can divide both sides by π
d = 11.99/π
Using a calculator, we get
d ≈ 3.82 cm
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the horizontal, continuous lintel on a classical building supported by columns is called a stylobate. T/F
Answers
The statement "the horizontal, continuous lintel on a classical building supported by columns is called a stylobate" is False.
The horizontal, continuous lintel on a classical building supported by columns is called an entablature, while the stylobate is the platform on which the columns stand.
In classical architecture, the entablature is the horizontal, continuous lintel that rests on top of the columns and consists of three parts: the architrave (the bottom layer), the frieze (the middle layer), and the cornice (the top layer). The entablature helps to unify the columns and create a sense of continuity across the facade of the building.
The stylobate, on the other hand, is the platform or base upon which the columns stand, and is usually elevated above ground level. Together, the stylobate and entablature form the colonnade, a defining feature of classical architecture.
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