The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified? y > x2 – 2 y ≥ –x2 + 5
Answers
Two rigid transformations must be applied:
Vertical translation 7 units in the +y direction.Reflection around the line y = 5.The solution set can be identified by the fact that domain of quadratic functions is the real domain.
How to use rigid transformations
In the field of the Euclidean geometry rigid transformations are transformations applied on geometric loci such that Euclidean distances within the latter are conserved and herein we must determine what rigid transformations we should apply on f(x) to obtain g(x).
After a careful examination, we conclude that following two rigid transformations must be applied:
Vertical translation 7 units in the +y direction.Reflection around the line y = 5.The solution set represents the set of x-values such that the function exists. As both functions are quadratic equations, then their solutions are described the entire real domain.
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Related Questions
find the measure of angle 8
Answers
Answer:
99 degrees.
Step-by-step explanation:
m < 8 = 99 (corresponding angles are congruent).
Write the quadratic equation in standard form: -7x+11= −2x^2
Answers
Answer:
[tex]x=\frac{7-\sqrt{137} }{4} =-1.76[/tex]
Step-by-step explanation:
2x8 - (29x34)+ 38-12 (4x960)=
Answers
a rectangle has an area of 54 square inches the width of the rectangle is 9 inches what is the langth
Answers
Answer:
As per Provided Information
Area of rectangle is 54 square inchesWidth of the rectangle is 9 inches.We have to calculate the length of rectangle .
As we know the formula to find the Area of rectangle .
[tex] \boxed{\bf \: Area_{(Rectangle)} = length \: \times width}[/tex]
On substituting the value we obtain
[tex] \sf \qquad \: \longrightarrow 54 = length \times 9 \\ \\ \\ \sf \qquad \: \longrightarrow \cfrac{54}{9} = length \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = \cfrac{54}{9} \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = \cancel \cfrac{54}{9} \\ \\ \\ \sf \qquad \: \longrightarrow \: length \: = 6 \: inches[/tex]
Therefore,
Length of the rectangle is 6 inches .Can anyone pls draw the reflected shape for the middle one the lines are mirror lines 50 points for this
Answers
Step-by-step explanation:
All drawn are correct except the middle one you need to draw down the shape size of given parallelogram
Just count the diagonal from each of the to the line and draw the points
Which graph represents the solution to the given system? Y=5x+4 and 5=5x-3
Answers
y = 5(x) + 4
for this function,
y-intercept: 4x-intercept:-0.85=5(x)-3
for this function,
y-intercept: nonex-intercept: 1.6A company is sued for job discrimination because only 39% of the newly hired candidates were minorities or women when 47% of all applicants were minorities or women. Is this strong evidence that the company’s hiring practices were discriminatory? a) Is this a one-tailed or two-tailed test? b) In this context what is a Type I error? c) In this context what is a Type II error? d) Which type error would the company consider to be more serious? e) Which type error might job applicants consider to be more serious?
Answers
The research is a one-tailed test because the company won't be sued if many minorities were hired.
How to illustrate the research?In the context, the type I error will be deciding the company is discriminating or not. The type II error will be deciding the company is not discriminating when it is.
The power of the test is the probability of correctly detecting actual discrimination. The type of error that the company consider to be more serious is the type I error.
In conclusion, the type of error that job applicants might consider to be more serious is type II error.
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(a+3b)(2c+d+4e) simplify
Answers
Answer:
2ac + ad + 4ea + 6bc + 3bd + 12be (Simplified)
ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ʙᴀꜱᴇʙᴀʟʟ ᴡɪᴛʜ ᴀ 3 ɪɴᴄʜ ᴅɪᴀᴍᴇᴛᴇʀ.
ᴜꜱᴇ 3.14 ꜰᴏʀ ᴘɪ
113.04 sq. in
28.26 sq. in
18.84 sq. in
9.42 sq. in
Answers
Answer:
As Per Provided Information
We have to use π = 3.14
Diameter of baseball is 3 inch
So, Radius of Baseball will be
Radius = Diameter/2Radius = 3/2 inch
Radius = 1.5 inch
we have been asked to determine the surface area of given baseball .
Using Formulae
[tex] \boxed {\bf \: Surface \: Area_{(Baseball)} \: = 4 \pi {r}^{2} }[/tex]
substituting the value and let's solve it
[tex] \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = 4 \times 3.14 \times {1.5}^{2} \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 4 \times 3.14 \times 2.25 \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 12.56 \times 2.25 \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 28.26 \: {inch}^{2} [/tex]
Therefore,
Surface Area of baseball is 28.26 sq. inch .So, your answer is 28.26 sq.in
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What types of angles are in each of these quadrilaterals?
Answers
Answer:
all the quadrilaterals have acute angles!
Given quadrilateral ABCD with vertices A(0, 0), B(3, 4), C(8, 4), and D(5, 0). Complete the statements
below.
Part A: The quadrilateral ABCD is a
A. rectangle
B. rhombus
C. square
D. trapezoid
Part B: The quadrilateral ABCD can be identified as the geometric shape in Part A because
A. all sides are congruent
B. only two sides are parallel
C.
- opposite sides are parallel and congruent
D. the diagonals are congruent
Answers
Part B: Only two sides are parallel
Answer:
Part A:
B. rhombus
Part B:
C. Opposite sides are parallel and congruent
In circle H with m∠GHJ=66 and GH=10 units, find the length of arc GJ. Round to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
arc length= central length/360 (circumference)
GJ=90/360 (2π20)
GJ= 31.42
31.42
The length of arc GJ is 11.5133 unit.
What is Arc length?In geometry, the arc length refers to the length of a portion of a curve or an arc of a circle. It is the distance along the curve between two endpoints of the arc.
We have,
m <GHJ = 66 and GH = 10 unit
Now, using arc length formula
= nπr / 180
= 66 x 3.14 x 10/ 180
= 11.5133 unit
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There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
Answers
Answer:
16/81
Step-by-step explanation:
Given
In the bag, there are : 4 blue and 5 red marblesProbability of blue (1st time)
P(1) = Total blue / Total marblesP(1) = 4 / (4 + 5)P(1) = 4/9Probability of blue (2nd time)
P(2) = Total blue / Total MarblesIt states it is replaced hence it is of the same constitution as the beginningP(2) = 4/9Probability of blue (both times)
P = P(1) x P(2)P = 4/9 x 4/9P = 16/81an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter?
Answers
The total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²
Since an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. The heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the length of the shorter base of each trapezoid is 1.5 centimeters, the radii of the hexagon, and the base of the trapezoid form a triangle of
height, h = apothem of the hexagon = 2 cm and base, b = length of shorter base of trapezoid. Area of the triangleSo, the area of this triangle is A = 1/2bh
= 1/2 × 1. 5 cm × 2 cm
= 1.5 cm × 1 cm
= 1.5 cm²
Area of the hexagonSince there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A
= 6 × 1.5 cm²
= 9.0 cm²
So, the total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²
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Write 9/10 as an equivalent fraction with a denominator of 100 then write the fraction as a decimal
Answers
Answer:
Since the denominator has to be 100 and 9/10, 0.90, and 90% are all equal the you would just need to make the 9 into a 90. Therefore, yout answer will be 90/100.
Find the zeros using the quadratic formula x^2-5x+4=y.
Answers
Answer:
(x-4) (x-1)
Step-by-step explanation:
X-4=0
x=4
X-1=0
X=1
What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1000?
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0.5934 = 59.34% probability that there is an error of at most $1000.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching the problem on the internet, it is found that the population has mean and standard deviation given, respectively, by [tex]\mu = 57300, \sigma = 9600[/tex].
For samples of 64, the standard error is given by:
[tex]s = \frac{9600}{\sqrt{64}} = 1200[/tex]
The probability of an error of at most $1000 is the probability of a sample mean between $56,300 and $58,300, which is the p-value of Z when X = 58300 subtracted by the p-value of Z when X = 56300, hence:
X = 58300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{58300 - 57300}{1200}[/tex]
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
X = 56300:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56300 - 57300}{1200}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
0.7967 - 0.2033 = 0.5934.
0.5934 = 59.34% probability that there is an error of at most $1000.
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The width of a rectangle with area 55in^2 depends on its length. write the formula that describes the width of the rectangle as a function of its length.
(screenshot attached if you need to see the problem better)
Answers
The formula that describes the width of the rectangle as a function of length is w = 55 / m.
How to find area of a rectangle?area of a rectangle = lw
where
l = lengthw = widthTherefore,
area = 55 inches²
length = m
width = w
Hence,
area = mw
55 = mw
divide both sides by m
55 / m = wm / m
w = 55 / m
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Find the sum of
-3/7 and its opposite
Answers
If I were to be walking 8MPH How fast would I be walking per minute? PLEASE HELP. (Hint: Half of 8MPH is 4, so that would be 4 Miles every 30 minutes.)
Answers
Answer:
0.13 miles per minute
Step-by-step explanation:
If you walk 8 miles in an hour, that is 8 miles per 60 minutes. We can divide 8 by 60 to get the miles per minute because there are 60 minutes in an hour. 8/60 = 0.13 (3 is repeating)
Under a dilation, are the pre-image and the image always,
sometimes, or never congruent?
Answers
Answer:
Never congruent
Step-by-step explanation:
A dilation is a transformation that makes an image that is thr same shape as the original, but a DIFFERENT SIZE.
Congruent shapes means they both have the same shape AND size.
So a dilation of the new image/shape can NEVER have the same shape AND size with the original.
BRAINLIEST?? TY!! :DD
What is Earth's diameter, rounded to the nearest whole number?
Answers
Answer:
7918
Step-by-step explanation:
If you round Earth's diameter, I believe that it is 7,918 miles.
Please help!!
Sorry for the bad quality
Answers
Answer:
For the table I got 18 for the 5, 36 for the ten and not sure on the last one for the table and for the last one I got approx 5 mins but I’m not too sure
Step-by-step explanation:
Answer:
A.
5 mins = $5.20
10 = $7.20
M - i can't calculate that without having more info but the equation would be (M × 0.40) + 3.20 = Total amount in dollars.
B. 42 minutes
Step-by-step explanation:
Use the equation I listed before for A.
For B. 20.00 - 3.20 = 16.80. 16.80/0.40 = 42.
you should give me brainliest if im right
All digits in a dropdown number are different and one of its digits is the average of all its digits. It has at least two digits. For example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number. a Find the smallest dropdown number.
Answers
The dropdown numbers is an illustration of combination
The smallest dropdown number is 1025
How to determine the smallest dropdown number?From the question, we have the following parameters:
The dropdown number is 4-digitThe digits are different.We start counting from 1023, 1024, 1025, 1026...........
The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2The number 1025 satisfies the given conditions
Hence, the smallest dropdown number is 1025
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Design An art class is making a mural for their school which has a triangle drawn in the middle.
The length of the bottom of the triangle is X. Another side is 5 more than four times the length of the
bottom of the triangle. The last side is 11 more than the bottom of the triangle. Write and simplify
an expression for the perimeter of the triangle.
Answers
Answer:
6x+16
Step-by-step explanation:
Bottom :x
Side1:4x+5
Side2:x+11
perimeter = x+4x+5+x+11
=6x+16
Laura’s birthday party has three different colored tables: pink, purple, and green. The pink table has 8 seats. The purple table has 10 seats, and the green table has 8 seats. Laura will assign seats as her friends arrive at her party. What is the probability that the first guest at the party will be placed at the pink table?
Answers
8+10+8=26
if there is 26 seats and 8 of them are pink, then the probability of laura’s friend getting a pink seat is 8/26, or 4/13 simplified.
Evaluate the following expression. Round your answer to two decimal places.
logz 11
2.18?
2.40?
0.46?
0.84?
Answers
The correct answer would be- A: 2.18
Your friend leaves your house. She later calls you on her cell phone, saying that she's been driving at 60 miles an hour directly away from you the whole time and is now 60 miles away. How long has she been gone?
Answers
Answer: 1hr
Step-by-step explanation: Distance = speed × time
Time = Distance / Speed = 60/60
If £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after two years
Answers
Answer:
£2121.8
Step-by-step explanation:
2000 X 1.03 X 1.03 = 2121.8
Question below .....
Answers
Let the unknown angle be x.
Sum of all angles of triangle = 180
x + 55 + 55 = 180
x + 110 = 180
x = 180 - 110
x = 70
