Guys, can you please help me with The Question #47 of The Quadratic Relations for me, please? :)
Answers
Answer:
[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
Parent function
[tex]y=-x^2[/tex]
Reflected in the x-axis
[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]
Compressed vertically by a factor of 1/2
Multiply the whole function by the given scale factor:
[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]
Translated 3 units down
Subtract 3 from the whole function:
[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]
Translated 5 units left
Add 5 to the variable of the function:
[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]
To sketch the parabola
Vertex = [tex](-5, -3)[/tex]
Axis of symmetry: [tex]x = -5[/tex]
Plot points:
[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]
[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]
[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]
[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]
Related Questions
A whole year level of 164 students is to be divided into 18 groups. By rounding
both numbers to the nearest 10, approximate the number of students in each
group.
Answers
Answer:
10
Step-by-step explanation:
no. of students in each group=164/18=9.111111...=10 (nearest 10)
Answer:
8
Step-by-step explanation:
When rounding to the nearest 10:
If the units are 0, 1, 2, 3 or 4 → round downIf the units are 5, 6, 7, 8 or 9 → round upTherefore:
164 rounded to the nearest 10 = 160
18 rounded to the nearest 10 = 20
To approximate the number of students in each year group, divide the rounded number of students by the rounded number of groups:
⇒ 160 ÷ 20 = 8
hi can someone help me
Answers
B mode is 0 because there is no numbers that is shown more the. Twice the median is 138.5
Team b had to make dinner
There you go :]
Step-by-step explanation:
mean value is always the sum of all data divided by the number of data points.
we can see just by looking at the numbers that team B is way below team A.
mean team A : 1529/8 = 191.125
mean team B : 1141/8 = 142.625
so, clearly, team B had to make dinner.
the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.
in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :
median team A : (180+189)/2 = 184.5
median team B : (143+134)/2 = 138.5
the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.
mode team A : 212
mode team B : 99, 102, 105, 134, 143, 145, 202, 211
when factoring the following trinomial,you need two numbers that multiply to equal "-24" and add to "-10" choose the two correct numbers
6
-8
-3
4
-6
-4
12
3
8
-2
-12
2
Answers
Answer:
-12 and 2
Step-by-step explanation:
-12 × 2 is -24
and
-12 + 2 is -10
Alex got 27 questions out of 30 correct. what present of the questions did he get correct?(use fish method)
Answers
if we take 30 to be the 100%, what is 27 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]
Find the length of the arc
Answers
Answer:
A
Step-by-step explanation:
the length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 8 × [tex]\frac{1}{3}[/tex]
= 16π × [tex]\frac{1}{3}[/tex] = [tex]\frac{16\pi }{3}[/tex] m
First two two terms of the given number sequence 3n + 1 are...
Answers
Answer:
the sequence begins as {4, 7, ... }
Step-by-step explanation:
a(n) = 3n + 1
The first term is a(1) = 3(1) + 1 = 4, and
the second term is a(s) = 3(2) + 1 = 7
So the sequence begins as {4, 7, ... }
(x + 3) (x + 5) (x + 7) (x + 9) + 16
Answers
Move point C so that ∠BAC and ∠CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements for this case.
Answers
The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.
What are supplementary angles?Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;
adjacent non-adjacent. Adjacent supplementary anglesAdjacent supplementary are angles with a common vertex and arm.
Non-adjacent supplementary anglesNon- adjacent supplementary angles are angles without a common vertex or arm.
∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.
They add up to 180°.
∠ BAC = 110° and ∠CAD = 70°
Hence, the angles could be 110° and 70°.
Note, this is an overview as the question is not complete.
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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.
Step-by-step explanation: Edmentum Answer
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Answers
Answer: COSINE
Step-by-step explanation:
I PROMISE
Answer:
See below
Step-by-step explanation:
For a right triangle, with the information given, tangent function is most appropo
tan 41 = 4/x re-arrange to
x = 4 / tan(41) then x = 4.60
Does anyone know the answer to this question here ?
Answers
Answer:
True
Step-by-step explanation:
A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees. At some later time, Luis takes another measurement and finds the angle of depression to the boat (now at point B) to be 39 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Help pls serious answers only!!! HW DUE TODAY! pls show steps ;-;
Answers
Using the slope concept, it is found that the distance from point A to point B is of 465 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
To find the horizontal position at point A, we have that:
tan(10º) = 107/dA
dA = 107/tan(10º)
dA = 607.
For the horizontal position at point B, we have that:
tan(37º) = 107/dB
dB = 107/tan(37º)
dB = 142.
Hence the distance is given by:
D = dA - dB = 607 - 142 = 465.
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A subtrahend is the number being subtracted in a subtraction problem. Robert
misread the digit l in the ones place of the subtrahend as 7 and the digit 7 in the tens place of the subtrahend as 1. The difference in the subtraction then became 222. What would be the actual difference if he had read the numbers correctly?
Answers
From the calculation below, the actual difference, if Robert had read the numbers correctly, is 168.
How to use subtrahend in the calculation?Let X represents the number from which subtrahend is subtracted.
Therefore, we can calculate X as follows:
X – 17 = 222
X = 222 + 17 = 239
If the subtrahend is read correctly as 71 and then subtracted from 239, we have:
Actual difference = 239 – 71
Actual difference = 168
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What is the length of segment R S?
Answers
Answer:
C
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{RS}{FG}[/tex] = [tex]\frac{ST}{GH}[/tex] ( substitute values )
[tex]\frac{RS}{21}[/tex] = [tex]\frac{4}{12}[/tex] ( cross- multiply )
12 RS = 84 ( divide both sides by 12 )
RS = 7 cm
One week, Genesis earned $367.40 at her job when she worked for 22 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $584.50?
Answers
Answer:
35 hrs
Step-by-step explanation:
Hope this helps! Have a great day!!
Which expression gives the distance between the points
(-3, 4) and (6, -2)?
O A. (-3-4)²+(6+2)²
O B. (-3-6) +(4+2)²
O C. (-3-6)²+(4+2)²
O D. (-3-4)²+(6+2)²
Answers
The expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
How to determine the expression?The points are given as:
(-3, 4) and (6, -2)
The distance between two points is calculated using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
This gives
[tex]d = \sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
Hence, the expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]
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Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case. ( pls answer fast )
Answers
Answer:
95
Step-by-step explanation:
The smallest number that divided by 6, 15, and 18 leavses 5 in each case is 95
the situation.
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents her total income?
Answers
The expression which represents Sherly's total income is 7e + 13n.
What is Cost Price?The cost price represents the specific value that represents unit price purchased.
Here,
total pair of earrings = e
total pair of necklaces = n
Cost of 1 pair of earring = $ 7
Cost of 1 necklace = $ 13
earning from earring = 7e
earning from necklace = 13n
Total earning = earning from earring + earning from necklace
Total earning = 7e + 13n
Thus, the expression which represents Sherly's total income is 7e + 13n.
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Please help!! So confused
Answers
Answer:
A.2x^2 + 12x
Step-by-step explanation:
Here,
f(x) = 1/2 x^2 + 3x
Now,
4.f(x) = 4(1/2 x^2 + 3x) = 4/2 x^2 + 12x = 2x^2 + 12x
can someone please hepl me on tis
Answers
Answer:
Answer is in pictures
Step-by-step explanation:
36=6x6 90=9x10
256+7=263 104=98+6-2
678=678 81+9=90
Help me please!!!!!!!!
Answers
Answer:
the third option
Step-by-step explanation:
because the numbers down there are the coefficients of the top equations
An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.
Answers
Answer:
The airplane flies 95 miles.
Step-by-step explanation:
First we need to find the distance for the first segment using the formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]. Let's say [tex](x_{1},y_{1})[/tex] is (0, 0) and [tex](x_{2},y_{2})[/tex] is (33, 56). This gets us that the length of this segment is 65 miles.Next, we need to find the distance for the second segment. Using the same formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex], we can say [tex](x_{1},y_{1})[/tex] is now (33, 56) and [tex](x_{2},y_{2})[/tex] is now (23, 32). This gets us that the length of this segment is 26 miles.To get the total distance traveled, add the length of these two segments together (65 miles + 26 miles) to get 91 total miles traveled.Question:
An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.
Answer:
The plane flew 91 miles.
Step-by-step explanation:
City 1 - City 2
---------------------------------------------------------------------------------------------------------
[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]
[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]
[tex]d_1[/tex] = [tex]65[/tex]
---------------------------------------------------------------------------------------------------------
City 2 - City 3
[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]
[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]
[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]
[tex]d_2[/tex] = 26
---------------------------------------------------------------------------------------------------------
[tex]d_1 + d_2 = 65 + 26[/tex]
[tex]d_1 + d_2 = 91[/tex]
---------------------------------------------------------------------------------------------------------
Therefore, the airplane flew a total of 91 miles through every city
---------------------------------------------------------------------------------------------------------
Key words: the airplane, 91 miles, through, every, city, flies, City 1, City 2, City 3, total, number, unit, represent, mile.
<3 Lots of love!
-The Book Worm.
n music, a quaver is one-eighth of a semibreve (whole note). What fraction of a semibreve is a hemidemisemiquaver? (Hint: hemi-, demi-, and semi- are prefixes each of which represents a multiplication by one-half).
Answers
Answer:
[tex]\dfrac{1}{64}[/tex]
Step-by-step explanation:
Hemi-, demi- and semi- are prefixes which mean half.
When applied to musical notation, each time a prefix is added it means the note's value is halved.
Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.
[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]
Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.
I need help finding both volume and surface area
Answers
Answer:
Volume
For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3
For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, [tex]\pi[/tex] = 3.14
V = radius^2 x height x [tex]\pi[/tex]
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)
Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3
Surface Area
Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2
A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)
Semi-circular prism:
A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2
Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2
Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.
In the past week, Joe has recorded the number of tickets that a movie theater has sold during each day from Monday to Saturday. This information was shown through the following Bar Graph.
How does the Bar Graph misrepresent the data?
A. The scale along the vertical axis is divided into unequal intervals.
B. The categories along the horizontal axis are missing one of the days.
C. The widths of the bars are not equal.
D. The heights of the bars representing Monday and Thursday are not same.
Answers
Based on the information shown through the bar graph, a misrepresentation of the data is that: B. the categories along the horizontal axis are missing one of the days.
What is a bar graph?A bar graph can be defined as a type of chart that is used for the graphical represent of data (information), especially through rectangular bars or vertical columns.
Based on the information shown through the bar graph in the image attached below, we can logically deduce that a misrepresentation of the data is that the categories along the horizontal axis are missing one of the days (Friday).
In conclusion, this bar graph misrepresented the data because Friday is missing from the categories along the horizontal axis.
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A high school track coach wanted to test whether giving the students an energy drink could affect performance during the 100 meter race. The coach split the 18 boys into two equal sized groups, where Group 1 was given the energy drink and Group 2 was not. The 100 meter race times were recorded during practice and shown in the table below. What inference can be made about the results?
Answers
Based on the difference in the observed means given, we can infer that energy drink does indeed have an effect on performance.
Can the energy drink affect performance?First find the observed mean difference:
= 11.6 - 10.8
= 0.8 seconds
When the exercise is done only once, we see that on average, those who took the energy drink were faster and so finished earlier than those who didn't.
We can therefore infer that the energy drink has an effect on performance.
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A pool is being filled with water. First, 14 liters are poured into the pool. Then, another 7 liters are poured into the pool.
How many liters of water are poured into the pool in all?
Enter your answer in the box.
Answers
Answer:
21 liters
Step-by-step explanation:
14 liters + 7 liters = 21 liters
Hope this helped :)
What is the perimeter of the following shape? (use an approximate value) pie = 3.14
Answers
===========================================================
Explanation:
A full circle of radius r = 14 cm has a circumference of...
C = 2pi*r
C = 2*3.14*14
C = 87.92
This is the approximate distance around the circle, aka the perimeter.
Half of this is 87.92/2 = 43.96 which is the curved distance of this semicircle.
The straight line portion is 14+14 = 28 cm long.
The total perimeter of the semicircle shown is 43.96+28 = 71.96 cm
13) Greenhouse gases are contributors to climate change as they absorb outgoing solar radiation and convert it to thermal energy. The main contributors to the
warming are carbon dioxide, methane, dinitrogen monoxide, and F-gases. The sources of these gases are shown in the pie chart here. What questions are relevan
these gases and their impacts on the climate change over the past 100 years? Select ALL that apply.
A) Does an increase in fossil fuel combustion create a local weather change?
B) Can a legislation that reduces the F-gases help prevent a global climate change?
C) Can reforestation of trees reduce the amount of carbon dioxide that is present in the atmosphere?
D) Can an increase in meat production occur without increasing methane and nitrogen from fertilizers?
E) Can a reduced reliance on fossil fuels decrease the atmospheric carbon dioxide and prevent rising global temperatures?
Answers
Answer:
e)as we know in this current century many modern country is polluting air pollution that may lead to impact our health
Factor 6x¹ − 5x² + 12x² − 10 by grouping. What is the resulting expression?
(6x + 5)(x²-2)
(6x - 5)(x²+2)
(6x² + 5)(x-2)
(6x²-5)(x+2)
Answers
Answer:
[tex](6x-5)(x^2+2)[/tex]
Step-by-step explanation:
[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]
You are choosing a student council president by lots.. If you have 10 pieces of paper numbered 0-9 and you draw 2 pieces (where order does NOT matter), how many candidates can get a unique number sequence?
Select one:
a.
90
b.
45
c.
60
d.
30
Answers
Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:
b. 45.
The order of the pieces is not important, hence the combination formula is used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:
[tex]C_{10,2} = \frac{10!}{2!8!} = 45[/tex]
Which means that option b is correct.
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