Answer:
2.625
Step-by-step explanation:
2 2/7 in decimal form is 2.2857
6 / 2.2857 = 2.625
The table lists the speeds of the fastest roller coasters in North America and Asia.
Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .
The difference of the means of the two data sets is = 4.57
The mean absolute deviation of the roller coaster speeds in North America is 13.3
The mean absolute deviation of the roller coaster speeds in Asia is 16.8
How to solve for the meansFirst we have to start with the data for North America
128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77
To get the mean you have to sum up the values and divide through by the total number 10
937.8/10
Mean = 93.78
Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10
133.32/10 = 13.3
For Asia, we have the data as
149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4
Mean for Asia = 892.1/10
= 89.21
Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10
= 168.32/10
16.8
The difference in the means = 93.78 -89.21
= 4.57
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pls explain and provide calculation thank you
Answer:
At least 18 solid balls
Step-by-step explanation:
Volume of rectangular tank:[tex]\sf \boxed{\bf Volume \ of \ rectangular \ tank = length* width * height}[/tex]
Volume of empty space = Volume of the full tank - Volume of the tank till the water.
= 20*10*13 - 20*10*11
= 2600 - 2200
= 400 cm³
Volume of 1 solid ball = 23 cm³
Number of solid ball to make the tank overflow = 400 ÷ 23
≈ 18 solid balls
The following dot plot shows the number of players at each table in Bill's Bingo Hall. Each dot represents a different table.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
What is the lowest number of players at a table?
players
The lowest number of people at a table is 0.
What is the lowest number of people at a table?A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.
Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.
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using the order of operations, which operation in the expression 3x2-2³÷4 should be completed first
A.multiply 3 and 2
B.divide 2³ by 4
C.cube 2
D.subtract 2³ from 2
Answer:
C. Cube 2.
Step-by-step explanation:
Using PEMDAS the first operation to be done is E (Exponent) which is
2³.
How many 5-letter words can be made using exactly 5 of the letters from
TEXAS and MEXICO? Letters may only be used as many times as they appear. (For
example, XETEX is allowed. However, MATEA is not allowed, since the A appears twice
in MATEA but only once in the given words.)
Step-by-step explanation:
for TEXAS using permutation formula
we have:5!/1!1!1!1!1!=5!=120
for MEXICO using permutation formula
we have:6!/1!1!1!1!1!1!=6!=720
PLS HELP OR ILL FAIL MY CLASSES I RLLY NEED HELP PLEASE + 30 POINTS + BRAINLIST
PLS HELP
PLS
PLS
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I NEED HELP
HELP
I’ll appreciate it so much please don’t skip and read this please
Answer:
See the attached picture.
Step-by-step explanation:
The number of pennies on square 64 is the total number of pennies on the first 63 squares.
Answer:The number of pennies on square 64 is greater than the pennies on 63 squares since 64 is already greater 63 that when 63 gets bigger 64 will also get bigger so it will always be greater than 63
Step-by-step explanation:
Answer:
Step-by-step explanation:
greater than
help pls with math lotsss of points!!!
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Calculate the value of the expression
1.) 18/3+2(12-5)
a) 33 1/3
b)10 2/3
c) 40
d)56
e)20
2.) 30+4(4+1)/2 -2(3+1)
a)77
b)46
c)92
d)21
e)17
Answer:
1. e
Step-by-step explanation:
18/3 +2(12-5)
=6+2(7)
=6+14
=20
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]
Divide 18 by 3 to get 6.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2(12-5) \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2\times7 \ \to \ \ [Multiply] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+14 \ \to \ \ [Add] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 20 \end{gathered}$} }[/tex]Therefore, the correct option is "E".
================================================================
===> Exercise 2[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4\times5}{2}-(3+1) \ \to \ \ [Multiply \ 4 \ by \ 5] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{20}{2}-(3+1) \ \to \ \ [Divide \ 20 \ by \ 2] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+10-2(3+1) \ \to \ [Add \ 30 \ and \ 10] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 4-2(3+1) \ \to \ [Add \ 3 \ and \ 1] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-2\times4 \ \ \to \ \ [Multiply \ 2 \ and \ 4.] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-8 \ \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 32 \end{gathered}$} }[/tex]It seems that none of the options is correct.
Help me pls this is very hard for me and plus i gotta turn this in tomorrow
Answer: [tex]\Large\boxed{x=40^\circ}[/tex]
Step-by-step explanation:
Given information
∡ 1 = 90°
∡ 2 = 50°
∡ 3 = x°
Total Angle = 180° (Triangle angle sum theorem)
Given formula
∡ 1 + ∡ 2 + ∡ 3 = Total Angle
Substitute values into the formula
(90) + (50) + (x) = (180)
Combine like terms
140 + x = 180
Subtract 140 on both sides
140 + x - 140 = 180 - 140
[tex]\Large\boxed{x=40^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Multiply (x - 3)(x2 + 7x - 2)
Answer:
x^3+4x^2−23x+6
Step by Step:
(x−3)(x2+7x−2)
=(x+−3)(x2+7x+−2)
=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)
=x3+7x2−2x−3x2−21x+6
=x3+4x2−23x+6
How many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1. 4) to within 0. 0001?
We need at least 7 terms of the Maclaurin series for ln(1 + x) to estimate ln 1.4 to within 0.0001
For given question,
We have been given a function f(x) = ln(1 + x)
We need to find the estimate of In(1.4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)
The expansion of ln(1 + x) about zero is:
[tex]ln(1+x)=x-\frac{x^2}{2} + \frac{x^3}{3} -\frac{x^4}{4} +\frac{x^5}{5} -\frac{x^6}{6} +.~.~.[/tex]
where -1 ≤ x ≤ 1
To estimate the value of In(1.4), let's replace x with 0.4
[tex]\Rightarrow ln(1+0.4)=0.4-\frac{0.4^2}{2} + \frac{0.4^3}{3} -\frac{0.4^4}{4} +\frac{0.4^5}{5} -\frac{0.4^6}{6} +.~.~.[/tex]
From the above calculations, we will realize that the value of [tex]\frac{0.4^5}{5}=0.002048[/tex] and [tex]\frac{0.4^6}{6}=0.000683[/tex] which are approximately equal to 0.001
Hence, the estimate of In(1.4) to the term [tex]\frac{0.4^6}{6}[/tex] is enough to justify our claim.
Therefore, we need at least 7 terms of the Maclaurin series for function ln(1 + x) to estimate ln 1.4 to within 0.0001
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Simplify: 7^x+1 + 7^x / 2×7^x
The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.
What is the simplified form of the expression 7^x+1 + 7^x / 2×7^x?It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.
On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.
Hence, we have; 7^x(7+1 ) / 2×7^x.
And upon simplification, we have; 8/2 = 4.
Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.
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Evaluate, leave ur answer in index form. 2³ × 2^-1
Multiply = add powers
3 + - 1 = 2
- - means +
+ + means +
- + means -
Thus, answer is 2^2
Hope this helps!
Find the smallest number by which 35280 must be multiplied so that the product is a perfect square.
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
What number must be an integer multiplied by to find a perfect square?
A number is a perfect square if the following property is satisfied:
a = b², where is a natural number.
Please notice that b can be either a prime number or a product of prime numbers.
Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of prime numbers:
35280 = 2⁴ × 3² × 5 × 7²
35280 = (2²)² × 3² × 5 × 7²
35280 = 4² × 3² × 5 × 7²
Then, we must add a 5 to find a product that is a perfect square:
4² × 3² × 5² × 7² = 176400
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
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What is the weight (in grams) of a liquid that exactly fills a 202 milliliter container if the density of the liquid is 0.685grams over milliliter? round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point.
Answer:
138.37 g
Step-by-step explanation:
Mass is the product of density and volume.
MassM = ρV = (0.685 g/mL)(202 mL) = 138.37 g
Select the order in which the operations should be performed
12-4/4
Divide 12 by 4, then subtract 4 from that number.
Divide 4 by 4, then subtract that number from 12.
Subtract 4 from 12, then divide that number by 4.
Subtract 4 from 12, then multiply that number by 4.
None of the above
Answer: Divide the 4/4 then subtract that from 12.
Step-by-step explanation:
Use PEMDAS. The Division comes first, then the subtraction.
How do I write a comment on the data following the completion of the scatterplot
What is the result of subtracting the second equation from the first?
- 2x + y = 0
-7x + 3y = 2
The result is [tex]5x-2y=-2[/tex].
The odds in favor of a horse winning a race are 9:5. find the probability that the horse will win the race.
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.
PLS HELP, WLL GIVE BRAINLEST, AND DONATE POINTS, PLEASE HELP ASAP!!!!!! ALSO GIVING 30 POINTS
The answer is J.
The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.
2/81/4The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.
2/61/3The probability is equal to :
1/4 × 1/31/12Answer:
J [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
• First, let's find the probability of landing a letter B in Spinner 1.
We have a total of eight possibilities, and two of them are the letter B.
∴ [tex]P(B) = \frac{2}{8}[/tex]
= [tex]\bf \frac{1}{4}[/tex]
• Next, let's find the the probability of landing the number 1 on Spinner 2.
There are a total of six possibilities, and two of them are the number 1.
∴ [tex]P(1) = \frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
• Now we have to calculate the probability of spinning a letter B and the number 1:
[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]
= [tex]\bf \frac{1}{12}[/tex]
Select the correct answer from each drop-down menu. Consider circle C with diameter DE. Diameter shows a circle centered at C. Points D and E lies on the circumference of the circle. Point E is labeled (13, 11) and point D is labeled (minus 3, 3). The equation of circle C is
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard equation of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the circle center and r is the radius of the circle.
The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:
h = (13 + (-3))/2 = 5
k = (3 + 11)/2 = 7
(h, k) = (5, 7)
[tex]Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}[/tex]
Radius = diameter / 2 = 8√5 ÷ 2 = 4√5
The equation of the circle is:
(x - 5)² + (y - 7)² = (4√5)²
(x - 5)² + (y - 7)² = 80
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
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The Library is having a book sale. Hardcover books sell for $4 each, and paperbacks sell for $2 each. If Connie spent $26 on 8 books, how many hard covers did she buy?
Please show work with a system of equations!!!!!!!!!!!!!
If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
Number of hardcover boughtLet h represent hard cover
Let p represent paperbacks
Formulate an equation
h + p= 8.......(1)
4h + 2p= 26......(2)
Multiply equation (1) by -2
-2h + -2p = -16
4h + 2p = 26
2h + 0p =10
2h = 10
Divide both side by 2h
h=10/2
h =5 hard covers
Paper backs
P=5-2
P=3 paper backs
Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
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What is the location of point g, which partitions the directed line segment from d to f into a 5:4 ratio? a number line goes from negative 5 to positive 10. point d is at negative 2 and point f is at positive 7. a line is drawn from point d to point f.
the location of the g point is 3.
What is Proportion?Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.
According to the given Information:Point G Partition the directed line segment form d to f into a
5:4 ratio
so,
g - d = (5/9) x (f - d)
We have that d = -2 and f = 7, Therefore
g - d = (5/9) x (f - d)
g + 2 = (5/9) x (7 + 2)
g + 2 = 5
g = 3
Therefore the location of the g point is 3.
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Answer: OPTION D
Step-by-step explanation:
Which of the following is the domain and range of the ellipse with equation 4x2 + 25y2 – 8x + 100y + 4 = 0?
The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
How to determine the domain and the range of the ellipse?The equation of the ellipse is given as:
4x^2 + 25y^2 – 8x + 100y + 4 = 0
Next, we plot the graph of the ellipse
See attachment for the graph of the ellipse
The domain
From the attached graph the minimum and the maximum values of x are:
Minimum = -4
Maximum = 6
So, the domain of the ellipse is [-4. 6]
The range
From the attached graph the minimum and the maximum values of y are:
Minimum = -4
Maximum = 0
So, the range of the ellipse is [-4. 0]
Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
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Help please!!!!!!! (im bad at math)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
The probability that the person is over 40 and prefers cola exists at 1.3725.
What is probability?The probability of an event exists in the ratio of the size of the event space to the size of the sample space.
The size of the sample space exists the entire number of possible outcomes.
The event space exists the number of outcomes in the event you exists interested in.
So, P = size of the event space/size of the sample space
To estimate the probability that the person exists over 40 years.
Size of the sample size = 255
Size of the event space = 85
P = 85/255
P = 1/3
To estimate the probability that they drink cola.
Size of the sample size = 255
Size of the event space = 95
P = 95/255
P = 19/51
To estimate the probability that the person exists over 40 years of age or that they drink cola
So, P = (1/3) + (19/51)
[tex]$P = (51*3+3*19)/153[/tex]
P = 1.3725
Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.
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Evaluate the integral, show all steps please!
Answer:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]
Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:
[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]
[tex]\textsf{Let }x=3 \sin \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]
Find the derivative of x and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]
[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]
[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]
[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]
[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]
[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]
[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
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Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x³
a=0
b=3
3 Intervals
Split up the interval [0, 3] into 3 equally spaced subintervals of length [tex]\Delta x = \frac{3-0}3 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3]
The left endpoint of the [tex]i[/tex]-th subinterval is
[tex]\ell_i = i - 1[/tex]
where [tex]i\in\{1,2,3\}[/tex].
Then the area is given by the definite integral and approximated by the left-hand Riemann sum
[tex]\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}[/tex]
Question
What are the coordinates of the point (−4, 2) after a translation 2 units left and 2 units up?
(−6, 4)
begin ordered pair negative 6 comma 4 end ordered pair
(−6, 0)
begin ordered pair negative 6 comma 0 end ordered pair
(−2, 0)
begin ordered pair negative 2 comma 0 end ordered pair
(−2, 4)
begin ordered pair negative 2 comma 4 end ordered pair
Answer:
(-6,4)
Step-by-step explanation:
You started at (-4,2) The first number in the ordered pair moves the number left and right and the second number moved the point up and down.
We are first told to move the point 2 units to the left. -4 is my left right number. If I am at -4 and I go to unites to the left, I will be at -6. My new point is now (-6,2). Next we are told to go up 2. The 2 number in my ordered pair tells me that I am 2 above the x axis. Now I am going to go two more units up. I am now at 4, so my new ordered pair after the translation is (-6,4)
coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).
What is Translation ?
"Translation" moves points the same distance along lines that are parallel to each other.
Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.
Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points
We are asked to find the coordinates of the points (-4,2) after a translation 2 units left and 2 units up.
We know that translating a point to the left by 'a' units means we need to subtract 'a' units from x-coordinate of the point.
Translation to 2 units left:
(-4,2) → (-4-2, 2) → (-6, 2)
We know that translating a point to upwards by 'a' units means we need to add 'a' units to y-coordinate of the point.
Translation to 2 units up:
(-6, 2) → (-6, 2+2) → (-6, 4)
Therefore, coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).
Read more about Translation at:
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