Answer:
The coordinates of the dillated vertices are [tex]A'(x,y) = (2,2)[/tex], [tex]B'(x,y) = (4,4)[/tex], [tex]C'(x,y) = (8,2)[/tex] and [tex]D'(x,y) = (4,-2)[/tex].
Step-by-step explanation:
From Linear Algebra, we define dilation by the following equation:
[tex]P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation, dimensionless.
[tex]P(x,y)[/tex] - Original point, dimensionless.
[tex]k[/tex] - Scale factor, dimensionless.
[tex]P'(x,y)[/tex] - Dilated point, dimensionless.
If we know that [tex]O(x,y) = (0, 0)[/tex], [tex]k = 2[/tex], [tex]A(x,y) = (1,1)[/tex], [tex]B(x,y) = (2,2)[/tex], [tex]C(x,y) = (4,1)[/tex] and [tex]D(x,y) = (2,-1)[/tex], then the dilated points are, respectively:
Point A
[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)
[tex]A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)][/tex]
[tex]A'(x,y) = (2,2)[/tex]
Point B
[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)
[tex]B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)][/tex]
[tex]B'(x,y) = (4,4)[/tex]
Point C
[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex]
[tex]C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)][/tex]
[tex]C'(x,y) = (8,2)[/tex]
Point D
[tex]D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)][/tex]
[tex]D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)][/tex]
[tex]D'(x,y) = (4,-2)[/tex]
The coordinates of the dillated vertices are [tex]A'(x,y) = (2,2)[/tex], [tex]B'(x,y) = (4,4)[/tex], [tex]C'(x,y) = (8,2)[/tex] and [tex]D'(x,y) = (4,-2)[/tex].
Cornelius has 25 nickels, 39 dimes, 22 quarters, and 12 fifty-cent pieces. How
much money does he have?
Answer:
16.65$
Step-by-step explanation:
Answer:
16.65
Step-by-step explanation:
Lisa reads 45 pages in 8 minutes. How many minutes will it take her to read 36 pages. Use a proportion or unit rate to solve.
Answer:
Step-by-step explanation:
if Lisa Read
45pages/8minutes she will read 36 pages/? minutes
45/8=5.62 pages/minute
36/5.62=6.4 minutes
roughly 6 minutes
Jamison wants to save up his money to buy a car. His parents said they will match what he saves, up to $2000. Jamison mows lawns in the summer, and shovels snow in the winter. He charges $25 per lawn, and $20 per driveway. Let X represent the amount of money that Jamison can save so that his parents will match the amount. Let L represent the number of lawns he mows , and T represent the number of driveways he shovels. Which of the following inequalities need to be part of the system? Select all that apply.
25L + 20d < x
x (greater than or equal to) 2000
20L+25d=x
25L+20d=x
x(less that or equal to)2000
Answer:
25l+20d=x and x ≤ 2000 needs to be part of the system.
Step-by-step explanation:
Given that:
Amount charged per lawn = $25
Number of lawns = l
Amount charged per driveway = $20
Number of driveways = d
Amount saved by Jamison = x
[tex]25l+20d=x[/tex]
Amount given by parents = upto $2000
It means the parents will not give more money than $2000, therefore, we will use less than equal to inequality
x ≤ 2000
Hence,
25l+20d=x and x ≤ 2000 needs to be part of the system.
4х + 3y = 12
х = 5y - 20
Solve the system by substitution
Answer:
y=4 and x=0
Step-by-step explanation:
4(5y-20)+3y=12
20y-80+3y=12
23y-80=12
23y=92
y=4
Substitute y as 4 to get x.
Answer:
y=4
x=0
Step-by-step explanation:
4x + 3y = 12
X - 5y =-20
Multiply second equation by 4
4x + 3y = 12
4x - 20y = - 80
Subtract
23y = 92
y = 92/23
y =4
Put the value in first equation
4x + 12 =12
So 4x = 0
Therefore x= 0
Find the h.c.f by division method:
399, 665, 1463.
Help!! Teachers,students,etc
Answer:
6 8 8 8 89 9 8 8 66 4 4 4 57 8c8 7 54
How do you convert a rational exponent into a radical? Use proper terminology (numerator, denominator, index, radicand, power).
Answer: 1. Well, for one they both have a 'radicand' and you can arrange both of them in a fraction form.
2. Graph is increasing, there's an asymptotic value, the domain is all real numbers, the range is y > 0. If you add a constant, you are shifting it vertically, which means it's y-intercept will change by the magnitude of the constant.
3. Linear functions are a straight line with one definite slope. Exponential functions are basically curves with their slopes, not constantly, but changing. As you increase your x-values, the linear functions lacks behind, and the exponential one becomes very large.
4. I really don't know how to explain this, it's kind of confusing.
5. You can use the slope formula: (y2-y1)/(x2-x1). Plug in values, you get:
(12-8)/(4-2). This can be simplified to 4/2 or just 2. That's his average rate of change: 2 balls per day.
6. An arithmetic sequence adds on a specific value every time. For example: {1, 3, 5, 7...}
A Geometric sequence increases every time by a common ratio. For example: {2, 6, 18, 54...}
6. If it's relative to time, then you have a parametric equation dealing with time. Just like that, you can see that 1 variable changes with respect to the other, and that implies parametricity.
Step-by-step explanation:
9514 1404 393
Answer:
[tex]x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a[/tex]
Step-by-step explanation:
The denominator of the fractional exponent becomes the index of the root. The exponent numerator is left as the power of the base. The exponent can be inside or outside the radical.
[tex]x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a[/tex]
Find the value of two numbers if their sum is 17 and their difference is 3.
Step-by-step explanation:
x+y=17 (First equation)
x-y=3 (Second equation)
Solving Equation (i)
x+y=17
x=17-y(First equation)
Putting value of x in equation (ii)
x-y=3
x=3+y
17-y=3+y
17=3+y+y
17=3+2y
2y=17-3
y=14/2
y=7
Putting value of y in equation(i)
x=17-y
x=17-7
x=10
PLEASE HELP ME IM RUNNING OUT OF TIME
The graph of a linear function is shown.
Which word describes the slope of the line?
A. positive
B. negative
C. zero
D. undefined
Answer:
negative
Step-by-step explanation:
its below the negative mark and its not verticle so it can't be undefined
Answer this thanks!!!!
Answer:
B
Step-by-step explanation:
$65×6%=$3.90
$3.90+$65=$68.90
m I right
ILL GIVE BRAINLIEST IF CORRECT!! Stacey is standing in a field. She walks 11 meters west, 30 meters north, 4 meters west and finally 22 meters south. How many meters is she from her starting point?
Answer:
21 meters
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
Out of 40 students in class 8,20% were absent.How many students were present?
Understanding:
The total number of students is 40. 8.20% of them were absent, which means the rest were present, or in other words, (100-8.20)% were present or 91.8%. We can find the actual number of present students by multiplying the percentage of present students by the total number of students.
Solution:
Present Percentage = 91.8% or [tex]\frac{91.8}{100}[/tex]
Present Students = [tex](\frac{91.8}{100})(40)=36.72[/tex], since we are dealing with people we have to round it, so the present students are actually 37.
HELP PLZ
find the value of x
Answer:
x=8
Step-by-step explanation:
Solve the system.
x + 2y – 4z = 4
2x – y + 2z = 3
3x – 8z = -2
Enter answer as ordered triple.
(2,[?],[?])
From second equation :
2x - y + 2z = 3
z = (3 + y - 2x)/2
Putting value of z in equation 1 and 3, we get :
x + 2y - 4( 3 + y - 2x )/2 = 4
x + 2y - 2( 3 + y - 2x ) = 4
x + 2y - 6 -2y +4x = 4
5x = 10
x = 2
Putting value of x in third equation, we get :
8z = 3( 2 ) + 2
z = 1
Putting value of x and z in equation 2, we get :
y = 2( x+z) - 3
y = 2( 1 + 2) - 3
y = 3
Therefore, the answer as an ordered triple is ( 2, 1, 3 ).
Grocery store sells tangerines in 2/5 kg bags. A customer bought 4kg of tangerines for a school party. How many bags did he buy
In order to have 4 kg, he must have 20/5 kg. Each bag is 2/5 kg, so 2/5 times 10 is 20/5 or 4kg. Therefore, he bought 10 bags of tangerines for the school party.
Find the values of a and b so that the linear system has the given solution.
Given Solution: (2, 1)
Equation 1: ax - by'= 4
Equation 2: bx - ay = 10
Answer:
a = 6, b = 8
Step-by-step explanation:
given (2,1)
2a - 1b = 4
-1a + 2b = 10
this gives us:
a + b = 14
solve for a
a = 14 - b
plug into first equations
2(14-b) - b = 4
28 - 2b - b = 4
28 - 3b = 4
24 = 3b
b = 8
now plug b back into your equation for a, and you get:
a = 14 - 8
a = 6
The dot plot show the heights of the players on two basketball teams
Answer:
Okay and? im confused there is no dot plot or question here...
Step-by-step explanation:
Answer:
H. Team B has a greater range in player heights than Team A has.
Step-by-step explanation:
just did the quiz
An 8 ounce tube of toothpaste costs $1.69. What is the Unit Price per ounce?
Answer:
$0.21 per ounce (rounded to nearest cent)
Step-by-step explanation:
8 ounces --- $1.69
1 ounce --- [tex]\frac{1}{8}[/tex] × $1.69 = $0.21 (rounded to nearest cent)
Question:
What is the Unit Price per ounce?
Answer:
If 8 ounces cost $1.69, then 1 ounce costs $1.69/8 = $0.21125, which is 21.125 cents, which rounds to 21.1 cents (because 2 is less than 5)
Completely factor the polynomial. 12x2 + 2x - 4
help now fast i will mark brainlest and please don't just put the answer work it out
Answer:
a. 6276
b. 5590
c. 23128
d. 17325
e. 15090
f. 40419
g. 10496
h. 15000
i. 15648
99% sure
write the number with the least value using the digits 1 through 9. use each digit only once. explain your reasoning
Answer: 123456789
Step-by-step explanation:
We need to write a 9-digit number using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9.
(where we can use each digit only one time)
We want the value of this 9-digit to be the smallest as possible, then:
The largest single value digit (9), needs to be in the smallest value place (in the units place)
The second larger digit (8), must be in the second smallest value place (in the tens)
And so on, then the 9-digit number will be something like:
123456789
Any other permutation will be larger than this number.
Function for g whose graph is similar to f(x)=3x^2 shifted right 6 units and upward 5 units
[tex]f(x) = 3 {x}^{2} [/tex]
function g has to be the transformation of function f. Therefore,
[tex]g(x) = 3 {(x - 6)}^{2} + 5[/tex]
is the answer.
Ethan sold 2/3 gallon of lemonade. Kayla sold some lemonade too. Together, they sold
1/4 gallons. Who sold more lemonade, Ethan or Kayla? How much more?
Answer:
Ethan sold more
Step-by-step explanation:
2/3 and 1/4
Simplify to 8/12 and 4/12
8/12 is more
Teen Court is a juvenile diversion program designed to circumvent the formal processing of first-time juvenile offenders within the juvenile justice system. An article reported on a study in which offenders were randomly assigned either to Teen Court or to the traditional Department of Juvenile Services method of processing. Of the 57 Teen Court individuals, 18 subsequently recidivated during the 18-month follow-up period, whereas 11 of the 54 Department of Juvenile Services individuals did so. Does the data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals who do so
Answer:
Z-statistic = 1.4017 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals
Step-by-step explanation:
Step(i):-
Given first sample size (n₁ ) = 57
Of the 57 Teen Court individuals, 18 subsequently recidivated during the 18-month follow-up period
First sample proportion
[tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{18}{57} =0.3157[/tex]
Second sample proportion
[tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{11}{54} =0.2037[/tex]
Null Hypothesis : p₁⁻ = p₂⁻
Alternative Hypothesis : p₁⁻ ≠ p₂⁻
Step(ii):-
Test statistic
[tex]Z = \frac{p_{1} ^{-} -p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }[/tex]
where
[tex]P = \frac{n_{1}p^{-} _{1} +n_{2} p^{-} _{2} }{n_{1} +n_{2} }[/tex]
[tex]P = \frac{57 X0.3157+0.2037X54}{54+57} = 0.2612[/tex]
Q = 1 - P = 1 - 0.2612 = 0.7387
[tex]Z = \frac{0.3157-0.2037}{\sqrt{0.2612 X0.7387 (\frac{1}{57} +\frac{1}{54} )} }[/tex]
Z = 1.4017
Level of significance ∝ =0.05
The tabulated value Z₀.₀₅ = 1.96
Z-statistic = 1.4017 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals
please help me with this question
1. 400 +4
2. 320+ 4
3. 360 +9
4. 5,0005
5. 3,000 +5
Answer:
1. 400 ÷ 4 = 100
2. 320 ÷ 4 = 80
3. 360 ÷ 9 = 40
4. 5000 ÷ 5 = 1000
5. 3000 ÷ 5 = 600
Answer:
1:100
2:80
3:40
4:1000
5:600
Step-by-step explanation:
I really need help on this
Answer:
i think its c i could be wrong but just go with your gut felling
Step-by-step explanation:
Please help thank you.
Solve the following equation algebraically:
x = 20
a. 4.47
b. -3.97, 3.97
C. -10, 10
d. 4.47, 4.47
Please select the best answer from the choices provided
A
B
Mark this and return
SU
Answer:
Option D
Step-by-step explanation:
Whenever we take a square root of a number the ± sign is with it like here in the question
[tex]x^2=20\\\\Apply\ square\ root\ on\ both\ sides\\sqrt{x^2}=\sqrt{20} \\\\The\ square\ cancels\ out\ with\ the\ root\x=\sqrt{20}[/tex]
And then x = ±4.47 which means x has two values one is +4.47 and the other is -4.47 so Option D is our answer.
Answer:
D
Step-by-step explanation:
Please Help
3x^2-5x+2=0
Answer: C
Step-by-step explanation:
to find the quotient 3/4 by 1/8
0 multiply 4/3 by 1/8
0 multiply 3/4 by 8
0 multiply 4/3 by 8
0 multiply 3/4 by 1/8
PLZ ASAP
Answer: D is 0.93
Step-by-step explanation:
(3/4 x 1/8 = 0.93 ) We are looking for 0.93.
4/3 x 1/8 = 0. 16
4/3 × 8 = 10.6
3/4 × 1/8 0.93
Nia has 19 apples. She wants to divide
them evenly into 4 bags. If she eats 3
apples, how many will she put into each
bag?
Answer: 4
Step-by-step explanation:
19 - 3 = 16
16/4 = 4
Answer: 4 apples
Step-by-step explanation:
19 - 3 = 16.
16 ÷ 4 = 4.
She will put 4 apples into each bag.