enlarge the triangle by a scale factor of -1.5 with centre of englargement (3,6)
Answers
The coordinates of the enlarged and reflected triangle are A'(x, y) = (6, 3), B'(x, y) = (3, 3) and C'(x, y) = (6, 0).
How to enlarge a triangle on a Cartesian plane by rigid transformation
In this problem we find a triangle whose vertices have the following coordinates: A(x, y) = (1, 8), B(x, y) = (3, 8), C(x, y) = (1, 10), and we are asked to enlarge the triangle by a scale factor of - 1.5 and with a centre of enlargement at (3, 6). Please notice that the negative sign of the scale factor involves both enlargement and reflection. Then, the operation can be done by the following operation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of enlargementk - Scale factorP(x, y) - Original pointP'(x, y) - Resulting pointIf we know that O(x, y) = (3, 6), k = - 1.5, A(x, y) = (1, 8), B(x, y) = (3, 8) and C(x, y) = (1, 10), then the coordinates of the resulting expression:
A'(x, y) = (3, 6) + (- 1.5) · [(1, 8) - (3, 6)]
A'(x, y) = (3, 6) + (- 1.5) · (- 2, 2)
A'(x, y) = (3, 6) + (3, - 3)
A'(x, y) = (6, 3)
B'(x, y) = (3, 6) + (- 1.5) · [(3, 8) - (3, 6)]
B'(x, y) = (3, 6) + (- 1.5) · (0, 2)
B'(x, y) = (3, 6) + (0, - 3)
B'(x, y) = (3, 3)
C'(x, y) = (3, 6) + (- 1.5) · [(1, 10) - (3, 6)]
C'(x, y) = (3, 6) + (- 1.5) · (- 2, 4)
C'(x, y) = (3, 6) + (3, - 6)
C'(x, y) = (6, 0)
The coordinates of the enlarged and reflected triangle are A'(x, y) = (6, 3), B'(x, y) = (3, 3) and C'(x, y) = (6, 0).
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Related Questions
Nvm, I know it's KM for this one y'all.
Answers
Answer:
If the question is asking which line is the radius then yes
Step-by-step explanation:
The expression 2 - x-1/x+2
is equivalent to
A. 1 - 3/x+2
B. 1 + 3/x+2
C. 1 - 1/x+2
D. 1 + 1/x+2
Answers
The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
We have to find, which equation is equivalent to the given expression.
The given expression is,
[tex]= 2- \dfrac{x-1}{x+2}[/tex]
To determine the equivalent expression following all the steps given below.
Step1; Taking LCM in the equation,[tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]
Step2; Solving the equation,[tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]
Step3; rewrite the equation in the small factors,[tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]
Step4; By using partial fraction rewrite the equation,[tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]
Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
For more details refer to the link given below.
https://brainly.com/question/2264568
Algebra Mary decided to travel from home to school which is 600 metres away. She started by walking “x” metres, then ran for twice the distance she walked. Mary then decided to take the bus for the rest of the journey which 65 metres more than the distance she ran. a) State an expression in terms of x for; i) the distance Mary ran [1 mark] ii) the distance Mary travelled by bus . [2 marks] iii) the total distance travelled [ 2 marks] b) Using the balancing method, solve the equation, hence state the distance Mary walked. [4 marks]
Answers
Answer:
Step-by-step explanation:
Distance traveled by walking = x
i) The distance Mary run = 2 *x = 2x
ii) Distance traveled by bus = 65 m more than the distance she ran
= 65 m more than 2x
Distance traveled by bus = 2x + 65
Total distance traveled = 600 m
x + 2x + 2x +65 = 600
5x + 65 = 600
5x = 600 - 65
5x = 535
x = 535/5
x = 107
Distance Mary walked = 107 m
(ii) Using a calculator, or otherwise, determine the exact value, to one decimal place, of 8792-6886 12 X 9
Answers
Answer: I did it in the explanation thingy-
Step-by-step explanation:
Step 1. 8792 - 6886 = 1906
Step 2. 12 x 9 108
That... OR the answer is 205848X
Solve the given portion 4/x=3/6 x=?
Answers
Answer:
8
Step-by-step explanation:
4/x=3/6
4=3/6x
4*6=3x
24/3=x
8=x
Please mark me as brainliest
I don’t wanna get wrong
Answers
Answer:
I think the answer is yes
Multiply x by 12 to get y
Please help. Thank you. (30 points included) (Shown work)
Answers
Answer:
True
Step-by-step explanation:
Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.
Please help I’ll give brainliest
Answers
Answer:
R = 13%
Step-by-step explanation:
P = $4000
I = $780
T = 18 months = 18/12 years
[tex]I = \frac{PRT}{100} \\\\780 = \frac{ 4000 \times R \times \frac{18}{12}}{100}\\\\780 = \frac{6000 \times R }{100}\\\\780 = 60R\\\\R = \frac{780}{60} = 13 \%[/tex]
can someone please explain to me how to do this?
Answers
Answer:
The fourth coefficient is 4.
Step-by-step explanation:
Pascal's Triangle in this case has 5 rows of coefficients because the highest power in (y + w)^4 is 4. 4 plus 1 is 5.
Here's the appropriate Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1 Use this row when expanding the 4th power of (v + w).
Notice that in the given expansion, the coefficients are
1, 4, 6, 4 1
This corresponds to the last (5th) row of Pascal's Triangle (above).
So the correct coefficient to be placed in the box is 4.
I need help i'm struggling with this work
Answers
Answer:
[tex]y=0.5x+2[/tex]
Step-by-step explanation:
Finding the inverse of a function is essentially finding the complete opposite of a given function. An easy trick can be used to find the inverse of a function. This trick is essentially thinking of the evaluator (f(x)) as another variable. Solve the function for (x) in terms of (f(x)); use inverse operations to do so. After completing this process, rewrite the function such that it is in the inverse function notation; switch the position of the (f(x)) and the (x), then indicate that it is an inverse function.
[tex]f(x)=2x-4[/tex]
Inverse operations,
[tex]f(x)=2x-4[/tex]
[tex]f(x)+4=2x[/tex]
[tex]\frac{f(x)+4}{2}=x[/tex]
Simplify,
[tex]0.5f(x)+2=x[/tex]
Rewrite in inverse function notation,
[tex]f^-^1(x)=0.5x+2[/tex]
[tex]y=0.5x+2[/tex]
FREE
y
A
What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the y-
axis?
8
X
0 (-8,-6)
O (-6, 8)
O (86)
O (6.-8)
C
B
Mark this and return
Save and Exit
Next
Submit
Answers
Find numbers a and b, or k, so that f is continuous at every point.
Answers
Answer:
[tex] \boxed{k = 7} [/tex]
Step-by-step explanation:
When interpreting this piecewise function, to determine whether or not the function is continuous, the limit to the left must be the same as the limit to the right.
Therefore to find an a value where the function is continuous at every point, we must determine where the limit is for the function.
In this case, the function is continuous at x = 7.
lim x→7 [x²] = lim x→7 [kx].
(7)² = k(7)
49 = 7k
÷7 ÷7
7 = k
k = 7.
En un colegio la cantidad de cuadernos y libros estan en la razon 2 es a 3. Si en total hay 126 cuadernos cuantos libros hay
Answers
Answer:
The number of books are 189.
Step-by-step explanation:
ratio of note books to the books = 2 : 3
total notebooks = 126
Let the number of books is x.
So, the ratio is
[tex]\frac{2}{3} = \frac{126}{x}\\\\x = 189[/tex]
So, the number of books are 189.
[tex]why \: \: do \: we \: need \: food \: \: \: \: {?} [/tex]
Answers
Answer:
to survive
Step-by-step explanation:
if you don't eat you are gonna died➡
At a sale on winter clothing, Cody bought four pairs of gloves and four hats for $36.00. Tori bought three pairs of gloves and four hats for $31.00. What were the prices for the gloves and hats?
Answers
Answer:
gloves cost $5
hats cost $4
Step-by-step explanation:
four pairs of gloves and four hats for $36.00
4g + 4h = 36
three pairs of gloves and four hats for $31.00
3g + 4h = 31
-------------------------
Subtract the second equation from the first
4g + 4h = 36
-( 3g + 4h = 31 )
––––––––––––
g = 5
gloves cost $5
substitute for g = 5 into either equation
4(5) + 4h = 36
20 + 4h = 36
Subtract 20 from both sides
4h = 16
Divide both sides by 4
h = 4
hats cost $4
haven't had luck with this question in the past and I need help.
Answers
Answer:
pi
Step-by-step explanation:
First find the area of a full circle with radius 2
A = pi r^2
A = pi 2^2
A = 4 pi
We know that this is 1/4 of a circle so take 1/4 of the area
1/4 A = 1/4 (4 pi) = pi
If you deposit $350 in an account that compounds interest continuously at 6.3%, how long will ittake to double your money?
Answers
Answer:
11 years
Step-by-step explanation:
Double of the amount deposited = $350 × 2 = $700
First, convert R as a percent to r as a decimal
r = R/100
R = 6.3%
Hence,
r = 6.3/100
r = 0.063 per year,
Then, solve the equation for t = time, the formula is given as:
t = ln(A/P) / r
A = Doubled amount = $700
P = Principal = Initial amount = $350
t = ln(700.00/350.00) / 0.063
t = 11.002 years
Approximately , t = 11 years
Therefore, it will take 11 years for your money to double.
Product of additive identity and multiplicative identity of -1/2 is
Answers
Answer:
1
Step-by-step explanation:
additive identity =1/2
multiplicative =2
Product = 1/2*2
So the answer is 1
A camera and a case cost 100 dollars. If the camera cost 90 more dollars than the case. How much does the case cost.
Answers
Answer:
Cost of case = $5
Step-by-step explanation:
x = cost of camera and y = cost of case
x = y + 90
x + y = 100
y + 90 + y = 100
2y = 10
y = 5
x = y + 90
x = 5 + 90
x = 95
Therefore, the cost of the camera is $95 and the cost of the case is $5.
The cost of case is 5 dollars.
What is the equation?The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Let,
Cost of camera = a and
Cost of case = b
Given that, camera and a case cost 100 dollars
a + b = 100
Since, the camera cost 90 more dollars than the case
So, a = b + 90
Substitute the value in the equation a + b = 100
b + 90 + b = 100
2b = 10
Divided by 2 both the sides
b = 5
Substitute the value of b in equation
a = b+ 90
a = 5 + 90
a = 95
So, the cost of the camera is $95 and the cost of the case is $5.
Hence, the cost of the case is 5 dollars.
Learn more about equation here:
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If k = -18 and m = 7, what is m - k?
Submit
Answers
Answer:
5
Step-by-step explanation:
Evaluate and substitute:
Sqrt of 7 - (-18)
Sqrt of 7 + 18 = 25
Sqrt of 25 = 5
Therefore, our answer!
Hope this helps, best of luck! :p
Please answer these tree questions in detail...
Will give Brainliest for the best...
Want answer in detail ASAP
Answers
Answer:
Step-by-step explanation:
14.
A.
x = 5.0081818181..
10x = 50.08181818181....
100x = 500.81818181818...
100x - x = 500.8181818... - 5. 008181818....
99x = 495.81
[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]
[tex]x = \frac{5509}{1100}[/tex]
14.
B.
[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]
15.
[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex] [tex][ \ rationalizing \ the \ denominator \ ][/tex]
[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex] [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]
[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]
[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]
16
[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]
[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex] [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]
[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex] [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]
What kind of sequence is this? (Need an answer fast lol.)
Answers
i dont know anymore
ok it was arithmetic
Answer:
arithmetic
Step-by-step explanation:
because this number is increasing by 7 in each
Really need help ?????pls
Answers
Answer:
34,833.21 ft³
Step-by-step explanation:
Volume of a cylinder = πr²h
r is the radius
h is the height
Given
height h = 19 3/4 ft
d = 1 1/5h
d = 6/5 * h
d = 6/5 * 19 3/4
d = 6/5 * 79/4
d = 474/20
radius r = 474/20 * 1/2
radius r = 474/40
radus r = 11 34/40
radus r = 11 17/20 ft
Get the volume
V = 3.14 * (474/40)² * 79/4
V = 3.14 * 561.69 * 19.75
V = 34,833.20535
Hence the volume of the cylinder to the nearest hundredth is 34,833.21 ft³
QUICKK a Square board has area of 2 ft.² what is the length of one side of the board
Answers
Answer:
√2 ft.
Step-by-step explanation:
⇒ Area of square board = 2 ft.²
⇒ (Side of the board)² = 2 ft.²
⇒ Side of the board = √(2 ft.²)
⇒ Side of the board = √2 ft.
I really help on this question
Answers
Answer:
jojo reference
Step-by-step explanation:
x = 180 - 129 = 51 degrees
If you need to show reasons
Adjacent angles on a straight line add to 180 (supplementary)
Corresponding angles on parallel lines are equal
simple interest 34,100 at 4% for 3 years
Answers
Answer:
Step-by-step explanation:
.....
1% = £341
4% = 341 X 4 = £1364
£1364 X 3 years = £4092
Based on the 4% interest per year
If it was 4% interest per month...
£1364 X 36 months/3years = £49,104
Lexon is standing 7.05 meters away from the statue off the Merlin mp at Merlin park Singapore the height of her eyes from her feet is 1.55 meters given that the angle of elevation of the top of the statue from her eyes is 42ﾟ find the height of the statue
Answers
Answer:
7.9m
Step-by-step explanation:
We solve using the Trigonometric function of Tangent
tan θ = Opposite/Adjacent
Opposite = x
Adjacent = 7.05m
We solve for x
tan 42 = x /7.05m
Cross Multiply
tan 42 × 7.05 = x
x = 6.3478485123m
Approximately = 6.35m
Height of the statue = x + 1.55
Hence, = 6.35m + 1.55m
= 7.9m
The height of the statue = 7.9 meters
What is the remainder when 19x^2+15x+12 is divided by x-2?
Answers
Answer:
118
Step-by-step explanation:
you save 2/5 of your allowance every week. if you receive $40 per week
how much money will you have after 8 weeks
Answers
Answer:
$128
Step-by-step explanation:
2/5 × $40= $16
$16×8= $128
En la inaguracion de unos juegos olimpicos, los 38 representantes de una nacion quieren desfilar formando columnas de 6¿es posible?¿de que modo podria desfilar formando columnas iguales?
Answers
Answer:
a) No
b) Sí
Step-by-step explanation:
a) En la inauguración de unos Juegos Olímpicos, los 38 representantes de una nación quieren desfilar en columnas de 6, ¿es posible?
Esto se calcula como
38 representantes / 6 columnas
= 6 2/6 = 6 1/3 columnas
No, no es posible, tendríamos 7 columnas con 6 columnas con representantes iguales de 6 y la séptima columna tendría solo 2 representantes allí
b) ¿Cómo podrían desfilar en columnas iguales?
Sí pueden
Esto se calcula como 38 representantes ÷ 2
= 19 columnas
Podemos tener 19 columnas con 2 representantes cada una