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
Using the equation
[tex] \sqrt{x + 7} + 5 = x[/tex]
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.
Answers
Given:
The equation is:
[tex]\sqrt{x+7}+5=x[/tex]
To find:
Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.
Solution:
We have,
[tex]\sqrt{x+7}+5=x[/tex]
Subtract 5 from both sides.
[tex]\sqrt{x+7}=x-5[/tex]
Taking square on both sides, we get
[tex]x+7=(x-5)^2[/tex]
[tex]x+7=x^2-10x+25[/tex]
[tex]0=x^2-10x+25-x-7[/tex]
[tex]0=x^2-11x+18[/tex]
Splitting the middle term, we get
[tex]x^2-2x-9x+18=0[/tex]
[tex]x(x-2)-9(x-2)=0[/tex]
[tex](x-2)(x-9)=0[/tex]
[tex]x=2,9[/tex]
Now, substitute [tex]x=2[/tex] in the given equation.
[tex]\sqrt{2+7}+5=2[/tex]
[tex]\sqrt{9}+5=2[/tex]
[tex]3+5=2[/tex]
[tex]8=2[/tex]
This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.
Substitute [tex]x=9[/tex] in the given equation.
[tex]\sqrt{9+7}+5=9[/tex]
[tex]\sqrt{16}+5=9[/tex]
[tex]4+5=9[/tex]
[tex]9=9[/tex]
This statement is true. So, 9 is a solution of given equation.
Therefore, 2 is an extraneous solution and 9 is a solution of given equation.
cho số phức z thỏa mãn 2iz-5+i=i-(z-2i) tính modun của số phức w=z-1+i
Answers
Solve the given equation for z :
2iz - 5 + i = i - (z - 2i )
2iz - 5 = 2i - z
(2i + 1) z = 2i + 5
z = (2i + 5)/(2i + 1)
z = (2i + 5)/(2i + 1) × (2i - 1)/(2i - 1)
z = (4i ² + 10i - 2i - 5) / (4i ² - 1)
z = (8i - 9)/(-5)
z = 9/5 - 8/5 i
Then
w = z - 1 + i = 4/5 - 3/5 i
Which side lengths form a right triangle?
Answers
Answer:
[tex]\text{B. }1.5, 2, 2.5,\\\text{C. }4, 4, \sqrt{32}[/tex]
Step-by-step explanation:
All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.
Verify:
[tex]1.5^2+2^2=2.5^2\checkmark,\\4^2+4^2=\sqrt{32}^2\checkmark[/tex]
s
is inversely proportional to
t
.
When
s
=
0.5
,
t
=
7
Work out
s
when
t
=
0.8
Answers
Answer:
4.375
Step-by-step explanation:
s=1/t
s=k/t
0.5=k/7
k=7x0.5=3.5
s=3.5/0.8
s=4.375
a circle shown below, m AC = 89° and m BC = 153°. Determine m∠ACB.
Answers
Answer:
m<ACB = 59degrees
Step-by-step explanation:
To get <ACB, first we need arcAB
arcAB + arcAC + arcBC = 360
arcAB + 89 + 153 = 360
arcAB+242 = 360
arcAB = 360 - 242
arcAB = 118
Also, m<ACB = 1/2arcAB
m<ACB = 1/2*118
m<ACB = 59degrees
Triangle ABC is reflected across the line y= x. What are the coordinates of the vertex B'of the resulting triangle a'b'c?
Answers
A teacher recorded the number of days her students went on vacation. Which statements describe the data? Select all that apply. Please help
Answers
Answer:
The students went on vacation for average 40 days.
The high school students went for more days than college students.
Step-by-step explanation:
The data shows number of students who went for vacation. The data class frequency shows that students who are in high school went for more days in vacation than college students. The students went for average of 40 days on vacation.
What is the volume of the cylinder shown below?
15
10
Answers
Answer:
option B
Step-by-step explanation:
Given r = 10 , h = 15
[tex]Volume = \pi r^2 h = \pi \times 10^2 \times 15 = \pi \times 100 \times 15 = 1500 \pi \ cubic \ units[/tex]
the ratio of blue to yellow paint when mixed to make green paint is 3:2 what percentage of the green paint is made from yellow paint
Answers
Answer:
40%
Step-by-step explanation:
3 + 2 = 5
Since 2 is the ratio of yellow paint, 2/5 x 100 = 40%
Hope this helped!
can someone help please...
Answers
Answer:
C. 8
Step-by-step explanation:
You double the distance of the x coordinate (ignore the sign in front of it) because you reflect it across the y-axis. So your math should look like this:
4*2= 8
2x+3y=15
X+y=6
Simultaneously equations
Answers
Answer:
Step-by-step explanation:
Let's solve your system by substitution.
2x+3y=15;x+y=6
Rewrite equations:
x+y=6;2x+3y=15
Step: Solvex+y=6for x:
x+y=6
x+y+−y=6+−y(Add -y to both sides)
x=−y+6
Step: Substitute−y+6forxin2x+3y=15:
2x+3y=15
2(−y+6)+3y=15
y+12=15(Simplify both sides of the equation)
y+12+−12=15+−12(Add -12 to both sides)
y=3
Step: Substitute3foryinx=−y+6:
x=−y+6
x=−3+6
x=3(Simplify both sides of the equation)
Answer:
x=3 and y=3
Answer:
x = 3, y = 3
Step-by-step explanation:
Given the 2 equations
2x + 3y = 15 → (1)
x + y = 6 → (2)
Multiplying 2) by - 2 and adding to (1) will eliminate x
- 2x - 2y = - 6 → (3)
Add (1) and (3) term by term to eliminate x
y = 3
Substitute y = 3 into either of the 2 equations and solve for x
Substituting into (1)
2x + 3(3) = 15
2x + 9 = 15 ( subtract 9 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Factorise fully 2a^2b + 6ab^2
Answers
Answer:
Step-by-step explanation:
2a^2b + 6ab^2
take common
2 can be taken common because there is 2in first term and there is 6 in second term and 2 can exactly divide 6 .there is a*a in first term and only a in second term so u can take a as common.There is only b in first term and b*b in second term so take u can take b as common.
total we can take
2ab as common.So,
2ab(a+3b)
therefore 2ab(a+3b) is the required answer.
The required factorization is 2ab(a+3b).
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Expanding brackets in reverse is a procedure known as factorizing.
Fully factorizing an equation entails putting it in brackets by eliminating the components with the highest common denominator.
Finding the highest common factor between all the terms in the phrase is the easiest technique to factorize.
We have, 2a²b + 6ab²
Here,
we have the highest common factor 2ab,
So, 2ab (a + 3b)
Therefore, 2ab(a+3b) is the required factorization.
To learn more about the factorization;
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pls help me i need help asap 30!! points pls help on all 4 questions
Answers
Answer:
b
d
a
d
Step-by-step explanation:
find out the arc length of DG and the measure of angle DHG
Answers
Answer:
is it timed, because i need like 20 mins to answer this question.
Step-by-step explanation:
(a)Find the commission on Rs65 000 if 4% commission is paid.
(b)On selling an article for Rs2700,a shopkeeper made a profit of 8%.find cost price of the article.
Answers
Answer:
Step-by-step explanation:
commission amount = 4 % of Rs 65000
=4/100 * 65000
=260000/100
=2600
therefore commision amount is Rs 2600
SP od an article = Rs 2700
profit %=8%
let CP be x
SP=CP + profit% of CP
2700=x + 8/100 *x
2700=100x + 8x/100
2700*100 = 108x
270000=108x
270000/108=x
2500=x
therefore cost price (CP) of an article is Rs 2500.
1) Find the remainder when 4x3 - 5x2 + 2x - 14 is divided by x -2
with the help of remainder theorem.
{ANS: R=2}
Answers
Answer:
remainder = 2
Step-by-step explanation:
A polynomial f(x) is divided by (x - a) then the remainder is f(a)
Here f(x) = 4x³ - 5x² + 2x - 14 is divided by (x - 2) then remainder is f(2)
f(2) = 4(2)³ - 5(2)² + 2(2) - 14
= 4(8) - 5(4) + 4 - 14
= 32 - 20 - 10
= 12 - 10
= 2
factorise:
k² - 2k - 8
with explaining the steps
Answers
Answer:
( k-4)(k+2)
Step-by-step explanation:
k² - 2k - 8
What 2 numbers multiply to -8 and add tp -2
-4*2 = -8
-4+2 = -2
( k-4)(k+2)
Refer to the attachment for steb-by-step explanation.
Please help if you can!!!!
Answers
Answer:
about 22 square units
Step-by-step explanation:
sana makatulong
Answer:
C: About 22 square units
Step-by-step explanation:
YW
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answers
Answer:area of the circle=πr²
3.14 =3.14 ×r²
r²= 1
r. =1 millimeters
the sum of the squares of two consecutive integers is 481. Find the integers
Answers
Answer:
{15, 16} or {-15, -16}
Step-by-step explanation:
Quick solution:
take half of the sum (approx. 240), sqrt(240)=15.5
So the numbers are 15 and 16. and also the negative equivalents since squares are always positive.
Exact method:
Let
x=smaller integer,
x+1 = next integer.
sum:
x²⁺(x+1)^2 = 481
2x^2 + 2x + 1 = 481
2x^2 + 2x - 480 = 0
x^2 + x -240 = 0
x = 15 or x = -16
so the integers are
either
{15, 16} or {-15, -16}
The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.
Assume 'x' is the number and the successive number is (x + 1).
The sum of the square of the consecutive number is 481. Then the equation of the number is given as,
x² + (x + 1)² = 481
Simplify the equation, then we have
x² + (x + 1)² = 481
x² + x² + 2x + 1 = 481
2x² + 2x - 480 = 0
x² + x - 240 = 0
x² + 16x - 15x - 240 = 0
x(x + 16) - 15(x + 16) = 0
(x + 16)(x - 15) = 0
x = 15, -16
Then the successive numbers are given as,
x + 1 = 15 + 1
x + 1 = 16
x + 1 = - 16 + 1
x + 1 = - 15
More about the solution of the equation link is given below.
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These two lines represent a system of equations.
What is the solution to that system?
Help ?
Answers
Answer: (-1,1)
Step-by-step explanation: Look at the intersection point of the lines
if im writing 200 post cards , and stamps are 0.36 cents a piece, how much money would 200 stamps be?
Answers
Answer:
72
Step-by-step explanation:
1 stamp costs 0.36 cents
Then, 200 post cards will cost 0.36 × 200 = 72
Answer:
$72 dollars
Step-by-step explanation:
200 x 0.36 = 72
In a class, 60% of the students are girls. There are 18 girls in the class.
a. How many students are in the class?
b.How many boys are in the class?
Answers
Answer:
a. Total of 45 students.
b. 18 Boys.
Answer:
There are 45 students and 18 boys in the class
plzzz anserw ill give you more points and crown if correct plzzz =D
From midnight to 7:00 am, the temperature rose 3/10 °C each hour. If the temperature at midnight was −1°C, what was the temperature at 7:00 am?
Answers
Answer:
11/10°C
Step-by-step explanation:
7 x 3/10 = 21/10
Temperature at Midnight = -1°C
Temperature at 7.00am = 21/10 + (-1°C)
= 11/10°C
PLEASE HELP ME WITH THIS
Answers
Which graph shows the solution to the system of linear inequalities?
x+5y>5
Y<2x+4
PLEASE HELP!!!
Answers
Answer:
x+5y >5 => red
y< 2x+4 => blue
Step-by-step explanation:
you can substitute x and y in each inequality to determine
This is my hw. heelp
Answers
Answer:
1/14
Step-by-step explanation:
Edwin is an insurance broker. Yesterday, he sold the Fredericks family a $425,000 insurance policy. And he also sold the Guthrie family a $379,000 insurance policy. If Edwin gets a 2.35% commission for all his sales. How much commission did he get paid for these two policies he sold?
Answers
Answer:
425000×0.0235=9987.5
379000×0.0235=8906.5
9987.5+8906.5=18894 that is the amount he gonna get
Encuentra el volumen de un prisma rectangular que mide 14m de largo y 10 m de ancho 34m de altura.
Answers
14x10x34
140x34=4760
Pls help I need this
Answers
Answer:
what you need help in we see nothing
