Mathematics High School

What is the image point of (4, 6) after the
transformation T5,2 O ry=-x?

Answers

Answer 1

Answer:

The image point is (-1,-2)

Step-by-step explanation:

Firstly, we have to reflect the given point over the line y = -x after which we perform the translation using the coordinate (5,2)

Mathematically;

If we reflect a point (x,y) over the line y = -x

we have the coordinate change to (-y,-x)

so, (4,6) becomes (-6,-4)

Then for the translation, we add 5 to the new x-axis coordinate, then add 2 to the new y-axis coordinate

we have this as;

(-6 + 5, 2-4) = (-1,-2)

Related Questions

D and E are points on sides AB and AC respectively of triangle ABC such that DE || BC. If AD = x-1, DB = x – 3, AE = x + 3 and EC = x , the value of x is: ​

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

The triangles are similar, so corresponding sides are proportional.

  AE/AD = EC/DB

  (x+3)/(x -1) = x/(x -3)

  x^2 -9 = x^2 -x . . . . . . . cross multiply

  x = 9 . . . . . . . . . . . add x+9-x^2 to both sides

The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240. A) Find the first term. B) Find the common ratio. C) Justify your answers by showing steps that demonstrates your answers generate S8=19680 and S4=240.

Answers

Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .

Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .

The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .

Now, on solving  [tex]\frac{S_{8} }{S_{4} }[/tex]  we get,

[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]  

[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]

[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )

So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .

mow much would 600$ invested at 8% interest compounded continuously be worth after 3 years?

Answers

The amount would be 2,250.

WILL MARK BRANLIEST
When describing a rotation, what
information must you include?

Answers

Answer:

The point you are rotating at (also called the centre of rotation)

The angle of rotation (usually in degrees but I don't know your school)

Direction of the turn

Step-by-step explanation:

state wether the product of √3 and √9 is rational or irrational. explain your answer​

Answers

√9 is rational and √3 irrational number

9 What is the volume of the cone below? * 267.95 in3 33.49 in3 133.97 in3

Answers

Answer:

Volume of cone = 33.49 inch³

Step-by-step explanation:

Missing information;

Height of cone = 8 inch

Diameter of cone = 4 inch

Find:

Volume of cone

Computation:

Radius of cone = Diameter of cone / 2

Radius of cone = 4 / 2

Radius of cone = 2 inch

Volume of cone = [1/3][πr²h]

Volume of cone = [1/3][(3.14)(2)²8]

Volume of cone = [1/3][(3.14)(4)8]

Volume of cone = [1/3][(3.14)(32)]

Volume of cone = [1/3][100.48]

Volume of cone = 33.49 inch³

Please help me!! Perimeter: about ______ ft squared
Area: about ________ ft squared

Answers

Answer:

55.1 ft ; 236.7 ft^2

Step-by-step explanation:

radius = 7.5 ft

Perimeter of the semicircles = 2 * radius * pi = 2 * 7.5 * pi = 47,12389 ft

Perimeter of the rectangle = 4 * 2 = 8 ft

Total perimeter = 55,12389 ft

Area of the semicircles = radius^2 * pi = 7.5^2 * pi = 176,714587 ft^2

Area of the rectangle = 4 * 15 = 60 ft^2

Total area = 236,714587 ft^2

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