MATHEMATICS HIGH SCHOOL

Please Help!!!a. Write in words, a two-step sequence of transformations, that maps ΔABC to ΔA’B’C’.

b. Write a two-step ordered-pair rule, for the transformation sequence.

Answers

Answer 1

Answer:

Answer:

a) Δ ABC is rotated around the origin by angle 180° and then translated 1

unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180° then its image

is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

then its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

then its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

then its image is = (x , y + k)

- If the point (x , y) translated vertically down by k units

then its image is (x , y - k)

* Lets solve the problem

∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant

and reverse its direction Point A up and its image A" down

∵ No change in its size

∴ Triangle ABC rotates 180° clockwise around the origin

# Remember : There is no difference between rotating 180° clockwise

or anti-clockwise around the origin

∵ The vertices of Δ ABC are:

# A = (-3 , 5)

# B = (-3 , 2)

# C = (-1 , 2)

∵ If point (x , y) rotated about the origin by angle 180° then its image

is (-x , -y)

∴ A'' = (3 , -5)

∴ B'' = (3 , -2)

∴ C'' = (1 , -2)

∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"

∵ The vertices of Δ A'B'C are:

# A' = (4 , -2)

# B' = (4 , 1)

# C' = (2 , 1)

- By comparing the x-coordinates and y-coordinates of points of

Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1

and every y-coordinate add by 3

∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates

∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates

∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form

Δ A'B'C'

a) Δ ABC is rotated around the origin by angle 180° and then

translated 1 unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

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I just need help on confirming my answers please.

Answers

Both A. and D. are increasing.

Answer:

A and D would be the correct answers

Step-by-step explanation:

N a water treatment plant, water passes through a cone-shaped filter with a height of 4 m and a diameter of 9 m. The water flows from the filter into a cylinder below it. One full cone-shaped filter fills one-fifth of the cylinder.What are the dimensions of the cylinder? Use 3.14 to approximate pi.
A. h = 3 m; r = 3 m
B.h = 4.23 m; r = 5 m
C.h = 15 m; r = 6 m
D.h = 33.75 m; r = 2 m

Answers

Given:
Cone-shaped filter: height = 4m ; diameter = 9m
cylinder: one full cone-shape filter fills 1/5 of the cylinder

volume of the cone = π r² h/3 = 3.14 * (4.5m)² * 4m/3
V = 3.14 * 20.25m² * 1.33m
V = 84.57 m³

84.57 m³ ÷ 1/5 = 84.57 m³ * 5 = 422.85 m³ volume of the cylinder

Volume of cylinder = π r² h

Choice A: V = 3.14 * (3m)² * 3m = 3.14 * 9m² * 3m = 84.78 m³
Choice B: V = 3.14 * (5m)² * 4.23m = 3.14 * 25m² * 4.23m = 332.10 m³
Choice C: V = 3.14 * (6m)² * 15m = 3.14 * 36m² * 15m = 1695.60 m³
Choice D: V = 3.14 * (2m)² * 33.75 m = 3.14 * 4m² * 33.75m = 423.90 m³

The closest answer is Choice D. height = 33.75 m ; radius = 2 m

there is a circular path around a sports field Soniye X 18 minutes drive one round of the field while Ravi takes 12 minutes for the same the first they both started the same point in same time I am going the same direction after how many minutes will they meet again at the starting point

Answers

Yes it is 14 The answer to the question

A private school opened in 2005 with an initial enrollment of 85 students. The enrollment has increased by an average of 18 students each year since the school opened. A nearby public school had an enrollment of 95 in 2005, and its enrollment has increased by an average of 15 students per year. Interpret the point of intersection in the context of the problem.

Answers

1. Let t = time in years, with t = 0 representing the year 2005. Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school. Create the two functions to represent the situation.

f(t) = 85 + 18t ⇒ y = 85 + 18x
g(t) = 95 + 15t ⇒ y = 95 + 15x

y = y
85 + 18x = 95 + 15x
18x - 15x = 95 - 85
3x = 10
x = 10/3
x = 3 1/3

y = 85 +18(10/3) = 85 + 180/3 = 85 + 60 = 145
y = 95 + 15(10/3) = 95 + 150/3 = 95 + 50 = 145

x = 10/3 or 3 1/3
y = 145

Help answer 1/5x-2/3y=30 when y = 15

Answers

The value of the variable x at y = 15 will be 200.

What is the solution to the equation?

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation is given below.

(1/5)x - (2/3)y = 30

Solve the equation for x, then we have

(1/5)x = 30 + (2/3)y

x = 150 + (10/3) y

The value of the variable x at y = 15 will be

x = 150 + (10/3) × 15

x = 150 + 50

x = 200

The value of the variable x at y = 15 will be 200.

More about the solution of the equation link is given below.

brainly.com/question/545403

#SPJ2

$\frac{1}5x-\frac{2}3y=30$

Plug in 15 for y.

$\frac{1}5x-\frac{2}3(15)=30$

2/3 of 15 is 10.

$\frac{1}5x-10=30$

Add 10 to each side.

$\frac{1}5x=40$

Divide each side by 1/5.
(dividing by a fraction is the same as multiplying by its reciprocal...flip 1/5...×5)

$\boxed{x=200}$