All categories

3 years ago

===============================================================

Mathematics

1 answer:

MAXImum [283]3 years ago

6 0

Answer: A. Figure ABCD is similar to figure A'B'C'D'.

Step-by-step explanation:

Given : Figure ABCD is reflected about the x-axis to obtain figure A'B'C'D'.

Since a reflection is a rigid transformation which produces congruent images.

⇒ Figure ABCD must be congruent to figure A'B'C'D'.

⇒ Figure ABCD has same size as figure A'B'C'D'.

⇒ Figure ABCD must be similar to figure A'B'C'D'. [ ∵ If two figures are congruent then they are also similar.]

Reflection preserves side length and measure of angles .

⇒ Corresponding angles and side lengths of figure ABCD must be congruent to figure A'B'C'D'.

⇒ The measure of angle D is equal to the measure of angle D'.

Hence, the statement best describes the relationship between the two figures is :-

A. Figure ABCD is similar to figure A'B'C'D'.

You might be interested in

PLEASE HELP! WILL GIVE 70 POINTS!!

Tresset [83]

Answer:

$A=189\ mm^2$

Step-by-step explanation:

Surface Areas

Is the sum of all the lateral areas of a given solid. We need to compute the total surface area of the given prism. It has 5 sides, two of them are equal (top and bottom areas) and the rest are rectangles.

Computing the top and bottom areas. They form a right triangle whose legs are 4.5 mm and 6 mm. The area of both triangles is

$\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2$

The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus

$A_f=b.h=(7.5)(9)=67.5 \ mm^2$

The back left area is another rectangle of 4.5 mm by 9 mm

$A_l=b.h=(4.5)(9)=40.5 \ mm^2$

Finally, the back right area is a rectangle of 6 mm by 9 mm

$A_r=b.h=(6)(9)=54 \ mm^2$

Thus, the total surface area of the prism is

$A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2$

$\boxed{A=189\ mm^2}$

4 0

3 years ago

A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day. Another day she s

Eduardwww [97]

The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

Solution:

Let "a" be the cost of each ribeye steak dinners

Let "b" be the cost of each grilled salmon dinners

A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day

Thus we frame a equation as:

11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63

$11 \times a + 12 \times b = 560.63$

11a + 12b = 560.63 -------- eqn 1

Another day she sold 16 ribeye steak dinners and 6 grilled salmon dinners, totaling $584.46

Thus we frame a equation as:

16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46

$16 \times a + 6 \times b = 584.46$

16a + 6b = 584.46 ------------ eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 2 by 2

32a + 12b = 1168.92 ------- eqn 3

Subtract eqn 1 from eqn 3

32a + 12b = 1168.92

11a + 12b = 560.63

( - ) ----------------

21a = 1168.92 - 560.63

21a = 608.29

Divide both sides by 21

$a = 28.96 \approx 29$

Substitute a = 29 in eqn 1

11(29) + 12b = 560.63

319 + 12b = 560.63

12b = 560.63 - 319

12b = 214.63

Divide both sides by 12

$b = 20.13 \approx 20$

Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

5 0

3 years ago

9×6=30+? please help me with it

7nadin3 [17]

Hi there
let me help you out

9 x 6 = 30 + x

9 x 6 = 54

54= 30 + x

54 - 30 = x

24 = x

x = 24

6 0

3 years ago

Read 2 more answers

Brent needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference b

Advocard [28]

The difference of the area of the two right triangles is 33.0 cm^2.

5 0

3 years ago

A-plus Auto Body is painting designs on a customers car. They had 18pints of blue paint on hand. They used 1/2 of it for the fla

Mashutka [201]

1/2 of 18 pints is 9 because 18/2=9

They have 9 pints left.

1/3 of 18 pints is 6 because 1/3*18=6

9-6=3

There are 3 pints left.

They need 7.75 pints and they only have 3 so 7.75-3=4.75 (or 4 3/4)

They need 4 3/4 more pints of blue paint

7 0

3 years ago

Read 2 more answers