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9966 [12]
3 years ago
12

How many solutions does this system have?

Mathematics
1 answer:
poizon [28]3 years ago
7 0

Answer:

Step-by-step explanation:

5x - y = 3.......(1)

2y = 10x+2.....(2)

Rearranging (2)

-10x + 2y = 2......(3)

Multiply equation (1) by 2

10x - 2y = 6..........(4)

Adding (3) and (4)

-10x + 10x + 2y - 2y = 2 + 6

No solution since both x and y are eliminated.

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A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?
Alexxx [7]

<u>Answer</u>:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of  larger square to smaller square is 9:1

<u>Step-by-step explanation:</u>

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side  of the small square is 2 units

so the are of the small square is 2^2 = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=>\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}

=>\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}

=>\sqrt{(3 +3)^2 +(-3 +3)^2}

=>\sqrt{(6)^2 +(0)^2}

=>\sqrt{36}

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

6^2

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0
3 years ago
What is 3p + 2 &gt; -10
bezimeni [28]

Answer:

p> -4

Step-by-step explanation:

3p + 2 > -10

3p > -10 -2

p> -4

7 0
2 years ago
What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?
NNADVOKAT [17]

Answer:

search it on googIe Imao

Step-by-step explanation:

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4 0
3 years ago
You throw a ball at a height of 5 feet above the ground. The height h (in feet)
Serjik [45]

Answer:

b

Step-by-step explanation:

4 0
3 years ago
On a map, the distance between two historical markers is 4.5 inches, and 2.5 inches represents 10 miles.
Morgarella [4.7K]

Answer:

The actual distance between the historical markers is 18 miles.

Step-by-step explanation:

Given : On a map, the distance between two historical markers is 4.5 inches, and 2.5 inches represents 10 miles.  

To find : What is the actual distance between the historical markers?

Solution :

We have given that,

2.5 inches represents 10 miles.

i.e, 1 inch represent \frac{10}{2.5} miles.

1 inch = 4 miles.

Now, The distance between two historical markers is 4.5 inches.

The actual distance between the historical markers in 4.5 inch is

4.5 \text{ inch}=4.5\times 4\text{ miles}

4.5 \text{ inch}=18\text{ miles}

Therefore, The actual distance between the historical markers is 18 miles.

7 0
3 years ago
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