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Anit [1.1K]
3 years ago
9

10. When you add the same number to both sides of an inequality, is the inequality still true? Explain how you know your stateme

nt holds for subtracting the same number?
Mathematics
1 answer:
avanturin [10]3 years ago
6 0

The inequality is still true! If you add a number, say 5 to both sides of the following inequality, does anything change?

3 < 6

3 + 5 < 6 + 5

8 < 11

The inequality is still true. We know the statement holds for subtracting the same number because, in a way, addition and subtraction are pretty much the same operation. If I subtract 5 from both sides, I can think of it like "I add negative 5 to both sides" or something along those lines. It's kind of backwards thinking.

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Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the orig
gayaneshka [121]

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

7 1
2 years ago
A system of equations is shown below,
Vikki [24]
Answer: No solution
Step by step:
10x-2(5x+2)=12
10x-10x-4=12
0x=16
No solution
4 0
3 years ago
What is the number written in standard notation?
expeople1 [14]

Answer:

option B

Step-by-step explanation:

To find the number which is written in the standard form,5 \times {10}^{3}

We expand {10}^{3} and multiply by 5 to get

= 5 \times (10 \times 10 \times 10)

=5\times 1000

=5000

5 0
3 years ago
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Heather purchased a new $1,500 laptop by using a credit card with a 17% interest rate. She will pay off the balance in 2 years b
olga2289 [7]

Answer:

1779.84

Step-by-step explanation:

7 0
2 years ago
How do I do number 2 ? Someone please helpp w
Alexxandr [17]

Answer:

yes it is a function

Step-by-step explanation:

You have to take the numbers and see if any of them are the same in the X column if their are some of the same numbers you only write the number once. than you connect the numbers to the given output. If any numbers have 2 outputs it is not a function.

7 0
3 years ago
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