Line segment AB measures 18 unit

The required expression that has an even integer value for all integers a and c is F. 8a + 2ac.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
We can determine which expressions have an even integer value for all integers a and c by looking at their factors.

An integer is even if and only if it is divisible by 2. Therefore, an expression will have an even integer value for all integers a and c if and only if it contains a factor of 2.

Let's look at each of the given expressions:

F. 8a + 2ac = 2(4a + ac)

This expression has a factor of 2, so it has an even integer value for all integers a and c.

G. 3a + 3c = 3(a + c)

This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.

H. 2a + c

This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.

J. a + 2c

This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.

K. ac + a²

This expression does not have a factor of 2, so it does not have an even integer value for all integers a and c.

Therefore, the expression that has an even integer value for all integers a and c is F. 8a + 2ac.

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The required fraction when multiplied by 8 1/2 so the product is about 5 is 10/17.

Given that,
what fraction would you multiply 8 1/2 so that the product is about 5 is to be determined.

What is the fraction?

Fraction is defined as the number of compositions that constitute the Whole.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
let the fraction b x
according to question
5 = x * 8 1/2
5 = x * 8.5
x = 5 / 8.5
x = 10 / 17

Thus, the required fraction when multiply by 8 1/2 so the product is about 5 is 10/17.

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Answer:

A'(1, 1); B'(3, 2); C'(1, 2)

Step-by-step explanation:

The original points are A(1,1 ), B(2, 3) and C(2, 1).

Reflecting the triangle across the x-axis will negate every y-coordinate; this maps

(1, 1)→(1, -1); (2, 3)→(2, -3); (2, 1)→(2, -1)

Rotating the figure 90° clockwise about the origin switches the x- and y-coordinates and negates the x-coordinate; this maps

(1, -1)→(-1 -1); (2, -3)→(-3, -2); (2, -1)→(-1, -2)

Reflecting across the line y=x will negate both the x- and y-coordinates; this maps

(-1, -1)→(1, 1); (-3, -2)→(3, 2); (-1, -2)→(1, 2)

Final answer:

To find the coordinates of ∆ABC after reflection across the x-axis, rotation by 90°, and reflection across y = x, we would apply these transformations to each point. Initially reflected across x-axis results in (x, -y), the 90° rotation gives (-y, x), and final reflection over y = x gives (x, -y). To find A′B′C′ we would need original coordinates, but general rule follows this pattern.

Explanation:

In this mathematics problem, we will find the coordinates for vertex A′, B′, and C′ of ∆A′B′C′. Given a triangle ∆ABC reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x, we need the original coordinates of A, B, and C to find A′B′C′. However, if we take a generic point (x, y), we can assume the following:

1. The reflection about the x-axis would turn it into (x, -y).
2. The 90° clockwise rotation about the origin would give the new coordinates (-y, x).
3. Finally, the reflection over the line y = x would change (-y, x) to (x, -y).

Assuming these transformations, we can find the final coordinates for A′, B′, and C′.

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