Few questions explain too, very confusedPLEASE HELP

1. twice the difference between a number and ten

2. if 5 is subtracted from twice a number the result is 11

3. if 5 is added to the quotient of a number and 4 , the result is 10

4. associative property use: 4x5n

The equation in slope-intercept form of the line that passes through (-2,17) and (3,-13) is y = -6x + 5

What is linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two points:

(-2, 17) and (3, -13)

The equation is:

[y - (-13)] = (-13-17)/(3+2)[x-3]

y + 13 = -6(x - 3)

y = -6x + 18 - 13

y = -6x + 5

Thus, the equation in slope-intercept form of the line that passes through (-2,17) and (3,-13) is y = -6x + 5

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The value of the verbal expression is -2.

Given that a verbalexpression negative 4 minus negative 2, we need to solve this,

To subtract a negative number, you can rewrite it as adding the opposite. Therefore, "negative 4 minus negative 2" can be rewritten as "negative 4 plus positive 2."

When you add a negative number and a positive number, you can simply combine them by their absolute values and use the sign of the larger number. In this case, the absolute values of 4 and 2 are the same, so the result will have the same sign as the larger number, which is negative.

Therefore, "negative 4 plus positive 2" equals -2.

So, negative 4 minus negative 2 is equal to -2.

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The length of Line BC is 10

What is a triangle?

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

What are similar triangles?

Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.

How to find the length of the line BC?

Considering Δ AXY    and    ΔABC

                      ∠AXY       =      ∠ACB  (corresponding angles are equal)

                       ∠AYX       =      ∠ABC   (corresponding angles are equal)

                       ∠A is common in both the triangles

∴ We can say the triangles are similar .

Now, let H be the height of ΔABC and h be the height of ΔAYX

So, we can say,  

• Now, we know that area of the triangle can be found with the help of the formula (1/2)x(base)x(height)

So,  

⇒    

Now, substituting XY = 5 and    in the above equation, we get

⇒ BC² = 100

⇒ BC = ± 10

Since BC is the length , so it cannot be negative.

So, the negative value is rejected.

∴  BC = 10

Option B is correct.

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