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3 years ago

Suppose that 3<a<4 and 4<b<5. Find all possible values of:a-b

Mathematics

2 answers:

aleksley [76]3 years ago

5 0

If 4 < b < 5, then -4 > -b > -5, or -5 < -b < -4.

Then

3 < a < 4 ==> 3 - 5 < a - b < 4 - 4 ==> -2 < a - b < 0

Ber [7]3 years ago

5 0

Answer: -2 < a - b < 0

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2 years ago

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3 years ago

What is the distance between the lines y = 2x and y = 2x+5? Round your answer to the nearest tenth.

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The distance between both lines is 2.24 units

Step-by-step explanation:

There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.

Given

$y=2x\\Putting\ x=1\\y=2(1)\\y=2\\So, the\ point\ on\ y=2x\ is\ (1,2)$

We have to find the distance of this point from y=2x+5

$y=2x+5\\Subtracting\ y\ from\ both\ sides\\y-y=2x+5-y\\2x-y+5=0$

The formula for finding distance of a point (x,y) from a line is:

$d=\frac{|Ax+By+C|}{\sqrt{A^2+B^2}}$

A=2

B=-1

C=5

Putting the values in the formula

$d=\frac{|(2)(1)+(-1)(2)+5|}{\sqrt{(2)^2+(-1)^2}}\\d=\frac{|2-2+5|}{\sqrt{4+1}}\\d=\frac{|5|}{\sqrt{5}}\\d=\frac{5}{\sqrt{5}}\\d=2.236\ units$

Rounding off will give: 2.24 units

The distance between both lines is 2.24 units

Keywords: Equations of lines

Learn more about distance in lines at:

#LearnwithBrainly

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3 years ago

Suppose that 3<a<4 and 4<b<5. Find all possible values of:a-b​

Suppose that 3<a<4 and 4<b<5. Find all possible values of:a-b