If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation.
1 answer:
Answer:
This is the interval from -9 to 16. Exclude -9 but include 16.
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Work Shown:
The idea is to multiply all sides by 5, then add 1 to all sides
This converts to the interval notation
note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.
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Answer:
Length of right-angle triangle 'a' = 4
b)
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Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given b = 3 and hypotenuse c = 5
Given ΔABC is a right angle triangle
By using pythagoras theorem
c² = a² + b²
⇒ a² = c² - b²
⇒ a² = 5²-3²
=25 - 9
a² = 16
⇒ a = √16 = 4
The sides of right angle triangle a = 4 ,b = 3 and c = 5
<u><em>Step(ii):-</em></u>
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Answer:
The equation of the line is y - 3 = 2.5(x - 2) ⇒ D
Step-by-step explanation:
The rule of the slope of a line is m = , where
- (x1, y1) and (x2, y2) are two points on the line
The point-slope form of a line is y - y1 = m(x - x1), where
- (x1, y1) is a point on the line
From the given figure
∵ The line passes through points (2, 3) and (0, -2)
∴ x1 = 2 and y1 = 3
∴ x2 = 0 and y2 = -2
→ Substitute them in the rule of the slope to find it
∵ m =
∴ m = 2.5
→ Substitute the values of m, x1, y1 in the form of the equation above
∵ m = 2.5, x1 = 2, y1 = 3
∵ y - 3 = 2.5(x - 2)
∴ The equation of the line is y - 3 = 2.5(x - 2)