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icang [17]
3 years ago
10

Solve the “and” compound inequality for –1 < 6x + 1 ≤ 13

Mathematics
1 answer:
ser-zykov [4K]3 years ago
8 0

Answer:

-1/3 < x <(or equal to) 2

Step-by-step explanation:

Firstly divide your inequality into two separate inequalities...

1) -1 < 6x + 1...then solve for the first one..,which then gives you....;

-2 < 6x....which gives us our first solution (x > -1/3)

Then the second inequality

2) 6x + 1 <(or equal to) 13

which then gives you....,

6x <(or equal to) 12...which then gives our second solution...( x <(or equal to) 2)

Then combine the two solutions into a compound solution

-1/3 < x <(or equal to) 2

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Use calculus to find the area of the triangle with the vertices (0, 5), (2, -2), and (5, 1).
guajiro [1.7K]

The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is  21 square unit.

We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate

Equation of line passing through (0,5) and (2,-2) is

y-5 = [(-2-5)/(2-0)](x-0)

=>y-5 = (-7) /2x

=>y= (-7/2x)+5 -------(eq1)

Equation of line passing through (0,5) and (5,1) is

y-5 = [(1-5) / (5-0)](x-0)

=>y-5 = (-4/5)x

=>y = (-4/5)x+5-------(eq2)

Equation of line passing from (2,-2) and (5,1) is

y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)

=>y+2=(3/3)(x-2)

=>y=x-4--------(eq3)

Now, we use definite integration to find the area between the different equation of line.

So, area enclosed between the equations is given by the

area =\int\limits^5_2[(-4/5)x+5 - (-7/2)x + 5)dx  + \int\limits^5_1[(-4/5)x+5 -(x-4)]dx

=>area=\int\limits^5_2(7/2-4/5)x dx + \int\limits^5_1((-9/5)x+9)dx

Using properties of integration,\int\limits x\, dx=x^{2}/2

=>area=\int\limits^5_2(27/10)x dx + \int\limits^5_1(-9/5)x+9)dx

=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)

=>area=(27/20)×(25-4) + (-9/5)×24+9×4

=>area = (27×21)/20 + (-216)/5+ 36

=>area=(567/20) - (216/5) + 36

=>area= [(567-261×4)+(36×20)]/20

=>area=[(567-864)+720]/20

=>area=423/20

=>area=21 square unit.

Hence, area of triangle is 21 square unit.

To know more about area of triangle, visit here:

brainly.com/question/19305981

#SPJ4

4 0
1 year ago
What is the solution to 4x+6 is less than or equal to 18?
Sunny_sXe [5.5K]

Hey there! :)

Answer:

x ≤ 3

Step-by-step explanation:

Given:

4x + 6 ≤ 18

Subtract 6 from both sides:

4x ≤ 12

Divide both sides by 4:

4x/4 ≤ 12/4

x ≤ 3

6 0
3 years ago
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An art class costs $45 for materials and then
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45+10x the x stands for how many classes you take
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3 years ago
Write an equivalent expression for (x - 11)(x + 9).
vodka [1.7K]

Answer:

x²-2x-99

Step-by-step explanation:

(x-11)(x+9) - foil method

x times x = x squared

x times 9 = 9x

-11 times x = -11x

-11 times 9 = -99

x squared + 9x + 11x + -99

x squared-2x-99

7 0
3 years ago
Can someone please help me? :(
Sholpan [36]
The answer is attached, hope this helps!

5 0
3 years ago
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