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2 years ago

Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.

Mathematics

1 answer:

Vikentia [17]2 years ago

3 0

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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3 years ago

Four usual dice are thrown on the ground. The total of numbers on the top faces of these four dice is 13 as the top faces showed

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The total of the faces touching the ground is 15.

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Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Given that:

Four usual dice are thrown

Total of numbers on the top faces of these four dice = 13

we know that in a dice, the sum of the numbers on any two opposite faces is always 7.

So,1 is opposite 6,

2 is opposite 5

and 3 is opposite 4.

Now, when 4,3,1 and 5 are the numbers on the top faces, then 3,4,6 and 2 respectively are the numbers on the face touching the ground as they sum upto 7.

Hence, total o faces touching the ground =3+4+6+2=15.

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1 year ago

Round 16.05792 to the nearest tenth

Alex

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3 years ago

Read 2 more answers

Solve for the equation of value of x(show your solution)

sertanlavr [38]

Answer:

2. ) {25}^{2x} - 1 = {125}^{3x} + 4

=> {25}^{2x} = {125}^{3x} + 4 +1

=> {(5)^(2)}^{2x} = {(5)^(3)}^{3x} + {5}^{1}

=> {5}^{4x} = {5}^{9x} + {5}^{1}

=> 4x = 9x + 1

=> 4x - 9x = 1

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3 years ago

Find the value of x for which the function y = x5-x³ + x² - 1 has a local minimum.

melisa1 [442]

The given function presents a local minimum in the coordinates (0,-1).

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In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

For solving this question, the given equation should be rewritten from the factoring.

$x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0$ . Then, you have 3 equations.

From the Zero Factor Principle, you can write

Equation 1

(x+1)²=0

x+1=0

x= -1

Equation 2

x-1=0

x=1

Equation 3

x²-x+1=0

$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}$

From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).