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Paul [167]
2 years ago
15

Write a proof. Given x = 2 = 3 (x - 4) Prove x = 5

Mathematics
1 answer:
Galina-37 [17]2 years ago
6 0

Step-by-step explanation:

The equation in the question is false.

x - 2 = 3(x - 4)

x - 2 = 3x - 12

3x - x = 12 - 2

2x = 10

x = 10 \div 2

x = 5

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NEED ASAP 50 PTS FOR ANSWER
vladimir2022 [97]

Answer:

This says that the product of 3 numbers (x, x-6 and x+2) is greater than zero. In other words the product of three numbers is positive. The key to the solution is the answer to the question: "How can is it possible to get a positive result when you multiply 3 numbers?" I hope the answer is obvious to you. You get a positive result when multiplying 3 numbers when a) all 3 numbers are positive, or b) two of the numbers are negative and the third one is positive. Any other combination of 3 numbers will have a negative or zero result. So the solution to this inequality will be all the x values that make

all 3 factors positive, or

make two of the factors negative and the third one positive

Now we just have to figure out how to translate this idea into number sentences. Making this translation is easier if we take time to figure out the order of the factors, if possible. Which one is the largest? Which one is the smallest? And which one is the middle factor? Even though we do not know what value x may be, it is possible, with these 3 factors, to know the order of them. After thinking about this for a while I hope you can see that (x+2) will always be greater than the other two factors, no matter what x happens to be. Similarly (x-6) will always be less than the other two no matter what x happens to be. And that makes x the in between factor. If you have trouble seeing this:

Picture a number line.

Picture any random point on this number line. (This is our "x").

x+2 will be two units to the right of x. Being to the right makes x+2 greater than x.

x-6 will be 6 units to the left of x. Being to the left makes x-6 less than x.

With x-6 to the left and x+2 on the right, x is the in-between number.

Knowing the order of the factors, combined with some logic, will make expressing the ideas "the three factors are positive" and "two factors are negative and one is positive" easier.

"The three factors are positive"

Without using the order or any logic we could say:

x+%3E+0 and x-6+%3E+0 and x+%2B+2+%3E+0

This is not terribly difficult to solve. But if we use the order and some logic we can come up with something much easier. Think about this: If the lowest of three numbers is positive, wouldn't the other two have to be positive, too? In other words, if the lowest of three numbers is to the right of zero on the number line, wouldn't the other two numbers, which are to the right of the lowest, also be to the right of zero? I hope you can see the logic of this. So to make all three factors positive we just have to make sure the lowest one is positive:

x-6+%3E+0

"Two factors are negative and one is positive"

Without using the order or any logic we would have to describe every possible combination of two negative factors and one positive factor:

((x+%3C+0) and x+-+6+%3C+0 and x+%2B+2+%3E+0) or (x+%3C+0) and x+-+6+%3E+0 and x+%2B+2+%3C+0) or (x+%3E+0) and x+-+6+%3C+0 and x+%2B+2+%3C+0))

Yikes!! This is solvable but it will take a lot of work. But if we use the order sand some logic we can get something much simpler to solve. When we know the order of the factors, in order to have 2 of three factors negative and one of them positive we only have to make sure that the in between factor is negative and the largest factor is positive. This is so because if the in-between factor is negative then the smallest of the three would have to be negative, too. So to make two factors negative and one positive all we have to say is:

(x+%3C+0 and x+%2B+2+%3E+0)

I hope you agree that using the order and some logic makes this problem much easier to solve. When you know the order of the factors this way is much easier. (Note: if it is not possible to figure out the order of the factors, then you must use the much longer, more complicated compound inequalities.)

Remember that our solution is the set of x values that make "all three factors positive or make two factors negative and one positive". Using what we figured out above this is:

(x+-6+%3E+0) or (x+%3C+0 and x+%2B+2+%3E+0)

Now we solve this compound inequality:

(x+%3E+6) or (x+%3C+0 and x+%3E+-2)

In interval notation (x+%3E+6) is (6, infinity)

In interval notation (x+%3C+0 and x+%3E+-2) is (-2, 0)

As for "My teacher is also asking me to find the vertex, axis and symmetry.": I agree, WHAT??. Even though I think it was phrased "axis of symmetry" not "axis and symmetry" it still doesn't make sense. The words "vertex", "axis of symmetry" apply to graphs of two variable sentences (usually parabolas). But we do not have a y. And if the inequality was x%28x-6%29%28x%2B2%29+%3E+y it would simplify to x%5E3+-4x%5E2+-12x+%3C+y. This is a cubic inequality not a quadratic inequality. Its graph would not be a parabola, would not have a vertex and would not have an axis of symmetry.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Solve the equation for all values of x in simplest form:<br> (x - 2)2 = 49
marin [14]
2x-4=49
2x=54
x is equal to 27
3 0
3 years ago
Volume of prisms just 3 problems
Vladimir79 [104]

Answer:

2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

4 0
3 years ago
Help me plzzzz and tyyyy
marin [14]

Answer:

her language arts hw takes longer and it takes 2/9 hr longer

Step-by-step explanation:

first of all, 4/9 > 2/9

4/9-2/9=2/9

5 0
3 years ago
PLSSS HELP IF YOU TURLY KNOW THISS
kirill [66]

Answer:

C) 3/4

Step-by-step explanation:

It is three steps out of four.

6 0
2 years ago
Read 2 more answers
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