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babunello [35]
3 years ago
11

Solve for x: |1/3-x/4|=7/12

Mathematics
1 answer:
ozzi3 years ago
4 0

Your answer is x={-1, 11/3}

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What is the volume of the rectangular prism shown below?
Fiesta28 [93]

Answer:

48

Step-by-step explanation:

times 4 times 3 times 4 + 48

3 0
3 years ago
Jerome bought a sweater that was on sale for 20 percent off. Jerome paid $25.10 for the sweater, including sales tax of 8.25 per
Over [174]
Let the original price of the sweater be = X
Then the amount Jerome pays for the sweater after 20% discount = X - (20X/100)
                                                                                                           = X - 0.2X
                                                                                                            = 0.8X
Now on this price the 8.25% tax needs to be added to get to the amount actually paid by Jerome.
So,
0.8X + [(8.25/100) * (0.8X) = 25.1
This is the equation from which the actual price of the sweater bought by Jerome can be determined.
So
0.8X + [(.0825) * ( 0.8X) = 25.1
0.8X + 0.066X = 25.1
0.866X = 25.1
X = 25.1/0.866
   = 28.98
So the actual price of the sweater is $28.98.
8 0
3 years ago
Cot (15 degrees)
STatiana [176]

Answer:

Part I: cot(15 degrees) = cot(45 - 30)

Part II: Evaluation is below

Step-by-step explanation:

<em>Everything is done in degrees</em>

<em />

Two angles that differ by 15 degrees that is easy to evaluate is 30 degrees and 45 degrees. The cot(15 degrees) = cot(45 - 30) = 1/tan(45-30) = (1+tan45tan30)/(tan30 - tan45) = (1+ sqrt(3))/(sqrt(3) - 1)

We rationalize this by multiplying 1+ sqrt(3) in the top and bottom, getting:

(4 + 2sqrt(3))/2 = 2 + sqrt(3)

I hope this helps! :)

8 0
2 years ago
Help me ASAP PLEASE
lina2011 [118]

Answer:

  4. Functions: 1, 2, 4, 5, 7, 8, 11, 12

  5. y = -1/2x+5/2, x ≤ -1; 2x +1, x > -1.

      y = 2, x < 0; x, 0 ≤ x ≤ 3; 3 x > 3.

Step-by-step explanation:

4. A list of ordered pairs is a function of no x-values are re-used. In (3) and (6), the value x=2 is used more than once.

A graph represents a function if it passes the "vertical line test." A vertical line cannot intersect the graph in 2 or more points. (9) and (10) both fail that test.

If the relation is not listed here as being "not a function," then it is one of the answers to question 4.

__

5. The first step in writing the equation of a piecewise function is to identify the pieces. These are generally bounded by points of discontinuity--jumps in the function value, or changes in the slope of lines.

The second step is to identify the section of the function that boundary points belong to. Solid dots are part of the function definition; open circles are not.

<u>Left Graph</u>

The left piece ends at x=-1. There is a solid dot attached to the left piece, so its definition will be for the domain x ≤ -1. That line has slope -1/2, since is drops 1 unit for each 2 to the right. If extended, it would intersect the y-axis at y = 2 1/2 = 5/2. So, the piece on the left is y = -1/2x + 5/2 for x ≤ -1.

The right piece starts at x=-1, but does not include that point. It has a rise of 2 for each 1 to the right, so its slope is 2. It crosses the y-axis at y=1, so the piece on the right is y = 2x + 1 for x > -1.

You can use the method of your textbook author to combine theses pieces into one equation. The method shown above is one way to do it.

__

<u>Right Graph</u>

This graph has a discontinuity at x=0 and a change in slope at x=3. It can be described by 3 pieces. The point at x=0 does not belong to the left piece, but goes with the middle piece.

The left piece of the function is the constant 2, so has the equation y = 2 for x < 0.

The middle piece has a slope of 1 and a y-intercept of 0, so has the equation y = x for 0 ≤ x ≤ 3.

The point at x=3 belongs to both the middle piece and the right piece, so can be part of both function definitions, if you like. Generally, it is better form to include any given x-value in only one of the pieces of the function. So the equation for the right piece can be y = 3 for x > 3.

4 0
3 years ago
Identify the x-intercept and the y-intercept of the graph of 6x + 15y = −30.
Hunter-Best [27]

Answer:

D. x-intercept is -5 and the y-intercept is -2

5 0
2 years ago
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