Help!!! 1/3x - 3/4 + 5/6x = -2
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<h3>Answer: </h3><h3>See the attached image below for the table</h3>
In column 1 we have the x values 0, 4, 8, 12
In column 2, we have the y values 1, 2, 3, 4
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Explanation:
We can start with any x value we want. I find that 0 is easiest to work with, so why not start at x = 0. For the sake of not repeating, I'll use y = 1 as the start value for y.
The first row of the table is x = 0 and y = 1.
A slope of 1/4 means rise/run = 1/4. So rise = 1 and run = 4.
A rise of 1 indicates y goes up by 1. A run of 4 means x increases by 4.
So put together, slope = 1/4 means each time x goes up by 4, y goes up by 1.
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If we started at x = 0, then going up by 4 leads to x = 4. If y starts at y = 1, then going up by 1 leads to y = 2.
The second row of the table is x = 4 and y = 2
We'll repeat the pattern of "add 4 to x, add 1 to y" getting the third row having x = 8 and y = 3
We can repeat as many times as we want. Doing another "up 1, over to the right 4" movement lands us on (x,y) = (12, 4)
The completed table is shown below in the attached image.
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If you were to use the slope formula with any two rows of the table, then you should get m = 1/4
Let's do the first two rows
m = (y2-y1)/(x2-x1)
m = (2-1)/(4-0)
m = 1/4
I'll let you check the other pairs of rows.
Length and width of rectangle is 15 inches and 6 inches respectively
<h3><u>Solution:</u></h3>Given that area of a rectangle is 90 square inch
Ratio of length to the width = 5: 2.
Need to determine length and width of rectangle.
As ratio of length to the width is 5 : 2
Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.
<em><u>The formula for area of rectangle is given as:</u></em>
Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:
On solving the above expression for x we get
Hence length and width of rectangle is 15 inches and 6 inches.
The values of the angles are; x = 12°, m∠PQS = 71°, m∠PQT = 142° and m∠TQR = 41°
<h3>What are the measure of the each angle?</h3>The required angles; x, m∠PQS, m∠PQT, and m∠TQR
The given parameters are bisects ∠PQT
m∠SQT = (8·x - 25)°
m∠PQT = (9·x + 34)°
m∠SQR = 112°
We have;
m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)
m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)
m∠SQT = m∠PQS by Definition of congruency
m∠PQT = 2 × m∠SQT
Therefore;
(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°
Collecting like terms gives:
(34 + 50)° = 16·x - 9·x = 7·x
7·x = 84°
x = 84°/7 = 12°
x = 12°
m∠SQT = (8·x - 25)°
Therefore;
m∠SQT = (8 × 12 - 25)° = 71°
m∠SQT = 71°
m∠PQT = 2 × m∠SQT
∴ m∠PQT = 2 × 71° = 142°
m∠PQT = 142°
m∠PQS = m∠SQT (Angles formed by the same bisector )
∴ m∠PQS = m∠SQT = 71°
m∠PQS = 71°
m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)
m∠SQT = 71°
∴ m∠SQR = 112° = 71° + m∠TQR
m∠TQR = 112° - 71° = 41°
m∠TQR = 41°
Learn more about angles here:
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