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liraira [26]
3 years ago
15

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the s

olutions of the equation 4-x = 2x + 3.
Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.
Part C: How can you solve the equation 4-x = 2x + 3 graphically?
Mathematics
1 answer:
ale4655 [162]3 years ago
3 0
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the solutions of the equation 4-x = 2x + 3.

Because the point where the graphs intersect is a point that meets both rules (functions) y = 4 - x and y = 2x + 3 meaning that y from y = 4 - x equals y from 2x + 3 and also both x have the same value.

Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.

x values    4 -x         2x + 3

-3              4-(-3)=7     2(-3)+3 =-3
-2              4-(-2)=6     2(-2)+3 =-1
-1              4-(-1)=5     2(-1)+3 = 1
0                4-0=4        2(0)+3 = 3
1                4-1=3         2(1)+3=5
2                4-2=2        2(2)+3 = 7
3                4-3=1        2(3)+3 = 9

The the solution is between x = 0 and x =1

Part C: How can you solve the equation 4-x = 2x + 3 graphically?

Draw in a same graph both functions  y= 4 - x and y = 2x +3.

Then read the x-coordinates of the intersection point. That is the solution.

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kozerog [31]

Hello from MrBillDoesMath!


Answer: infinite solutions


Discussion: I did a double take on this one but  the left hand is

a + 3 + 2a =  3a +3

and the right hand side is

-1 + 3a + 4 = 3a + (4-1) = 3a + 3


The left and right sides of the equation are identical for all "a", i.e. for infinitely many "a" values.


Regards, MrB.







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For angles in first quadrant, the reference angle is itself. In second quadrant, the equation would be 180 - x where x is the measure of the angle. In third quadrant, x - 180. Lastly, in the fourth quadrant, the reference angle is 360 - x. From the second set of angles in the given, the reference angles are.
              (1) 135 ; RA = 180 - 135 = 45
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2 years ago
What is the next letter a z b y c x d
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Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separate
Nata [24]

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

_____

A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

7 0
3 years ago
In 1982 Abby’s mother scored at the 93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the
oksian1 [2.3K]

Answer:

The percentle for Abby's score was the 89.62nd percentile.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation(which is the square root of the variance) \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Abby's mom score:

93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the scores was 9604.

93rd percentile. X when Z has a pvalue of 0.93. So X when Z = 1.476.

\mu = 503, \sigma = \sqrt{9604} = 98

So

Z = \frac{X - \mu}{\sigma}

1.476 = \frac{X - 503}{98}

X - 503 = 1.476*98

X = 648

Abby's score

She scored 648.

\mu = 521 \sigma = \sqrt{10201} = 101

So

Z = \frac{X - \mu}{\sigma}

Z = \frac{648 - 521}{101}

Z = 1.26

Z = 1.26 has a pvalue of 0.8962.

The percentle for Abby's score was the 89.62nd percentile.

3 0
3 years ago
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