Solution:
Given:
To find f(g(x)):
Therefore, f(g(x)) = 3x + 5
To find g(f(x)):
Therefore, g(f(x)) = 3x + 1
Elizabeth is going to roll a fair 6-sided die 600 times. Complete the following statement with the best prediction. Elizabeth wi
2 answers:
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The equation is
This case asking the end result in the form of a slope-intercept.
<u>Step-1: find out the gradient. </u>
10x + 2y = -2
We isolate the y variable on the left side. Subtract both sides by 10x, we get:
2y = - 10x - 2
Divide both sides by two
y = -5x -1
The slope-intercept form is , with the coefficient m as a gradient. Therefore, the gradient is m = -5.
If you want a shortcut to find a gradient from the standard form, implement this:
10x + 2y = −2 ⇒ a = 10, b = 2
<u>Step-2:</u> the conditions of the two parallel lines
The gradient of parallel lines is the same . So
<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)
We use the point-slope form.
Given that
- m = -5
- (x₁, y₁) = (0, 12)
y - 12 = - 5(x - 0)
y - 12 = - 5x
After adding both sides by 12, the results is
<u>Alternative steps </u>
Substitutes m = -5 and (0, 12) to slope-intercept form
12 = -5(0) + c
Constant c is 12 then arrange the slope-intercept form.
Similar results as above, i.e.
<u>Note: </u>
- A similar problem brainly.com/question/10704388
- Investigate the relationship between two lines brainly.com/question/3238013
- Write the line equation from the graph brainly.com/question/2564656
Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant
Answer:
We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489
Step-by-step explanation:
- Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.
This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.
However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.
Observe that:
- 1+2+4+8+16+32+64+128+256+489=1000
- Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
- If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since
, by 2) we know that this would be possible.