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aksik [14]
3 years ago
13

The graph shows the functions f(x), p(x), and g(x):

Mathematics
2 answers:
AleksandrR [38]3 years ago
7 0
Um yes lol beat me to it, but yes ^they^ are correct
Savatey [412]3 years ago
3 0
Part A:
The solution of the equations p(x) and g(x) is the intersection of the two lines.
p(x): y=3x-15..................(1)
g(x): y=-2x+5..................(2)

By comparison, 3x-15=-2x+5 => 5x=20 => x=4 
Substitute x=4 in (1), y=3(4)-15=12-15=-3
=>  Solution: (4,-3)
(see second attached image)

Part B: write any two solutions for g(x).
We cannot write a solution to a function unless there is an equation.
ASSUMING what is meant is to write two points that lie on the line g(x), then we can assume any two values of x, say x1, x2, and evaluate y1=g(x1) and y2=g(x2).
If x1=0, then g(x1)=g(0)=-2(0)+5=5 => point is (0,5)
If x2=1, then g(x2)=g(1)=-2(1)+5=-2+5=3 => point is (1,3) .... and so on.

Part C: what is the solution to the equation g(x)=f(x)
g(x)=f(x) => -2x+5=4+1.5^x => 1.5^x+2x-1=0 .......................(3)
There is no analytic solution to solve this kind of problems.  However, we can always solve it graphically and check the answer algebraically.
As we can see from the third graph, the solution is (0,5).
Check: 1.5^(0)+2(0)-1 = 1+0-1 = 0    => solution (0,5) is good.
Answer: solution is (0,5)

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Step-by-step explanation:

The function ⌊x⌋ rounds the value x to the lower whole number.

for example:

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then, the graph of ⌊x⌋ will be a black dot in the each whole number, and a horizontal segment to the right that ends with a white dot in the next whole number. Right above the white dot, we have another black dot, and it repeats.

if we have ⌊x⌋ + 2, we move te previous graph 2 units upwards, then the correct option is the top right graph.

You can check some points if you like:

f(0) = ⌊0⌋ + 2 = 2

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f(1) = ⌊1⌋ + 2 = 3

So in x = 0 we have a black dot in y = 2, and in x = 1 we have a white dot in y = 2 and a black dot in y = 3.

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Simplify the following expresión by combining like terms: 8x +7 - 2x + y
beks73 [17]

Simplifying the expression 8x +7 - 2x + y, by combining like terms is 6x + y + 7

<h3>How to simplify an expression?</h3>

The expression have to be simplified by combining the like terms.

Like terms are terms whose variables (and their exponents such as the 2 in y²) are the same.

Therefore,

8x +7 - 2x + y

The like terms are 8x and 2x . Therefore, lets combine it.

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