The graph of a function never has two different points with the same x-coordinate because.. A. the graph of a function cannot be a straight line. B. each input value is mapped to a single output value. C. each input value is mapped to more than one output value. D. the graph of a function is a vertical line.
Answers
Answer: The correct reason is (B) each input value is mapped to a single output value.
Step-by-step explanation: The given statement is:
"The graph of a function never has two different points with the same x-coordinate."
We are to select the correct reason for the above statement.
The definition of a FUNCTION is as follows:
In simple language, a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
That is, if y = f(x) is a function of a variable 'x', then we have
(A) The first statement is "the graph of a function cannot be a straight line."
The statement is false. For example, let us consider y = x + 2. Obviously, it is a function because every value of 'x' will result in only one value of 'y'.
Also, the graph here will be a straight line as shown in the attached figure (1).
(B) The first statement is "each input value is mapped to a single output value."
The statement is true according to the definition of a function.
(C) The third statement is "each input value is mapped to more than one output value."
The statement is false by the definition of a function.
(D) The fourth statement is "the graph of a function is a vertical line."
The statement is false. For example, if we consider the vertical line x = 2. Then, we see from the attached figure (2) that the points (x, y) = (2, 1), (2, 0), (2, 3), etc. all lie on the line.
This shows that one input value leads to infinitely many values of 'y'. Hence, this vertical line cannot be the graph of a function.
Thus, (B) is the correct statement.
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Answers
The rate of change of y is proportional to y. when x=0, y=4 and when x=3, y=10 then the value of y is 12 when x =6.
The two points from the given information are (0, 4) and (3, 10).
Let us find the
=6/3
=2
Now let us find the y intercept to write the equation in slope intercept form.
Consider the point (0, 4) to find y intercept.
Plug in the point values in slope intercept form:
4=2(0)+b
Solve for b:
b=4
The equation in slope intercept form is y=2x+4.
Now let us find the value of y when x=6.
Plug in x as 6 in the equation y=2x+4.
y=2(6)+4
y=12+4
y=16
Hence, the value of y is 16 when x is 6.
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We know x+y=0; so, if x=6 y= -6
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Y is up and down, vertically & x is horizontal.
There is positive and negatives in coordinates.
The way the negatives and positives are positioned is like this:
The left hand side of the 'x axis' is negative.
The right hand side of the 'x axis' is positive.
The top part of the 'y axis' is positive.
The bottom part of the 'y axis' is negative.
Whilst plotting, you always start with the x axis. Considering 3 is a positive, you plot it on the right hand side. With your finger, mark out where the 3 is, and slide it down until you get to -7 on the plane.
Answers
3x²-x+9=0
==>x²-x/3+3=0
p+q=1/3
pq=3
p/q+q/p=[(p+q)²-2pq]/(pq)=[(1/3)²-2*3]/3=[1/9-6]/3=-53/27
also x² - (1/3)x + 3 = 0
p,q are roots so
(x - p)(x - q) = x² - (1/3)x + 3 = 0
x² - (p+q)x + pq = x² - (1/3)x + 3 = 0
compare coefficients we have
p+q = 1/3 ... (1)
pq = 3 ... (2)
(1)/(2) ... (p+q)/pq = (1/3)/3
p/q + q/p = 1/9
Answers
Answers
Let's solve your equation step-by-step. x2+5x−6=0
Step 1: Factor left side of equation. (x−1)(x+6)=0
Step 2: Set factors equal to 0. x−1=0 or x+6=0
x=1 or x=−6
Car payment: $203.34
Gas bill: $96.67
Check deposit: $1289.60
Cash deposit: $45
Debit card transaction: $67.12
ATM withdrawal: $30
Find the current account balance to date.
A. $1,923.71
B. $937.47
C. $1,726.52
D. $1,555.33
Answers
Answer:
Option A. $1,923.71would be correct
Step-by-step explanation:
Account balance : $986.24
Total deductions = Car payment + Gas bill + Debit card transaction + ATM withdrawal
Total deductions = 203.34 + 96.67 + 67.12 + 30 = $397.13
Now subtract the total of payments and withdrawals from initial balance
986.24 - 397.13 = $589.11
Now add all the check and cash deposits
Total deposits = Check deposit + Cash deposit
Total deposits = 1289.60 + 45.00 = $1334.60
$589.11 + 1334.60 = $1923.71
Current account balance to date would be $1923.71.
Final answer:
The current balance of the account is $1923.71. This is calculated by adding the deposits to the initial balance and then subtracting the various expenses and withdrawals.
Explanation:
To find the current bank account balance, we start with the initial balance and add any deposits. After that, we subtract all the expenses and withdrawals. In this case, the initial balance is $986.24. We add the check deposit of $1289.60 and the cash deposit of $45, and get $2320.84. Then we subtract the car payment of $203.34, the gas bill of $96.67, the debit card transaction of $67.12, and the ATM withdrawal of $30. The resulting balance, $1923.71, is the final balance to date.
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