72. Solve for the variable in the equation:
4.9x + 4.4 = 19.1
x=3?
71. Does a machine that takes one quarter at a time into its input and produces one gumball in its output act like a function?
Yes?
69. Does a machine that takes one quarter at a time into its input and produces two gumballs in its output at like a function?
No?
65. Solve for a in the equation:
2 1/2 a= -25
(That's written: two and a half a equals negative twenty five)
I got a=-10
62. Determine if y=x/2 is a function.
Yes
58. An equation is not a function if even one x value produces _____ corresponding y values(s).
a. one
b. less than one
c. more than one
d. zero for a
C?
69,yes, it is a function,for each input, y=2
all others correct.
72. To solve for the variable in the equation 4.9x + 4.4 = 19.1, we need to isolate the variable x. To do this, we subtract 4.4 from both sides of the equation:
4.9x + 4.4 - 4.4 = 19.1 - 4.4
This simplifies to:
4.9x = 14.7
To isolate x, we divide both sides of the equation by 4.9:
(4.9x)/4.9 = 14.7/4.9
This gives us:
x = 3
So the value of x that satisfies the equation is 3.
71. Yes, a machine that takes one quarter at a time into its input and produces one gumball in its output acts like a function. In a mathematical sense, a function is a relation between sets of inputs and outputs, where each input has a unique output. In this case, when you input one quarter, the output is one gumball, and this remains consistent for each quarter you input. Therefore, this machine can be considered a function.
69. No, a machine that takes one quarter at a time into its input and produces two gumballs in its output does not act like a function. As mentioned earlier, for a relation to be a function, each input should have a unique output. In this case, when you input one quarter, there are two possible outputs (two gumballs). Therefore, this machine does not satisfy the definition of a function.
65. To solve for a in the equation 2 1/2 a = -25, we need to isolate the variable a.
First, we convert the mixed number 2 1/2 to an improper fraction. Multiplying the whole number (2) by the denominator (2) and adding the numerator (1), we get:
2 * 2 + 1 = 5
So, 2 1/2 is equivalent to 5/2. The equation now becomes:
(5/2) * a = -25
To isolate a, we need to divide both sides of the equation by 5/2:
(5/2) * a / (5/2) = -25 / (5/2)
Dividing fractions is the same as multiplying by the reciprocal, so we have:
a = -25 * (2/5)
Simplifying this expression, we get:
a = -10
So, the value of a that satisfies the equation is -10.
62. The equation y = x/2 represents a linear function. In this equation, the variable y represents the output, and x represents the input. The equation states that the output (y) is half of the input (x). Each input has a unique output, so this equation represents a function.
58. An equation is not a function if even one x value produces more than one corresponding y value(s). Therefore, the correct answer is option c. "more than one." If for any x value, there are multiple possible y values, then the relation described by the equation violates the definition of a function.