Use factoring. What is the solution of 2x² = 14x + 60? a. x = -15, x = 4 b. x = -10, x = 3 c. x = 15, x = 12 d. x = 10, x = -3
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Answer: d. x = 10, x = -3
Step-by-step explanation:
We will solve by factoring as asked.
Given:
2x² = 14x + 60
Subtract 2x² from both sides of the equation:
0 = -2x² + 14x + 60
Factor:
0 = −2(x − 10)(x + 3)
Zero-product property:
x - 10 = 0 x + 3 = 0
x = 10 x = -3
d. x = 10, x = -3
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The perimeter of a regular heptagon with each side 4.5 cm is ____
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The initial value of the function is 2.5.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers.
The range of the function is all real numbers greater than 3.
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The statements which are true of the function; f(x) = 3(2.5)^x and there explanations are below;
- The function is exponential;Traditional to every exponential function is that the independent variable is usually an exponent of a constant. Hence, we can conclude the function is an exponential function.
- Yes,the function increases by a factor of 2.5 for each unit increase in x. Hence, the slope of the function is; 2.5.
- The domainof the function is all real number, because, the value of y is defined for all real number values of x.
Read more on exponential functions;
This is an exponential function since the x is in the exponent's place instead of in the place of a "regular" variable. The first statement is true.
The initial value of this particular function is 3 (the other number is the multiplier), so choice 2 is NOT true.
The function increases by its multiplier, which is 2.5, so statement 3 is true.
The equation allows us to enter any x value we want to determine the y, so the domain is in fact all real numbers. So, this statement is also true.
If you were to graph this on a calculator, you would see that the range, the "allowed" y values for our function, do not touch or ever drop below the x-axis. That means that the range is all numbers greater than 0. So that statement is false. No matter what value we pick for x, we will NEVER get back a negative y value or that y = 0. For example, if x = 0, y = 3; if x = -5, y = .03; if x = -10, y = .0003; if x = 5, y = 292.97; if x = -100, . Y will never be equal to 0 or less than 0.
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Answer:
see below
Step-by-step explanation:
(a) 48% is a sample statistic because it's based on the responses of 1,259 US residents. It's used to estimate a population parameter.
(b) We can calculate a 95% confidence interval for the proportion of US residents who support marijuana legalization. This interval provides a range, and we can be 95% confident that the true proportion falls within this range.
(c) The confidence interval calculation assumes the data follows a normal distribution. To use this method, we need a sufficiently large sample size, which is met in this case.
(d) To justify the news piece's statement that a majority of Americans support marijuana legalization, we need to check if the confidence interval includes values above 50%. If it does, then it supports the statement.
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wish it helps
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Answer:
-44
Step-by-step explanation: