(6y - 11)(6y + 11) = ay
² - b |use (a - b)(a + b) = a² - b²
(6y)² - 11² =ay² - b
36y² - 121 = ay² - b |add b to both sides
ay² = 36y² - 121 + b |divide both sides by y² ≠ 0
a = (36y² - 121 + b)/y²
Expanded FormExpanded form refers to a base and an exponent written as repeated multiplication. ExponentExponents are used to describe the number of times that a term is multiplied by itself. ExpressionAn expression is a mathematical phrase containing variables, operations and/or numbers.
Answer:
an acute triangle
Explanation:
All of the angles are less than 90 degrees, which is an acute triangle.
Answer:
Part 1) The explanatory variable is the type of oven
It is a categorical variable
Part 2) The response variable is the baking time
It is a quantitative variable
part 3) two-sample z-test for proportions should be used for the test
Step-by-step explanation:
An explanatory variable is an independent variable that is not affected by all other variables. In this experiment, the type of oven is the input variable and it is not affected by any other variable
A categorical variable is one that has two or more categories without any intrinsic ordering of the categories. The type of oven is either gas or electric, so it is categorical.
A response variable is a dependent variable whose variation depends on other variables. The baking time in this experiment depends on the type of oven used
A quantitative variable is one that take on numerical values.
A two proportion z-test allows you to compare two proportions to see if they are the same. The null hypothesis (H0) for the test is that the proportions are the same. The alternate hypothesis (H1) is that the proportions are not the same.
<h3>
Answer: n+15</h3>
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Explanation:
- n = number of minutes
- cost of company X = 3n+30
- cost of company Y = 2n+15
To find out how much more company X charges, we subtract the two cost expressions
CompanyX - CompanyY = (3n+30)-(2n+15) = 3n+30-2n-15 = n+15 which is the final answer.
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An example:
Let's say you talk on the phone for n = 20 minutes.
Company X would charge you 3n+30 = 3*20+30 = 90 cents
Company Y would charge you 2n+15 = 2*20+15 = 55 cents
The difference of which is 90-55 = 35 cents.
If you plugged n = 20 into the n+15 expression we got, then n+15 = 20+15 = 35 matches up with the previous 35 cents.
This example helps confirm the answer. I'll let you try out other examples.
