You'll want to work with the center-radius form of a circle equation for this. the center formula is <span>(x – h)</span>²<span> + (y – k)</span>²<span> = r</span>², where (h, k) is your center and r is your radius. plug in the information your circle gives you: A(-3, 12), radius = 5
(x + 3)² + (y - 12)² = (5)² ... simplify the right side
(x + 3)² + (y - 12)² = 25 ... from here, you need to foil both of your binomials to convert this to the "general form" that your answer choices are in.
(x + 3)² = (x + 3)(x + 3) = x² + 6x + 9
(y - 12)² = (y - 12)(y - 12) = <span>y² - 24y + 144
</span>
x² + 6x + 9 + y² - 24y + 144 = 25 ... combine like terms
x² + 6x + y² - 24y + 153 = 25 ... subtract 25
x² + 6x + y² - 24y + 128 = 0 is your equation. reorder it so that it's from the highest degree to the lowest: x² + y² + 6x - 24y + 128 = 0 is your result (C).
10.8 4/5 is equal to 10.8.
Answer:
x = 18.8
Step-by-step explanation:
(6x + 19) is in linear pair vertically so,
it's value will be 180 - 6x + 19. ......( angles in linear pair are supplementary)
now, 180 - 6x + 19 is corresponding with (4x + 11)
therefore, 4x + 11 = 180 - 6x + 19
4x + 6x = 180 + 19 - 11
10 x. = 180 + 8
10 x. = 188
x = 188/10
x. = 18.8
Cross - check:-
4x + 11 = 180 - 6x + 19
4 * 18.8 + 11 = 180 - ( 6 * 18.8 +19)
86.2. = 86.2
therefore, x = 18.8 is the correct answer
Answer:
B
Step-by-step explanation:
Absolute value works like this.
For any number you put inside the absolute value bars, it will always come out positive, so -5 and 5 can work.
Answer:
We can assume that the statistic is 
So the p value obtained was a very high value and using the significance level given 
we have 
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
Step-by-step explanation:
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion 
is significantly different from a hypothesized value 
.
Calculate the statistic
We can assume that the statistic is
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5
