Given: a and b are parallel and c is a transversal. Prove: ∠2 ≅ ∠7

Parallel lines b and a are cut by transversal c. On line b where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 5, 6, 2. On line a where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 3, 7, 8, 4.
Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent.

We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because
angles are congruent. Angles 5 and 7 are congruent because
angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the

What is the solution to the division problem below x3+x2-11x+4/x+4

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?

Amayoral candidate would like to know her residents’ views on a tax on sugar drinks before the mayoral debates. she asks one thousand registered voters from both parties. these voters are an example of a census population convenience sample simple random sample