An isosceles triangle abc with the base bc is inscribed into a circle. find the measure of angles of it, if measure of arc bc=102°.

The measures of the angles of ΔABC are

m∠A = 51° , m∠B = 64.5 , m∠C = 64.5°

Step-by-step explanation:

* Lets revise some facts in the circle

- The measure of the circle is 360°

- Equal chords intercept equal arcs

- The measure of an inscribed angle equals half the measure

 of the intercepted arc

* Lets solve the problem

- ΔABC is isosceles withe base BC

∴ AB = AC

- The vertex angle is A

∵ ∠A is an inscribed angle subtended by arc BC

∴ m∠A = 1/2 the measure of arc BC

∵ The measure of arc BC = 102° ⇒ given

∴ m∠A = 1/2(102) = 51°

- In ΔABC

∵ AB = AC ⇒ proved

∴ m∠B = m∠C ⇒ base angles of isosceles Δ

- The sum of the interior angles in any Δ = 180°

∵ m∠A = 51 ⇒ proved

∴ m∠B = m∠C = (180 - 51) ÷ 2 = 129 ÷ 2 = 64.5°

* The measures of the angles of ΔABC are

  m∠A = 51° , m∠B = 64.5° , m∠C = 64.5°

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows: