Geometry Answers

Given: m<1+m<2=m<4

prove: m<3+m<1+m<2=180

PQ = 3x + 7, QR = 5x − 19

Provide the missing statement and reasons for the following proof:

Given: <BDA ~= <A

Prove:  x=3

statement reason

S1. <BDA ~= <A R1. Given

S2. <BDA ~= <CDE R2.

S3. <CDE ~= <A R3. Transitive Property of Congruence

S4. m<CDE = m<A R4.

S5. R5. Substitution Property of Equality

S6. 14x = 13x + 3 R6.

S7. x = 3 R7. Subtraction Property of Equality

A survey crew worker uses a site instrument that is on a 4-ft stand. He sites a spot on the road 66 feet away. What is the grade, to the nearest whole percent?

A construction worker needs to raise some materials to the top of a 20-ft tall building by using a computer-controlled crane. If the materials are 28 feet away from the base of the building, what slope needs to be programmed into the computer to accomplish the delivery? State your answer as a fraction in lowest terms

The stack on the left is made up of 15 pennies, and the stack on the right is also made up of 15 pennies. If the volume of the stack of pennies on the left is 390 mm³, what is the volume of the stack of pennies on the right in cubic millimeters? (Hint: only enter numerals in the answer blank) (4 points)  

PQ=3x+14 and QR=7x-10; Find x

The drawing below shows a right-angled triangle. A straight line crosses the triangle parallel to

the line z and encloses an angle of α. The lengths x and y of the bottom and top line segments

as well as the angle α are given. Find an equation for the length z.

A circle has an area equal to 25pi cm². Its diameter AB coincides with one of the sides of triangle ACB whose vertex C lies on the circle. If the triangle has an area equal to 11 cm², find the perimeter of the triangle.

Point M lies on side AC of an equilateral triangle ABC; circles   \Omega _1  and   \Omega _2  are circumcircles of triangles MAB and MBC respectively. It is known that point   A  divides arc   MAB  of circle in the ratio of   \Omega _1  that MA:AB = 28:41. Find the ratio on which point C devides arc   MCB  of circle   \Omega _2 . In the answer indicate MC:CB