9514 1404 393
Answer:
Step-by-step explanation:
Angles A and P are marked congruent; angles B and Q are marked congruent, so the triangles are similar by the AA similarity postulate. The similarity statement can be written ...
ΔABC ~ ΔPQR by AA similarity
__
The ratio of sides of PQR to ABC is the ratio QR/BC = 12/6 = 2. That is, each side in the larger triangle is 2 times the length of the corresponding smaller side.
PQ = 2·AB = 2·4 = 8
PR = 2·AC = 2·7 = 14
The side lengths of interest are ...
PQ = 8, PR = 14
For this, all you have to do is create equations where all you have to do is change the x value. The equation for gym A would be 35 + 42x, where x is the number of months he has the membership, and the first number is the initial fee. The equation for gym B would be 65 + 36x, following the same rules. Now all you have to do is set both of these equations equal to each other:
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245
Answer:
56 + 53pi
Step-by-step explanation:
<u><em>Area of small circles:</em></u>
diameter of small circle: 4cm
forumla to find area of circle: A = pir^2
r is radius = half of diameter -> d/2 = 4 / 2 = 2cm
A = pi (2cm)^2
A = pi (4cm)
A = 4pi
<u><em>Area of large circle:</em></u>
diameter of small circle: 4cm
forumla to find area of circle: A = pir^2
r is radius = half of diameter -> d/2 = 14 / 2 = 7cm
A = pi (7cm)^2
A = pi (49cm)
A = 49pi
<u><em>Area of rectangle:</em></u>
Area = width x length
Area = 14cm x 4cm
Area = 56cm
<u><em>Add all three areas:</em></u>
Area of rectangle + large circle + small circle
56cm + 49pi + 4pi = 56cm + 53pi
Answer:
(-1,-1)
Step-by-step explanation:
If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).
Answer:
tan56°
Step-by-step explanation:
The Addition identity for tangent ratio is
tan(x + y) = 
, thus
= tan(24 + 32)° = tan56°
