Dan and Mario went to a sandwich shop to buy sandwiches for their group of friends. Dan bought 2 tuna and 5 vegetarian sandwiche
2 answers:
Answer:
Step-by-step explanation:
Given : Dan bought 2 tuna and 5 vegetarian sandwiches for $37. Mario bought 4 tuna and 3 vegetarian sandwiches for $39.
To Find: Which system of equations can be used to solve for the cost of each kind of sandwich
Solution:
Let the cost of 1 tuna be x
Cost of 2 tuna = 2x
Cost of 4 tuna = 4x
Let the cost of 1 vegetarian sandwich be y
Cost of 5 sandwiches= 5y
Cost of 3 sandwiches= 3y
Since we are given that Dan bought 2 tuna and 5 vegetarian sandwiches for $37
So, equation becomes:
Mario bought 4 tuna and 3 vegetarian sandwiches for $39.
So, equation becomes:
Hence system of equations can be used to solve for the cost of each kind of sandwich :
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<h2>Answer:</h2>
∠ABC = 76°
BC = 20.1
CA = 28.0
<h2>Step-by-step explanation:</h2>Solving the triangle means finding all unknown angles and sides of the triangle.
(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>
Therefore, the sum of angles of the triangle ABC is 180°. i.e
∠ABC + ∠BCA + ∠CAB = 180°
=> ∠ABC + 60° + 44° = 180°
=> ∠ABC + 104° = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;
=>
=>
<em>Substitute the necessary values</em>
---------------------(ii)
(a) To get side BC, use the first two terms of equation (ii)
<em>Cross multiply</em>
BC x sin 60 = 25 x sin 44
BC x 0.8660 = 25 x 0.6947
0.8660 x BC = 17.3675
BC =
BC = 20.05
=> BC = 20.1 to the nearest tenth
(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;
<em>Cross multiply</em>
CA x sin 60 = 25 x sin 76
CA x 0.8660 = 25 x 0.9703
0.8660 x CA = 24.2575
CA =
CA = 28.01
=> CA = 28.0 to the nearest tenth
Answer:
g = 36
Step-by-step explanation:
We have the equation + 7 =19
Subtract 7 from both sides: = 19 - 7 = 12
= 12
Now, multiply by 3 to both sides: 3 × = 3 × 12
g = 36