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1 answer:
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11 weeks are required for Riley to work to save enough money to buy the new television
<h3><u>Solution:</u></h3>Given that Riley needs a total of $1,049.77
Riley has saved $200.79 already and earns $77.18 per week at her job
To find: Number of weeks Riley need to work to save enough money to buy the new television
Remaining amount needed = $1,049.77 - $200.79
Remaining amount needed = $ 848.98
Let "n" be the number of weeks Riley need to work to save enough money to buy the new television
Also she earns $77.18 per week at her job
1 week ⇒ $ 77.18
"n" weeks ⇒ $ 848.98
Therefore, by cross multiplication,
Therefore 11 weeks are required for her to work to save enough money to buy the new television
<h3><u>Method 2:</u></h3><em>Total amount = amount already saved + ($77.18 per week at her job)("n" weeks)</em>
1,049.77 = 200.79 + (77.18)(n)
1049.77 - 200.79 = 77.18n
848.98 = 77.18n
n = 11
Therefore 11 weeks are required for her to work to save enough money to buy the new television
Answer:
Length of the rectangle = 9.58 feet and width = 27.14 foot
Step-by-step explanation:
Let the length of the rectangular area is = x feet
and the width of the area = y feet
Area of the rectangle = xy square feet
Or xy = 260
y = -------(1)
Cost to fence the three sides = $3 per foot
Therefore cost to fence one length and two width of the rectangular area
= 3(x + 2y)
Similarly cost to fence the fourth side = $14 per foot
So, the cost of the remaining length = 14x
Total cost to fence = 3(x + 2y) + 14x
Cost (C) = 3(x + 2y) + 14x
C = 3x + 6y + 14x
= 17x + 6y
From equation (1)
C =
Now we take the derivative,
C' = 17 -
To minimize the cost of fencing,
C' = 0
17 - = 0
= 17
x = 9.58 foot
and y =
y = 27.14 foot
Answer:
5 cm
Step-by-step explanation:
If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.
If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.
Consider two right triangles ABO and ACO. In these triangles:
- AO is common hypotenuse;
- ∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;
- OB=OC as radii of the circle k(O).
By HL theorem, triangles ABO and ACO are congruent. Then
- ∠OAB=∠OAC=30°;
- AC=AB=5 cm.
Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.
Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus
∠CBA=∠BCA=1/2(180°-60°)=60°.
Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.
