Which one of the following options have the same value as 65 percent of 20
2 answers:
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The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20
<em><u>Solution:</u></em>
Let "a" be the cost of each ribeye steak dinners
Let "b" be the cost of each grilled salmon dinners
<em><u>A waitress sold 11 ribeye steak dinners and 12 grilled salmon dinners, totaling $560.63 on a particular day</u></em>
Thus we frame a equation as:
11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63
11a + 12b = 560.63 -------- eqn 1
<em><u>Another day she sold 16 ribeye steak dinners and 6 grilled salmon dinners, totaling $584.46</u></em>
Thus we frame a equation as:
16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46
16a + 6b = 584.46 ------------ eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 2 by 2</u></em>
32a + 12b = 1168.92 ------- eqn 3
<em><u>Subtract eqn 1 from eqn 3</u></em>
32a + 12b = 1168.92
11a + 12b = 560.63
( - ) ----------------
21a = 1168.92 - 560.63
21a = 608.29
Divide both sides by 21
<em><u>Substitute a = 29 in eqn 1</u></em>
11(29) + 12b = 560.63
319 + 12b = 560.63
12b = 560.63 - 319
12b = 214.63
Divide both sides by 12
Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20
The length of DZ is 4 units ⇒ 3rd answer
Step-by-step explanation:
Triangle X Y Z is cut by line segment C D, where
- C lies on side XY and D lies on the side YZ
- The length of C D is 15
- The length of X Z is 18
- The length of C Y is 25
- The length of Y D is 20
- C D and X Z are parallel
- CX = 5 units
We need to find the length of DZ
In Δ XYZ
∵ C ∈ XY and D ∈ YZ
∵ CD // XZ
∴ m∠YCD = m∠YXZ ⇒ alternate angles
∴ m∠YDC = m∠YZX ⇒ alternate angles
In Δs YCD and YXZ
∵ m∠YCD = m∠YXZ
∵ m∠YDC = m∠YZX
∵ ∠Y is a common angle
∴ Δ YCD is similar to Δ YXZ by AAA postulate
- There is a constant ratio between their corresponding sides
∴
∵ YC = 25 units
∵ CX = 5 units
∵ YX = YC + CX
∴ YX = 25 + 5 = 30 units
∵ YD = 20 units
∵ YZ = YD + DZ
∴ YZ = 20 + DZ
Let us use the ratio of the corresponding side
∵
∴
- Simplify by dividing up and down by 5
∵
∴
- By using cross multiplication
∴ 5(20 + DZ) = 6(20)
∴ 100 + 5 DZ = 120
- Subtract 100 from both sides
∴ 5 DZ = 20
- Divide both sides by 5
∴ DZ = 4 units
The length of DZ is 4 units
Learn more:
You can learn more about triangles in brainly.com/question/3202836
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