Angel, Juan y Ricardo son hermanos. Durante el mes de agosto viajaron a visitar a sus padres que viven en Huancayo. Angel llega
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Answer:
Step-by-step explanation:
Given that lines l and m are parallel and there is a transversal cutting through these lines.
5). (9x + 2)° = 119° [by alternate interior angles]
9x = 117 ⇒ x = 13
6). (12x - 8)° + 104° = 180°
12x = 180 - 96
x = ⇒ x = 7
7). (5x + 7) = (8x - 71) [by alternate exterior angles]
8x - 5x = 71 + 7
3x = 78
x = 26
8). (4x - 7) = (7x - 61) [by corresponding angles]
7x - 4x = -7 + 61
3x = 54
x = 18
9). (9x + 25) = (13x - 19) [by corresponding angles]
13x - 9x = 25 + 19
4x = 44
x = 11
(13x - 19)° + (17y + 5)° = 180° [linear pairs of angles sum to supplementary]
(13×11) - 19 + 17y + 5 = 180
129 + 17y = 180
17y = 180 - 129
y = 3
10). (3x - 29) + (8y + 17) = 180 [linear pairs of angles sum to supplementary]
3x + 8y = 180 + 12
3x + 8y = 192 -----(1)
(8y + 17) = (6x - 7) [by alternate exterior angles]
6x - 8y = 24
3x - 4y = 12 -----(2)
From equation (1) subtract equation (2)
(3x + 8y) - (3x - 4y) = 192 - 12
12y = 180
y = 15
Plugging into equation (1),
3x + 8(15) = 192
3x + 120 = 192
x = 24
11). (3x + 49)° = (7x - 23)° [by corresponding angles]
7x - 3x = 49 + 23
4x = 72 ⇒ x = 18
(11y - 1)° = (3x)° [by corresponding angles]
11y = 3×18 + 1
11y = 55 ⇒ y = 5
12). (5x - 38)° = (3x - 4)° [by corresponding angles]
5x - 3x = 38 - 4
2x = 34
x = 17
(7y - 20)° + (5x - 38)° + 90° = 180°
[The angles within a triangle sum to 180°]
7y + 5x - 58 = 90
5x + 7y = 148
5×17 + 7y = 148
85 + 7y = 148
7y = 148 - 85
y =
Answer:
(1) The necessary proportion of spirit to varnish stands at 1:3.
(2) A total of 80 ml of mineral spirit is required.
(3) The ratio of the heights to the widths of the tapestries is 3:2.
Step-by-step explanation:
(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.
Therefore,
Consequently, the proportion of spirit to varnish is 1:3.
(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.
Let the total solution quantity be .
Thus, .
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This means the total solution amounts to 320 ml.
Now, calculating Spirit = Total solution - Varnish
⇒Spirit = 320ml-240ml
⇒Spirit = 80ml
Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.
(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.
Thus, the dimensions become 15m long and 10m wide.
Now, the proportion of Height to Width is 15:10
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Thus, the proportion of the heights of the tapestries to their widths is 3:2.