Answer:
The total distance Remy will swim is approximately 236 meters
Step-by-step explanation:
From the given diagram, of triangle ΔCAB, we have that the path Remy is to swim are;
1) Length of segment C to A
2) Length of segment A to B
3) Length of segment B to C
The length of the perpendicular at point D on segment AB to C = 60 meters
Therefore, DC = 60 m
By trigonometric ratios, we have;
We are given the values of the trigonometric ratios of the following angles;
tan(27°) = 0.51
tan(43°) = 0.93
cos(27°) = 0.89
cos(43°) = 0.73
∴ tan(43°) = AD/DC = 0.93
Where the lengths of AC, AD, DB, DC and BC
AD = DC × tan(43°)
∴ AD = 60 × 0.93 ≈ 55.8
Similarly, we have;
tan(27°) = DB/DC
∴ DB = DC × tan(27°)
DB = 60 × 0.51 ≈ 30.6
From , we have;
cos(43°) = DC/AC
AC = DC/(cos(43°))
∴ AC = 60/0.73 ≈ 82.2
Similarly, we have;
cos(27°) = DC/BC
BC = DC/(cos(27°))
∴ BC = 60/0.89 ≈ 67.4
The total distance Remy will swim = AC + AD + DB + BC
∴ The total distance Remy will swim = 82.2 + 55.8 + 30.6 + 67.4 = 236
The total distance Remy will swim = 236 meters
Answer:
(b) c2+6x+9=16
(e) (x+)2=16
Step-by-step explanation:
Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20
Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4
She spent $26 more on books than on pens which means
Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26
Sinplifying it
(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104
She spent $394 which means
Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394
Simplifying it
(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576
Now, we have two equations,
(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576
Now we need to find a third equation with either x or y as the subject of any of both the previous equations.
Let's make y the subject of (2) equation
8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)
Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)
8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3
Now find the value of y by substituting the value of x in either equation, preferably (3)
y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80
Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50
3 sodas cost $2.97 +.15 tax total $3.12
Answer:
The number is 27
Step-by-step explanation:
Let the 10s digit be x
Let the units digit be y
y = x + 5
10x + y = 3(x + y) Remove the brackets
10x + y = 3x + 3y Substitute the x + 5 into the second equation for y
10x + x + 5 = 3x + 3(x + 5) Remove the brackets on the right.
10x + x + 5 = 3x + 3x +15 Collect like terms on each side.
11x + 5 = 6x + 15 Subtract 5 from both sides
11x + 5 - 5 = 6x + 15 - 5 Collect like terms
11x = 6x + 10 Subtract 6x from both sides
11x - 6x = 6x - 6x + 10
5x = 10 Divide by 5
5x/5 = 10/5
x = 2
y = x + 5
y = 2 + 5
y = 7
