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suter [353]
3 years ago
5

Ocean waves move in parallel lines toward the shore. The figure shows the path that a windsurfer takes across several waves. For

this exercise, think of the windsurfer's wake as a line. If m∠1 = (5x + 3y)° and m∠2 = (5x + y)°, find x and y.

Mathematics
1 answer:
grandymaker [24]3 years ago
3 0
If you look at the figure, the angle marked red is equal to 70° because vertical angles are equal. So, that also means that the opposite angle 2 is also 70°. So, the first equation is:

70 = 5x + y

Next, the green angle as marked is equal to
Green angle = 180 - 70 = 110
Being vertical angles, angle 1 is then equal to 110°. So,the second equation is

110 = 5x + 3y

Subtract the two equations:

    5x + y = 70
 -  5x + 3y = 110
________________
           -3y = -40
             <em> y = -40/-3 = 13.33°</em>

Substituting y to either one of the equations,
5x + 13.33 = 70
Solving for x,
<em>x = 11.33°</em>

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Use the discriminant to find the number and type of solution for x^2+6x=-9​
likoan [24]

Answer:

D = 0; one real root

Step-by-step explanation:

Discriminant Formula:

\displaystyle \large{D =  {b}^{2}  - 4ac}

First, arrange the expression or equation in ax^2+bx+c = 0.

\displaystyle \large{ {x}^{2}  + 6x =  - 9}

Add both sides by 9.

\displaystyle \large{ {x}^{2}  + 6x + 9 =  - 9 + 9} \\  \displaystyle \large{ {x}^{2}  + 6x + 9 =  0}

Compare the coefficients so we can substitute in the formula.

\displaystyle \large{a {x}^{2}  + bx + c =  {x}^{2}  + 6x + 9 }

  • a = 1
  • b = 6
  • c = 9

Substitute a = 1, b = 6 and c = 9 in the formula.

\displaystyle \large{D =  {6}^{2}  - 4(1)(9)} \\  \displaystyle \large{D =  36 - 36} \\  \displaystyle \large{D =  0}

Since D = 0, the type of solution is one real root.

6 0
3 years ago
A bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. If x represen
Maksim231197 [3]
The function would be 12.50+.45x
5 0
3 years ago
Read 2 more answers
your friend claims that two isosceles triangles ABC and DEF are congruent if two corresponding sides are congruent. he explains
Svetach [21]
Think about the fact that you can have two types of isosceles triangle: one of them that is a right triangle (isosceles right triangle) such as a 45-45-90 triangle and the other type can be just a regular triangle that has two sides that are congruent but it isn't a right triangle. 

Thus, you would need more info about the triangles in order to conclude that the two isosceles triangles are congruent to each other. 
7 0
3 years ago
If α, β are the zeroes of the polynomials f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) =
Pavlova-9 [17]

Answer:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

Step-by-step f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)explanation:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(xf(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(xf(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1) + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

4 0
3 years ago
Wyatt's dog is tethered to a post in his yard. if the rope tied to the dog is 12 feet long, how many square yards does the dog h
Amiraneli [1.4K]
Radius = 4 yards
Area = PI * radius^2
Area = 3.14 * 16
Area = 50.24 square yards
 

8 0
3 years ago
Read 2 more answers
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