3*(x+5)^(1/2)=-9
(x+5)^(1/2)=-3
x+5=9
x=4
3*(4+5)^(1/2)=-9
3*(9)^(1/2)=-9
3*3=-9
4 is an extraneous solution
Answer:
14. x=-2.5, y = -7
15. x=28 y = -20
Step-by-step explanation:
14. Let's solve this system by elimination. Multiply the first equation by -1.
-1*(4x-y)= -1*(- 3)
-4x +y = 3
Then add this to the second equation.
-4x+y = 3
6x-y= - 8
--------------
2x = -5
Divide each side by 2
x = -2.5
We still need to find y
-4x+y =3
-4(-2.5) + y =3
10 +y =3
Subtract 10 from each side.
y = 3-10
y = -7
15.I will again use elimination to solve this system, because using substitution will give me fractions which are harder to work with. I will elimiate the y variable. Multiply the first equation by 11
11(
5x+6y)= 11*20
55x+66y = 220
Multiply the second equation by -6
-6(9x+11y)=32*(-6)
-54x-66y = -192
Add the modified equations together.
55x+66y = 220
-54x-66y = -192
---------------------------
x = 28
We still need to solve for y
5x+6y = 20
5*28 + 6y =20
140 + 6y = 20
Subtract 140 from each side
6y = -120
Divide by 6
y = -20
6 + 4 + 4 = 14 cm
2 * pi * r =
2 * 3.14 * 3 = 18.84 / 2 = 9.42
14 + 9.42 = 23.42
Answer:
25. If you look at angle B from the first figure you see a square that indicates a 90 degrees angle, thus the figure shown is a right triangle. You can also see that angle C is said to have 60 degrees. a right triangle has a total angle of 180 degrees. so, 180 - 90 - 60 = 30 degrees. Therefore, angle A is 30 degrees.
27. Now you want the measure of the hypotenuse, and you know this a right triangle. so, simply use the law of sines to find the measure of AC :
4cm/sin(60) = AC/Sin90
AC = 4.62 cm
29. angle z is in the other figure and same stuff, just substract the angles, you have 90 degrees and 30 degrees... 180 - 90 - 30 = 60 degrees
31. Angle Y = 90 degrees
this value is already given, it's the little square that indicates a 90 degrees angle.
26. 5 cm
28. 90 degrees
30. You already found AC, use the pythagorean theorem. sqrt((4.62)^2 - 4^2) = 2.31 cm
32. use pythagoras again, square root(5^2 - 3^2) = 4
So as you can see all the measurements are the same because if you see at the very top of your figures it says ABC = XYZ which means pretty much that they have the same values (notice that there is a little something added to the = sign, watch out for that because that's what indicates that two figures are equal in terms of angles and measures.
