Answer:
Step-by-step explanation:
4x - 3/2 - 5 - 2x/3 - 3x - 4/3 = 5
Give all terms least common denominator of 6:
4x(6/6) - 3/2(3/3) - 5(6/6) - 2x/3(2/2) - 3x( 6/6)- 4/3(2/2) = 5(6/6)
24x/6 - 9/6 - 30/6 - 4x/6 - 18x/6 - 8/6 = 30/6
Combine x terms and numerical terms:
2x/6 - 47/6 = 30/6
2x/6 = 77/6 (Add 47/6)
2x = 77 (Multiply both sides by 6)
x = 77/2 = 38.5
Problem 1)
Let p = distance from V to Y
By the angle bisector theorem, we can form the proportion
VT/VY = TK/KY
57/p = 129.2/68
57*68 = p*129.2
3876 = 129.2p
3876/129.2 = 129.2p/129.2
30 = p
p = 30
Use the value of p to find x
x = VY+YK
x = p+68
x = 30+68
x = 98
Answer: 98 mm
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Problem 2)
The triangles are similar, so we can form a proportion of the corresponding sides
MN/MA = MP/MB
67.2/(67.2-32) = 81.9/x
67.2/35.2 = 81.9/x
67.2*x = 35.2*81.9
67.2*x = 2882.88
67.2*x/67.2 = 2882.88/67.2
x = 42.9
Answer: 42.9 meters
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Problem 3)
Similar to problem 1, we use the same theorem
EG/GD = EH/HD
44.8/(x+4) = 56/35
44.8*35 = 56(x+4)
1568 = 56x+224
1568-224 = 56x+224-224
1344 = 56x
56x = 1344
56x/56 = 1344/56
x = 24
Answer: 24 millimeters
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Problem 4)
We'll use a similar idea used in problem 2
9/(9+72) = (3x-20)/((3x-20)+56)
9/81 = (3x-20)/(3x+36)
1/9 = (3x-20)/(3x+36)
1*(3x+36) = 9(3x-20)
3x+36 = 27x-180
3x+36+180 = 27x-180+180
3x+216 = 27x
3x+216-3x = 27x-3x
216 = 24x
24x = 216
24x/24 = 216/24
x = 9
Answer: 9 centimeters
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Problem 5)
Area of triangle
A = 0.5*b*h
Plug in A = 210 and h = 35; solve for b
A = 0.5*b*h
210 = 0.5*b*35
210 = 0.5*35*b
210 = 17.5*b
12 = b
b = 12
Now use the base and height to find the hypotenuse
a^2 + b^2 = c^2
h^2 + b^2 = c^2
35^2 + 12^2 = c^2
1369 = c^2
c^2 = 1369
sqrt(c^2) = sqrt(1369)
c = 37
Answer: 37 inches
Answer:
2.5
Step-by-step explanation:
4*2.5 = 10
Why?
4*2 = 8
4*.5 = 2
Answer:
<em>Center ~ ( -4, 3 ), Radius ~ 2; Option A</em>
Step-by-step explanation:
<em>~ We know that the standard circle equation ( x - a )^2 + ( y - b )^2 = r^2 provided r ⇒ radius of the circle, centered at ( a, b ) ~</em>
1. If we are given the circle formula ( x + 4 )^2 + ( y - 3 )^2 = 4, it would be that the center points ( a, b ) would be the inverse of 4 and -3, provided the formula is -a and -b: center ( -4, 3 )
2. Now the radius in the formula ( x - a )^2 + ( y - b )^2 = r^2, is noted by r such that in ( x + 4 )^2 + ( y - 3 )^2 = 4, r^2 is 4 ⇒ r = √4 = 2
3. We now know that the center of this circle is ( -4, 3 ) with a radius of 2, and the only graph that represents that function is the first graph ~
<em>Answer: Center ~ ( -4, 3 ), Radius ~ 2</em>
You solve this by first determining how many years is it from 2004 to 2016. It is 12 years. Now you do 0.07 (which is 7% in decimal form) times 12 which gives you 0.84. To find 84% of 12,500, you just multiply them two together and get 10,500. You finish this by subtracting 10500 from 12500 and you get $2,000 as your final answer.
For 2020, you determine how many years it is from 2004 to 2020 and you get 16. So you multiply 0.07 times 16 giving you 1.12. You multiply 1.12 times 12,500 and you get 14,000. Finally, you subtract 14,000 from 12,500 giving you -1500.