We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.
PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE
Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5
So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5
Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20
So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25
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<span>Finally, we check our solution against the original question. </span>
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔
Hope that helped :)
I cant solve the last part at the moment but i think 20. 49
21. 81
22. m
23. 49
Answer:
(B) (1.50, 2.0)
(E) (1 and one-half, 2)
Step-by-step explanation:
On the coordinate plane
The bleachers is 1.5 units to the right and 2 units up.
1.5 units to the right indicates a positive value on the x-axis. Therefore, the bleachers x-coordinate is 1.5.
2 units up indicates a positive value on the y-axis. Therefore, the bleachers y-coordinate is 2.
Therefore, we can write the bleachers location in the (x,y) coordinate system as: (1.5,2)
The following ordered pairs shows the bleacher's location.
- (B) (1.50, 2.0)
- (E) (1 and one-half, 2)
Answer:
B = 40°
a = 23.0
b = 19.3
Step-by-step explanation:
✔️B = 180° - (90° + 50°) => sum of triangle
B = 40°
✔️Reference angle = 50°
Opp = a
Hypotenuse = 30
Adjacent = b
Find a by applying the trigonometric function, SOH:
Sin 50 = Opp/Hyp
Sin 50 = a/30
30 × Sin 50 = a
23.0 = a
a = 23.0 (nearest tenth)
To find b, apply CAH:
Cos 50 = Adj/Hyp
Cos 50 = b/30
30 × Cos 50 = b
b = 19.3 (nearest tenth)
1.
slope = (5/3 - 2/3)/((3/2 - 1/2)
slope = 1/1 = 1
answer
1
2.
slope = (8-3)/(9-8)
slope = 5/1 = 5
answer
5
3.
m = -1, b = -3
y = mx + b
so
equation
y = -x - 3
answer
y = -x - 3
4. m = 0 b = -4
y = mx + b
so
equation
y = -4
answer
y = -4