Answer:
y=-5
Step-by-step explanation:
-3(-4-6y)+7(-y+5)=-8
12+18y-7y+35=-8
11y+47=-8
11y=-8-47
11y=-55
y=-55/11
y=-5
Answer:
∠C = 106.7°, ∠D = 73.3°, CD = 104.4
Step-by-step explanation:
As shown in the diagram attached, let a point E be made on line BD.
Hence, BE = 130 m
BE + ED = BD
ED = BD - BE
ED = 160 m - 130 m = 30 m
Also, CE = 100 m
Using Pythagoras theorem in triangle CDE:
CD² = CE² + ED²
CD² = 100² + 30²
CD² = 10000 + 900 = 10900
CD = √10900
CD = 104.4
Using sine rule in triangle CDE:
![\frac{sin(D)}{CE}=\frac{sin(E)}{CD}\\ \\sin(D)=\frac{sin(E)}{CD} *CE\\\\sin(D)=\frac{sin(90)}{104.4}*100\\ \\sin(D)=0.9578\\\\D=sin^{-1}0.9578\\\\D=73.3^o](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28D%29%7D%7BCE%7D%3D%5Cfrac%7Bsin%28E%29%7D%7BCD%7D%5C%5C%20%20%5C%5Csin%28D%29%3D%5Cfrac%7Bsin%28E%29%7D%7BCD%7D%20%2ACE%5C%5C%5C%5Csin%28D%29%3D%5Cfrac%7Bsin%2890%29%7D%7B104.4%7D%2A100%5C%5C%20%5C%5Csin%28D%29%3D0.9578%5C%5C%5C%5CD%3Dsin%5E%7B-1%7D0.9578%5C%5C%5C%5CD%3D73.3%5Eo)
In trapezoid ABCD, the sum of angles in a quadralateral is 360°, hence:
∠A + ∠B + ∠C + ∠D = 360
90 + 90 + ∠C + 73.3 = 360
∠C + 253.3 = 360
∠C = 360 - 253.3
∠C = 106.7
Answer:
x
=
e
y
+
3
−
4
Step-by-step explanation:
Algebra Examples
Popular Problems Algebra Find the Inverse y=e^(x+3)-4
y
=
e
x
+
3
−
4
Interchange the variables.
x
=
e
y
+
3
−
4
Solve for
y
.
Tap for fewer steps...
Since
y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
e
y
+
3
−
4
=
x
Add
4
to both sides of the equation.
e
y
+
3
=
x
+
4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln
(
e
y
+
3
)
=
ln
(
x
+
4
)
Use logarithm rules to move
y
+
3
out of the exponent.
(
y
+
3
)
ln
(
e
)
=
ln
(
x
+
4
)
The natural logarithm of
e
is
1
.
(
y
+
3
)
⋅
1
=
ln
(
x
+
4
)
Multiply
y
+
3
by
1
.
y
+
3
=
ln
(
x
+
4
)
Subtract
3
from both sides of the equation.
Answer: 101
Step-by-step explanation:
45 women total
17 women will not watch the game
So 33 people did not want to watch the game and 17 are women
33-17 = 16 men who won’t watch the game
So 40 men who will and 16 men who won’t equals 56 men and 45 women
56+45= 101
Answer:
B
Step-by-step explanation:
Given
2x + 3y = 36 ← substitute y = 6
2x + 3(6) = 36
2x + 18 = 36 ( subtract 18 from both sides )
2x = 18 ( divide both sides by 2 (
x = 9 → B