Answer:
<em>The sea cow can stay under water for 16 minutes.</em>
Step-by-step explanation:
A hippopotamus can stay under water for 15 minutes.
A sea cow can stay under water
minutes and this is 11 minutes longer than one-third the time a hippopotamus can.
So, "11 minutes longer than one-third the time a hippopotamus can" means: ![[\frac{1}{3}(15)+11] minutes](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B3%7D%2815%29%2B11%5D%20minutes)
Thus, the equation will be: ![y= \frac{1}{3}(15)+11](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B3%7D%2815%29%2B11)
Now, solving the above equation, we will get.........
![y= \frac{1}{3}(15)+11 \\ \\ y=5+11= 16](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B3%7D%2815%29%2B11%20%5C%5C%20%5C%5C%20y%3D5%2B11%3D%2016)
So, the sea cow can stay under water for 16 minutes.
The length of AC is 16 km.
Solution:
Given data:
AB = c = 14 km, ∠A = 30° and ∠B = 89°
AC = b = ?
<u>Let us first find angle C:</u>
<em>Sum of all angles in a triangle = 180°</em>
m∠A+ m∠B + m∠C = 180°
30° + 89° + m∠C = 180°
119° + m∠C = 180°
Subtract 119° from both sides, we get
m∠C = 61°
<u>To find the length of AC:</u>
<em>Using sine formula:</em>
![$\frac{b}{\sin B } =\frac{c}{\sin C}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bb%7D%7B%5Csin%20B%20%7D%20%3D%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
Substitute the given values in the formula.
![$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }](https://tex.z-dn.net/?f=%24%5Cfrac%7Bb%7D%7B%5Csin%2089%5E%5Ccirc%20%7D%20%3D%5Cfrac%7B14%7D%7B%5Csin%2061%5E%5Ccirc%20%7D)
Multiply by sin 89° on both sides.
![$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ](https://tex.z-dn.net/?f=%24%5Csin%2089%5E%5Ccirc%20%5Ctimes%20%5Cfrac%7Bb%7D%7B%5Csin%2089%5E%5Ccirc%20%7D%20%3D%5Cfrac%7B14%7D%7B%5Csin%2061%5E%5Ccirc%20%7D%20%5Ctimes%20%5Csin%2089%5E%5Ccirc)
![$b=\frac{14}{0.8746 } \times0.9998](https://tex.z-dn.net/?f=%24b%3D%5Cfrac%7B14%7D%7B0.8746%20%7D%20%5Ctimes0.9998)
![b=16](https://tex.z-dn.net/?f=b%3D16)
The length of AC is 16 km.
Answer:
A) 7 is the greatest common factor of the expression.
B) factoring the expression
we get ![\mathbf{7(2x+4y+3)}](https://tex.z-dn.net/?f=%5Cmathbf%7B7%282x%2B4y%2B3%29%7D)
Step-by-step explanation:
We are given the expression: ![14x + 28y + 21](https://tex.z-dn.net/?f=14x%20%2B%2028y%20%2B%2021)
Part A: What is the greatest common factor of the expression?
We need to find the greatest common factor of the expression.
The expression is divisible by 7
So, 7 is the greatest common factor of the expression.
Part B: Factor the expression
We need to factor the expression: ![14x + 28y + 21](https://tex.z-dn.net/?f=14x%20%2B%2028y%20%2B%2021)
Taking 7 common:
![14x + 28y + 21\\=7(2x+4y+3)](https://tex.z-dn.net/?f=14x%20%2B%2028y%20%2B%2021%5C%5C%3D7%282x%2B4y%2B3%29)
So, factoring the expression
we get ![\mathbf{7(2x+4y+3)}](https://tex.z-dn.net/?f=%5Cmathbf%7B7%282x%2B4y%2B3%29%7D)
Answer:
Sine angle A = 1,050 / 2,800
Sine angle A = .375
arc sine (.375) = Angle A
Angle A = 22.024 Degrees
(THIS REPLACES THE PREVIOUS ANSWER.)
Step-by-step explanation:
Answer:
Regular hexagon =720
Regular octagon=1080
Step-by-step explanation:
The formula is (n-2) x 180, «n» is the side number of the polygon
The first one
So (n-2) x 180
(6-2) x 180
4 x 180
720
And the second polygon
(n-2)x 180
(8-2) x 180
6 x 180
1080