25 students
194 balloons
194/25 = 7.76
Each student gets 7 balloons, 7 x 25 = 175 balloons will be used
194 - 175 = 19 balloons remaining (Answer to part 1 of this question)
If each student needs 8 balloons
8 * 25 = 200
200 - 194 = 6 ballons needed (Answer to part 2 of this question)
We also could have found the answer to part 2 by saying that we had 19 balloons left over when the students each were given 7 balloons
Each student needs another 1 balloon = 25 balloons,
We have 19 left over
25 - 19 = 6 balloons need to be purchased (we got the same answer both ways so it is very likely we have the correct answer)
Answer:
A) y =
is logarithmic function.
Step-by-step explanation:
Given : Options.
To find : which of the following is a logarithmic function.
Solution : We have given option
Logarithmic function : The function which have log init.
We can see from given options
y =
is logarithmic function.
Therefore, A) y =
is logarithmic function.
Answer: 24.2° SouthWest
<u>Step-by-step explanation:</u>
First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
<u>Perpendicular (x):</u>
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
<u>Angle (θ):</u>
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
![{\qquad\qquad\huge\underline{{\sf Answer}}}](https://tex.z-dn.net/?f=%20%7B%5Cqquad%5Cqquad%5Chuge%5Cunderline%7B%7B%5Csf%20Answer%7D%7D%7D%20)
Let's solve ~
![\qquad \sf \dashrightarrow \: 10x + 30 = 90](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%2010x%20%2B%2030%20%3D%2090)
[ according to given figure ]
![\qquad \sf \dashrightarrow \: 10x = 90 - 30](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%2010x%20%3D%2090%20-%2030)
![\qquad \sf \dashrightarrow \: 10x = 60](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%2010x%20%3D%2060)
![\qquad \sf \dashrightarrow \: x = 60 \div 10](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20x%20%3D%2060%20%5Cdiv%2010)
![\qquad \sf \dashrightarrow \: x = 6 \degree](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20x%20%3D%206%20%5Cdegree)
Correct choice is D
<u>Answer:</u>
D) 6x^2 - 8y^2 = 50
-6x^2 - 2y^2 = 11
<u>Step-by-step explanation:</u>
We are given the following two expressions:
![3x^2-4y^2=25](https://tex.z-dn.net/?f=3x%5E2-4y%5E2%3D25)
and
![-6x^2-2y^2=11](https://tex.z-dn.net/?f=-6x%5E2-2y%5E2%3D11)
Now if we look at the option D)
and
, we can observe that the earlier part in the given expression is just a simplification of 6x^2 - 8y^2 = 50.
![6x^2 - 8y^2 = 50\\\\2(3x^2-4y^2) = 50\\\\3x^2-4y^2 = \frac{50}{2} \\\\3x^2-4y^2=25](https://tex.z-dn.net/?f=6x%5E2%20-%208y%5E2%20%3D%2050%5C%5C%5C%5C2%283x%5E2-4y%5E2%29%20%3D%2050%5C%5C%5C%5C3x%5E2-4y%5E2%20%3D%20%5Cfrac%7B50%7D%7B2%7D%20%5C%5C%5C%5C3x%5E2-4y%5E2%3D25)
and the later part
is already the same.
Therefore, the correct answer option is D) 6x^2 - 8y^2 = 50
-6x^2 - 2y^2 = 11.