Answer: 1. 63; 2. 84; 3. 104 4. 1:2
Step-by-step explanation: Since Zoey has $28, and the ratio is 4:5, we can multiply the ratio by 7 on both sides so that it is 28:35, giving $35 for andrew, and this $28+$35=$63. Since the ratio of red to white marbles has a sum of 10, but there are 120, we multiply the ratio by 120/10=12, to make the ratio applicable to the scenario, so 7 times 12 = 84 red marbles. Same way for the theater question, 195/15=13, so 8 times 13= 104, and so 104 people are boys. For the last question you can simply divide both sides by 5 (or think of it as a fraction, 5/10=1/2).
Answer:
To solve for n you need to get it by itself
First you want to distribute your 2 through the (3n+14)
-2n+6n+28=-20 (2*3n+2*14= 6n+28)
Now you want to combine any like terms if possible
4n+28=-20 (-2n+6n=4n, both like terms)
Then you want to subtract -28 from both sides
4n=-48 (28-28=0, -20-28=-48)
Lastly you want to divide both sides by 4
n=-12 (4n/4=n, -48/4= -12)
Answer:
Average rate of change: 
Step-by-step explanation:
<u>Remember:</u>
The average rate of change of a function over an interval ![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
is 
<u>Given:</u>
![[a,b]=[1,7]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%3D%5B1%2C7%5D)
<u>Calculation:</u>
Therefore, the average rate of change of the function 
over the interval 
is .
For this case, what you must do is take out the area of two triangles and add it to the area of a rectangle to find the total area.
We have then:
Triangle area:
A = (1/2) * ((13-9) / (2)) * (10) = 10 in ^ 2
Rectangle area:
A = (9) * (10) = 90 in ^ 2
Total area:
At = 2 * (10) + 90 = 110 in ^ 2
answer:
110 in²
Answer:
21.9°
Step-by-step explanation:
In ΔHIJ, the measure of ∠J=90°, HI = 8 feet, and JH = 1.9 feet. Find the measure of ∠H to the nearest tenth of a degree.
We solve this above question using the Sine rule
a/sin A = b/sin B
In ΔHIJ, the measure of ∠J=90°, HI = 8 feet, and JH = 1.9 feet.
Hence:
HI/∠J = JH/∠H
= 8/sin 90° = 1.9/sin ∠H
Cross Multiply
∠H = arc sin(sin 1.9 × 90/8)
∠H = 21.9°
