Answer:
(-1, 6)
Step-by-step explanation:
A graphing calculator shows the vertex to be (x, y) = (-1, 6).
__
You can also find it by putting the equation into vertex form.
y = -2(x^2 +2x) +4
y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside
y = -2(x +1)^2 +6
Compare to ...
y = a(x -h)^2 +k
and you see a=-2, h=-1, k=6
The vertex is (h, k) = (-1, 6).
#1) A
#2) E
#3) C
#4) 0.5840
#5) 0.6945
#6) 0.4911
#7) D
#8) G
#9) 0.4375
#10) 0.5203
The formula we use for this is
,
where
is the speed of sound, f is the frequency (or pitch) of the note, and λ is the wavelength.
#1) 0.77955f = 343
Divide both sides by 0.77955:
0.77955f/0.77955 = 343/0.77955
f = 439.997 ≈ 440. This is the pitch for A.
#2) 0.52028f = 343
Divide both sides by 0.52028, and we get f = 659.260. This is the pitch for E.
#3) 0.65552f = 343
Divide both sides by 0.65552, and we get f = 523.25. This is the pitch for C.
#4) 587.33λ = 343
Divide both sides by 587.33 and we get λ = 0.583999 ≈ 0.5840.
#5) 493.88λ = 343
Divide both sides by 493.88, and we get λ = 0.6945.
#6) 698.46λ = 343
Divide both sides by 698.46 and we get λ = 0.49108 ≈ 0.4911.
#7) 0.5840f = 343
Divide both sides by 0.5840 and we get f = 587.3288 ≈ 587.33. This is the pitch for D.
#8) 0.4375f = 343
Divide both sides by 0.4375 and we get f = 784. This is the pitch for G.
#9) 783.99λ = 343
Divide both sides by 783.99 and we get λ = 0.4375.
#10) 659.26λ = 343
Divide both sides by 659.26 and we get λ = 0.52028 ≈ 0.5203.
In this big ol' word problem, this is just an instance of basic multiplication/division.
If it takes it 1 hour for 3 meters...
12 ÷ 3 = 4.
It would take 4 hours for the water level to change to 12 meters.
Answer: 1. 7
2. 100
3. 193.8
4. 0.8
5. 90.6
Step-by-step explanation:
1. Given the data 9,3,10,12,4,5,12,2
For finding the median we arrange it in ascending order
2,3,4,5,9, 10,12,12
Since the no of observations are even
∴ median =
= 
=
=7
i.e. Median =7
2. Given the data
23, 95,100,23,100,100
Since the no 100 is repeated thrice i.e. the maximum no of times
∴ Mode=100
3.
Given the data
108, 305,252,113, 191
Mean=
=
=193.8
4. Money spent in the first week
= $11.52, $6.48, $5.99, $14.00, and $9.50
Total for the first week
=11.52+6.48+5.99+14.00+9.50
=$47.49
Now she spent $4 more in the second week
i.e.$47.49+4
=51.49$
Increase in mean =
=0.8
5.
Given
2 students scored 100 each
9 students scored 95 each
10 students scored 90 each
3 students scored 80 each
1 student scored 70
Total score of students =
=2265
The average score
=
=90.6
Answer:
×=3
Step-by-step explanation:
you have to do 3×-2×=1x
and than the formal look like ×+4=4×-5
and move × to other side so that become 3x
and move 5 to +5 so that become 9
the formal look like 9=3×
and divide 3/9 is your answer
×=3
