X2 + 16x – 2 = 111) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (x - c)2 = d.
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Answers
The equation with completing the squares is (x + 8)² = 77.
What is an equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + 16x - 2 = 11
We can make completesquares.
x² + 16x - 2 - 11 = 0
x² + 16x - 13 = 0
x² + 2 x 8 x (x) -8² + 8² - 13 = 0
(x² + 16x + 8²) - 64 - 13 = 0
(x + 8)² - 77 = 0
(x + 8)² = 77
Thus,
The equation is (x + 8)² = 77.
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Answer:
(x+8)^2=77 and x=negative 8±√77
Step-by-step explanation:
After watching a video, I got it right on Khan
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Answers
Answer:
1 whole and 5/8 as a decimal is 1.625
Steps: Convert 1 5/8 to a improper fraction-> 13/5 and dived the numerator by the denominator. 13/5= 1.265
Answers
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
= 4/3 x π x 4^3
= 268.08
= 85.33 π
~ 300 units ^3
Answers
Answer:
B.
Step-by-step explanation:
9 (x + 1) = 9*x + 9*1 = 9x + 9
Answers
Answer:
a. The biomass weighs 2.30 * 10^7 kg after a year
b. It'll take 2.56 years to get to 4*10^7kg
Step-by-step explanation:
a.
k = 0.78,K = 6E7 kg
Given
dy/dt = ky(1- y/K)
Make ky dt the subject of formula
ky dt = dy/(1-y/K) --- make k dt the subject of formula
k dt = dy/(y(1-y/K))
k dt = K dy / y(K-y)
k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides
kt + c = ln(y/(K-y))
Ce^(kt) = y/(K-y)
Substitute the values of k and K
Ce^(0.78t) = y/(6*10^7 - y) ----- (1)
Given that y(0) = 2 * 10^7kg
(1) becomes
Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)
Ce° = (2*10^7)/(4*10^7
C = 2/7
Substitute 2/7 for C in (1)
2/7e^0.78t = y/(6*10^7 - y) ---(2)
We're to find the biomass a year later
So, t = 1
2/7e^0.78 = y/(6*10^7 - y)
0.62 = y/(6*10^7 - y)
y = 0.62(6*10^7 - y)
y = 0.62*6*10^7 - 0.62y
y + 0.62y = 0.62*6*10^7
1.62y = 0.62*6*10^7
1.62y = 3.72 * 10^7
y = 2.30 * 10^7kg.
Hence, the biomass weighs 2.30 * 10^7 kg after a year
b.
Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg
Substitute 4*10^7 for y in (2)
2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)
2/7e^0.78t = 4*10^7/2*10^7
2/7e^0.78t = 2
e^0.78t = (2*7)/2
e^0.78t = 2
t = 2 * 1/0.78
t = 2.56 years
Hence, it'll take 2.56 years to get to 4*10^7kg
Answers
Answer:
c. One sided t-test
Step-by-step explanation:
One sided t test because we want to compare two means and alternative hypothesis is directional.
Answers
7 is the factor of 14 and 7 has 14 as its multiple.
What is Factor?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Given:
We have the Number 14.
So, the factors of 14 = 1, 2, 7, 14.
and, 7 can act as factor of 14.
also, 7 has multiple 14.
Hence, 7 is the required number.
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Answer:
7 is both a factor and a multiple