Answer:
The measure of the angle is 150°, the measure of its supplementary is 30°
Step-by-step explanation:
The given parameters are;
The measure of the given angle = 5 × The measure of its supplementary angle
Let "x" represent the given angle, and let "y" represent its supplementary angle, we have;
x = 5 × y...(1)
x + y = 180°...(2)
By substituting the value of x = 5 × y, from the first equation into the second equation, we have;
x + y = 180°
x + y = 5 × y + y = 5·y + y = 6·y = 180°
y = 180°/6 = 30°
y = 30°
x = 5 × y = 5 × 30° = 150°
x = 150°
The measure of the angle = x = 150°, the measure of its supplementary = y = 30°.
In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 8 million? d) Find the doubling time. a) The exponential growth function is P(t) nothing, where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)
Answer:
a) The exponential growth function
P(t) = 5,690,000(1.0287)^t
b) 6,742,868.7374 million
c) 12.04 years
d) 2439.0243902
Step-by-step explanation:
In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year.
The formula for exponential growth is given as:
P(t) = Po( 1 + r) ^t
Where P = Population size after time t
Po = Initial population size
r = Growth rate in percentage
t= time in years
a) Find the exponential growth function.
P(t) = Population size after time t
Po = Initial population size = 5.69 million
r = Growth rate in percentage = 2.87% = 0.0287
t= time in years
The Exponential growth function
P(t) = 5,690,000(1 + 0.0287)^t
P(t) = 5,690,000(1.0287)^t
b) Estimate the population of the city in 2018.
From 2012 to 2018 = 6 years
t = 6 years
Hence,
P(t) = Po( 1 + r) ^t
P(t) = 5,690,000(1 + 0.0287)^6
P(t) = 5,690,000(1.0287)^6
P(t) = 6,742,868.7374 million
c) When will the population of the city be 8 million?
P(t) = 8,000,000
P(t) = Po( 1 + r) ^t
P(t) = 5,690,000(1 + 0.0287)^t
8,000,000 = 5,690,000(1 + 0.0287)^t
8,000,000 = 5,690,000(1.0287)^t
Divide both sides by 5,690,000
8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000
= 1.4059753954 = 1.0287^t
Take logarithm of both sides
log 1.4059753954 = log 1.0287^t
Log 1.4059753954 =t Log 1.0287
t = Log 1.4059753954/Log 1.0287
t = 12.041740264
t = 12.04 years
d) Find the doubling time.
The formula is given as 70/Growth rate
= 70/0.0287
= 2439.0243902
Ana and Chuyen are exploringunderwater sea life while on a helmet divingadventure. Ana's location ismath−30feet below sealevel, and Chuyen's location ismath−12feet belowsea level. Which girl is located farther from sealevel?
Answer:
Ana
Step-by-step explanation:
Given that:
Ana's location = −30feet below sealevel
Chuyen's location = − 12feet below sea level
Sea level = point 0 ;
-30 feets below sea level
A depth of - 30, below the water surface.
A depth of - 12 below sea level ; a depth of 12 feets below the water surface
-30 feets is farther below the water surface than - 12 feets
Hence, Ana is farther below the sea level than Chuyen
Which expression represents the completely factored form of 2x3 + x2 - 8x - 4?
a (x2 - 4)(2x + 1)
6 (x - 2)2(2x - 1)
0 (x - 2)(x + 2)(2x - 1)
d (x-2)(x + 2)(2x + 1)
Answer:
D
Step-by-step explanation:
D is also equivalent
what is the meaning of life
Answer:
The meaning of life, or the answer to the question: "What is the meaning of life?", pertains to the significance of living or existence in general. Many other related questions include: "Why are we here?", "What is life all about?", or "What is the purpose of existence?"
Step-by-step explanation:
Answer:
Step-by-step explanation:
The meaning of life, or the answer to the question: "What is the meaning of life?", pertains to the significance of living or existence in general. Many other related questions include: "Why are we here?", "What is life all about?", or "What is the purpose of existence?"
if g(x) = 8x -20, find g(-4)
Answer:
g(-4)= -52
Step-by-step explanation:
g(x) = 8x -20
Substitute -4 for x
g(-4) = 8(-4) -20
g(-4) = -52
Given the table on the right, what is the slope?
Answer:
hi
Step-by-step explanation:
Is the relation a function?
Answer:
yes
Step-by-step explanation:
For a relation to be a function each value of x in the domain must map to exactly one unique value of y in the range.
Since the relation is a straight line , then each value of x will only map to one unique value of y ( passes the vertical line test )
Please help me with this
Answer:
A
Step-by-step explanation:
what is the answer?????????????????????????????????????
Answer:
A
Step-by-step explanation:
tell me your opinions on the following image
Answer:
gorgeous
Step-by-step explanation:
Answer:
i am disturbed.
Step-by-step explanation:
this image is disturbing to me, because he is staring at you in your sleep too
A collector has a box of 32 figurines. The value of each figurine increased by $2.32 over the past year. The box of figurines is now worth $114.24. What was the original cost, x, of one figurine? The original cost of one figurine was .
Answer:
$1.25
Step-by-step explanation:
step 1:
2.32 x 32
answer:
74.24
step 2:
114.24 - 74.24
answer:
40
step 3:
40 divided by 32
FINAL answer:
40 divided by 32 = x
x =
1.25--------------
the original cost was $1.25! :D
the lamp is $10 and the sales tax is 5% whats the total cost of the lamp
Answer:
10.50
Step-by-step explanation:
Answer:
10.50
Step-by-step explanation:
multiply 10 by .5 and you get 50cents so add that to 10 and you get 10.50
A shop keeper purchased 200 bulbs for Rs.10 each. However 5 bulbs were fused and had to
be thrown away. The remaining were sold at Rs.12 each. Find the gain or loss %
Answer: 17%
Step-by-step explanation:
A shop keeper purchased 200 bulbs for Rs.10 each. Therefore, the cost price:
= 200 × 10
= 2000
Since 5 bulbs were fused and had to
be thrown away and the remaining were sold at Rs.12 each. Therefore, selling price would be:
= 195 × 12
= 2340
Gain would be:
= 2340 - 2000
= 340
Gain percent would be:
= Gain / Cost price × 100
= 340/2000 × 100
= 17%
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 15% real fruit juice. The company used 100.5 liters of real fruit juice to make 30 more liters of Drink A than liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Answer:
There needs to be 300 liters of Drink A and 270 liters of Drink B
Step-by-step explanation:
Let a = the amount of Drink A and b = the amount of Drink B
Multiplying a number by 0.2 is the same as calculating 20% of it and same goes with 15% and 0.15. This makes our equation for the amount of fruit juice:
0.2a + 0.15b = 100.5
We know what the difference between a and b will be 30 liters so:
a - b = 30
Now we have our system of equations
To cancel out a, we can multiply the first equation by -5 so we will now have:
-a - 0.75b = -502.5
a - b = 30
Adding these two equations together, we get:
-1.75b = -472.5
Both sides are negative, so we can take the negative signs away.
1.75b = 472.5
Now divide both sides by 1.75
b = 270
Plugging 270 into b, we have:
a - b = 30
a - 270 = 30
Add 270 to both sides
a = 300
There needs to be 300 liters of Drink A and 270 liters of Drink B
The system of linear equations which could be used to find the amount in litres of drinks A and B are :
(0.2a + 0.15b) = 100.5a - b = 30Let :
Amount of drink A = a
Amount of drink B = b
Percentage of real fruit juice for drink A = 20%
Percentage of real fruit juice for drink B = 15%
Total litres made = 100.5
(Amount of drink A × percentage) + (Amount of drink B × percentage) = Total litres
(0.2a + 0.15b) = 100.5 - - - - - (1)The difference between the amount of drink A and B made :
Drink A is 30 liters more than B :
a - b = 30 - - - - - (2)The system of equations required to determine the amount of drink A and B made are :
(0.2a + 0.15b) = 100.5a - b = 30Learn more : https://brainly.com/question/20379472?referrer=searchResults
Which is greater: 6/30 or 12/40
Answer:
12/40
Step-by-step explanation:
match the denominators so have 6/30 be multiplies with 40/40 and 12/40 multiplied with 30/30
6/30(40/40) = 240/1200
12/40(30/30) = 360/1200
As we can see, 360/1200 is bigger than 240/1200, therefore 12/40 is bigger
Answer: [tex]\frac{12}{40}[/tex]
Step-by-step explanation:
Hey there!
-If we were to simplify [tex]\frac{6}{30}[/tex] we would be able to simplify it to [tex]\frac{1}{5}[/tex].
-Multiply [tex]\frac{6}{30}[/tex] by 100 and you get 20 .
-Now compare that with [tex]\frac{3}{10}[/tex] which is [tex]\frac{12}{40}[/tex] simplified.
-Multiply [tex]\frac{12}{40}[/tex] by 100 and you get 30.
-We can now tell that [tex]\frac{12}{40}[/tex] is greater than [tex]\frac{6}{30}[/tex].
~I hope I helped :)~
What is the area of the triangle?
48 in 2
28 in 2
96 in 2
24 in 2
Answer:
48 in^2
Step-by-step explanation:
To find the area of a triangle is (1/2)*base*height, so (1/2)*4in*24in = 2in*24in = 48 in^2.
Answer:
48 in2
Step-by-step explanation:
when finding area we use the equation A= 1/2bh
b meaning base and h meaning height
so for this we would use A= 1/2(24)(4)
multiply them both to get A=1/2(96)
and then take half of 96 to get 48
so the answer is 48in 2
3n +15 for n =4
what is the answer
Answer:
the correct answer would be 27
Step-by-step explanation:
So first things first you need to replace n with 4
3n+15
(3)(4)+15
=12+15
=27
Hope this helps have an amazing day!!
Answer: 27
Step-by-step explanation:
-We would need to substitute the value of the variable into the equation and simplify.
-We will be plugging in 4 for n.
Step 1: Plugging in.
3 * 4 = 12
Step 2: Addition.
12 + 15
Final Answer: 27
helppppp pleaseeeeeeeeeeeeeeeeeeeee
Answer:
Communicative property is the third one second one is assositave and first one is distributive
Step-by-step explanation:
If 4 raffle tickets is 6 dollars how much is 1 raffle ticket
Is 5+x equal to 8+0.75x
Answer:
1.2
Step-by-step explanation:
X×5=0.75
X=(6, 5)
x=1.2
Answer:
no
Step-by-step explanation:
5+x=8+0.75x
x=12
HURRYYYYY!!!
If f(x) = |x + 7| find f(-12).
I’d appreciate an answer ;)
Answer: Hope you have a good day or night!
Step-by-step explanation:
What is 56/5 simplest form???
Answer:
9 1/3
Step-by-step explanation:
this is what i think and i hope im right
Answer:
11 1/5
Step-by-step explanation:
You can do 56 divided by 5 to answer this.
56 / 5 = 11 and 1/5
11 1/5
Simplify: 1/2 (24q -1)
Answer:
12q -1/2
Step-by-step explanation:
Answer:
12q -1/2
Step-by-step explanation:
Question 3 HELPPPPPPPPPPPPPPPP
Answer
The following is a picture of the number with a point on -2
Order the following numbers from least to greatest (15 Pts)
Answer:
-5.1 , -14/3, -4
Step-by-step explanation:
In the negative side of the numberline -5 is lesser than -14/3 and -4.
Also -14/3 is aproximatedly -4. 6. so its less than -4
Answer:
1. -5.1
2. - 14/3
3. -4
Explanation:
- 14/3 is equal to -4.6 repeating. We can check this by dividing 14 by 3 and adding the negative sign. So -4 is the greatest number of the numbers, and -5.1 is the least since it is the most of the negative numbers. - 14/3 would go in the middle because it isn't greater than -4 nor less than -5.1.
Hope this helps!
I hope I explained well!
PLEASE HELP DUE IN 6 MINS!!!!!!!!!!!!!!!!!!!!!
Box of nails: $3.80
Box of screws:$5.25
Claw Hammer:$12.95
Electric Drill:$42.50
a.Write two expressions to represent the total cost of 3 boxes of nails, 2 boxes of screws, 2 hammers, and 1 electric drill.
b.What is the total cost of the items purchased?
Answer:
Step-by-step explanation:
a. 3n+2s+2h+1x=42.50
b. 90.3
Which equation represents a linear function? (5 points)
Equation 1: y3 = 2x + 1
Equation 2: y = 3x + 1
Equation 3: y = 5x2 − 1
Equation 4: y = 4x4 − 1
75 POINTS!WILL MARK BRAINLIEST
m(x) = 2xto the 2nd power+3x-5
m(-2)=-19 right?
Answer:
Yes
Step-by-step explanation:
Answer:
2mx³+3x−5
Step-by-step explanation:
In the system of equations, b is a constant. If the system has infinitely many solutions, what is the value of b?
Answer:
The value of b is 9.5
Step-by-step explanation:
If a system of equations has infinitely many solutions, that means the two equations are equal
If the system of equations ax + by = c, dx + ey = f, then
a = d ⇒ coefficients of xb = e ⇒ coefficients of yc = f ⇒ numerical termsLet us use this fact to solve the question
∵ 3x - y = 19 ⇒ (1)
∵ 1.5x - 0.5 y = b ⇒ (2)
∵ This system of equations has infinitely many solutions
∴ The coefficients of x must be equal
∴ The coefficients of y must be equal
∴ The numerical terms must be equal
→ Multiply equation (2) by 2 to make the coefficients of x and y on it
equal the coefficients of x and y in equation (1)
∵ 2(1.5x) - 2(0.5y) = 2(b)
∴ 3x - y = 2b ⇒ (3)
→ By comparing equations (1) and (3), 19 must equal 2b
∵ 2b = 19
→ Divide both sides by 2
∴ b = 9.5
∴ The value of b is 9.5