Answer:
y = 2(4^(x))
Step-by-step explanation:
In 2012, the park has a population of 32 lions. A year later, in 2013, the park has 128 lions.
This means in 2012, it was 2^(5) lions while after 1 year it was 2^(7) lions
Thus, it increases every year by a ratio of 2^(2)
Thus, in 2011, it was 2^(5) - 2^(2) = 2^(3) lions
In 2010, it was 2^(3) - 2^(2) = 2
Since Lions were introduced in the park in 2010, using f(x), it means;
at x = 0, f(x) = 2
at x = 1, f(x) = 2^(3)
at x = 2, f(x) = 2^(5)
at x = 3, f(x) = 2^(7)
To find an exponential function that models the situation, let's use the generic formula: y = ab^(x)
At x = 0 and y = 2, we have;
2 = a × b^(0)
Thus,a = 2
At x = 1, y = 2^(3)
Thus; 2^(3) = 2 × b^(1)
b = 8/2
b = 4
So the exponential equation is;
y = 2(4^(x))
You can use the fact that the given figures are expressible as 2 raised to some powers.
The exponential function modeling the number of lions to the years passed since 2010 is given as
[tex]f(x) = 2^{1+2x}[/tex]
What is an exponential function?Those functions which are expressed as some constant raised to the power of the argument called exponential function.
How to find which function can model the given condition?Since 2012 - 2010 = 2 and the number of lions = 32 = [tex]2^5[/tex]
and 2013 -2010 = 3 and the number of lions =128 = [tex]2^7[/tex]
Thus, there is increment of 2 exponent as 1 year was changed.
Thus, we have:
[tex]f(x) = 2^{2x + a}[/tex] where a might be some constant( i took this form of exponent just by trial and error. It was already visible that one year was increasing double output, thus 2x and since there was just double increase and no other effect, there might be some non variable thing(a constant) so i thought to try some variable and see if this can work)
Since at x = 2, we get 2 raised to the power 5
thus.
[tex]2(2) + a = 5\\a = 1[/tex]
Thus,
The exponential function modeling the number of lions to the years passed since 2010 is given as
[tex]f(x) = 2^{1+2x}[/tex]
You can see that this will give correct output for x = 2 and x = 3
Learn more about exponential functions here:
https://brainly.com/question/15680851
(5x² + 25x + 30)– (3x² + 6x + 3)
Notice that the second polynomial is subtracted from the first.
It's important to understand that the minus sign outside the
second set of parenthses can be thought of as a -1.
So we need to distribute the -1 through each of
the terms in the second set of parenthses.
So our problem will now look like 5x² + 25x + 30 - 3x² - 6x - 3.
Now, we combine like terms.
So we have 2x² + 19x + 27.
If y varies inversely as x. Using the coordinates (5, 3) and (x, 2.5), find the missing value x.
Answer:
(6, 2.5 )
Step-by-step explanation:
Given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k substitute the coordinate point (5, 3 ) into the equation, that is
3 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )
15 = k
y = [tex]\frac{15}{x}[/tex] ← equation of variation
Using (x, 2.5 ) with y = 2.5 , then
2.5 = [tex]\frac{15}{x}[/tex] ( multiply both sides by x )
2.5x = 15 ( divide both sides by 2.5 )
x = 6
Thus point is (6, 2.5 )
What are the answers to these two things? 3x -2 + 4 = x - 6 and x + 8 = 5x + 6 Im gonna need step by step also, thanks!
Answer:
For 3x-2+4=x-6
[tex]3x - 2 + 4 = x - 6 \\ 3x - x = - 6 - 4 + 2 \\ 2x = - 8 \\ x = \frac{ - 8}{2} \\ x = - 4[/tex]
for x+8=5x+6
[tex]x + 8 = 5x + 6 \\ x - 5x = 6 - 8 \\ - 4x = - 2 \\ x = \frac{ - 2}{ - 4} \\ x = \frac{1}{2} [/tex]
Alicia ran 5 miles over the weekend. Approximately how many kilometers did she run? [Use the conversion 1 mile ≈ 1.6 kilometers. Type your answer as a number.] kilometers
Answer:
Total distance Alicia run in kilometer = 8 Kilometer
Step-by-step explanation:
Given:
Total distance Alicia run = 5 miles
1 mile ≈ 1.6 kilometer
Find:
Total distance Alicia run in kilometer
Computation:
Total distance Alicia run in kilometer = 1.6 × 5
Total distance Alicia run in kilometer = 8 Kilometer
Stacey has earned $9 interest over the past 20 months with an initial investment of $150. What is the simple interest rate she is earning? Express your answer to the nearest tenth of a percent. (It wants me to use the formula I=Prt which I don't remember)
Answer:
3.6%
Step-by-step explanation:
We are solving the above question, using the simple interest Formula:
I = PRT
Where
I = Interest = $9
P = Principal = $150
R = Interest rate = ??
T = Time in years = 20 months
We convert this to years
12 months = 1 year
20 months = x
x = 20/12
x = 1.67 years
Hence, making R the subject of the formula
R = I/PT
R = 9/150 × 1.67
R = 9/250.5
R = 0.0359281437
Converting to percentage
R = 0.0359281437 × 100
R = 3.59281437%
R = 3.6 %
The simple interest rate she is earning is 3.6%
8x + 7 + 7x - 2=90
I need this to be solved ASAP
Answer:
ok so
Step-by-step explanation:
8x + 7 + 7x - 2=90=>
=> 15x+5= 90
=> 15x=90 - 5=>
=> 15x =85= x= 5.6666...
Hey there!
“8x + 7 + 7x – 2 = 90”
• FIRST: COMBINE your LIKE TERMS
(8x + 7x) + (7 – 2) = 90
‘8x + 7x = 15x’
‘7 – 2 = 5x’
“15x + 5 = 90”
• SECOND: SUBTRACT by 5 on BOTH SIDES
15x + 5 – 5 = 90 – 5
CANCEL out: 5 – 5 because that gives you 0
KEEP: 90 – 5 because it helps us solve for your x-value
‘90 – 5 = 85’
NEW EQUATION:
“15x = 85”
• THIRD: DIVIDE by 15 on BOTH SIDES
15x/15 = 85/15
CANCEL out: 15/15 because that equals 1
KEEP: 85/15 because it gives us our x-value
Reduce: 85/15 and it gives us: x
Answer: x = 17/3 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Please help me ASAP
Answer:
A, y-intercept = (0,24)
Step-by-step explanation:
The y intercept is the one without a variable. You have to solve to find it in the other options.
Answer:
The first choice would be the best one.
Step-by-step explanation:
The y intercept occurs when x = 0 of the given polynomial.
All 3 answers will give you the correct answer. The y intercept is (0,24)
but the first one will be the quickest because all you need to do to find it is just eliminate any term with x in it.
2x^2 when x = 0 is 0
16x when x = 0 is 0.
That only leaves m(0) = 24 found just by looking at it.
The second one also works. 2 (0+4)^2 - 8 = 32 - 8 = 24
And the third one as well 2(6)(2) = 24
question in pic help
Answer:
B
Step-by-step explanation:
Explain your reasoning for why -3/4 is less than 5/8
Answer:
Step-by-step explanation:
-3/4 and 5/8
bc it's a negative number and not a positive number. When numbers are negative, the number keeps getting smaller and smaller. And when you add a positive number to a negative number, then the number will start increasing it's value.
Hope it helped a little
find the quotient of 1 1\3 and 5\6
Answer:
1 3/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 1/3=4/3
4/3 *6/5(division)
=24/15
=8/5
= 1 3/5
2% of 65 answer fast please
Answer:
2% of 65
2/100*65
13/10
1 3/10
There is an assortment of shirts in store at the mall. The shirts come in 4 different colors. There are 36 red shirts, 12 blue shirts, 42 black shirts, and 60 white shirts. What is the ratio of black shirts to blue shirts?
Answer:
The ratio of black shirts to blue shirts is 7:2
Step-by-step explanation:
Ratios
A ratio is a way to compare two numbers of the same kind. We use ratios to compare things of the same type. For example the ratio of boys and girls in a class. Ratios as expressed in the form n:m.
There are 36 red shirts, 12 blue shirts, 42 black shirts, and 60 white shirts. It's required to calculate the ratio of black shirts to blue shirts. We'll use fractions to express the relationship. The fraction will divide 42 by 12:
[tex]\frac{42}{12}[/tex]
Simplifying by 6:
[tex]\frac{42}{12}=\frac{7}{2}[/tex]
Thus, the ratio of black shirts to blue shirts is 7:2
Answer:
black shirts to blue shirts is 7:2
Step-by-step explanation:
What is the value of
[tex]3 \sqrt{64} [/tex]
8
4
-8
-4
Answer:
4
Step-by-step explanation:
4 * 4 * 4 = 64
Does anyone know this?
Answer:
42 cm²
Step-by-step explanation:
Length of the shaded rectangle = 7 cm
Width of the shaded rectangle= 7 - (0.5 + 0.5) = 7 - 1
Width of the shaded rectangle = 6 cm
Area of the shaded rectangle = L × W
Area = 7 × 6 = 42 cm²
Solve.
5.25t + 5 = 16.5t + 14
The solution is t =
i realy need helpppppp
Answer:
-0.8 is the correct answer for this question
Step-by-step explanation:
mark me as brainliest
Answer:
t=-0.8
Step-by-step explanation:
You want to get the 't' by itself, so you will subtract 5 from both sides
5.25t=16.5t+9
Now, you want to subtract 16.5t from both sides
-11.25t=9
now you divide -11.25 from both sides.
t=-0.8
A builder is using the drawing below to build a house. If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?
Answer:
The correct answer is A
Step-by-step explanation:
20% x 12 = 2.4
2.4 + 12 = 14.4
20% x 8 = 1.6
1.6 + 8 = 9.6
✧brainliest appreciated✧
What is the length of DF?
Answer:
6x-5=3x+10
6x-3x=10+5
3x=15
3x÷3=15÷3
x =5
Step-by-step explanation:
pliz mark brainliest
help :( it's 4:36am and i still have a bunch of geometry hw to do and i have school tomorrow at 7. i just need some emotional support haha :') thanks.
Answer:
My emotional speech to you : Yolo UWU or you got this, I believe you can achieve great things, and you probs think hah no, but lOOk Me DeAd In thE EyE thrOuGh The scReen, HUnNy U GOt thIs, RePeAt It :)
Help pls I don’t remember how to do this so how do u find x, y, and z in this
Answer: 3) x = 87°; y = 93°; z = 63°
Step-by-step explanation:
x + 33 + 60 = 180 since they form a triangle.
x + 93 = 180
Subtract 93 from both sides
x = 87°
x and y are linear pairs so they're supplementary.
y + x = 180
y + 87 = 180
Subtract 87 from both sides
y = 93°
z + y + 24 = 180 since they also form a triangle
z + 93 + 24 = 180
z + 117 = 180
Subtract 117 from both sides
z = 63°
Hope this helped!
Oh and nannara nanke demo ii yo, ikasete yaru kara. :p
IM CONFUSED PLEASE ANSWER THIS
We know he traveled 4.8 miles in 3 hours. However, since the question asks for his speed in miles per hour, we only want to know how far he travels in one hour. To find this, we just divide 4.8 by three, and find that he is traveling at 1.6 miles per hour.
Answer:
Speed = 1.6
Step-by-step explanation:
[tex]Speed=\frac{Distance}{Time} \\\\Speed = \frac{4.8}{3}=1.6[/tex]
Enjoy? here a math question you guys might knoew
What do you know about the solution(s) to the system of linear equations?
The solution is (-2,0).
There are infinitely many solutions.
There is no solution
The solution is (4, -1).
Answer:
No solutions.
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect is the solution set to the systems of equations.
If the lines are the same, they will have infinite solutions (will always intersect).
If the lines are parallel, they will have no solutions (will never intersect).
According to the graph, we see that the lines are parallel. Therefore, the systems has no solutions.
What is an equation of the line that passes through the point (−6,−1) and is perpendicular to the line 6x−y=7?
Answer:
y=-1/6x-2
Step-by-step explanation:
Lets find the slope of the given line
6x-7=y,m=6
The slope of the perpendicular line would be=-1/6
Using the point-slope form y-y1=m(x-x1)
y--1=-1/6(x--6)
y+1=-1/6(x+6)
6y+6=-x-6
6y=-x-6-6
6y=-x-12
y=-1/6x-2
Which property is represented 7(t+u)= 7t + 7u
Answer:
distributive property
Step-by-step explanation:
The distributive property is
a(b + c) = ab + ac
where each term in the parenthesis is multiplied by the value outside.
Then
7(t + u) = 7t + 7u
can someone pls help with this asap
2,4,5 = Obtuse angle triangle
3,4,5 = Right angled triangle
6,7,8 = Acute angle triangle
7,9,15= Obtuse angle triangle
3,3,10 = Cannot form a triangle
A list or set of numbers in a certain order is called
p^2-4p+4=0
is this a quadratic equation
Answer:
2-4+4=0
Step-by-step explanation:
A train leaves at 0836 and arrives at 1057. It travelled at an average speed of 85 km/h. How far did it travel?
Answer:
199.75km
Step-by-step explanation:
Step one:
given data
We are told that the time of travel is from
8:36- to 10:57
which is 2 hours 21 minutes
Hence the time taken is 2.35 hours
the speed is 85km/h
Step two:
From the expression
speed= distance/time
85= distance/2.35
distance= 85*2.35
distance= 199.75km
Answer: it traveled a distance of 199.75Km
Step-by-step explanation:
From the question , Let 0836 be 8:36
and 1057 be 10:57
Time of departure= 8:36
Time of arrival = 10:57
Time traveled = 10:57- 08:36= 2 Hours 21 minutes
changing trhe time to hours becomes 21/60 = 0.35 hours + 2 HOURS = 2.35 hours
Step 2
Speed = Distance / Time
Distance = Speed x Time
=85 km/hr x 2.35 hours
=199.75Km
Choose the correct exponential form for the expression. 0.3 × 0.3 × 0.3 × 0.3 (0.3)3 (0.3)4 40.3 43
Answer:
It is B. (0.3)4
Step-by-step explanation:
(0.3)4
0.3 × 0.3 × 0.3 × 0.3
Answer:
(0.3)4 or B
can i has brainlyiest
Step-by-step explanation:
Subtract-3c2 + 12cd – 4d2 from 4c2 + 3cd + 2d?.
Your answer should be a polynomial in standard form.
Answer:
Subtract [tex]-3c^2 + 12cd - 4d^2[/tex] from [tex]4c^2 + 3cd + 2d^2[/tex] we get [tex]\mathbf{7c^2-9cd+6d^2}[/tex]
Step-by-step explanation:
We need to Subtract [tex]-3c^2 + 12cd - 4d^2[/tex] from [tex]4c^2 + 3cd + 2d^2[/tex]
(Note: Considering 2d^2 instead of 2d as thinking it typo error)
Subtracting from means we have to subtract [tex]4c^2 + 3cd + 2d^2 -(-3c^2 + 12cd - 4d^2)[/tex]
Subtracting:
[tex]4c^2 + 3cd + 2d^2 -(-3c^2 + 12cd - 4d^2)\\=4c^2 + 3cd + 2d^2 +3c^2 - 12cd + 4d^2[/tex]
Combining like terms (Like terms are those that have same variables like 4c^2 and 3c^2 are like terms, 3cd and -12cd are like terms, 2d^2 and 4d^2 are like terms)
[tex]=4c^2+3c^2 + 3cd-12cd + 2d^2+4d^2 \\=7c^2-9cd+6d^2[/tex]
So, Subtract [tex]-3c^2 + 12cd - 4d^2[/tex] from [tex]4c^2 + 3cd + 2d^2[/tex] we get [tex]\mathbf{7c^2-9cd+6d^2}[/tex]