a) If N is the population of the city and is the time in years, N expressed as a function of t is; N(t) = N₀*e^(kt)
b) The population 2 years from now will be; 25198 people
How to solve the exponential growth model?The general formula for exponential growth model is;
N(t) = N₀*e^(kt)
where;
f(x) is exponential growth function
N₀ is initial amount
t is time
k is constant
a) We are told that;
N is the population of the city.
t is the time in years
Thus, N expressed as a function of t is;
N(t) = N₀*e^(kt)
b) We are told that the population doubled in size over an 18-month
period . Thus, the equation would now be;
N(t) = N₀*2^(t/18)
Thus, if the current population is 10000, then it means that 2 years from now, we will have;
N(2) = 10000 * 2^(24/18)
I used 24 because 2 years is 24 months
Thus;
N(2) ≈ 25198 people
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On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time using another common denominator. Explain how you found your answers
Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.
Given,
In the question:
There are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time using another common denominator.
Explain how you found your answer.
Now, According to the question:
There are 60 min in an hour
and, 60 as a common denominator.
So, 45/60 and 10/60
Explanation: Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.
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A work ladder can extend to 8 meters. How many centimeters is that? How many kilometers is that? Use 1000 m) unit analysis to solve this conversion problem (1 km ==
Answer:
8m = 800cm
8m = 0.008km
Step-by-step explanation:
1 kilometer is 1000 meters
1 meter is 100 centimeters
You'd only have to multiply in the first one:
[tex]8 \times 100 = 800[/tex]
8m = 800cm
Remember that when multiplying by 100 you only have to add zeros.
For km, as it is bigger than m you have to divide by 1000, when dividing this time you only have to carry an imaginary point starting from right to left, the amount of zeros there are:
[tex]8. \\ .8 \\ .08 \\ .008 \\ 8 \div 1000 = .008[/tex]
8m = 0.008km
If you run out of numbers when carrying the point, just add zeros.
Use the equation y=x2−3x+2 to answer the following questions. Part A: What numeric expression should be added in order to complete the square for the given equation? Part B: What equation is equivalent to the given equation after completing the square? Select two answers: one for Part A and one for Part B.
Part A
[tex](b/2)^2 =(-3/2)^2 =\boxed{9/4}[/tex]
Part B
[tex]-x^2 -3x+2\\\\=-(x^2 +3x)+2\\\\=-(x^2 +3x+2.25-2.25)+2\\ \\=-((x+1.5)^2 -2.25)+2\\\\=-(x+1.5)^2 +2.25+2\\\\\boxed{y=-(x+1.5)^2 +4.25}[/tex]
Fill in the blank. (Please help)
Answer: Table
Step-by-step explanation: Hope you find it helpful!
which of the following are possible rational roots of the polynomial function
check all that apply
F(x)=2x^2-3x+7
a.+_2
b.+_1/2
c.+_1
d.+_1/7
e.+_7
help me
±1/2, ±1, ±7 are the possible rational roots of the polynomial function.
What is the rational root theorem?The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.
An anXn+ an− 1xn − 1 + … + a1x1 + a0 = 0 is a polynomial equation in one variable (x), where a0, a1,..., and an are regular integers. Therefore, q must divide a and p must divide a0 for a polynomial equation to have a rational solution, p/q.
It is given in the question,
F(x)=2x^2-3x+7
Here, p is a 7-fold factor.
p, thus, might have a value of 1, -1, 7, or -7.
and q is a two-fold factor.
Thus, q might have a value of 1, -1, 2, or -2.
Hence, ±1/2, ±1, ±7 are the possible rational roots of the polynomial function.
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Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.
Area of the sheep pen = 1600feet square
What is area?The amount of space occupied by a flat (2-D) surface or form of an object is known as its area.
180 feet of fence were purchased.
The perimeter of a rectangular sheep pen is equal to two times the length plus the width, or two times the length plus 180. One side of the rectangular sheep pen is covered with a barn, which equals the width.
The rectangular sheep pen's covered side:
180 =2 length + width
180 = 2 x80 +width
180 - 160 = width
20= width
Area = l*b = 80*20
Area of sheep pen = 1600 feet square
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f’’(x)=cos(x), f’(pi)=2, f(pi)=-1
f(x)=?
PLS URGENT
The required function f(x) is represented by -1 + F(x + sin(x)).
To find the function f(x), you can use the formula for integration by substitution:
f(x) = F(g(x)) + C
where F is an antiderivative of f, g is a function such that g'(x) = f(x), and C is a constant.
In this case, we can take g(x) = x + sin(x). Then g'(x) = cos(x), so f(x) = F(g(x)) + C = F(x + sin(x)) + C.
We are given that f'(π) = 2 and f(π) = -1, so we can use these values to find the constants C and F.
First, we can find F by taking the derivative of F(x + sin(x)). This gives us:
F'(x + sin(x)) = f(x) = cos(x)
Substituting x = π and using the fact that F'(x + sin(x)) = f'(π) = 2, we get:
F'(π + sin(π)) = 2
Since sin(π) = 0, this simplifies to:
F'(π) = 2
Then, using the fact that F(x + sin(x)) = f(π) = -1 when x = π, we can find the value of F(π):
F(π) = -1
Now that we have found the values of F and F', we can use these to find the value of C.
Since F(x + sin(x)) = F(x) + F'(x) sin(x), we can substitute x = π to get:
F(π + sin(π)) = F(π) + F'(π) * sin(π)
Substituting the values we found above, this becomes:
F(π + 0) = -1 + 2 x 0
Which simplifies to:
F(π) = -1
Since F(π) = -1, we can conclude that C = -1.
Therefore, the function f(x) is given by:
f(x) = F(x + sin(x)) + C = F(x + sin(x)) - 1
= -1 + F(x + sin(x))
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In which way should the graph of f(x) = x2 be shifted to produce the graph of g(x) = (x - 3)2?
A.
3 units to the left
B.
3 units to the right
C.
3 units down
D.
3 units up
Answer:
g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x)
Step-by-step explanation:
Answer:
uh nose
Step-by-step explanation:
which point is not on the graph of 5x+6y=-42
The slope is m = RISE / RUN, and the change in y is frequently referred to as "RISE."
Step-by-step explanation:[tex]5*x-6*y-(42)=0[/tex]
Tiger understands that this is a straight line equation. Typically, this equation is expressed as y=mx+b (or "y=mx+c" in the UK).
A straight line drawn using the Cartesian coordinate system has the formula "y=mx+b," where "y" denotes the vertical axis and "x" denotes the horizontal axis.
In this equation, y represents how high the line rises, x represents how far it travels along, m represents the slope or gradient, or how steep the line is, and b represents the Y-intercept, or the point at which the line crosses the Y axis.
The X, Y, and slope are collectively referred to as the line properties. We will now plot the line 5x-6y-42 = 0 and determine its characteristics.
x = 0 the value of y is 7/-1 so this line "cuts" the y axis at y=-7.00000
y-intercept = 42/-6 = 7/-1 = -7.00000
y = 0 the value of x is 42/5 Our line therefore "cuts" the x axis at x= 8.40000
x-intercept = 42/5 = 8.40000
Slope = 1.667/2.000 = 0.833 x-intercept = 42/5 = 8.40000 y-intercept = 42/-6 = 7/-1 = -7.00000To learn more about 5x+6y=-42 refer to:
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Please help
Evaluate numerical expression !
After evaluation of the given expression, the value obtained in mixed fraction form is equal to -4 3/10.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given expression in the question,
(-5 - (-4 1/2)) × 3 + (-2 4/5)
The expression in simplified form will be,
(-5 + 9/2) × 3 - 14/5
(-10 + 9) × 3 -14/5
-3/2 - 14/5
= (-15 - 28)/10
= -43/10
It can also be written in mixed fraction form,
= -4 3/10
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Find the value of the variable. Type your number answer into box. (This is the same picture as #5.)
the answer to 5 was 1.67
Answer:
x = 21
Step-by-step explanation:
[tex]\frac{x}{9}[/tex] = [tex]\frac{35}{15}[/tex]
[tex]\frac{35}{15}[/tex] can be simplified to [tex]\frac{7}{3}[/tex] if we divide the numerator and denominator by 5
[tex]\frac{x}{9}[/tex] = [tex]\frac{7}{3}[/tex] cross multiply and solve for x
3x = 63 Divide both sides by 3
x = 21
QUICKKKKK!!
Graph the image of the figure using the transformation given.
91) translation: (x, y) →(x+3, y-5)
92.) translation: (x,y) →(x,y -2)
93) reflection across x = -2
94.) reflect across y = 1
95) rotation 180° about the origin
96) rotation 90° counterclockwise about the
origin
I’ll give you all the points just helppppp me outttt!!
The image after the transformations of rotation, translation or reflection can be found by certain operation or rotation.
We can find how to know the image of certain figures after the given transformations are done.
91) Here it is translation.
x coordinates are shifted to right by 3 units and y coordinates are shifted to down by 5 units.
So the entire graph will be shifted to right by 3 units and down by 5 units.
92) Here, the translation is by not shifting the x coordinates and shifting the y coordinates 2 units to the down.
So the entire graph will be shifted to down by 2 units.
93) When a graph is reflected across x = -2, then the graph is moved horizontally such that the original figure and the image will be at the same distance from x = -2.
94) When a graph is reflected across y = 1, then the graph is moved vertically such that the original figure and the image will be at the same distance from y = 1.
95) When a graph is rotated about the origin 180°, if it is clockwise or anticlockwise, each of the coordinates (x, y) in the graph will become (-x, -y).
96) If the rotation is 90° counterclockwise about the origin, the coordinates (x, y) in the original graph becomes (-y, x).
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2 1/2 divided by 4 Anwser quick please
Answer:
5/8
Step-by-step explanation:
We can solve this by turning 2 1/2 into a decimal.
2 1/2 = 2.5
2.5 ÷ 4 = 0.625
0.625 = 5/8
2 1/2 divided by 4 is 5/8
question is attached
Answer:
56
Step-by-step explanation:
Top line:
100% - 80% = 20%
20% of 60 = 0.2 × 60 = 12
Small piece on top is 12.
Second line:
Small piece is 12.
100% - 60% = 40%
Small piece is also 40%.
40% of x = 12
0.4x = 12
x = 12/0.4
x = 30
The entire second line is 30.
60% of 30 = 0.6 × 30 = 18
60% of second line is 18.
Third line:
30% of third line = 18
100% - 30% = 70%
30/18 = 70/x
30x = 18 × 70
x = 42
Larger part of third line is 42.
Fourth line:
75% of 4th line is 42.
100/x = 75/42
75x = 100 × 42
x = 56
Answer: 56
If y varies directly as x and y = 15 when
x = -3. What is y when x = 6?
The value of y is -30.
Direct variation is y = kx
15 = k(-3)
Divide by -3 on both sides
-15/3 = k
-5 = k -------> 1
Substituting 1 and x = 6, in Direct Variation
y = -5*6
y = -30
Therefore, the value of y is -30.
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P---> P' (2,-4) for (x,y) ---> (x-3, y-3) and reflection line y=x Find the coordinates of P
The coordinates of P' after the transformation are (-1, 1)
How to determine the coordinates that describe the transformation of P?From the question, we have the following parameters that can be used in our computation:
Point P' = (2, -4)
This point can be represented as
(x, y) = (2, -4)
Also, from the question, we have the transformation to be:
(x-3, y-3) and reflection line y=x
Mathematically, this can be expressed as
(x, y) = (y - 3, x - 3)
So, we have
Point P' = (2, -4)
This means that
y -3 = 2
x - 3 = -4
Evaluate
y = 1
x = -1
Hence, the point P after transformation is (-1, 1)
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Follow the steps to solve this equation. 3(2x 6) â€"" 4x = 2(5x â€"" 2) 6 1. use the distributive property: 6x 18 â€"" 4x = 10x â€"" 4 6 2. combine like terms: 2x 18 = 10x 2 3. use the subtraction property of equality: 18 = 8x 2 4. use the subtraction property of equality: 16 = 8x 5. use the division property of equality: = x
The solution of given equation by using the property of equality is x = 2.
Explain the distributive property?The distributive property states that multiplying the total of two or even more operand by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.An equation has been presented to us.
3(2x + 6) -4x = 2(5x -2) + 6
Our given equation has to be solved step-by-step.
Step 1: Utilize the distributive property;
3×2x + 3×6 - 4x = 2×5x -2×2 + 6
6x + 18 -4x = 10x - 4 + 6
Step 2: combine similar phrases.
6x + 18 -4x = 10x - 4 + 6
2x + 18 = 10x + 2
Step 3: Apply the equality's subtraction property
2x - 2x + 18 - 2 = 10x + 2 - 2x - 2
16 = 8x
Step 4: Apply the equality's divisional property:
16/8 = 8x/8
x = 2
As a result, is our given equation's answer is x = 2.
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The correct question is-
Follow the steps to solve this equation. 3(2x + 6) – 4x = 2(5x – 2) + 6 1. Use the distributive property: 6x + 18 – 4x = 10x – 4 + 6 2. Combine like terms: 2x + 18 = 10x + 2 3. Use the subtraction property of equality: 18 = 8x + 2 4. Use the subtraction property of equality: 16 = 8x 5. Use the division property of equality:
help with example 4!!! first answer gets brainliest
Answer:
Assuming angle 1 is 75º.
1 -> 75
2 -> 105
3 -> 75
4 -> 105
5 -> 75
6 -> 105
7 -> 75
8 -> 105
simultaneous equations x+5y=6
x+3y=2
Answer:
(- 4, 2 )
Step-by-step explanation:
x + 5y = 6 → (1)
x + 3y = 2 → (2)
subtract (2) from (1) term by term to eliminate x
(x - x) + (5y - 3y) = 6 - 2
0 + 2y = 4
2y = 4 ( divide both sides by 2 )
y = 2
substitute y = 2 into either of the 2 equations and solve for x
substituting into (1)
x + 5(2) = 6
x + 10 = 6 ( subtract 10 from both sides )
x = - 4
solution is (- 4, 2 )
someone help me pls i would appreciate
Answer:
Addition, Distributive, Addition, Multiplication, Division
Step-by-step explanation:
A recipe calls for 3/2 cups of flour. You only have a 1/2 cup measuring cup. What fraction of a cup of flour, in halves, do you need?
To obtain an amount of 3 / 2 cups of flour, then we need three halves of cup by means of a 1 / 2 cup measuring cup.
How many cups are needed to get the require amount of flour
In this problem we have the case of recipe that requires 3 / 2 cups of flour in terms of certain number of measuring cups with an amount of 1 / 2 cups. The number of measuring cups (n) is equal to the total required by the recipe (M) divided by the amount of the measuring cup (m), both in cups. That is:
n = M / m
If we know that m = 1 / 2 cup and M = 3 / 2 cup, then the number of measuring cups is:
n = (3 / 2 cup) / (1 / 2 cup)
n = 3
In other words, we need 3 halves of a cup of flour to obtain the required amount of 3 / 2 cups.
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Help with this ixl please
Answer:
25°
Step-by-step explanation:
We know the opposite angles must be equal when two lines intersect, so 67 = 42+t. Subtracting 42 from both sides gives t=25, which is our answer
answer:
25 degrees
step-by-step explanation:
67=42+t so using that equation the answer can be determined. hope that helps!
Angel corre en un maratón de 500m y lo hizo en 1,5 horas. ¿Cuál fue la velocidad de
Angel?
Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.
Select all of the measurement pairs that could be the dimensions of Rectangle B.
4.5 inches by 1.5 inches
8 inches by 2 inches
10 inches by 4 inches
13.5 inches by 4.5 inches
90 inches by 30 inches
Answer:32
Step-by-step explanation:
In problems 7-11, use the diagram to find the measure of each angle.
From the given triangle diagram figure, angles are -
m∠1 = 72°
m∠2 = 114°
m∠3 = 66°
m∠4 = 66°
m∠5 = 56°
m∠6 = 32°
What is triangle?Depending on how many sides a polygon has, it is given a unique name. Because "tri" is a word that indicates "three," the polygon with three sides is known as a triangle. This polygon has three angles, as indicated by its name. Poly means numerous in the prefix.
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
In the given problem,
m∠6 = 180° - (90° + 58°)
so, m∠6 = 32°
Next, m∠1 +m∠6 = 180° - (42° +34°)
= 104°
so, m∠1 = 104° - 32°
= 72°
Next, m∠5 = 90° - 34°
m∠5 = 56°
Again, m∠4 = 180° - (56° + 58°)
m∠4 = 66°
Now from the figure, m∠3 and m∠4 are vertically opposite angle.
So, m∠3 = 66°
Again, m∠2 = 180° - 66° = 114°
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5. What are the real and complex solutions of the polynomial equation? (1 point)
x^3-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i
Given polynomial equation x3 - 8 = 0
x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)
x3 - 23 = (x - 2)(x2 + 2x + 4)
One root is 2
x2 + 2x + 4 = 0
x = -b ± √(b2 - 4ac) / 2a
x = -2 ± √22 - 4(4) /2
x = -2 ± √4 - 16 /2
x = -2 ± √-12 /2
x = -1 ± √3i
Therefore, x = 2, -1 ±√3i
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Given,
polynomial equation x3 - 8 = 0
x3-8 is a cubic polynomial is in the form a3 - b3 = (a - b)(a2 + ab + b2)
x3 - 23 = (x - 2)(x2 + 2x + 4)
One root is 2
x2 + 2x + 4 = 0
x = -b ± √(b2 - 4ac) / 2
x = -2 ± √22 - 4(4) /2
x = -2 ± √4 - 16 /2
x = -2 ± √-12 /2
x = -1 ± √3i
Therefore, x = 2, -1 ±√3i
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What is the value of t?
Answer: t = 37.8 degree
Step-by-step explanation:
We know that a circle has 360 degrees, this is half a circle, so it total is 180 degrees.
We add 63.7 with 78.7 = 142.4 degree
Take 180 - 142.2 = 37.8 degree
For each value of u, determine whether it is a solution to 9u-7≥65.
function rule to find f(9).
Answer: 12
Step-by-step explanation:
[tex]f(9)=3+9=12[/tex]
What is the solution to this system of equations? 2x+y=40 x-2y=-20
Answer: the solution to the system of equations is x = 12 and y = 16.
Step-by-step explanation: To solve this system of equations, you can use the method of substitution.
First, solve one of the equations for one of the variables. For example, you can solve the first equation for x:
2x + y = 40
2x = 40 - y
x = (40 - y)/2
Then, substitute this expression for x in the second equation:
x - 2y = -20
(40 - y)/2 - 2y = -20
Multiplying both sides by 2, we get:
40 - y - 4y = -40
-5y = -80
y = 16
Substituting this value for y in the first equation, we can solve for x:
2x + 16 = 40
2x = 24
x = 12
Therefore, the solution to the system of equations is x = 12 and y = 16.