Final answer:
The most helpful form to determine the time for the ball to hit the ground is Option A, h(t) = -16(t - 3)(t + 1), as it is already in factored form, making it easy to find the positive root, which represents the time when the ball would hit the ground.
Explanation:
When attempting to determine the time required for the ball to hit the ground in a quadratic model, we are essentially looking for the time when the height of the ball, h(t), is zero. To find this, we need to find the roots of the quadratic equation. Function A, h(t) = -16(t - 3)(t + 1), is already factored, which makes finding the roots straightforward. When dealing with quadratic equations, remember that negative time values do not make sense in this context, so we are only interested in the positive root.
The most helpful form for this task would therefore be Option A, h(t) = -16(t - 3)(t + 1), as the roots can be easily read from the factored form, which directly gives the times when the ball reaches the ground level without further calculation. In this case, the positive root t = 3 seconds represents the time when the ball would hit the ground. Ignoring the root t = -1 because time cannot be negative.
Which function results after applying the sequence of transformations to f(x) = x5?
stretch vertically by 3
reflect across the x-axis
shift right 1 unit
shift up 2 units
A. f(x) = -(3x - 1)5 - 2
B. f(x) = -3(x - 1)5 + 2
C. f(x) = 3(x5 - 1)5 + 2
D. f(x) = -3(x + 1)5 + 2
Answer: B
Step-by-step explanation:
The function results [tex]f(x) = -3(x - 1)5 + 2[/tex] after applying a sequence of transformations [tex]f(x) = x^5[/tex].
We have to determine, which function results after applying the sequence of transformations [tex]f(x) = x^5[/tex].
According to the question,
To find the sequence of the transformation of the given function following all the steps given below.
Function; [tex]f(x) = x^5[/tex]
Step1; Stretch vertically by 3 in the negative x-axis.
[tex]f(x) = -3[(x )^5][/tex]
Step2; Reflect the function across the x-axis,[tex]f(x) = -3(x)^5[/tex]
Step3; Shifting the function 1 unit right,[tex]f(x) = -3(x-1)^5[/tex]
Step4; Shifting the function upward 2 units,[tex]f(x) = -3(x-1)^5 +2[/tex]
Hence, The function results [tex]f(x) = -3(x - 1)5 + 2[/tex] after applying a sequence of transformations [tex]f(x) = x^5[/tex].
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Consider the following geometric series. Rewrite the series using sigma notation. 4-10+25-62.5+156.25-390.625
Answer:
See below.
Step-by-step explanation:
The common ratio = -10/4 = -5/2 and the first term is 4.
The sigma notation is:
n=6
∑ 4(-5/2)^n-1. (answer).
n=1
Answer:
[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]
Step-by-step explanation:
We are given the geometric series [tex]4 + -10+ 25+ -62.5+ 156.25+ -390.625[/tex]
General geometric series is of the form
[tex]a, ar, ar^2, ar^3, ar^4,\text{ and so on}[/tex], where a is the first term and r is the common ration.
The common ratio for given geometric series is [tex]\frac{\text{Second Term}}{\text{First Term}}[/tex] = [tex]\frac{-10}{4} = \frac{-5}{2}[/tex]
[tex]a = 4\\r = \frac{-5}{2}[/tex]
To write the series in summation form we use:
[tex]\sum_{k=0}^{k=n} a(r)^{k}[/tex]
Thus, the given geometric series is
[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]
Please help me I need it fast
Answer:
b and c
Step-by-step explanation:
i think its b and c
Answer:
A, D, and E
Step-by-step explanation:
They all have ten 0.1 square which equals 1.
How can you solve linear inequalities in one variable?
Answer:
There can be three solution sets of linear equalities. They can have one solution, or they can have no solutions or they can have infinitely many solutions. System of linear inequalities that have many or infinite solutions are called ” dependent”.
Step-by-step explanation:
A ladder leans against the side of a house. The angle of elevation of the ladder is 69 degrees, when the bottom of the ladder is 12 ft from the side of the house . Find the length of the ladder.
Final answer:
To find the length of the ladder, use the tangent of the angle of elevation. The height of the ladder is equal to the distance from the house multiplied by the tangent of the angle of elevation.
Explanation:
To find the length of the ladder, we can use the trigonometric relationship of the angle of elevation. The tangent of the angle of elevation is equal to the opposite side (height of the ladder) divided by the adjacent side (distance of the ladder from the house).
Tan(69°) = height/12 ft
height = 12 ft x tan(69°)
Using a calculator, we can determine that the height of the ladder is approximately 31.99 ft.
An archeologist has found a fossil in which 35% of its carbon-14 remains. Hold old is the fossil?
Answer:
8,680 years old
Step-by-step explanation:
The fossil is 8,680 years old if 35% of its carbon-14 remains.
Find the median.
12, 8, 5, 6, 1, 10, 13, 11
A. 8.25
B. 9
C. 12
D. 66
Your answer asks to find the median of the given numbers.
Answer: B). 9To find the median, you would need to sort of the numbers from least to greaters.
The given numbers we have:
12, 8, 5, 6, 1, 10, 13, 11
Now, just sort them from least to greatest.
1, 5, 6, 8, 10, 11, 12 ,13
What you would do next is eliminate the numbers on the side, one by one, in order to get your median.
[tex]1, 5, 6, 8, 10, 11, 12 ,13\\\\5, 6, 8, 10, 11, 12\\\\6, 8, 10, 11\\\\8, 10[/tex]
We ended up with two numbers, 8 and 10. Since we didn't end up with one number, we're going to have to add those numbers, and then divide it by two.
[tex]8+10=18\\\\18\div2=9[/tex]
You should get 9.
Therefore, the median would be 9.
B). 9 should be your FINAL answer
I hope this helps!Best regards, MasterInvestorAnswer:
The correct answer is option B. 9
Step-by-step explanation:
Median:
Median of a data set means that, the central data when arrange all the in ascending or descending order
It is given a data set ,
12, 8, 5, 6, 1, 10, 13, 11
To find the median of data set
Here there are 8 items, median is average of 4th and 5th terms
Ascending order,
1, 5, 6, 8, 10, 11, 12, 13
Median = (8 + 10)/2 = 18/2 = 9
The correct answer is option B. 9
What is the midpoint of the segment shown
Answer:
B) (-⁷/₂, ³/₂)
Step-by-step explanation:
Midpoint equation: ( (x₁ + x₂)/2, (y₁ + y₂)/2 ), when the two points are (x₁, y₁) and (x₂, y₂).
Plug in: ( ⁽⁻⁶ ⁺ ⁻¹⁾/₂, ⁽⁻² ⁺ ⁵⁾/₂ )
Add: (-⁷/₂, ³/₂)
Answer:
B
Step-by-step explanation:
Using the midpoint formula
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
let (x₁, y₁ ) = (- 6, - 2) and (x₂, y₂ ) = (- 1, 5)
midpoint = [ [tex]\frac{1}{2}[/tex](- 6 - 1), [tex]\frac{1}{2}[/tex](- 2 + 5)]
= (- [tex]\frac{7}{2}[/tex], [tex]\frac{3}{2}[/tex] ) → B
1. Which of the following is equal to
40 + 55?
A. 40 X 55
B. 40 - 55
C. 40 + 40
D. 55 + 40
Answer:
D
Step-by-step explanation:
These I's are being used as sticks
lets say i have 40 sticks then i add 55 more sticks to them
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII + IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII If i were to reverse the sequence and use the 55 sticks and add 44 sticks to them it would be the same as me having 44 sticks and adding 55 more.
By commutative property, the following which is equal to 40 + 55 is Option(D) 55 + 40.
What is commutative property ?The commutative property is a math rule that says that the order in which we find the sum of the numbers does not change the sum up value of the numbers.
By the statement,
A + B = B + A , where A and B are any numbers
How to apply the property in the question ?The original expression given is 40 + 55 .
Therefore by commutative property, the equivalent expression is -
40 + 55 = 55 + 40
Thus, by commutative property, the following which is equal to 40 + 55 is Option(D) 55 + 40.
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the solution to a system of linear equations is (-3, -3). Which system of linear equations has this point as its solution?
I'm being timed!
Answer:
x - 5y = 12 and 3x + 2y = -15Step-by-step explanation:
[tex](-3,\ -3)\to x=-3,\ y=-3\\\\\text{Put the values of x and y to the equations and check equality:}\\\\x-5y=-12\\-3-5(-3)=-12\\-3+15=-12\\12=-12\qquad\bold{FALSE}\\\\x-5y=12\\-3-5(-3)=12\\-3+15=12\\12=12\qquad\bold{TRUE}\\\\3x+2y=-15\\3(-3)+2(-3)=-15\\-9-6=-15\\-15=-15\qquad\bold{TRUE}[/tex]
The system of linear equations has this point as its solution will be,x-5y=12 and 3x+2y=-15. Option C is correct.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The solution to a system of linear equations is (-3, -3).
x = -3
y= -3
After putting the value one by one in the given equations;
A)
[tex]\rm x-5y=-12\\\\\ -3-5(-3)=-12\\\\-3+15=-12\\\\12\neq-12[/tex]
B)
[tex]\rm x- 5y =12\\\\ -3-5(-3)=12\\\\-3+15=12\\\\12=12[/tex]
[tex]\rm 3x+2y=-15\\\\3(-3)+2(-3)=-15\\\\ -9-6 =-15\\\\ -15=-15[/tex]
The system of linear equations has this point as its solution will be,x-5y=12 and 3x+2y=-15.
Hence, option C is correct.
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What conclusion can be drawn from the following statements?
P(EF) = 0.3
P(E)= 0.3
A Events E and F are mutually exclusive.
B. Event F is a subset of event E.
C Events E and Fare equal.
D. Events E and Fare independent.
Answer:
D.
Step-by-step explanation:
The conclusion that can be drawn from the given statements is that " events E and F are independent".
When are independent events?Two events such as A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B. I.e.,
P(A ∩ B) = P(A)×P(B)
What is conditional probability?If A and B are two events in a sample space S, then the probability of event B after event A has occurred is called the conditional probability and it is denoted by P(B|A) = [P(A ∩ B)]/P(A).
Verifying how the given events are related:Given that E and F are two events.
P(E|F) = 0.3
P(E) = 0.3
So, the conditional probability is written as,
P(E|F) = P(E ∩ F)/P(F)
If E and F are independent events, then the probability P(E ∩ F) = P(E) × P(F).
On substituting,
P(E|F) = P(E) × P(F)/P(F)
= P(E)
Therefore, P(E|F) = P(E) = 0.3
Hence, events E and F are independent.
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The arena’s car park is shown below.
Area of a circle = πr2
π = 3.14
What is the area of the car park, not including the arena itself?
The area of the parking lot without considering the arena is determined to be 6518.75 square units.
To determine the parking lot area excluding the arena, the process involves multiple steps:
Parking Lot Area Calculation:
Utilize the formula A = B x H, where B is the base (100) and H is the height (75).
Compute A = 100 x 75, resulting in an initial parking lot area of 7500 square units.
Arena Area Calculation:
Employ the formula A = π r², where r is the radius (25) of the arena.
Calculate A = π x 25², yielding an arena area of 19625 square units.
Adjustment for Arena Area:
Observe the image indicating that the car park bisects the arena, cutting its area in half.
Subtract half of the arena's area from the parking lot area to obtain the adjusted area within the car park.
The adjustment equation is A = area - 0.5 x arena, where area is the parking lot area (7500) and arena is half of the arena's area (19625 / 2 = 981.25).
Final Result:
Perform the subtraction: A = 7500 - 981.25, yielding a final area of 6518.75 square units.
Therefore, the area of the parking lot without considering the arena is determined to be 6518.75 square units.
Given the table of value below, which of the following ordered pairs are found on the graph of the inverse function ?
Option: C is the correct answer.
The ordered pair which will be found in the graph of the inverse function is:
C. (0,-2) , (4,-1) , (8,0) , (12,1) , (16,2)
Step-by-step explanation:We are given a table of values as:
x f(x)
-2 0
-1 4
0 8
1 12
2 16
i.e. the domain of the function is: {-2,-1,0,1,2}
and range of the function is: {0,4,8,12,16}
We now that for any function f(x) and it's inverse function the x and y value get interchanged i.e. the domain of the function f(x) becomes the range of its inverse function and the range of the function f(x) becomes the domain of the inverse function.
Hence, for any function with given ordered pair the inverse function will have ordered pair with x and y-value getting swapped.
i.e. if (-2,0) is an ordered pair of f(x)
then (0,-2) will be an ordered pair in the inverse function of f(x).
Hence, similarly all the ordered pairs could be obtained.
The answer is:
Option: C
What 8/12+8/11 in another way than and improper fraction
Answer:
Step-by-step explanation:
8/12+8/11 needs to be converted, so the denominator (the bottom number) is the same. To do that, you can multiply them, so 12 x 11= 132
Now since you multiplied the bottom, you need to multiply the top of each equation.
88/132+96/132=184/132 or as a decimal, 1.3939393939....
Or a faster way is to just insert into a calculator 8 divided by 12 then add 8 divided by 11.
Answer:
16/23
Step-by-step explanation:
I added 12 and 11 and then I added 8 and 8
I will mark brainliest ,thank, and rate to to the best answer!Please help! ASAP
At Westside Middle School, 10 percent, or 140 students, participate in soccer. How many students are in the school? Check all that apply.
Answer:
1st, 3rd, and 6th
Step-by-step explanation:
Let's look at each statment...
1.) Correct
Explanation: 10 percent of the students at the school participate in soccer. If 140 is 10% of the number of students at the school, there is more than 140 students at this school.
2.) Incorrect
Explanation: We've already established that the # of students at the school is more than 140.
3.) Correct
Explanation: 10% as a decimal is 0.1 Divide 140 by 0.1 and you get 1,400. So, the total number of students is 1,400.
4.) Incorrect
Explanation: We've already established that the number of students is 1,400, not 290.
5.) Incorrect
Explanation: We've already established that the number of students is 1,400, not 150.
6.) Incorrect
Explanation: If the percent was a ratio, it would be 10:100 or 10/100. This is because a whole percent is 100% and the percent of students who play soccer is 10%.
7.) Correct
Explanation: We've already established that the ratio would be 10:100 or 10/100. Thus, this is correct.
I hope this helps! :)
If f(x) = 3x - 2 and g(x) = 2x + 1, find (f + g)(x).
Step-by-step explanation:
The answer to the question
what is x plus 2-5= 1/2
Answer this question thanks
First add 3 to both sides (what you do on one side you must do to the other). Since 3 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the right side and bring it over to the left side.
1 > s - 3
1 + 3 > s - 3 + 3
4 > s
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
4 > s OR s < 4
aka 4 is greater then s OR s is less then 4
This means that the graph will have an empty circle and the arrow will go to the left of 4. Look at image below.
Hope this helped!
~Just a girl in love with Shawn Mendes
a boat costs 19200 and decreases in value by 12% per year. how much will it cost in 5 years
Answer:
7,680
Step-by-step explanation:
I did 12% x 5 years and got 60
Then I decreased 19,200 by 60% to get 7,680
Hope this helps!
For which pairs of functions is (f•g)(x)=12x? f(x)=3-4x and g(x)=16x-3
F(x)=6x2 and g(x)= 2/x
F(x)= and g(x) = 144x
F(x)=4x and g(x) =3x
Answer:
F(x)=4x and g(x) =3x
Step-by-step explanation:
We will have to check each pair of functions one by one
So,
For f(x)=3-4x and g(x)=16x-3
For composition we have to put g(x) in place of x in f(x)
(fog)(x)=3-4(g(x))
= 3-4(16x-3)
=3-64x+12
=-64x+15
So first pair doesn't give 12x.
Now for,
F(x)=6x2 and g(x)= 2/x
(fog)(x)= 6(g(x))^2
=6(2/x)^2
=6*(4/x^2)
=24/x^2
For the last pair:
F(x)=4x and g(x) =3x
(fog)(x)=4(g(x))
=4(3x)=12x
So for the last pair of functions (fog)(x) is 12x ..
Answer:
d
Step-by-step explanation:
on edge
How many solutions does y=(0.5)x and y=6 have
Answer:
The system has one solution
Step-by-step explanation:
we have
[tex]y=(0.5)^{x}[/tex] ----> equation A
[tex]y=6[/tex] -----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
There is only one point of intersection
therefore
The system has one solution
see the attached figure
What is the solution to the equation 6x+2=9x-1
Answer:
X=1
Step-by-step explanation:
Subtract by 2 from both sides of equation.
6x+2-2=9x-1-2
Simplify.
1-2=-3
6x=9x-3
Then subtract by 9x from both sides of equation.
6x-9x=9x-3-9x
Simplify.
-3x=-3
Divide by -3 from both sides of equation.
-3x/3=-3/-3
Simplify, to find the answer.
-3/-3=1
X=1 is the correct answer.
Answer:
x=1
Step-by-step explanation:
PLEASE HELP!!! I don’t understand
Answer:
Step-by-step explanation:
Use the half angle identity for cosine:
cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)
I'm going to figure out the sign part first for cos(x/2)...
so x is in third quadrant which puts x between 180 and 270
if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)
cosine is negative in the second quadrant
so we know that
cos(x/2)=-sqrt(1+cos(x))/sqrt(2)
Now we need cos(x)... since we are in the third quadrant cos(x) is negative...
If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.
So let's plug it in:
cos(x/2)=-sqrt(1+4/5)/sqrt(2)
No one likes compound fractions (mini-fractions inside bigger fractions)
Multiply top and bottom inside the square roots by 5.
cos(x/2)=-sqrt(5+4)/sqrt(10)
cos(x/2)=-sqrt(9)/sqrt(10)
cos(x/2)=-3/sqrt(10)
Rationalize the denominator
cos(x/2)=-3sqrt(10)/10
The solution set for
6a^2-a-5=0
Answer:
a=1 or a=5/6
Step-by-step explanation:
I'm going to attempt to factor 6a^2-a-5
a=6
b=-1
c=-5
Find two numbers that multiply to be a*c and add to be b.
a*c=-30 =-6(5)
b=-1 =-6+5
So replace -a with -6a+5a in the expression we started with
6a^2-6a+5a-5
now we factor by grouping
6a(a-1)+5(a-1)
(a-1)(6a-5)
Now let's solve the equation:
(a-1)(6a-5)=0
So a=1 or a=5/6
Please help me thank you
Answer:
Yes
Step-by-step explanation:
Any relation is said to be a function , if and only if
i) every element of first ordered pair is mapped with some element of second ordered pair.
ii) every element in first ordered pair is mapped to only singe element from the ordered pair.
Here in this case we see that there is some value of y for every value of x Hence first condition satisfies.
Also , none of the value of x is mapped or resulting into a two different values of y
Hence both the conditions are fulfilled , there for it is a function.
Cindi bought a sheet pizza for a party. Some of the pizza has pepperoni, some has onions, and the rest of it has both. Two-fifths of the pizza has just pepperoni and one-third of the pizza has just onions. What fraction of the pizza has both pepperoni and onions? PLEASE ANSWER ASAP
Answer:
[tex]\frac{4}{15}[/tex] of the pizza has both pepperoni and onions.
Step-by-step explanation:
As we know, [tex]\frac{2}{5}[/tex] of the pizza has pepperoni and [tex]\frac{1}{3}[/tex] of it is onions.
1. Find the total of the two fractions above.[tex]\frac{2}{5}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{6}{15}[/tex] + [tex]\frac{5}{15}[/tex] (because you have to find like denominators when you add)
= [tex]\frac{11}{15}[/tex]
[tex]\frac{11}{15}[/tex] of the pizza have one topping.
2. Subtract [tex]\frac{11}{15}[/tex] from the whole.The whole is 1, or [tex]\frac{15}{15}[/tex]. So,
[tex]\frac{15}{15}[/tex] - [tex]\frac{11}{15}[/tex] = [tex]\frac{4}{15}[/tex].
[tex]\frac{4}{15}[/tex] of the pizza have both pepperoni and onions.
Final answer:
Two-fifths (2/5) of the pizza has just pepperoni and one-third (1/3) has just onions. Since the sum of these portions exceeds one, we find the overlap by subtracting one from the sum (11/15 - 15/15), resulting in 4/15 of the pizza having both pepperoni and onions.
Explanation:
Cindi bought a sheet pizza for a party with some sections having different toppings. To find out what fraction of the pizza has both pepperoni and onions, we'll first consider the fractions of the pizza with individual toppings. Two-fifths (2/5) of the pizza has just pepperoni and one-third (1/3) has just onions. The sum of these fractions exceeds one, indicating an overlap which must be the part with both toppings.
To calculate the overlap, we add the fractions for just pepperoni and just onions:
2/5 + 1/3 = 6/15 + 5/15 = 11/15.
Since the total cannot exceed one whole pizza, the overlap - the portion with both toppings - is the amount that the sum of individual parts exceeds one. Therefore, we subtract one from the combined fraction:
11/15 - 1 (which equals 15/15) equals -4/15. This negative value is indicative of the overlap. Therefore, 4/15 of the pizza has both pepperoni and onions.
What term best describes a line and a point that lie in the same plane?
A. Congruent
B. Coplanar
C. Collinear
D. Equal
Answer:
B AND C
Step-by-step explanation:
Collinear Points: points that lie on the same line.
Coplanar Points: points that lie in the same plane.
Apollo Spas services 105 hot tubs. If each hot tub needs 165 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
Answer:
17.325 liters
Step-by-step explanation:
Given
Muriatic acid needed by one hot tub = 165 ml
Total hot tubs: 105
So, in order to find the total quantity of muriatic acid, the quantity for one tub will be multiplied by total tubs
So,
Total quantity of muriatic acid: 105 * 165
= 17325 ml
Since we have to find the answer in liters.
1 liter contains 1000 milliliters.
So,
for 17325 ml
= 17325 / 1000 = 17.325 liters
Hence, Apollo Spas needs 17.325 liters of muriatic acid for all of the hot tubs ..
Answer:
17.325 liters
Step-by-step explanation:
Number of Apollo Spas Services= 105 hot tubs
Each hot tub needs Muriatic acid= 165 ml
We have to find the total liters of muriatic acid
Total number of liters required = Number of hots cups× 165 ml
Total number of liters required= 105×165 ml
Total number of liters required= 17,325 ml
1ml = 1/1000 liters
Total number of liters required= 17.325 liters
Hence, the correct answer is 17.325 liters
you are graphing y<2x +1 what type of line do you use and where do you shade ?
The graph is attached.
Why?To solve the problem, we need to look for the characteristics of the line.
We can see that:
- The line has a positive slope since the coefficient of the linear term is a positive number (2).
- Since the line has a positive slope, the line is increasing.
From the line we can calculate the axis intercepts:
For the x-axis intercept, making "y" equal to 0, we have:
[tex]y=2x+1\\\\0=2x+1\\\\x=-\frac{1}{2}=-0.5[/tex]
We have that the x-axis interception point is located at the point (-0.5,0)
For the y-axis intercept, making "x" equal to 0, we have:
[tex]y=2x+1\\\\y=2*0+1\\\\y=1[/tex]
We have that the y-axis interception point is located at the point (0,1)
Also, we have a "less" symbol for the inequality, meaning that the shade that represents the solution of the inequality is located under the pointed line.
The graph of the inequality is attached.
Have a nice day!
In 2012 the population at a middle school was 695 students. In 2016, the population had grown to 825 students. Assuming a constant rate of change, predict the population of the school in 2018.
890 students
725 students
850 students
760 students
Answer:
These kind of problem can be modeled by using the following equation
y = Po*e^(k*(t-to))
Where
Po = initial population
to = year of the initial population
y = Number of students at current year
k = constant rate of change
t = time in years
In 2012
695 = Po*e^(k*(2012 - 2012))
Po = 695
In 2016
825 = 695.e^(k*(2016-2012))
825/695 = e^(k*(4))
ln(825/695) = 4*k
k = ln(825/695) / 4
k = ln(825/695) / 4
k = 0.04287
in 2018
y = 695*e^(0.04287*(2018-2012))
y = 695*e^(0.04287*(6))
y = 695*e^(0.257)
y = 695*1.293
y = 898.85
approximately
899 students
Final answer:
The predicted school population in 2018, based on a constant rate of change, is 890 students. This is calculated by determining the annual rate of increase between 2012 and 2016 and applying it to the 2016 population.
Explanation:
To predict the population of the school in 2018, we need to calculate the constant rate of change between 2012 and 2016, and then apply that rate to extend the prediction to 2018. From 2012 to 2016, the school's population grew from 695 to 825 students. This is an increase of 825 - 695 = 130 students over 4 years.
The annual rate of change is thus 130 students
over 4 years = 32.5 students per year. To predict the population for 2018, we add twice the annual rate of change to the 2016 population (since 2018 is two years after 2016): 825 + (2 * 32.5) = 825 + 65 = 890 students.
Therefore, we can predict that the school population in 2018 will be 890 students.