The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is n³ - 6n² + 3n + 5 + 10/n - 8.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is given below:
(n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8)
The divisor is 8
The coefficients are:
1 -14 51 -19 -30
Using synthetic division:
the first coefficient is 1
the second coefficient = 1 * (8) + (-14)
the second coefficient = -6
the third coefficient = -6 * (8) + (51)
the third coefficient = 3
the fourth coefficient = 3 * (8) + (-19)
the third coefficient = 5
the remainder = 5 * (8) + (-30)
the remainder = 10
Therefore, the solution = 1(n⁴/n) -6(n³/n) + 3(n²/n) + 5(n/n) + 10/n - 8
The solution = n³ - 6n² + 3n + 5 + 10/n - 8
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Find the 14th term of the arithmetic sequence whose common difference is d = 8 and whoose first term is a1=5
The 14th term of the arithmetic sequence is 109 whose common difference is d = 8 and whose first term is a(1)=5.
The value of 14th term of an AP is 109.
In the given question
The common difference = 8
The value of first term=5
And we have to find the value of 14th term of Arithmetic progression
We utilize the method for locating the nth term to locate a specific term in an arithmetic series. An arithmetic sequence's nth term is determined by an = a + (n - 1)d in step 1.
Putting the given value in formula:
an = a + (n - 1)d
a 14th=5+(14-1)8
a 14th=5+13*8
a 14th=5+104
a 14th=109
So the value of 14th term of an AP is 109.
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Evaluate each of the following expressions given that: f ( x ) = √ x + 5 f(x)=x+5 g ( x ) = 3 x − 7 g(x)=3x-7 h ( x ) = 5x(x)=5x f ( g ( 5 ) ) = f(g(5))= Preview g ( f ( 78 ) ) = g(f(78))= Preview h ( g ( f ( 2 ) ) ) = h(g(f(2)))=
Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.
The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.
Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.
In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.
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What is the relationship between 30 hours and 15 hours complete this statement.
the number of hours spent using electronic devices is ? times the number of hours spent playing sports.
The relation between the number of hours spent using electronic devices is 2 times the number of hours spent playing sports.
The term called relation is defined as the relationship between sets of values of ordered pairs and the set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
Here we have know that the number of hours spent using electronic devices is 30 and the number of hours spent playing sports 15.
As per the definition of relation, in order to find the relation we need to do the division operation on then we get,
=> 30/15
=> 2
Which means that the first one is 2 times of the second one.
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Part 6
What is the mean absolute deviation for Doctor As data set on contacts? What is the mean absolute deviation for Doctor Bs data set on contacts
Write a sentence comparing these two data sets using their mean absolute deviations.
There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
Now, According to the question:
The doctors' mean absolute deviation on glasses
The dataset of doctor A is given as:
643 634 670 658 636 624 641 655 649 629
The dataset of doctor B is given as:
651 625 622 624 631 621 653 647 646 646
Using a statistical calculator, we have:
Doctor A
Doctor A: Mean Absolute Deviation (MAD) = 11.28
Doctor B: Mean Absolute Deviation (MAD) = 12
Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses
The variation of the two data
In a dataset, the larger the mean absolute deviations value, the larger the variation.
By comparison, 12 is greater than 11.28
Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
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The given question is incomplete, complete question is:
What is the mean absolute deviation for Doctor A’s data set on glasses? What is the mean absolute deviation for Doctor B’s data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.
Doctor A Doctor B
Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts
745 643 102 763 651 112
726 634 92 736 625 111
769 670 99 735 622 113
765 658 107 759 624 135
756 636 120 748 631 117
742 624 118 756 621 135
757 641 116 765 653 112
748 655 93 761 647 114
770 649 121 768 646 122
738 629 109 761 646 115
The trajectory of a golf ball hit from a tee on the ground at an angle of 50 degrees with an initial speed of 60 meters per second can be modeled by the parabola f(x) = 1. 19x − 0. 0033x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.
PLEASE HELP!
The height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground will be 360 .6 meters
Apparently, x is the distance from the place where the ball is impacted on the ground.
The ball's horizontal speed, given by s, can be calculated using the equation cos(50) = s/60, where s = 38.5 mps.
Size is represented by f(x). The highest point of the parabola would be at -b/2a = -1.19/-.0066 = 180.3 metres, meaning the ball has moved 180.3 metres.
Input 107.28 metres into the formula to find the height.
In order to calculate the distance travelled, the ball must be on the ground, hence f(x) = 0.
-.0033x^2 + 1.19x = 0
x*(-.0033x + 1.19) = 0
x= 1.19/.0033 = 360 .6 meters
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A class plants a tree. sketch the graph of the height of the tree overtime.
a. Identify the two variables.
b. How can you describe the relationship between the two variables?
c. Sketch the graph.
I will give brainiest for full answer!
Answer:
a) The two variables are the number of years and the height of the tree in feet
b) It is a positive linear relationship.
c) Put a point at (0,3) and one at (3,7), and connect the dots.
you have built a regression model to predict future crops of tomato based on a range of growing conditions. the model seems to fit well to the training data, but when any new data is tested it performs very poorly. how would you typically describe a model where this occurs?
That regression model is described as overfitting. The model has identified specific data points in the data that are not universal.
A regression model, which provides a function, describes the relationship between one or more independent variables and a response, dependent, or target variable. To explain the relationship between height and weight, for instance, a linear regression model might be utilized.
Regression analysis is the foundation for many forecasts and evaluations of the effects on target variables. Regression models are widely employed in research to support claims about fuel economy, the causes of pollution, or the effects of screen time on learning.
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Convert 9y^2+72y=72=6x-x^2 to standard form.
A) (x-3)^2/81 + (y-4)^2/ 9=1
B) (x+3)^2/81+(y+4)^2/9=1
C) (x-3)^2/81 + (y+4)^2/9=1
D) doesnt matter the answer is C
The standard form of the equation 9y^2+72y=72=6x-x^2 will be x-3)^2/81 + (y+4)^2/9=1.
Imagine that you are collaborating on a math assignment with students Andrea and Susan. To represent a word problem, you are looking for an equation. You each work on the problem independently, then compare your solutions. The formula 2x - y = -1 was created by you. The formula y = 2x + 1 was created by Andrea. Susan's final solution was the equation y - 3 = 2(x - 1).The given equation is :
[tex]x^{2} + 9y^{2} -6x +72 y = 72[/tex]
[tex]x (x-6) +9y (y+6) = 72[/tex] +1 +36
x(x-6) / 109 + 9y(y+6) / 109 = 1
Thus, by simplifying above equation
(x-3)^2/81 + (y+4)^2/9=1
In this case, Option C is correct.
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Answer:
C) (x-3)^2/81 + (y+4)^2/9=1
Step-by-step explanation:
in the equation 3(x-1)=2x+c, for what value of c will x = 3? Explain your reasoning
Brainliest Answer
By algebra properties, the value of variable c for linear equation 3 · (x - 1) = 2 · x + c such that x = 3 is equal to 0.
How to solve a linear equationIn this problem we need to find the value of a variable c such that the following system of linear equations exists:
3 · (x - 1) = 2 · x + c
x = 3
First, substitute x in the first equation:
3 · (3 - 1) = 2 · 3 + c
Second, simplify and clear the resulting expression:
3 · 2 = 6 + c
6 = 6 + c
c + 6 = 6
c = 0
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Rewrite the ff. Quadratic Formula from General Form to Vertex Form or vice versa.
1. y=x²+6x+14
2. y=2x²+8x+12
3. y=3(x+3)²-7
4. y=(x+2)²+4
Answer:
1. y= (x-3)^2+5 vertex form
2. y= 2(x+2)^2+4 vertex form
3. y= 3x^2+18x+20 general form
4. y= x^2+4x+8 general form
Isaac purchased a new car in 2004 for $16, 900. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $1,400 in the year 2012, then what would be the predicted value of the car in the year 2017, to the nearest dollar?
The value of the car in the year of 2017 would be of:
$295.
How to obtain the value of the car in 2017?A decaying exponential function is given as follows:
y = a(1 - r)^x.
In which:
a is the initial value.r is the decay rate, as a decimal.The initial value for this problem is of:
a = 16900.
After 8 years, the value was of 1400, hence the decay rate is obtained as follows:
16900(1 - r)^8 = 1400
(1 - r)^8 = 1400/16900
((1 - r)^8)^1/8 = (1400/16900)^1/8
1 - r = 0.73245368177
Hence the function is:
y = 16900(0.73245368177)^x.
2017 is 13 years after 2004, hence the value would be of:
y = 16900(0.73245368177)^13
y = $295.
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Find the length of the prism
The length of the rectangular prism is 4/5x.
What is a rectangular prism?
Six faces make up the three-dimensional shape of a rectangular prism (two at the top and bottom and four are lateral faces). The prism has rectangular shapes on each of its faces. There are therefore three sets of identical faces in this picture. A cuboid is another name for a rectangular prism because of its shape.
We know that Volume of a rectangular prism is a product of length, height and width.
We are given volume as (7/x)-(3/5x).
The width(w) is 2/x and the height(h) is 4/x
Using the formula, we get
⇒ V = lwh
⇒ (7/x)-(3/5x) = l * (2/x) * (4/x)
⇒ l = [(7/x)-(3/5x)] / [(2/x) * (4/x)]
⇒ l = (32/5x) /(8/x^2)
⇒ l = 4/5x
Hence, the length of the rectangular prism is 4/5x.
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Please Help Me AND HURRY!
Is \sqrt{5}+\sqrt{16} A Rational Or Irrational Number
The number √5 + √16 is an irrational number
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
\sqrt{5}+\sqrt{16}
Express properly
So, we have the following representation
√5 + √16
Take the square root of 16
This gives
√5 + 4
Rewrite as
4 + √5
The above expression is an irrational number
This is so because of the radical symbol on 5
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PLSSS HELP TURLY KNOW THISSS
Answer:
[tex] \sf \: x = 5[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 15 - x = 10
Then the value of x will be,
→ 15 - x = 10
→ -x = 10 - 15
→ -x = -5
→ [ x = 5 ]
Hence, the value of x is 5.
est scores for students on an easy test. approximately symmetric b) the numbers of hours of television watched by a large, typical group of americans. approximately symmetric c) the heights of a large, typical group of ad
Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.
A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.
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A helicopter is descending from an altitude of 1,500 feet. The helicopter descends at a constant rate of 280 feet per minute. Which function can be used to determine H, the height of the helicopter above the ground after m, minutes? A H=280m+1,500H=280m+1,500H=280m+1,500 B H=1,500−280mH=1,500-280mH=1,500−280m C H=1,500m+280H=1,500m+280H=1,500m+280 D H=280m−1,500H=280m-1,500H=280m−1,500
The function that can be used to get the height of the helicopter above the ground is: H=280m−1,500
What is a function in mathematics?A function is a statement, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable).
How to solve for the function
The value 280 is the constant rate that the helicopter is said to be descending.
The altitude from which it is coming down is given as 1500 feet
The function would be written as H=280m−1,500
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write a description of each inequality
-5a+3>1
show work
Answer:
Step-by-step explain
You have to solve for 5a
Find the logarithmic function f(x) = log a (x-h) that describes the graph *image included*
The logarithmic function that describes the graph is given as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
How to define the logarithmic function?The parent logarithmic function is defined as follows:
f(x) = log(x).
Which, no matter the base, has the vertical asymptote given as follows:
x = 0.
The vertical asymptote of the graphed function is given as follows:
x = -1.
Hence:
[tex]f(x) = \log_a{(x + 1)}[/tex]
When x = 3, f(x) = 2, hence the base a is obtained as follows:
[tex]2 = \log_a{(4)}[/tex]
Meaning that:
a² = 4.
a = 2.
And the function is then defined as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
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A scooter costs a retailer $75, but it sells for $125 at the local store. What is the percent markup? Be sure to round to the nearest hundreth.
Answer = ___%
The percent markup for the scooter that costs a retailer $75 but sells for $125 at the local store is 66.67%.
What is the markup?The markup is the additional price added to the cost of an item for retail sales.
Markups are usually expressed in percentages.
To express the markup in percent determine the difference between the retail price and the cost price. Then divide the difference by the cost price and multiply by 100.
The cost price of the scooter = $75
The selling price of the scooter = $125
The markup in dollars = $50 ($125 - $75)
The markup percent = 66.67% ($50/$75 x 100)
Thus, the scooter was marked-up at 66.67%.
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Can someone help me with this please?
Answer:
Scalene Triangle
Step-by-step explanation:
Right triangles have 90 degree angles. Isosceles triangles have 2 equal sides. While, equilateral triangles have 3 equal sides.
You have $80 in your bank account. Each week you plan to deposit $9 from your allowance and $25 from your paycheck. The equation b = 80+(25+9)w gives the amount b in your account after w weeks how many weeks from now will you have $245 in your bank account
Answer:
165/34
Step-by-step explanation:
245=80+(25+9)w We subtract 80 from each side and simplify
165=(34)w Divide each side by 34
165/34 = w
is the given value a root of the equation or not?
1. 8x-4= 2; 3
2. 4y + 5 = y-7; -4
Answer: To check if a given value is a root of the equation 8x-4 = 2, we can substitute the value into the equation and see if it makes the equation true.
When we substitute 3 for x in the equation 8x-4=2, we get 8(3)-4=2, which simplifies to 24-4=2, which is not true. So, 3 is not a root of the equation.
To check if a given value is a root of the equation 4y + 5 = y-7, we can substitute the value into the equation and see if it makes the equation true.
When we substitute -4 for y in the equation 4y + 5 = y-7, we get 4(-4) + 5 = -4-7, which simplifies to -16+5=-11=-4-7, which is true. So, -4 is a root of the equation.
Step-by-step explanation:
If f(x)=3x, g(x)=x+4 , and h(x)=x2−1 , find g[h(0)]
the value of function g[h(0)] at x = 0 is 3.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given that,the functions f(x) = 3x, g(x) = x + 4 , and h(x) = x² − 1
Since,
G(h(x)) = x² - 1 +4
G(h(x)) = x² + 3
Thus at x = 0
G(h(0)) = 0² + 3
G(h(0)) = 3
therefore, the value of function g[h(0)] at x = 0 is 3.
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Put the numbers in order from smallest to largest.
50.57
150
15.2
5.899
Answer:
Smallest to Largest =
5.899, 15.2, 50.57, and 150
Step-by-step explanation:
I hope this helps you out :D
Find the perimeter of the
polygon if ZB = ZD.
D
A
10.5 cm
12.5 cm
C
B
11.5 cm
P = [?] cm
Perimeter of Regular Polygon = 92cm (Number of sides) x (Side length of a polygon) units
What is Perimeter of Polygon?The total length of a polygon's boundary is calculated as the polygon's perimeter. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane. A polygon's perimeter is always measured in linear distances such as metres, centimetres, inches, feet, etc.
Based on the length of its sides, we can classify a polygon as either regular or irregular. The formula for several well-known polygons' perimeter is as follows:
A triangle's perimeter is equal to its three side lengths, a, b, and c.
A rectangle's perimeter equals 2 (length + width).
We first determine whether the given polygon is a regular polygon or an irregular polygon before computing the perimeter of the polygon. The polygon's perimeter is then determined using the proper Formula
Therefore, the formula to find the perimeter of a regular polygon is: Perimeter of regular polygon = (number of sides) × (length of one side)
From the given diagram;
Perimeter of the polygon = AB + BC+ CD + DA
Perimeter of the polygon = 10.5 + 11.5 + 12.5 + 11.5 + 11.5 + 12.5 + 11.5 + 10.5
Perimeter of the polygon = 22 + 24 + 24 + 22
Perimeter of the polygon = 46 + 46
Perimeter of the polygon = 92cm
Hence the Perimeter of the polygon is 92cm
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find the number in which when subtracted from both 17 and 12 , the product will be 1.04 (qudratic equation)
The required number in which when subtracted from both 17 and 12 , the product will be 1.04 is x = 11.8 or 17.2.
What is quadratic equation?ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
According to question:
Let the number is x, then
(17 - x)(12 - x) = 1.04
204 - 17x - 12x + x² = 1.04
x² - 29x + 204 = 1.04
x² - 29x + 202.96 = 0
On solving for x, we get
x = 11.8 or 17.2
Thus, the number can be x = 11.8 or 17.2.
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The needed value is either x = 11.8 or 17.2, which when deducted from both 17 and 12 will result in a product of 1.04.
What is a quadratic equation?A quadratic equation, or a second-order polynomial equation in a single variable, is defined as ax2 + bx + c = 0. a 0. Due to the fact that it is a second-order polynomial equation, which is ensured by the algebraic basic theorem, it must have at least one solutionIf the number is x, then(17 - x)(12 - x) = 1.04204 - 17x - 12x + x² = 1.04x² - 29x + 204 = 1.04x² - 29x + 202.96 = 0We obtain x by solving for it.x = 11.8 or 17.2Thus, the value of the number can be either x = 11.8 or x = 17.2.
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Find an equation of the plane through the point and perpendicular to the given line. (-2, 9, 10) x = 5 + t, y = 3t, z = 4 - 3t
Let A be the point (-2, 9, 10) and n be the normal vector of the plane. The direction vector of the line is <1, 3, -3>, and since the plane is perpendicular to the line, n is orthogonal to the direction vector.
So, n is a vector that satisfies:
n . <1, 3, -3> = 0
The equation of the plane can be written in the form:
n . (x - A) = 0
Where x = (x, y, z) is any point in the plane.
We can find n by taking the cross product of two non-parallel vectors in the plane, such as <1, 0, 0> and <0, 1, 0>. Then,
n = (1, 0, 0) x (0, 1, 0) = (0, 0, 1)
Substituting the values of A and n into the equation of the plane, we get:
0 . (x - (-2, 9, 10)) = 0
0 . (x + 2, y - 9, z - 10) = 0
z - 10 = 0
z = 10
So the equation of the plane is:
z = 10
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7. Calculate the selling price of a sound system costing R499 if it is sold at a loss of 45%. 8. The price of milk increased by 8%. If the original price is R10,84, what is the new price? 9. A cell phone costing R747 was advertised at a reduced price of R599. Calculate the percentage discount being offered.
10. Mandisa planned to spend RI 000 for shoes this week. On Monday she spent R228,95 and on Thursdays she spent R573,38 on shoes. How much money does she have left for the week?
II. Kate's food budget for the month is R700. The first week she spent R189,75, the second week she spent R203,20 and the third week she spent R146,95. How much does she have left for the last week?
The answers to all parts are shown below.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
7. CP of sound system = 499
loss= 45%
So, the selling price = 499 - 45% of 499
= R 274.45
8. original price is =1084
The new price = 1084 + 8% of 1084
= R 1,170.72
9. Percentage decreased
= ( 747 - 599) / 747 x 100
= 19.81%
10. Mandisa left with
= 1000 - (228.95 + 573.38)
= R 197.67
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HELP HELL GELP
HELPFBDNAKAKIWKW
seaview high school currently has 1,206 students and the town is predicting that they will receive 7 new students each year springtown high school currently had 1,074 students and the town is predicting that they will receive 19 new students each year how many years will it take for the schools to have the same number of students
The number of years that will take for the schools to have the same number of students is given as follows:
11 years.
How to define the linear functions?The number of students in each school is modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope, representing the yearly change.b is the intercept, representing the initial amount of students in each school.The functions for this problem are given as follows:
Seaview: Se(t) = 1206 + 7t.Springtown: Sp(t) = 1074 + 19t.They will have the same number of students when:
Sp(t) = Se(t).
Hence:
1074 + 19t = 1206 + 7t
12t = 132
t = 132/12
t = 11 years.
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