The Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1 is
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]
In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.
The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
In the scenario above, we are given the function f(x) = e and a = 1.
The first derivative of e^x is e^x,
the second derivative is e^x,
and the third derivative is also eˣ.
We then evaluate these derivatives at a = 1, we get:
f(1) = e¹ = e
f'(1) = e¹ = e
f''(1) = e¹ = e
f'''(1) = e¹ = e
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
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Ina Crespo rowed 16 miles down the Habashabee River in 2 hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current. I need help asap
Answer:ina can row 6mph in still water and 2 mph in current
Step-by-step explanation:
Find the lengths of each triangle…
2x ft
6x ft
200ft
Answer:
[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]
[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]
Step-by-step explanation:
Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.
Pythagoras Theorem[tex]\large{\boxed{a^2+b^2=c^2}[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.From inspection of the given diagram:
a = 2xb = 6xc = 200Substitute these values into the formula and solve for x.
[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]
Substitute the found value of x into the expression for each side length.
[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]
[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]
Therefore, the exact side lengths of the given right triangle are:
[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]
The side lengths to the nearest hundredth are:
63.25 ft189.74 ft200 fthelp please i need help with this answer
The initial value (a) of the exponential function f(x) = 4ˣ is 1.
How to solve an exponential equation?The standard form of an exponential equation is:
y = abˣ
where a is the initial value and b is the multiplication factor.
If b > 1, it is a growth function and if b < 1, it is a decay function.
Given the exponential function:
f(x) = 4ˣ
The initial value (a) = 1 and the multiplication factor (b) = 4.
The graph of the exponential function f(x) = 4ˣ is attached below.
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A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
The height of the person on the ferris wheel can be modeled by the equation:
h = 20sin(π/4*t) + 21
where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.
Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.
Answer:
x = 3, -5/2
Step-by-step explanation:
First, you move the 15 onto the left of the equation by subtracting it from both sides.
Second, you plug your info into the quadratic equation. (1 +- sqrt(1+4*15*2))/4
Who can help mee??
well, let's find out how much she made on each week
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]
Please I want the answer!
The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2
Writing the subtraction expressions to calculate the lengthsFrom the question, we have the following parameters that can be used in our computation:
O = (3, 2)
A = (-7, 5)
B = (-7, 2)
The distance between (or length of) the coordinates is calculated as
Length = √[(x2 - x1)² + (y2 - y1)²]
Using the above as a guide, we have the following:
OB = √[(3 -- 7)² + (2 - 2)²]
OB = √[(3 -- 7)² + 0²]
OB = √[(3 -- 7)²]
OB = 3 -- 7
AB = √[(-7 -- 7)² + (5 - 2)²]
AB = √[0² + (5 - 2)²]
AB = √[(5 - 2)²]
AB = 5 - 2
Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2
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This is so hard. Can you help me with this?
Answer: 70, 6
Step-by-step explanation:
(a) For <F that is the same as <D. The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same
All of the angles are = 180 if you subtract <E, you are left with 140 to be split between <F and <D
<F= 70
(b) all of the sides are the same because all the angles are the same
so AB=6
Given: rectangle MNPQ ~ rectangle RSTU
- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU
The perimeter of rectangle RSTU is 21 cm.
The area of the rectangle RSTU is 27 cm².
How to find the perimeter and area of a rectangle?A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.
Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.
Hence,
Let's find the width of the rectangle MNPQ
14 = 2(4 + w)
14 = 8 + 2w
14 - 8 = 2w
2w = 6
w = 6 / 2
w = 3 cm
Therefore, using similar ratio,
4 / 6 = 3 / RU
cross multiply
4RU = 18
RU = 18 / 4
RU = 4.5 cm
Therefore,
Perimeter of the rectangle RSTU = 2(6 + 4.5)
Perimeter of the rectangle RSTU = 2(10.5)
Perimeter of the rectangle RSTU =21 cm
Area of the rectangle RSTU = 4.5 × 6
Area of the rectangle RSTU = 27 cm²
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A side of the triangle below has been extended to form an exterior angle of 125°. Find the value of
From the given triangle, x has a value of 35°.
As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.
Which angles are adjacent?Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.
According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.
Now, 125°+ y =180°
y = 180°-125°
y = 55°
As a result, the supplied triangle's value for y is 55°.
The sum of the triangle law,
55°+ 90° + x = 180°
x = 35°
Therefore the value of x = 35°
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1. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
A 0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
B (0,1) is a zero of the quadratic because it is where the parabola crosses the y-axis.
C (-0,3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
D (0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.
The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.
plot the y-get at (0,1),
x = - b/2a
To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is
f(3/4) = 1/8.
Plot the vertex at (3/4, 1/8).
Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.
To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.
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You buy a $256,000 home with a down payment of 24%. Find the amount of the down payment and the mortgage amount.
The amount of the down payment and the mortgage amount are $61440 and $194560
Finding the amount of the down payment and the mortgage amount.From the question, we have the following parameters that can be used in our computation:
Buy a $256,000 home with a down payment of 24%
This means that
down payment = 24% * 256,000
So, we have
down payment = 61440
Next, we have
mortgage amount = (1 - 24%) * 256,000
So, we have
mortgage amount = 194560
Hence, the mortgage amount is 194560
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Fully factorise x ² + 18x
Answer: To factorize x² + 18x, we can first find the greatest common factor (GCF) of the two terms, which is x:
x(x + 18)
This is the fully factorized form of x² + 18x.
Help pleasee
here is the picture is about Row Ops
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
The given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
Now,
From the given information,
The operation we are to carry out is:
Add -4(row 1) to row 3
This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)
Multiplying by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result from the multiplication to the corresponding elements in row 3
Adding the results to corresponding elements in row 3
4 -1 6 | -8
+ -4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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Lisa an experienced shipping clerk, can fill a certain order in 9 hours. Felipe a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?
The solution is ___Hours
It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.
To solve this problem, we can use the formula:
1/T = 1/T₁ + 1/T₂
where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.
Substituting the given values into the formula, we get:
1/T = 1/9 + 1/11
Simplifying the right-hand side of the equation, we get:
1/T = (11 + 9)/(9 x 11)
1/T = 20/99
Multiplying both sides by 99, we get:
T = 99/20
Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.
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Help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
what is approximately ?
Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,
In the given question,
The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.
To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.
Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63
So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:
fraction remaining = (1/2)⁰°⁶³ ≈ 0.518
To find the remaining mass, we can multiply the fraction remaining by the initial mass:
remaining mass = fraction remaining x initial mass
remaining mass = 0.518 x 500 mg ≈ 259 mg
Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
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The solution set of the following equations 2x-y=8 , 3x+2y=5 is ..............
*
Answer:
x = 3,
y = -2
Step-by-step explanation:
Let's write the given equations into a system:
{2x - y = 8,
{3x + 2y = 5;
Let's make y the subject from the 1st equation:
-y = 8 - 2x / × (-1)
y = 2x - 8
Replace y in the 2nd equation with its value from the 1st one:
3x + 2(2x - 8) = 5
Expand the brackets:
3x + 4x - 16 = 5
Collect like-terms:
7x = 5 + 16
7x = 21 / : 7
x = 3
y = 2 × 3 - 8 = -2
Un elevador de taller mecánico tiene pistones de entrada y salida de 5 cm y de 60 cm de radio respectivamente. Con este dispositivo se mantiene levantado un auto de 2000 kg. ¿Cuál es la fuerza aplicada al pistón de entrada?
The force applied to the input piston is 136.25 N.
How to find the force applied to the intake piston?This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.
Thus, we can equate the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:
P₁ = P₂
F₁/A₁ = F₂/A₂ (Pressure = Force/Area)
F₂ = 2000 * 9.81 = 19620 N (F = mg)
A₁ = π * r₁² = π * 5² = 25π cm²
A₂ = π * r₂ ² = π * 60² = 3600π cm²
F₁ = F₂/A₂ * A₁
F₁ = (19620/3600π) * 25π
F₁ = 136.25 N
Therefore, the force applied to the input piston is 136.25 N.
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Question in English
A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?
Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q
Answer:
A. P
Step-by-step explanation:
You want to identify the point that represents a striking deviation in the given box plot.
IQRThe interquartile range for this box plot is the difference between the upper and lower quartiles:
29 -26 = 3
OutlierThe "fence" that is 1.5 times the IQR below the lower quartile is ...
26 -3·1.5 = 21.5
Point P lies beyond this fence, so is considered an outlier in the data set.
Point P represents a striking deviation, choice A.
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A student is solving the equation shown.
√x+1+2√x-1=0
For the first step in solving the equation, the student subtracts the second term from both sides of the equation.
For the second step, the student squares both sides of the equation.
What is the result of the second step?
Answer:
C) x + 1 = 4(x - 1)-----------------------
Given equation to solve:
[tex]\sqrt{x+1} +2\sqrt{x-1} =0[/tex]The result of the first step:
[tex]\sqrt{x+1} =-2\sqrt{x-1}[/tex]The second step:
[tex](\sqrt{x+1})^2 =(-2\sqrt{x-1} )^2[/tex]And its result is:
x + 1 = 4(x - 1)The matching choice is C.
how much money does she make all together in one week
needs more explanation
n/4.4 =7 Pls Help nowwwwwwwwwwwwwwwwwwwww
Answer:
n=7
Step-by-step explanation:
[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]
The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x − 0.0033x^2, 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.
Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The equation of the parabolic trajectory of the golf ball is given by:
f(x) = 0.84x - 0.0033x²
where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b / 2a
where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:
a = -0.0033 and b = 0.84
Substituting these values into the formula, we get:
x = -0.84 / 2(-0.0033)
= 127.27
So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:
f(127.27) = 0.84(127.27) - 0.0033(127.27)²
f(127.27) ≈ 21.67
So the highest point of the trajectory is approximately 21.67 meters above the ground.
To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:
0 = 0.84x - 0.0033x²
0.0033x² = 0.84x
x = 0 or x = 254.55
So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.
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Help pleaseeeee I would appreciate it
(1) The result of the row operation R₂ ↔ R₃ is [ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
(2) The result of the row operation 3R₁ ↔ R₁ is [24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
What is the result of the row operation?
The result of the row operation in the matrix is calculated as follows;
R₂ ↔ R₃, implies changing row 2 and row, and the result would be;
[ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
The result of obtained from 3R₁;
3R₁ = [24 - 27 -21 - 18]
3R₁ ↔ R₁ is determined as; (the row interchange)
[24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
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A laptop computer is purchased for $4700. Each year, it’s value is 80% of its value the year before. After how many years will the laptop computer be worth $1000 or less?
Answer:
Step 1:
Let x = number of years
Let y = Value of the laptop after x years
Step 2:
Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)
Step 3:
Set the equation equal to 1000 and solve for x
1000 = 0.8((4700)x)
1 = 0.8(4700)x
1/0.8 = 4700x
1.25 = 4700x
x = (1.25/4700)
Answer: The laptop will be worth $1000 or less after 0.0026608 years.
Answer:
1 year
Step-by-step explanation:
4700 x .8= 3760
4700 - 3760 = 940$
In 1 year the laptop will be $940
You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually
What is investment compounded annually?When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.
For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960
Then new total amount after one year will be $12,000 + $960 = $12 960 ,
This process will continue for each year of the investment and the formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n
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complete quesation:
You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
a.
3.99% compounded monthly
b.
4% compounded quarterly
c.
4.175% compounded annually
d.
4.2% simple interest
What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?
The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.
What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept
Given that; the line passing through the point (-3,-4) and parallel to the x-axis.
A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.
Hence;
The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.
To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:
-4 = b
Note that: y = b, where b is a constant.
y = -4
Therefore, the equation of the line y = -4.
Option C) y = -4 is the correct answer.
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1 Place an X in the table to show the solution that makes each equation true. 6+x=15 244 X 9x = 18 x=9
Step-by-step explanation:
| Equation | Solution |
| 6+x=15 | x = 9 |
| 9x = 18 | x = 2 |
The table would look like:
| Equation | Solution |
| 6+x=15 | X |
| 9x = 18 | X |
i need answer for this with explanation
Answer:
53yd
Step-by-step explanation:
SA1 = 2(4×2)
= 2×8
= 16
SA2 = 2(4×3)
= 2×12
= 24
SA3 = 2(3×2)
= 2×6
= 12
TOTAL SA
16+24+13
= 53
Please help!!!
The number of miles m (in billions) traveled by vehicles in City A can be modeled by
2.86 + 112 where t is the number of years since 1994. Use a graphing calculator to
approximate the year in which the number of vehicle miles of travel in City A was 140 billion.
m ==
Based on the linear model, the number of vehicle miles of travel in City A was 140 billion in the
year
The year in which the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.
What is a linear model?The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.
To derive the number of year,
140 = 2.86t + 112
Subtracting 112 from both sides gives:
28 = 2.86t
Dividing both sides by 2.86 gives:
t ≈ 9.79 years
See attached graph.
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