The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]
Domain of a function refers to the values or range of input values of a function for which the function exists in real.
In this problem the given function is
[tex]y=\sqrt{(x+6)}-7[/tex]
Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.
So, for existence of function it is must to
[tex]x+6\geq0[/tex]
[tex]x\geq-6[/tex]
Hence the domain of the given function is given by [tex]x\geq-6[/tex]
Hence the correct option is (B).
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How do l do this please help
The attached graph represents the graph of the parallel lines
How to plot the lines?The equation of the lines are linear equation
A linear equation is represented as:
y = mx + b
Where b represents the y-intercept.
Using the above form of linear equation as a guide, the equations of the lines are
y = -x + 5
y = -x + 2
y = -x - 3
y = -x - 2
Where -5, 2, -3 and -2 are the given y-intercepts and y = -x is the base equation.
Next, we plot the equations on a coordinate grid
See attachment
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Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
The foreign exchange market works according to the principles of firms, households, and investors:
These three constituent factors of the foreign exchange market determine the demand and supply patterns in the market. Demand for a foreign currency might increase in the foreign exchange market is linked to the expectation of an increase in the value of a foreign currency. Supply of a foreign currency in the foreign exchange market is linked to an inverse principle, where the expectation of a decrease in the value of foreign currency pushes supply upwards. If we are to suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A., then the value of the MXN will decrease, with everything being equal. A higher interest rate leads to the appreciation of a foreign currency relative to other currencies in the foreign exchange market. A lower interest rate leads to the depreciation of a foreign currency relative to other currencies in the foreign exchange market.Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
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Solve: 4 + 3x = 2(3x-7) +9
A. There are infinitely many solutions
B. x = 3
C. x = -3
D. x = 2/3
Answer:
B. x = 3
Step-by-step explanation:
Simplifying
4 + 3x = 2(3x + -7) + 9
Reorder the terms:
4 + 3x = 2(-7 + 3x) + 9
4 + 3x = (-7 * 2 + 3x * 2) + 9
4 + 3x = (-14 + 6x) + 9
Reorder the terms:
4 + 3x = -14 + 9 + 6x
Combine like terms: -14 + 9 = -5
4 + 3x = -5 + 6x
Solving
4 + 3x = -5 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
4 + 3x + -6x = -5 + 6x + -6x
Combine like terms: 3x + -6x = -3x
4 + -3x = -5 + 6x + -6x
Combine like terms: 6x + -6x = 0
4 + -3x = -5 + 0
4 + -3x = -5
Add '-4' to each side of the equation.
4 + -4 + -3x = -5 + -4
Combine like terms: 4 + -4 = 0
0 + -3x = -5 + -4
-3x = -5 + -4
Combine like terms: -5 + -4 = -9
-3x = -9
Divide each side by '-3'.
x = 3
Simplifying
x = 3
3+7=6-|-x|
Solve for x.
Thanks :)
Answer:
no solution
Step-by-step explanation:
| | is a notation for absolute value, which is the distance that a number is from 0.
you can think of this as the "positive version" of a number
so, |-x| will become: x
We can plug this into the equation, and solve like we would for any variable
3 + 7 = 6 - |-x| {simplify}
3 + 7 = 6 - x {simplify}
10 = 6 - x
Now, we can isolate x (isolate = get it alone)
10 = 6 - x
-6 - 6 {subtract 6 from both sides}
4 = -x {multiply both sides by -1 to get positive x}
·-1 ·-1
- 4 = x
{check solution:}
3 + 7 = 6 - | -4 |
10 = 6 - 4
10 = 2
FALSE
because this solution has been found to be false, there is no possible value for x
we write this as: no solution
[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]
Which number should replace the ç to make the subtraction problem correct?
9.866
- 7.97ç
1.889
Answer:
7
Step-by-step explanation:
for you to get the missing number just take the complete numbers and minus them then you'll get the incomplete digit needed good day.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the expressions given in words with their values when m = 6. 2 15 42 3 21
The matching is done below
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
1) 3 is the difference of 2 times d minus 3.
As, 2*d - 3
=2*3 - 3
=6 - 3
= 3
2) 4 is 4 added to the difference of d minus 3.
or, 4 + (d - 3)
or, 4 + (3 - 3)
or, 4 + 0 = 4
3) 0 is the difference of d minus 3 divided by 2.
(d - 3)/2
= (3 - 3)/2
= 0/2
= 0
4) 2 is the quotient of 12 divided by the difference of 3 times d minus 3.
12/(3d - 3)
=12/(3*3 - 3)
=12/(9 - 3)
=12/6
= 2
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what is the simplified equivalent of the terminating
The simplified fractional equivalent of 0.25 is 1/4 .
The complete question is
What is the simplified fractional equivalent of the terminating decimal 0.25?
What is simplified equivalent ?When a number is solved to a state where it cannot be further simplified , but can be written in a different format , the two numbers are then called the simplified equivalent of each other.
The given number is decimal 0.25
So this number is in its simplified state but can also be written as
0.25 * 1
= 0.25 * 100 /100
= 25/100
= 1/4
Therefore 1/4 is the simplified fractional equivalent of 0.25.
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Karl, Serene and Pauline have 1281 stickers altogether. 08
Pauline had 3 times as many stickers as Serene.
Karl had 175 stickers fewer than Pauline.
How many stickers did Pauline have?
Pauline has 371 stickers. Karl, Serene, and Pauline have 1281 stickers altogether.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Let Karl, Serene and Pauline have x, y, and z stickers.
Given condition;
Karl, Serene, and Pauline have 1281 stickers altogether;
x+y+z = 1281
Pauline had 3 times as many stickers as Serene.
z = 3 y
y=z/3
Karl had 175 stickers fewer than Pauline.
x=z -175
Substitute all the values in the terms of z;
x+y+z = 1281
z -175 + z/3 + z = 1281
8z/3 = 1281 +175
z=546
Pauline have;
x = z -175
x =546 -175
x = 371
Hence Pauline has 371 stickers.
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Find f(-4) for f(x)=9(3)^x
Answer:
[tex] f(-4) = \dfrac{1}{9} [/tex]
Step-by-step explanation:
[tex] f(x) = 9(3)^x [/tex]
[tex] f(-4) = 9(3)^{-4} [/tex]
[tex] f(-4) = 3^2 \cdot 3^{-4} [/tex]
[tex] f(-4) = 3^{-2} [/tex]
[tex] f(-4) = \dfrac{1}{9} [/tex]
Answer:
1/9
-------------
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
Answer:
1170$Step-by-step explanation:
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
we can solve with an equation
6 : 540 = 13 : x
x = 540 * 13 : 6
x = 7020 : 6
x = 1170
--------------------------
check
6 : 540 = 13 : 1170
0.01111111111 = 0.01111111111
the answer is good
help me with this please i will gave u bralinet answer who ever answer first
Answer:
[tex]\fbox {5 times}[/tex]
Step-by-step explanation:
Days where both will be done :
⇒ 2nd day × 3rd day
⇒ 6th day
Number of times in September :
⇒ The month has 30 days
⇒ Number of times = 30/6
⇒ Number of times = 5
Answer:
5 times
Step-by-step explanation:
• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:
LCM (2 and 3) = 2 x 3
= 6
This means, she will do both every 6th day.
• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:
⇒ 30 ÷ 6
= 5 times
Please solve these questions with an explanation
Answer:
Step-by-step explanation:
1.) I can find my Vulome if the vulome of cylinder is multiplied by 4/3 who am i?
2.)The Vulome is 1/3 that of a cylinder that has the same base and height with me. Who am I?
If the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Thus, you're a sphere.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this formula:
V = 4/3 × πr³
Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that if the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Also, multiplying the volume of a cylinder by 1/3 would produce the volume of a sphere.
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Consider a student loan of $12, 500 at a fixed APR rate of 9% for 25 years.
a. Calculate the monthly payment
b. Determine the total amount paid over the term of the loan
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
The monthly payment is; $104.9; The total amount paid over the term of the loan is; $31470
How to calculate APR?
We are given;
Loan principal = $12,500
Interest rate = 12%
Number of payments per year = 12 payments per year.
Loan term = 25 years.
Formula for monthly payment is;
PMT = (p * APR/n)/[1 - (1 + APR/n)^(-nY)]
Where;
p is principal
APR is interest rate
n is number of payments per year
Y is loan term
Thus;
PMT = (12500 * 0.09/12)/[1 - (1 + 0.09/12)^(-12 * 25)]
PMT = 93.75/(1 - 0.106288)
PMT = $104.9
B) Total amount paid over the loan term is;
A = PMT * m * n
where;
m is number of months in a year,
n is number of years
A = 104.9 * 12 * 25
A = $31470
C) The principal as a percentage of the loan is;
P/A = 12500/31470
P/A = 39.72%
Percentage paid for interest is = 100% - 39.72% = 80.28%
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In need of help in algebra, 4 questions help please
The solution to all the given equation has been determined.
What is an Intercept ?An intercept is the point at which a straight line intersects the x or y axis.
The equation given are
5x-4y = -20
x+5y = 5
x+4y = 4
x+2y = 6
All the equations are plotted on the graph and the value of the intercept are determined
For Equation 1
The solution is x = 0 , -4 , y = 4 , 0
For Equation 2
The solution is x = 0 ,5 , y=1 ,0
For Equation 3
The solution is x = 0,4 ; y = 1 ,0
For Equation 4
The solution is x =0,6 ; y = 3 ,0
The graph are attached with the answer.
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what is life?bhkbkbkjnmmkjopjlknm nbgvuyihjknm
Answer:
yessss
Step-by-step explanation:
yessssssss
The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.
En una tienda se fabrican dos tipos de mesas, de 3 y 4 patas. En total se tienen 89 mesas para vender. Se sabe que el quíntuple de las mesas de 3 patas más la cantidad de mesas de 4 patas es igual a 277. ¿ Cuántas mesas de 3 patas se tienen para vender?
En una tienda se fabrican
La cantidad de mesas de 3 patas que tiene para la venta la tienda que las
fabrica es: 47
¿Qué es un sistema de ecuaciones?
Es un arreglo de ecuaciones que se caracteriza por tener el mismo número de incógnitas que de ecuaciones.
Existen diferentes métodos para su resolución:
Sustitución: se despeja de una ecuación una variable, quedando en función de otra para luego sustituirla en otra ecuación y así obtener
Igualación: se despeja la misma variable en dos de las ecuaciones y se igualan los resultados.
Eliminación: se resta o suman dos ecuaciones para que quede un resultado en función una variable y así despejarla.
Gráfico: se grafican las rectas y el punto de intersección es la solución del sistema.
¿Cuántas mesas de 3 patas se tienen para vender?
Definir;
x: mesas de 3 patas
y: mesas de 4 patas
Ecuaciones
x + y = 89
5x + y = 277
Aplicar método de eliminación;
Restar 1 - 2;
x + y = 89
-5x - y = -277
-4x + 0 = -188
Despejar x;
x = 188/4
x = 47
Sustituir;
47 + y = 89
Despejar y;
y = 89 - 47
y = 42
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Which statement is true about the end behavior of the
graphed function?
As the x-values go to positive infinity, the function's
values go to negative infinity.
As the x-values go to zero, the function's values go
to positive infinity.
As the x-values go to negative infinity, the function's
values are equal to zero.
As the x-values go to positive infinity, the function's
values go tO positive infinity.
Answer:
As the x-values go to positive infinity, the function's
values go to negative infinity.
Step-by-step explanation:
upon viewing the graph you will notice that the function in blue will appear to go down (negative) as you follow the x to the right, in the positive direction.
Making your answer to be as the x goes to positive inf (right) the values of the function go to negative inf (down).
Write the ratio as a fraction in lowest terms.
Compare in inches.
4 feet to 49 inches
Answer:
48/49
Step-by-step explanation:
divison and multiplcation
Frankie’s weekly budget includes a long-term goal of purchasing a car. He is saving $15 a week toward that goal. He is considering saving up his money to purchase his grandmother’s older car. Frankie knows his grandmother has maintained the car and it is in good condition. She is also giving him a greatly discounted price of $800. What should Frankie consider before buying the car? Check all that apply. what he will be giving up if he spends $800 on the car the cost to maintain (oil, tires, gas, brakes) and insure the car how many of his friends have cars his short- and long-term financial goals if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs
The decision of purchasing a car must be taken by Frankie after considering the following points:
1. what he will be giving up if he spends $800 on the car
2. The cost to maintain and ensure the car
3. his short- and long-term financial goals
4. if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs.
What is the point he must know about purchasing a car?Frankie is an individual person when he wants to purchase a car that is his long-term goal.
he must consider various things before making such a big expenditure.
The points to be noted before purchasing a car are:
what is the cost for Frankie for spending $800?
What will be the maintenance and insurance cost?
He must check his other short and long-term goals before purchasing a car.
Is the expense of the car a necessity for Frankie or he can use public transport.
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Answer:
Step-by-step explanation: thank me later
A,B,E
Which expressions are completely factored?
30a^6-24a^2=3a^2(10a^4-8)
The factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
The given expression is [tex]30a^{6} -24a^{2}[/tex].
We need to factorise the given expression.
What are the factors?Each of these numbers and expressions is referred to as a factor of algebraic expressions if it is possible to express algebraic expressions as the product of numbers, algebraic variables, or algebraic expressions.
Now, [tex]30a^{6} -24a^{2}=6a^{2} (5a^{4}-4 )[/tex]
Therefore, the factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].
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If a-4b=18,what is 3a/81b
Answer:
You cannot solve this problem with only one given equation
Step-by-step explanation:
You need at least 2 equations to solve for two variables.
The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
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Answer:36
Step-by-step explanation:
Question 1(Multiple Choice Worth 5 points) (04.02 MC) What are the domain and range of the function f of x is equal to the quantity x squared plus 8x plus 7 end quantity divided by the quantity x plus 1 end quantity? D: {x ∊ ℝ | x ≠ 1}; R: {y ∊ ℝ | y ≠ 0} D: {x ∊ ℝ | x ≠ −1}; R: {y ∊ ℝ | y ≠ −6} D: {x ∊ ℝ | x ≠ −7}; R: {y ∊ ℝ | y ≠ 0} D: {x ∊ ℝ | x ≠ −1}; R: {y ∊ ℝ | y ≠ 6}
The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
The complete questionWhat are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1
The domain of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Set the denominator to 0
x + 1 = 0
Solve for x
x = -1
This means that the domain of the function is the set of all real numbers except -1
Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}
The range of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Factorize the numerator
[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]
Simplify
f(x) = x + 7
The function is undefined at x= -1.
So, we have:
f(-1) = -1 + 7
f(-1) = 6
This means that the range of the function is the set of all real numbers except 6
Hence, the range of the function is {y ∊ ℝ | y ≠ 6}
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Answer:
It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
Step-by-step explanation:
I took the test
Find the slope of the line that passes through the points (4, 4) and (5, 7).
Answer:
3
Step-by-step explanation:
Slope of a line between any two points (x1,y1) and (x2,y2) is given by the equation:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
let's take (x1,y1) as (4,4) and (x2,y2) as (5,7)
So slope = [tex]\frac{7-4}{5-4}[/tex] = 3
Answer:
y = 3x - 8
Step-by-step explanation:
y = Mx + c
m = 3 / 1
4 = 3(4) + c
4 - 12 = c
How do I graph y−3=1/2(x+3) on this graph? :c
From point (0, 9/2) and (-9, 0) we get a straight line.
What is Straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.
Here, given equation:
(y − 3) = 1/2(x + 3)
at x = 0,
y - 3 = 1/2 (0 + 3)
y - 3 = 1/2 X 3
y = 3/2 + 3
y = 9/2
at y = 0,
0 - 3 = 1/2 (x + 3)
-3 = 1/2 (x + 3)
-6 = x + 3
x = -6 - 3
x = -9
Thus, from point (0, 9/2) and (-9, 0) we get a straight line.
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pls see the attachment
24 of the 720 numbers have the numbers 1, 2 and 3 in that order
How to determine the number of arrangements?The digits are given as:
1, 2, 3, 4, 5, and 6
For 1, 2 and 3 to come in that order, then the three numbers must be treated as a digit
So, we have:
(123), 4, 5, and 6
Now, there are 4 digits.
The number of arrangements is then calculated as:
Arrangements = 4!
Expand
Arrangements = 4 * 3 * 2 * 1
Evaluate
Arrangements = 24
Hence, 24 of the 720 numbers have the numbers 1, 2 and 3 in that order
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Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2
The expanded expressions are shown below:
(x + 1)² = x² + 2 · x + 1(x - 3)² = x² - 6 · x + 9(x + 4)² = x² + 8 · x + 16(x - 1/2)² = x² - x + 1/43 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75(1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2How to expand perfect square trinomials
Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:
a) (x + 1)² = x² + 2 · x + 1
b) (x - 3)² = x² - 6 · x + 9
c) (x + 4)² = x² + 8 · x + 16
d) (x - 1/2)² = x² - x + 1/4
e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75
f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2
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Britney sells mattresses at a furniture store. She makes a 9.75% commission on each mattress she sells. Last week, Britney sold four mattresses. The sale price of each mattress is shown in the table.
How much did Britney earn last week?
Enter your answer in the box.
$
Mattress sale Amount
Mattress 1 $2400
Mattress 2 $3200
Mattress 3 $1900
Mattress 4 $800
Answer:
$809.25
Step-by-step explanation:
→ Find the sum of the sales amount
2400 + 3200 + 1900 + 800 = 8300
→ Find the amount that s commission
( 9.75 × 8300 ) ÷ 100 = $809.25
world problem in length (trigonometry) geometry not chemistry
Answer:
≈ 47.2 m
Step-by-step explanation:
let the height from the sea to the base of lighthouse be h₁
let the height from the sea to the top of the lighthouse be h₂
using the tangent ratio in the right triangle
tan55.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h_{1} }{610}[/tex] ( multiply both sides by 610 )
h₁ = 610 tan55.1°
tan56.5° = [tex]\frac{h_{2} }{610}[/tex] ( multiply both sides by 610 )
h₂ = 610 tan56.5°
then
height of lighthouse = h₂ - h₁
= 610 tan56.5° - 610 tan55.1°
= 610(tan56.5° - tan55.1° )
≈ 47.2 m ( to the nearest tenth )
