Answers
Answer:
The correct answer option is C. [tex] g ( x ) = | x - 4 | + 6 [/tex].
Step-by-step explanation:
We know that the transformation which shifts a function along the horizontal x axis is given by [tex]f(x+a)[/tex], while its [tex]f(x-a)[/tex] which shifts the function to the right side.
Here we are to shift the function 4 units to the right and 6 units up.
Therefore, the function will be:
[tex] g ( x ) = | x - 4 | + 6 [/tex]
Answer: Option C
[tex]g (x) = | x-4 | +6[/tex]
Step-by-step explanation:
If we have a main function and perform a transformation of the form
[tex]g (x) = f (x + h)[/tex]
So:
If [tex]h> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the left
If [tex]h <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the right
Also if the transformation is done
[tex]g (x) = f(x) + k[/tex]
So
If [tex]k> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units up
If [tex]k <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units downwards.
In this case the main function is [tex]f(x) = | x |[/tex] and moves 4 units to the right and 6 units to the top, then the transformation is:
[tex]g (x) = f (x-4) +6[/tex]
[tex]g (x) = | x-4 | +6[/tex]
Related Questions
What is the answer? Please help
Answers
Answer:
A
Step-by-step explanation:
One and three hundred and four thousand
1+ 3/100+ 4/1000
What's the answer of..
[tex] \frac{4a {}^{2} }{16a {}^{5} \: b {}^{2} } b {}^{5} [/tex]
Answers
Answer:
[tex]\large\boxed{\dfrac{1}{4}a^{-3}b^3=\dfrac{b^3}{4a^3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4a^2b^5}{16a^5b^2}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=\dfrac{4}{16}a^{2-5}b^{5-2}=\dfrac{1}{4}a^{-3}b^3\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=\dfrac{b^3}{4a^3}[/tex]
Which of the following is the radical expression of a to the four ninths power?
4a9
9a4
fourth root of a to the ninth power
ninth root of a to the fourth power
Answers
Step-by-step explanation:
[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\large\huge\boxed{a^\frac{4}{9}=\sqrt[9]{a^4}}[/tex]
The radical expression which represents a to the four ninths power is:
Ninth root of a to the fourth power.
Step-by-step explanation:We are asked to find the radical expression for the word phrase:
a to the four ninths power.
i.e. mathematically it could be written as:
[tex]a^{\dfrac{4}{9}}[/tex]
Now, we know that:
[tex]a^{\dfrac{m}{n}}=(a^m)^{\dfrac{1}{n}}=\sqrt[n]{a^m}[/tex]
Here we have:
[tex]m=4\ \text{and}\ n=9[/tex]
Hence, the expression cold be written as:
[tex]a^{\dfrac{4}{9}}=\sqrt[9]{a^4}[/tex]
Find the first three terms of the arithmetic series described.
a_1=1,a_n=19,S_n=100
Answers
Answer:
1, 3, 5
Step-by-step explanation:
The sum of an arithmetic series is:
S_n = n (a_1 + a_n) / 2
100 = n (1 + 19) / 2
n = 10
The nth term of an arithmetic sequence is:
a_n = a_1 + d (n − 1)
19 = 1 + d (10 − 1)
d = 2
The common difference is 2. So the first three terms are 1, 3, and 5.
A brand new motorcycle gets 70 miles per gallon of gas. If the motorcycle drives 520 miles before running out of gas, how much gas started in the tank? Write you answer as a mixed number.
Answers
Answer:
[tex]x=7 \frac{3}{7}[/tex] gallons
Step-by-step explanation:
So we are given:
70 miles -> 1 gallon is used.
520 miles -> x gallons is used.
Set up a proportional to solve.
I lined up everything already above:
[tex]\frac{70}{520}=\frac{1}{x}[/tex]
Cross multiply:
[tex]70(x)=520(1)[/tex]
[tex]70x=520[/tex]
Divide both sides by 70:
[tex]x=\frac{520}{70}[/tex]
Reduce the fraction (divide top and bottom by 10):
[tex]x=\frac{52}{7}[/tex]
How many 7's are in 52? 7 because 7(7)=49
How much is left over after seven 7's go into 52? 52-49=3
So the answer as a mixed fraction is:
[tex]x=7 \frac{3}{7}[/tex]
To find out how much gas was in the motorcycle's tank, divide the total distance driven by the fuel efficiency. In this case, 520 miles / 70 miles per gallon equals 7 2/5 gallons of gas.
To determine how much gas started in the tank of the motorcycle that gets 70 miles per gallon and drove 520 miles before running out of gas, we use the formula:
Calculate the number of gallons used by dividing the total distance driven by the mileage per gallon. This gives us the formula: Gallons Used = Total Miles Driven / Mileage (Miles per Gallon).Divide the total miles driven, which is 520 miles, by the mileage per gallon, which is 70 miles per gallon.The result is 520 miles / 70 miles per gallon = 7.4285714286 gallons.To express this as a mixed number, we take the integer part, which is 7 gallons, and then write the decimal part as a fraction. The decimal part is approximately 0.4286, which can be rounded to 4\/10 or simplified to 2/5. So the mixed number is 7 2/5 gallons.(3k/k-2)+(6/2-k)
3
-3
3k+6/k-2
3k+6/k+2
Answers
Answer:
Therefore, the answer is 3
Step-by-step explanation:
The given expression is:
[tex]\frac{3k}{k-2} + \frac{6}{2-k} \\\\Taking\ LCM\\= \frac{3k(2-k)+6(k-2)}{(k-2)(2-k)} \\=\frac{6k-3k^2+6k-12}{(k-2)(2-k)}\\= \frac{-3k^2+12k-12}{(k-2)(2-k)}\\\\Applying\ formula\\=\frac{-3(k^2-4k+4)}{(k-2)(2-k)}\\=\frac{-3((k)^2-2*2*k+(2)^2)}{(k-2)(2-k)}\\=\frac{-3(k-2)^2}{(k-2)(2-k)}\\=\frac{-3(k-2)}{(2-k)}\\=\frac{3(2-k)}{2-k}\\=3[/tex]
Answer: 2k
Step-by-step explanation:
-k + 3k = (-1 + 3)k = 2k
If f(x)=4x-12 what is f(2)
Answers
Answer:
-4
Step-by-step explanation:
plug 2 into the equation.
f(2)=4(2)-12
= 8-12
= -4
I hope this helped!
Answer:
f(2) =-4
Step-by-step explanation:
f(x)=4x-12
Let x=2
f(2) = 4(2) -12
=8-12
=-4
How do you find the focus and directrix of y=-2x^2 +8x-15?
Answers
Answer: [tex]\bold{focus: \bigg(2, -7 \dfrac{1}{8}\bigg), \quad directrix: y = -6 \dfrac{7}{8}}[/tex]
Step-by-step explanation:
First, rearrange the equation into vertex form: y = a(x - h)² + k where
(h, k) is the vertex[tex]a = \dfrac{1}{4p}[/tex]NOTE: p is the distance from the vertex to the focus
y = -2x² + 8x - 15
y + 15 = -2x² + 8x → added 15 to both sides
y + 15 = -2(x² - 4x) → factored out -2 from the right side
y + 15 + (-2)(4) = -2(x² - 4x + 4) → completed the square
y + 7 = -2(x - 2)² → simplified
y = -2(x - 2)² - 7 → subtracted 7 from both sides
Now it is in vertex form where:
(h, k) = (2, -7)a = -2 ⇒ [tex]-2=\dfrac{1}{4p}[/tex] ⇒ [tex]p=-\dfrac{1}{8}[/tex]Focus = (2, -7 + p) → Focus = (2, -7 + (-1/8)) → [tex]Focus = \bigg(2, -7 \dfrac{1}{8}\bigg)[/tex]
Directrix: y = -7 - p → Directrix: y = -7 - (-1/8) → [tex]Directrix: y = -6 \dfrac{7}{8}[/tex]
Find the sum of this infinite geometric series where a1=0.3 and r=0.1
Answers
Answer:
1/3
Step-by-step explanation:
The formula for computing the sum of an infinite geometric series is
[tex]S=\frac{a_1}{1-r}[/tex] where r is between -1 and 1 and [tex]r[/tex] is the common ratio, and [tex]a_1[/tex] is the first term of the series.
So let's plug in:
[tex]S=\frac{0.3}{1-0.1}[/tex]
[tex]S=\frac{0.3}{0.9}[/tex]
[tex]S=\frac{3}{9}[/tex] I multiplied bottom and top by 10.
[tex]S=\frac{1}{3}[/tex] I divided top and bottom by 3.
The sum is 1/3.
The sum of the infinite geometric series is 1 / 3.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.
Given that the first term a₁ = 0.3 and common ratio r = 0.1. The sum of the geometric series is calculated by using the formula below:-
S = a₁ / ( 1 - r )
S = 0.3 / ( 1 - 0.1 )
S = 0.3 / 0.9
S = 3 / 9
S = 1 / 3
Therefore, the sum of the infinite geometric series is 1 / 3.
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How do you Divide 7÷135
Answers
The area of the trapezoid is 40 square units.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
Answers
Hey there!
The area of a trapezoid is h(a+b/2), where h is the height and a and b are the two bases. We already have our area, so let's solve for our height in the equation.
40= x(16/2)
40=8x
x=5
Therefore, the height is B) five units.
I hope this helps!
Answer:
answer is 5
Step-by-step explanation:
Write an equation for a circle with a diameter that has endpoints at (-10, 1) and (-8, 5). Round to the nearest tenth if necessary.
Answers
Answer:
The equation is (x+9)^2 + (y-3)^2 = 5
Step-by-step explanation:
The standard form for the equation of a circle is:
(x−h)^2+(y−k)^2=r2
The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter at (-10, 1) and (-8, 5) can be determined as:
(-10 +(-8))/2 , (1+5)/2
= -10-8/2, 1+5/2
= -18/2 , 6/2
= -9 , 3
Thus(-9,3) is the center of the circle.
Now we will use the distance formula to find the radius of the circle.
r^2=(-10-(-9))^2 + (1-3)^2
r^2=(-10+9)^2 +(-2)^2
r^2=(-1)^2 + (-2)^2
r^2=1 + 4
r^2= 5
Take square root at both sides.
√r^2= √5
r=√5
Now put the values in the 1st equation.
(x−h)^2+(y−k)^2=r2
where h = -9, k =3 and r = √5
(x-(-9))^2 + (y-3)^2= (√5)^2
(x+9)^2 + (y-3)^2 = 5
Thus the equation is (x+9)^2 + (y-3)^2 = 5 ....
Ben and Arnoldo are sharing snacks. They have peanut treats and coconut treats. Ben ate 2 of the peanut treats and 4 of the coconut treats for a total of 160 calories. Arnoldo ate 3 of the peanut treats and 2 of the coconut treats for a total of 140 calories. They wrote the system below to represent the number of calories there are in the two types of treats.
Answers
Answer:
The number of calories in a peanut treat is 30.
The number of calories in a coconut treat is 25.
Step-by-step explanation:
So we have Ben ate 2 peanut treats (let p represent the calories in each peanut treat) and 4 coconut treats (let c represent the calories in each coconut treat). The sum of those calories is 160.
This is the equation for Ben:
2p+4c=160
I'm going to use the same representation here. p for the number of calories in each peanut treat and c for the number of calories in each coconut treat.
Arnold ate 3 p's and 2 c's for a sum of 140 calories:
Alrnoldo's equation is:
3p+2c=140
So we have the system:
2p+4c=160
3p+2c=140
I'm going to divide the first equation by 2 because each term is divisible by 2:
p+2c=80
3p+2c=140
This system is setup for elimination because the equations are in the same form and the second column have the same variable expression, 2c. So we are going to subtract to eliminate the variable c, that is 2c-2c=0.
p+2c=80
3p+2c=140
---------------------Subtract!
-2p+0=-60
-2p =-60
Divide both sides by -2:
p =30
So if p=30 and p+2c=80 , then 30+2c=80.
So let's solve:
30+2c=80 for c
Subtract 30 on both sides:
2c=50
Divide both sides by 2:
c=25
The number of calories in a peanut treat is 30.
The number of calories in a coconut treat is 25.
Which equations and/or functions represent the graphed line? Select three options.
f(x)=1/5x-4
f(x)=1/2x+2
f(x)=1/2x+1
y-3=1/2(x-2)
y-1=1/2(x+2)
Answers
Answer:
f(x) = 1/2x + 2
y - 3 = 1/2(x - 2)
y - 1 = 0.5(x + 2)
Step-by-step explanation:
The equations that represent the graphed line are f(x) = 1/2x + 2, f(x) = 1/2x + 1, and y - 1 = 1/2(x + 2).
Explanation:The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In the given options, the equations that represent the graphed line are:
f(x) = 1/2x + 2f(x) = 1/2x + 1y - 1 = 1/2(x + 2)These equations have the same slope and y-intercept as the graphed line.
Which two events are independent?
A and X
A and Y
B and X
B and Y
Answers
Answer:
A and X
Step-by-step explanation:
None
Is the following relation a function? {(3, 2), (3, −2), (1, −4), (−1, 2)}
Answers
Step-by-step explanation:
no it is not because if 3 maps on 2, then it cannot map on -2 at the same time
A relation is considered a function if each input has only one output. The given set contains the input '3' with two different outputs '2' and '-2', therefore, it is not a function.
Explanation:In mathematics, a relationship is considered a function if for every input there is only one output. In other words, no two pairs should have the same first element yet different second elements.
If we look at the set of ordered pairs provided, we have {(3, 2), (3, -2), (1, -4), (-1, 2)}. We can see that the input '3' corresponds to both '2' and '-2'. Since there are two outputs for the same input, we can determine that this relation is not a function.
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on the coordinate grid, the graph of y= 3/x-1+3 is shown. it is a translation of y =3/x
Answers
The question is about translating the graph of the function y = 3/x. The graph of y = 3/(x - 1) + 3 results from shifting the parent function to the right by 1 unit and upwards by 3 units on the coordinate grid.
Explanation:The question pertains to the translation of a rational function on the coordinate grid and is related to graph transformations. The function y = 3/x is known as the parent function, and y = 3/(x - 1) + 3 is the transformed function. To illustrate the translation, we can understand the changes in terms. Here x - 1 indicates a horizontal shift to the right by 1 unit, and +3 signifies a vertical shift upwards by 3 units. The new graph represents these translations on the coordinate system, which is a two-dimensional representation with x and y-axes as described in the reference information provided.
A circle has a radius of 25 centimeters and a central angle EOG that measures 100°. What is the area of sector EOG?
Answers
Answer:
≈ 545.42 cm²
Step-by-step explanation:
The area (A) of sector EOG is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{100}{360}[/tex]
= π × 25² × [tex]\frac{10}{36}[/tex]
= 625π × [tex]\frac{10}{36}[/tex]
= [tex]\frac{625(10)\pi }{36}[/tex] ≈ 545.42 ( to 2 dec. places )
Match each variable with what it represents in a sequence formula. 1. r the value of the first term 2. d the value of the nth term 3. n common ratio 4. an common difference 5. a1 term number
Answers
Answer:
r is the common ratio (in geometric sequence)
d is the common difference (in arithmetic sequence)
n is the term number
a1 is the value of the first term
an is the value of the nth term
Step-by-step explanation:
For the sequence formula, each term represent as follows,
[tex]r[/tex]: common ratio
[tex]d[/tex]: common difference
[tex]n[/tex]: term number
[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term
[tex]a_{1}[/tex]: the value of the first term
What is the sequence?"Sequence is defined representation of a number in a particular order using some formula."
According to the question,
For the sequence formula,
Each variable is matched with the following term,
[tex]r[/tex]: common ratio
[tex]d[/tex]: common difference
[tex]n[/tex]: term number
[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term
[tex]a_{1}[/tex]: the value of the first term
Hence, for the sequence formula, each term represent as follows,
[tex]r[/tex]: common ratio
[tex]d[/tex]: common difference
[tex]n[/tex]: term number
[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term
[tex]a_{1}[/tex]: the value of the first term
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Find X. Round to the nearest tenth if necessary.
Answers
Answer:
x = 9
Step-by-step explanation:
When 2 chords intersect inside a circle then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is
2 × x = 3 × 6, that is
2x = 18 ( divide both sides by 2 )
x = 9
What should be added to the difference of 1 and 1/2 and 2/6 to get 1 and 2/3?
Answers
Rewrite 1/2 to have a common denominator with 2/6
1/2 x 3 = 3/6
Now you have 1 and 3/6 - 2/6 = 1 and 1/6
Now rewrite 2/3 to have a common denominator with 1/6: 2/3 x 2 = 4/6
Subtract 1/6 from 4/6:
4/6 - 1/6 = 3/6 = 1/2
You will need to add 1/2
To get from the difference between 1 and 1/2 and 2/6 to 1 and 2/3, one must add 1/2 after ensuring both differences have a common denominator.
To find out what should be added to the difference between 1 and 1/2 and 2/6 to get 1 and 2/3, we need to perform a few steps involving fractions. First, let's convert 1 and 1/2 into an improper fraction by multiplying 1 (the whole number) by 2 (the denominator of the fractional part) and adding 1 (the numerator of the fractional part), which gives us 3/2. Now, to find the difference between 3/2 and 2/6, we must have a common denominator, which is 6 in this case. Multiplying the numerator and denominator of 3/2 by 3 gives us 9/6.
Now we subtract 2/6 from 9/6 to get the difference, which is 7/6 or 1 and 1/6. To find what needs to be added to this difference to get 1 and 2/3, we must also express 1 and 2/3 as an improper fraction. Multiplying 1 (the whole number) by 3 (the denominator) and adding 2 (the numerator) gives us 5/3.
To compare 7/6 with 5/3, we need the same denominator, which is 6. So we multiply the numerator and denominator of 5/3 by 2 to get 10/6. Subtracting 7/6 from 10/6, we find the missing number to be 3/6, which simplifies to 1/2.
u want to leave a 15% tip on a $33 meal. What is the total cost for the night?
Answers
Answer: The total cost would be 37.95
Step-by-step explanation:
The total cost for the night, including a 15% tip on a $33 meal, is $37.95.
Explanation:To calculate the total cost for the night, we need to add the meal cost and the tip. For a $33 meal, a 15% tip would be calculated using the formula tip = meal cost x tip percentage/ 100. In this case, tip = $33 x 15/100= $4.95. Therefore, the total cost for the night (meal cost + tip) would be $33 + $4.95 = $37.95.
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Find the range of the function f(x) = 4x - 1 for the domain (-1,0, 1, 2, 3}.
Answers
For this case we have a fucnion of the form [tex]y = f (x)[/tex]
Where:
[tex]f (x) = 4x-1[/tex]
By definition, the rank of a function is given by:
The set of the real values that the variable y or f (x) takes.
So:
[tex]f (-1) = 4 (-1) -1 = -4-1 = -5\\f (0) = 4 (0) -1 = 0-1 = -1\\f (1) = 4 (1) -1 = 4-1 = 3\\f (2) = 4 (2) -1 = 8-1 = 7\\f (3) = 4 (3) -1 = 12-1 = 11[/tex]
ANswer:
The range is: -5, -1,3,7,11
Answer:
{-5,-1,3,7,11}
Step-by-step explanation:
The range is the output of the function
We have the inputs
f(x) = 4x - 1
f(-1) = 4(-1)-1 = -4-1 = -5
f(0) = 4(0)-1 = 0-1 = -1
f(1) = 4(1)-1 = 4-1 = 3
f(2) = 4(2)-1 = 8-1 = 7
f(3) = 4(3)-1 = 12-1 = 11
The outputs for the given inputs are
{-5,-1,3,7,11}
NEED HELP PLEASE ASAP Given: AEDFG AABF
Name the postulate or theorem you can use to prove AADE & AEBA
е СРСтс
AAS Theorem
HL Theorem
ASA Postulate
Answers
Answer:
H-L Theorem
Step-by-step explanation:
They tell you that they are right triangles, and you have your congruency marks. If they never had right angle indicators, this theorem would never work.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
The lines shown below are perpendicular.if the green line has a slope of 3/4 what is the slope of the red line?
Answers
Answer:
-4/3
Step-by-step explanation:
because the line are perpendicular, so the slope of re line is -1/(3/4)=-4/3
How would you get the answer of how much change he received
Answers
$100- $61.25= $38.75
He would receive $38.75 in change.
Answer:
Step-by-step explanation:
Givens
I foot of sill = 1.75
35 feet of sill = x
Paid with 100 dollars.
Solution
First part
Solve the proportion
1/35 = 1.75/ x Cross multiply
1*x = 35 * 1.75
x = 61.25
=========
Second part
Get the change.
Change = 100 - 61.25
Change = 38.75
============
The change =
3 tens 30.00
1 five 5.00
3 ones 3.00
3 quarters .75
Total 38.75
emily bought a new car for $22000. She paid 93% of the list price. What was the list price?
Answers
To answer your question the list price for Emily's vehicle would have a $23,655.91 list price
Hope this helped
Aaron
Answer: The list price of the car was $ 23655.91.
Step-by-step explanation: Given that Emily bought a new car for $22000 and she paid 93% of the list price.
We are to find the list price of the car.
Let $ x denote the list price of the car.
Then, according to the given information, we have
[tex]93\%\times x=22000\\\\\\\Rightarrow \dfrac{93}{100}\times x=22000\\\\\Rightarrow 93x=22000\times100\\\\\Rightarrow 93x=2200000\\\\\Rightarrow x=\dfrac{2200000}{93}\\\\\Rightarrow x=23655.91.[/tex]
Thus, the list price of the car was $ 23655.91.
Find the surface area of the triangular prism
Answers
The formula for the area of a triangle is 1/2bh. So you multiply 36 by 38 and 1/2 to get 684
You then have to fine the area of the rectangles and since they’re three of them you multiply 3 by 36 and 41 to her 4428.
When you add 4428 and 684 you get 5112 square inches
Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.
What are the dimensions of one of the identical triangular pieces of the plane?
2 cm base, 3 cm height
3 cm base, 3 cm height
3 cm base, 4 cm height
3 cm base, 6 cm height
Answers
Answer:
2 cm base, 3 cm height
Step-by-step explanation:
Let
x -----> the height of one of the identical triangles pieces of the plane
y ----> the base of one of the identical triangles pieces of the plane
we know that
x=3 cm
2y+2=6
solve for y
2y=6-2
2y=4
y=2 cm
therefore
The dimensions of one of the identical triangles pieces of the plane are 2 cm base and 3 cm height
Answer:
The correct option is 1. The dimensions of one of the identical triangular pieces of the plane are 2 cm base and 3 cm height.
Step-by-step explanation:
From the given figure it is noticed that the length of parallel sides of the trapezoid are 6 cm and 2 cm.
The height of triangular pieces is same as the height of trapezoid. So the height of triangular pieces is 3 cm.
Let the measure of base of the triangular pieces be x.
[tex]x+2+x=6[/tex]
Combine like terms.
[tex]2x+2=6[/tex]
Subtract 2 form both the sides.
[tex]2x+2-2=6-2[/tex]
[tex]2x=4[/tex]
Divide both sides by 2.
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
The base of the triangles is 2 cm.
The dimensions of one of the identical triangular pieces of the plane are 2 cm base and 3 cm height. Therefore the correct option is 1.
What is the volume of the prism below 4 height length 18 9width
Answers
The volume of the prism is [tex]\(V = 648 \, \text{cubic units}\).[/tex]
The formula for the volume (V) of a rectangular prism is given by [tex]\(V = lwh\),[/tex] where (l) is the length, (w) is the width, and (h) is the height. In this case, the provided dimensions are length (l = 18), width (w = 9), and height (h = 4). Substituting these values into the formula: [tex]\[ V = 18 \times 9 \times 4 = 648 \, \text{cubic units}. \][/tex] Therefore, the volume of the prism is [tex]\(648 \, \text{cubic units}\).[/tex]
Understanding the concept of volume in three-dimensional geometry is vital. The formula [tex]\(V = lwh\)[/tex] reflects the relationship between the length, width, and height of a rectangular prism. Multiplying these dimensions provides the total space enclosed by the prism in cubic units. In this instance, with a length of 18 units, a width of 9 units, and a height of 4 units, the volume calculation yields [tex]\(648 \, \text{cubic units}\),[/tex] representing the spatial capacity of the given prism.
Calculating the volume of prisms is a fundamental skill in geometry and has practical applications in various fields, including architecture and engineering. This calculation allows us to quantify the amount of space a three-dimensional object occupies, providing essential information for design and analysis. In this case, the resulting volume, [tex]\(648 \, \text{cubic units}\),[/tex] represents the capacity of the rectangular prism specified by the given dimensions.