Answer:
The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]
Step-by-step explanation:
Given as :
The net force = F Newton
The mass of the object = m kg
The acceleration = a m/s²
Now, As The force is define as the product of mass and velocity
So, F = m × a
Now, Again , if the acceleration = 8 a
and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F
So, Let The mass = M
∵ F = m × a
∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]
Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]
or, M =0.0625 × [tex]\frac{F}{a}[/tex]
∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]
so, The mass = [tex]\frac{m}{16}[/tex]
Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex] Answer
Final answer:
According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.
Explanation:
According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.
If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:
(F/2) = m * (8a)
To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:
m = (F/2)/(8a)
Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).
What is the measure of < c
45°
56°
60°
66°
Answer:
c = 56
Step-by-step explanation:
The two angles 'c' and '124' form a straight angle. They add to 180
c+124 = 180
c+124-124 = 180-124 ... subtract 124 from both sides
c+0 = 56
c = 56
Answer:
56 <3
Step-by-step explanation:
Please check my work and if any answers wrong or you feel like it is not good enough feel free to correct me and let me know, Greatly appreciated.
Question 1
Is the expression x3•x3•x3 equivalent to x3•3•3? Why or why not? Explain your reasoning.
No, Because the given numbers have different value.
Question 2
Rewrite in simplest radical form
1
x
−3
6
. Show each step of your process.
If the symbols of the radicals are given by
It is possible to perform the simplification as well,
Question 3
Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.
Since these are both x terms and 4x= x*x*x*x, I can simply write 5x.
Question 4
Rewrite in simplest radical form
x
5
6
x
1
6
. Show each step of your process.
Question 5
Which of the following expressions are equivalent? Justify your reasoning.
A. 4√x3
B. 1
x−1
C. 10√x5•x4•x2
D.x^{\frac{1}{3} } multiply by
x^{\frac{1}{3} } multiply by
x^{\frac{1}{3} }
Question 1:
No, \(x^3 \cdot x^3 \cdot x^3\) equals \(x^9\), while \(x^3 \cdot 3 \cdot 3\) equals \(9x^3\), representing different operations and values.
Question 2:
Incomplete. The expression \(1/x^3\) can be rewritten as \(x^{-3}\) using negative exponents.
Question 3:
Incorrect. The product of \(\sqrt{x}\) and \(4\sqrt{x}\) equals \(4x\), not \(5x\). Use exponents to simplify.
Question 4:
The expression \(x^{5/6} \cdot x^{1/6}\) simplifies to \(x\). Show the steps of exponent addition.
Question 5:
Unjustified. Determine equivalent expressions by simplifying each and comparing results. Justify based on mathematical properties.
Here's a review of your work:
Question 1:
Your reasoning is incorrect. The expressions are not equivalent because they represent different operations. \( x^3 \cdot x^3 \cdot x^3 \) means \( x \) multiplied by itself 3 times, which is \( x^9 \). \( x^3 \cdot 3 \cdot 3 \) is a multiplication of constants, which equals \( 9x^3 \). So, the expressions are not equivalent because they result in different values.
Question 2:
Your answer is incomplete. It seems like you've provided a template for simplifying radicals, but you haven't actually applied it to the given expression. To simplify \( \frac{1}{x^3} \), you can rewrite it as \( x^{-3} \).
Question 3:
Your answer is incorrect. The product of \( \sqrt{x} \) and \( 4\sqrt{x} \) is not simply \( 5x \). To rewrite it in simplest rational exponent form, you should use the property of exponents which states that \( \sqrt{a} = a^{1/2} \). So, \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and \( 4\sqrt{x} \) is equivalent to \( 4x^{1/2} \). Multiplying these expressions together, you get \( 4x^{1/2} \cdot x^{1/2} = 4x^{1/2 + 1/2} = 4x^1 = 4x \).
Question 4:
You haven't shown your process for simplifying \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} \). To simplify, use the property of exponents which states that when you multiply two terms with the same base, you add their exponents. So, \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} = x^{\frac{5}{6} + \frac{1}{6}} = x^{\frac{6}{6}} = x^1 = x \).
Question 5:
You haven't justified which expressions are equivalent. To determine equivalence, you need to simplify each expression and compare them to each other.
One number is four more than four times another. If their sum is increased by five, the result is thirty-nine. Find the numbers.
Answer:
(6, 28) or x=6, y=28 or The numbers are 6 and 28.
Step-by-step explanation:
4x+4=y
x+y+5=39
--------------
4x+4=y
x+y=39-5
----------------
4x+4=y
x+y=34
------------
x+(4x+4)=34
x+4x+4=34
5x+4=34
5x=34-4
5x=30
x=30/5=6
4(6)+4=y
24+4=y
y=28
x=6, y=28
Which words or phrases describe parallel lines?
Select all that apply.
common points
coinciding
coplanar lines
perpendicular
never intersect
The never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.
What are parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.
Therefore, the never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.
To know more about parallel lines follow
https://brainly.com/question/16742265
#SPJ2
What value represents the vertical translation from the graph of the
(x+5)2+3?
0 -5
O-3
Answer:
The value 3 represents the vertical translation upwards of [tex]f(x)[/tex] to [tex]g(x)[/tex]
Step-by-step explanation:
The question is incomplete or missing data.
The correct question
What value represents the vertical translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function
[tex]g(x) = (x + 5)^2 + 3[/tex]?
Given functions:
Parent function
[tex]f(x) = x^2[/tex]
Translated function
[tex]g(x) = (x + 5)^2 + 3[/tex]
Translation rules
For horizontal shift
[tex]f(x)\rightarrow f(x+c)[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.
For vertical shift
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
From the functions given the translation rule can be given as:
[tex]f(x)\rightarrow f(x+5)+3[/tex]
[tex]g(x)=f(x+5)+3[/tex]
This shows the graph is shifted left by 5 units and upwards by 3 units.
Thus the value 3 represents the vertical translation of [tex]f(x)[/tex] to [tex]g(x)[/tex]
Mrs. Martini is 6 years more than 3 times as old as Tony. Eight years ago, she
was 2 years less than 9 times as old as he was then. Find each of their ages.
Mrs Martini age is 42 years and Tony age is 12 years
Step-by-step explanation:
The given is:
Mrs. Martini is 6 years more than 3 times as old as TonyEight years ago, she was 2 years less than 9 times as old as he was thenAssume that Tony is x years old now
∵ Mrs. Martini is 6 years more than 3 times as old as Tony
∵ Tony is x years old
- Multiply the age of Tony by 3 and add 6 to the product
∴ The age of Mrs Martini = 3 x + 6
8 years ago
- Subtract 8 from the age of each one
Tony age = (x - 8)
Mrs Martini age = (3 x + 6) - 8 = 3 x + 6 - 8 = 3 x - 2
∵ Eight years ago, Mrs Martini was 2 years less than 9 times as old
as Tony was then
- Multiply Tony age by 9 and subtract 2 from the product
∵ Tony age from 8 years ago = x - 8
∵ Mrs Martini age from 8 years ago = 3 x - 2
∴ 9(x - 8) - 2 = 3 x - 2
- Simplify the left hand side
∴ 9 x - 72 - 2 = 3 x - 2
- Add like terms
∴ 9 x - 74 = 3 x - 2
- Subtract 3 x from both sides
∴ 6 x - 74 = -2
- Add 74 to both sides
∴ 6 x = 72
- Divide both sides by 6
∴ x = 12
∵ x represents the age of Tony
∴ Tony is 12 years old
∴ 3 x + 6 is the age of Mrs Martini
- Substitute x by 12
∵ 3(12) + 6 = 36 + 6 = 42
∴ Mrs Martini is 42 years old
Mrs Martini age is 42 years and Tony age is 12 years
Learn more:
You can learn more about word problems in brainly.com/question/10557938
#LearnwithBrainly
What is the sum of the interior angles of an equilateral triangle?
A. 60°
B. 90°
C.180°
D.360°
Answer:
c
Step-by-step explanation:
Name one point on the line y - 4 = 3(x + 2)
Please help!!
write an expression with 4.3,-1.07 and 2.971. Use only subtraction and addition to come out with a negative number
Step-by-step explanation:
You could add (-1.07 + 2.971) to get (1.901)
Then do (1.901 - 4.3) to get a negative number; (-2.399)
I would double check this all with a calculator
A carpenter wants to cut a 6 foot board into pieces 2/3 foot long . How many pieces can the carpenter make
Answer:
The carpenter can make 9 pieces.
Step-by-step explanation:
6/(2/3)=(6/1)(3/2)=18/2=9
Which function represents the sequence: 4, 7, 10, 13, 16,...
Answer:
3n + 1
Step-by-step explanation:
Note the sequence has a common difference between consecutive terms, that is
7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3
This indicates that the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 4 and d = 3, thus
[tex]a_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1
Answer:
[tex]\large\boxed{a(n)=3n+1}[/tex]
Step-by-step explanation:
It's an arithmetic sequence:
[tex]a(1)=4\\\\a(2)=a(1)+3=4+3=7\\\\a(3)=a(2)+3=7+3=10\\\\a(4)=a(3)+3=10+3=13\\\\a(5)=a(4)+3=13+3=16\\\vdots[/tex]
An explicit formula of an arithmetic sequence:
[tex]a(n)=a(1)+(n-1)d[/tex]
d - common difference
We have
[tex]a(1)=4,\ d=3[/tex]
Substitute:
[tex]a(n)=4+(n-1)(3)[/tex] use the distributive property
[tex]a(n)=4+3n-3[/tex]
[tex]a(n)=3n+1[/tex]
A series of books has 30 volumes, each with 700 pages. What is the total number of pages in the series?
Answer:
Step-by-step explanation:
Here we have to multiply to find the total...
30 volumes, then each individual book with 700 pages, therefore, the answer would be 21,000 pages
To calculate the total number of pages in the series, multiply the number of volumes (30) by the pages per volume (700) to get a total of 21,000 pages.
Explanation:The question asks for the total number of pages in a series of books, assuming each of the 30 volumes has 700 pages. Therefore, the calculation we need to perform is: 30 volumes × 700 pages per volume.
The formula to calculate the total number of pages is:
Total Pages = Number of Volumes × Pages per Volume
By inserting the given values into the formula:
Total Pages = 30 × 700 = 21,000 pages.
Hence, the total number of pages in the series is 21,000.
write an inequality and that represents the graph.
Answer:
Part 16) [tex]y\leq -x+2[/tex]
Part 17) [tex]y>\frac{1}{3}x-1[/tex]
Step-by-step explanation:
Part 16) we know that
The solution of the inequality is the shaded area below the solid line
The slope of the solid line is negative
The y-intercept of the solid line is the point (0,2)
The x-intercept of the solid line is the point (2,0)
The slope of the solid line is
[tex]m=(0-2)/(2-0)=-1[/tex]
The linear equation of the solid line in slope intercept form is
[tex]y=-x+2[/tex]
therefore
The inequality that represent the graph is
[tex]y\leq -x+2[/tex]
Part 17) we know that
The solution of the inequality is the shaded area above the dashed line
The slope of the dashed line is positive
The y-intercept of the dashed line is the point (0,-1)
The x-intercept of the dashed line is the point (3,0)
The slope of the dashed line is
[tex]m=(0+1)/(3-0)=\frac{1}{3}[/tex]
The linear equation of the dashed line in slope intercept form is
[tex]y=\frac{1}{3}x-1[/tex]
therefore
The inequality that represent the graph is
[tex]y>\frac{1}{3}x-1[/tex]
define the solution to a system of linear inequalities.
The solution to a system of linear inequalities is the set of values that satisfy all the inequalities at once, graphically represented as the overlapping shaded region on a coordinate plane.
Explanation:The solution to a system of linear inequalities is defined as the set of values that satisfy all inequalities in the system simultaneously. To find this solution set, each inequality is graphed on the same coordinate plane to determine the region where all inequalities overlap. Within this region, any point represents a solution to the system. If an inequality is non-strict (less than or equal to or greater than or equal to), the boundary line is included in the solution set and is usually drawn as a solid line. If the inequality is strict (less than or greater than), the boundary line is not included in the solution set and is depicted as a dashed line. The solutions are typically represented graphically by shading the area of the plane that satisfies all conditions.
GETS BRAINILIST!!!!What number should be placed in the box to help complete the division calculation? long division setup showing an incomplete calculation. 13 is in the divisor, 3302 is in the dividend, and 2 hundreds and 5 tens is written in the quotient. 2600 is subtracted from 3302 to give 702. An unknown value represented by a box is being subtracted from 702. Numerical Answers Expected! Answer for Blank 1:
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Long division setup showing an incomplete calculation
13 is in the divisor3302 is in the dividend2 hundreds and 5 tens is written in the quotient2600 is subtracted from 3302 to give 702An unknown value represented by a box is being subtracted from 702We need to find this number
Lets write the steps above
∵ The dividend = 3302
∵ The divisor = 13
- 2 hundreds means 200 and 5 tens means 50
∵ The quotient = 200 + 50 + x
∵ Dividend = divisor × quotient
∴ (13 × 200) + (13 × 50) + (13 × x) = 3302
∵ 13 × 200 = 2600
- Subtract 2600 from the dividend
∴ 3302 - 2600 = 702
∵ 13 × 50 = 650
∴ 702 - 650 = 52 ⇒ 650 is the unknown value
∵ 13 × x = 13x
∵ 52 - 13x = 0
- Add 13 x to both sides
∴ 52 = 13x
- Divide both sides by 13
∴ x = 4
∴ 3302 ÷ 13 = 200 + 50 + 4
∴ 3302 ÷ 13 = 254
∴ From the steps above the missing number subtracted from
702 is 650
The unknown value is being subtracted from 702 is 650
Learn more:
You can learn more about the division operation in brainly.com/question/1747117
#LearnwithBrainly
Answer:
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Long division setup showing an incomplete calculation
13 is in the divisor
3302 is in the dividend
2 hundreds and 5 tens is written in the quotient
2600 is subtracted from 3302 to give 702
An unknown value represented by a box is being subtracted from 702
We need to find this number
Lets write the steps above
∵ The dividend = 3302
∵ The divisor = 13
- 2 hundreds means 200 and 5 tens means 50
∵ The quotient = 200 + 50 + x
∵ Dividend = divisor × quotient
∴ (13 × 200) + (13 × 50) + (13 × x) = 3302
∵ 13 × 200 = 2600
- Subtract 2600 from the dividend
∴ 3302 - 2600 = 702
∵ 13 × 50 = 650
∴ 702 - 650 = 52 ⇒ 650 is the unknown value
∵ 13 × x = 13x
∵ 52 - 13x = 0
- Add 13 x to both sides
∴ 52 = 13x
- Divide both sides by 13
∴ x = 4
∴ 3302 ÷ 13 = 200 + 50 + 4
∴ 3302 ÷ 13 = 254
∴ From the steps above the missing number subtracted from
702 is 650
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Dean is comparing prices on ground beef. Store A is selling 5 pounds of ground beef for $23.49. Store B is selling 8 pounds of ground beef for $36.96.
Which store is offering the better deal on ground beef?
Store B is offering the better deal on ground beef
Step-by-step explanation:
Dean is comparing prices on ground beef
Store A is selling 5 pounds of ground beef for $23.49Store B is selling 8 pounds of ground beef for $36.96We need to know which store is offering the better deal on ground beef
To find the better deal we must to find the unit price of each store
The unit price = total price ÷ number of pounds
∵ Store A is selling 5 pounds of ground beef for $23.49
∴ The unit price of Store A = 23.49 ÷ 5 = $4.698
∴ The unit price of Store A is $4.698 per pound
∵ Store B is selling 8 pounds of ground beef for $36.96
∴ The unit price of Store B = 36.96 ÷ 8 = $4.620
∴ The unit price of Store B is $4.620 per pound
∵ $4.620 < $4.698
∴ The unit price of Store B is less than the unit price of Store B
∴ Store B is cheaper than Store A, then it is offering the better deal
Store B is offering the better deal on ground beef
Learn more:
You can learn more about the word problems in brainly.com/question/317697
#LearnwithBrainly
p = $14,300
r = 7 1/2%
t = 4
What is i?
$4,290.00
$429.00
$4.29
Answer:
Value of I is $4290
Step-by-step explanation:
We have been given that,
Formula for simple interest is given by
Plugging the known values
On simplifying, we get
Hence, value of I is $4290
the jurassic zoo charges $5 for each adult and $3 for each child the total bill for the people from school trip was $420 how many adults and how many child went to the zoo
Answer:
The number of adults who went to the zoo was 21 and the number of children was 105.
Step-by-step explanation:
The complete question is
The Jurassic Zoo charges $5 for each adult admission and $3 for each child. The total bill for the 126 people from a school trip was $420. How many adults and how many children went to the zoo?
Let
x -----> number of adults
y ----> number of children
we know that
[tex]x+y=126[/tex] ------> equation A
[tex]5x+3y=428[/tex] ----> equation B
Solve the system by graphing
The solution is the intersection point both graphs
The solution is the point (21,105)
see the attached figure
therefore
The number of adults who went to the zoo was 21 and the number of children was 105.
Round 2,034,627,105 too the nearest ten thousand
Answer: 2,000,000,000
Step-by-step explanation:
Simplify the expression.
Answer:
[tex]19 - \frac{6}{5}j[/tex]
written out on a computer keyboard, you would type: 19 - (6/5)j
Step-by-step explanation:
The terms that dont have a 'j' attached to them all group up and combine to this: 18 + (-5) + 6 = 18-5+6 = 13+6 = 19
The rest of the terms have a 'j', and they combine to: [tex]-\frac{2}{5}j - \frac{4}{5}j = \left(-\frac{2}{5} - \frac{4}{5}\right)j = \frac{-2-4}{5}j = -\frac{6}{5}j[/tex]
After combining both sets of like terms, we have 19 as the first result and [tex]-\frac{6}{5}j[/tex] as the second result. They are then added to get [tex]19 + \left(-\frac{6}{5}j\right) = 19 - \frac{6}{5}j[/tex]
We cant simplify any further because there are no like terms left.
Which statements are true given the histogram? Check
all that apply.
The histogram is symmetrical.
The histogram is evenly distributed.
The cluster from 4 p.m.-10 p.m. means that most of
the texts were sent in the afternoon and evening.
U More texts were sent from 6 p.m.-8 p.m. than from 8
p.m.-10 p.m.
The peak from 4 p.m.-6 p.m. means that the highest
number of texts was sent during this interval.
10 pm-1159
Answer:
C and E
Step-by-step explanation:
The cluster from 4 p.m.–10 p.m. means that most of the texts were sent in the afternoon and evening.
The peak from 4 p.m.–6 p.m. means that the highest number of texts was sent during this interval.
How do you Graph this
Y = 5x + 12
y = 2x - 4
What is the value of f(x) = 2/3 x + 1/4 when x = 6?
Answer:
4 1/4
Step-by-step explanation:
f(x) = 2/3(6) + 1/4
f(x) = 4 + 1/4
f(x) = 4 1/4(4.25)
A)-124
B)-18
C)-36
D)-96
Answer:
It's Either B Or D
Step-by-step explanation:
only because They Only number that are closer so you can reverse it is 18 or 96
Which statement is true for the tables?
1) Both Table A and Table B represent functions.
2) Both Table A and Table B do not represent functions.
3) Table A does not represent a function, but Table B represents a function.
4) Table A represents a function, but Table B does not represent a function.
Answer:
Table A represents a function, but Table B does not represent a function.
Step-by-step explanation:
We have to select the correct option among the given 4 options after judging the given two tables attached to this question.
The first table shows that for each x values there is only one y value. Therefore, this is a function.
But in the second table shows that for each x value there are multiple y values since we are getting y = 1 and 2 for x = 5.
Hence, table B is not a function. it is just a relation. (Answer)
Answer:
d.
Step-by-step explanation:
What is
The equation of the line that passes through the points (5,-1) and (4,-5)
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have two points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4[/tex]
Thus, the equation is of the form:
[tex]y = 4x + b[/tex]
We substitute one of the points and find b:
[tex](x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21[/tex]
Finally, the equation is:
[tex]y = 4x-21[/tex]
Answer:
[tex]y = 4x-21[/tex]
5. Describe the pattern below.
9, 12, 15, 18, 21, 24
Answer:
The numbers increase by 3
Step-by-step explanation:
The difference between all the numbers in the sequence have a gap of 3
9 and 12 --gap of 3
12 and 15--gap of 3
18 and 21--gap of 3
21 and 24--gap of 3
Answer
y=3+ before
Step-by-step explanation:
you add 3 to every number
A pool gained 10 gallons of water on Friday due to rain. How could the owner of the pool bring the water level back to its previous level? Select all that apply.
A) Let her kids play in the pool and splash out 10 gallons
B) Let 10 gallons of water evaporate
C) increases the amount of water by 10 gallons due to rain
D) add 10 gallons of water with hose
E) drain 10 gallons of water from the pool
F) fill 10 old milk gallons with water and dump them into the pool
Answer:
A) B) E)
Step-by-step explanation:
I had this question on one of my tests and I got it right :)
Mary had back surgery and was given a prescription with instructions to take 4 tablets twice a day for pain. How many tablets will Mary take in 7 days
Answer:
56
Step-by-step explanation:
4 x 2 = 8
8 x 7 = 56
Answer = 56
The shorter leg of a right triangle is 6 feet shorter than the longer leg. The hypotenuse is 6 feet longer than the longer leg. Find the side lengths of the triangle.
The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Step-by-step explanation:
Let,
Longer leg = a = x
Shorter leg = b = x - 6
Hypotenuse = c = x + 6
As the triangle is right angles, therefore, using pythagoras theorem;
[tex]a^2+b^2=c^2\\(x)^2+(x-6)^2=(x+6)^2\\x^2+(x^2-12x+36)=x^2+12x+36\\x^2+x^2-12x+36=x^2+12x+36\\ 2x^2-12x+36=x^2+12x+36[/tex]
Adding (-x² - 12x-36) on both sides
[tex]2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\\x^2-24x=0[/tex]
Taking x common;
[tex]x(x-24)=0\\[/tex]
Either,
x=0
or,
x-24 = 0 => x=24
As length cannot be 0 therefore,
Longer leg = x = 24 feet
Shorter leg = x-6 = 24-6 = 18 feet
Hypotenuse = x+6 = 24+6 = 30 feet.
The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Keywords: triangle, addition
Learn more about triangles at:
brainly.com/question/2927458brainly.com/question/2959656#LearnwithBrainly