The answer after simplifying the expression, [tex]x^{-10} *x^{6}[/tex], will be [tex]1/x^{4}[/tex].
According to the question,
We have the following expression:
[tex]x^{-10} *x^{6}[/tex]
Now, we know that if two numbers are being multiplied with the same base but different powers then their powers are added.
(More to know: if the numbers are in division with the same base but different powers then their powers are subtracted.)
So, we have:
[tex]x^{-10+6}[/tex]
[tex]x^{-4}[/tex]
Now, we know that if powers are in negative then the number can be inverted to make the power positive (because it is given that the answer should have only positive exponents).
[tex]1/x^{4}[/tex]
Hence, the value after solving the expression is [tex]1/x^{4}[/tex].
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What type of transformation is this? Be specific
A circle passes through the points (3, 2) and (7, 2) and has radius 2√2. Find the two possible equations for this circle.
Answer:
(x-5)²+y² = 8(x-5)²+(y-4)² = 8Step-by-step explanation:
radius, r = 2√2
let the center be A(a, b):
The distance from the center to any of the 2 points is r.
So for (7, 2):
it satisfies the equation:
(x-a)²+(y-b)² = r²
Substituting x and y:
(7-a)²+(2-b)² = (2√2)²
squaring both sides:
(7-a)² + (2-b)² = 8
a² +b² - 14a -4b + 49+ 4= 8
a² +b² - 14a -4b + 45= 0 (Eqn 1)
For (3, 2):
it also satisfies the equation:
(x-a)²+(y-b)² = r²
Substituting x and y:
(3-a)²+(2-b)² = (2√2)²
squaring both sides:
(3-a)² + (2-b)² = 8
a² +b² - 6a -4b + 9+ 4= 8
a² +b² - 6a -4b + 5= 0 (Eqn 2)
We can now proceed by elimination:
(Eqn 2) - (Eqn 1):
(a² +b² - 6a -4b + 5) - (a² +b² - 14a -4b + 45) = 0
- 6a - -14a+ 5 - 45 = 0
8a - 40 = 0
8a = 40
a = 40/8
a = 5Putting a back into (Eqn 2):
a² +b² - 6a -4b + 5= 0
5² +b² - 6(5) -4b + 5= 0
25 +b² - 30 -4b + 5= 0
b² -4b = 0
b(b -4) = 0
Values of b:
b = 0 and b = 4POSSIBLE EQUATIONS OF CIRCLE:
Since we have 2 values of b, we have 2 possible centers:
(5, 0) and (5, 4)
Putting the centers into the standard equation of the circle above, we obtain:
(x-5)²+y² = 8 and(x-5)²+(y-4)² = 8PLEASE VOTE AS BRAINLIEST.
BLAISE M.
A fish tank sprung a leak and loses 45% of its water.
There is now 363 litres of water in the fish tank.
How much water was in the fish tank before the leak?
Answer:
689.7
Step-by-step explanation:
Are null and alternative hypotheses statements about samples, about populations, or does it depend on the situation? explain.
The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
stuck on this math question for years,! if anyone helps 12 points !!!
Answer:
3
Step-by-step explanation:
There are 4.5 diamonds, which represent 9 hours in total.
This corresponds to 9/3 = 3 circles.
Answer:
3 circles
Step-by-step explanation:
For the pig, it's 4.5 squares. Each square is two hours, and 4.5*2 is 9. Each circle is 3 hours, and 9 divided by 3 is 3. Therefore, the answer is 3 circles.
if the scale in the drawing is 1/4inch=3miles, what is the distance, in miles between Hawthorne an Doylestown?(help)
We will investigate how to use ratios to determine the actual distance between cities as per defined scale.
We are given a scale conversion ( ratio ) at which distances are scaled down:
[tex]\begin{gathered} \text{Scale : Actual} \\ \frac{3}{4}\text{ in : }3\text{ miles} \end{gathered}[/tex]We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.
[tex]\text{Scale distance = 1.75 in}[/tex]Now utilize the scale conversion ratio to determine the actual distance:
[tex]\begin{gathered} \text{Scale : Actual } \\ \frac{3}{4}in\text{ : 3 miles} \\ \\ 1.75\text{ in: x} \\ ======= \\ \\ \frac{3}{4}\cdot x\text{ = 3}\cdot1.75 \\ \\ x\text{ = }\frac{3\cdot1.75\cdot4}{3} \\ \\ x\text{ = 7 miles} \end{gathered}[/tex]Therefore, the distance between Hawthorne and Doylestown is:
[tex]7\text{ miles}[/tex]
I need some explanation on how to do piece wise functions? Where do I even start with this equation, can you explain this step by step? Including breaking down the graphing of absolute functions?
A piecewise function is basically a function that behaves differently at different domain intervals.
The given piecewise function is
[tex]\begin{cases}2x\quad \quad \quad \quad \quad \quad x\le3 \\ \frac{1}{3}x^2-2x+9\quad x>3\end{cases}[/tex]As you can see, the function has a different expression for the interval x is less than or equal to 3 and a different expression for the interval x is greater than 3.
The easiest way to determine which graph corresponds to the given piecewise function is to evaluate the piecewise function at different values of x and graph it.
Evaluate the piecewise function for the interval x is less than or equal to 3.
[tex]\begin{gathered} 2x \\ x=1\rightarrow2(1)=2 \\ x=2\rightarrow2(2)=4 \\ x=3\rightarrow2(3)=6 \end{gathered}[/tex]Evaluate the piecewise function for the interval x is greater than 3.
[tex]\begin{gathered} \frac{1}{3}x^2-2x+9 \\ x=4\rightarrow\frac{1}{3}(4)^2-2(4)+9=6.33 \\ x=6\rightarrow\frac{1}{3}(6)^2-2(6)+9=9 \\ x=8\rightarrow\frac{1}{3}(8)^2-2(8)+9=14.33 \end{gathered}[/tex]Now, let us graph these points
As you can see from the graph, it matches with the graph of the 2nd option.
Therefore, the correct graph of the given piecewise function is the 2nd graph.
Devon is saving to buy a telescope. If he saves 7$ a week for 14 weeks which equation can be used to fund the total cost
Answer: Multiply 7 and 14
Step-by-step explanation: to find the answer you multiply 7 and 14 you get 98$ which is the total cost pls consider making me brainliest if im correct i really hope i am :)) make sure to tell me if im wrong
Answer:
Step-by-step explanation:
Step 1: Assume your variables
We can see that the money is being saved on a weekly basis.
So, let's assume the number of weeks for which the money is being saved to be the variable: [tex]x[/tex]
And let's consider the total cost after [tex]x[/tex] weeks to be: [tex]y[/tex]
Step 2: Manipulate the variables according to the information given
$7 is being saved each week.
So, in one week, [tex]\$7[/tex] is saved.
In two weeks, [tex]\$(7\times 2)[/tex] is saved.
So, in [tex]x[/tex] weeks, [tex]\$(7\times x)[/tex] is saved.
Step 3: Create the equation
In words, the equation will be as such:
Total cost after [tex]x[/tex] weeks = Amount saved in [tex]x[/tex] weeks
Upon representing this mathematically, we get:
[tex]y=7\times x\\y=7x[/tex]
The equation [tex]y=7x[/tex] can be used to find the total cost.
Seth buys last year's best-selling novel, in hardcover, for $21.75. This is with a 25% discount from the original price. What was the original price of the novel?
Price after the 25% discount: $21.75
This means that $21.75 is 75% of the original price. If x is the original price, then:
[tex]\begin{gathered} 75\text{\% of }x=21.75 \\ \frac{75}{100}\cdot x=21.75 \\ x=\frac{100\cdot21.75}{75} \\ \Rightarrow x=\text{ \$}29 \end{gathered}[/tex]2. How do you determine the equation of the asymptote of an exponential function?
The general form of exponential function is given below:
[tex]\begin{gathered} y=a.b^x+c \\ \text{When a.b}^x=0,\text{ the asymptote of the function becomes } \\ y\text{ = c , which is, y-intercept} \\ \text{But where c=0, the asymptote is the line y = 0} \end{gathered}[/tex]4x - 2y = 5 if the range is {-5,-3,0,7}
The domain of the given function given range is {1.25, -0.25, 1.25, 4.75}
Domain and range of a functionThe range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f(x) make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of value.
Given the range of the function as {-5, -3, 0, 7}
Determine the domain from the function 4x - 2y = 5
4x - 2y = 5
4x - 2(-5) =5
4x + 10 = 5
4x = 5
x = 5/4 = 1.25
If y = -3
4x - 2y = 5
4x - 2(-3) =5
4x + 6 = 5
4x = -1
x = -1/4 = -0.25
If y = 0
4x - 2(0) =5
4x - 0 = 5
4x = 5
x = 5/4 = 1.25
If x = 7;
4x - 2y = 5
4x - 2(7) =5
4x - 14 = 5
4x = 19
x = 19/4 = 4.75
Therefore the equivalent domain of the function is {1.25, -0.25, 1.25, 4.75}
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3,4,16/3 find the 10 term
The 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The [tex]n^{th}[/tex] term of the Geometric Sequence is
given by the formula
aₙ = a*rⁿ⁻¹
where , a is the first term , r is the common ratio .
in the question ,
the sequence is given as {3,4,16/3....}
here we need to find the common ratio(r) ,
we know , r = a₂/a₁
So , r= 4/3 .
Since we need to find the 10th term , so n=10 .
Substituting the values in the nth term formula , we get
a₁₀ = (3)*(4/3)¹⁰⁻¹
= 3* (4/3)⁹
= 4⁹/3⁸
= 262144/6561
The 10th term is 262144/6561.
Therefore , the 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The given question is incomplete , the complete question is
Find the 10th term of the Sequence {3,4,16/3....} ?
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Math
Simplify each expression. show your solution
To simplify a phrase, create an equivalent expression without any terms that are identical.The expression will then be rewritten using the fewest terms feasible.
What is an equation to simplify?
A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants together. Add numbers
2+1
= 3
2³ = 8
first one 8
2. x²× x°
= x ²+°
3.a6_a4
= a2
4. x×x×y×y
=x²y²
5 x²×x×y×y²
= x³y³
6.(mn)5
= m5N5
7 (abc)²
= a²b²c²
8.(p²q)³
p6q3
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write the slope-intercept form of the equation for each line
bro i need sm to help me quick
Answer:
y = x + 7
Step-by-step explanation:
The line rises at a slope of 1 and intercepts the y-axis at 7.
Consider the line whose equation is y=-1/2x+3
any line that is perpendicular to this line is
Answer:
positive
Step-by-step explanation:
for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)
y = -1/2x+3 = Line A
y = 2x+3 = PERPENDICULAR to Line A
24. OPEN-ENDED Complete the table so that when t is the
independent variable, the relation is a function, and when
t is the dependent variable, the relation is not a function.
The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.
The independent variable is the input, while the dependent variable is the output.
Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.
However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
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Can someone please answer this!
Answer: see the attachment
Step-by-step explanation:
h = # of hours worked
{10h and {15(h-40)+400 are both functions i.e. simplified equations
simply fit the # of hours worked in each equation to get the values. you can also double check your work or to understand better
to do so, take (h) # of hours worked and multiply by the pay rate. This gives the total pay over the work week. then take the extra hours beyond the 40. ie 7. if $10 is the pay rate per hour and OT is 1.5xnormal pay then 10x1.5=15. Multiply 15x7 and you get 105 then add to 400 and you get $505. 400 comes from 10(40).
part b and c is just setting the functions.
so instead of 40 hrs per week your full-time rate is now 38 and anything beyond would be counted as overtime. so a normal work week of 38 hrs x the $10/hr would equate to $380 for the week.
part c, if the hours per week were kept normal at 40hrs/week but the pay rate is increased this then changes 10 = h to 12 = h. if 12=h and you work 40hrs/week, then 12(40)=$480 for the normal work week. also this changes your OT pay from 10(1.5)=15 to 12(1.5)=$18
Explain what is 20 divided by 5/3 show work
Answer:
12
Step-by-step explanation:
Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes. If she continues at the same rate, how many hours will it take for Selena to make 264 more pancakes?
Selena needs 4 more hours to prepare 264 more pancakes.
What is unitary method?Unitary method is a process of finding the value of a single unit, and use this value to find the value of the required number of units.
Given is Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes.
We have -
The rate at which Selena is making pancakes = 132 pancakes in 2 hours.
Number of pancakes left to be made = 264
Now, in 2 hrs she makes 132 pancakes
Then, in 1 hr she will make (132/2) or 66 pancakes.
Now, she makes 66 pancakes in 1 hour.
So, she will make 1 pancake in (1/66) hours
Therefore, she will make 264 pancakes in (264/66) or 4 hours.
Therefore, she will need 4 more hours to prepare 264 more pancakes.
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simplify 4√(384.5)³ using logarithm
After simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. When measuring the relative change of a value rather than its absolute difference, logarithmic scales are helpful. Moreover, logarithmic scales are used to compress large-scale scientific data because the logarithmic function log(x) grows very slowly for large x. Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular types of logarithms.So, 4√(384.5)³ using logarithm:
(Refer to the image attached below for calculations.)= 30158.13684Therefore, after simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
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In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.
What is the profit from 2021? Write & solve an Algebraic Equation.
suppose that the average price for a gallon of gasoline in the united states is 3.75 and in russia it is . assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of in the united states and a standard deviation of in russia. a. what is the probability that a randomly selected gas station in the united states charges less than per gallon (to 4 decimals)? b. what percentage of the gas stations in russia charge less than per gallon (to 2 decimals)? c. what is the probability that a randomly selected gas station in russia charged more than the mean price in the united states (to 4 decimals)?
Using probability, we know that the left-tailed area exists at 17.87%.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.So, now calculate as follows:
Let the critical value be x= $ 3.5Mean µ = $ 3.73Standard deviation σ = $ 0.25Using formula:
z = (x - µ) / σSubstitute the values in the above equation, and we obtain:
= (3.5-3.73) / 0.25Simplifying the equation, we will get:
= (-0.23) / 0.25= -0.92Finally, by using a table we calculate the left-tailed area:
P(z < -0.92) = 0.17878638 = 17.87 %Therefore, using probability, we know that the left-tailed area exists at 17.87%.
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Complete question:
The average price for a gallon of gasoline in the United States is $3.73 and in Russia, it is $3.40. Assume these averages are the population means in the two countries and that the standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon?
been stuck on this for ages
A bearing is a measurement of direction that uses North as a point of reference. Your bearing is 00° if you are moving north.
The angle from north to this bearing, measured counterclockwise, is the actual bearing. Utilize the knowledge that west is 270° from the north, south is 180°, and east is 90°.
The number of degrees in the angle measured counterclockwise from the north line to the line connecting the center of the compass is the bearing of a point.
How do you determine bearing angle?
The bearing is the angle subtracted in a clockwise direction from north to west. The bearing is 270° - 17° = 253° since the angle from north to west is 270°.
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Tom’s car has 11 1/9 gallons of gas. If he uses 38 of the gas, how much gas does the car have left?
Answer: 6 [tex]\frac{17}{18}[/tex] gallons of gas left in the car
Step-by-step explanation:
Upon further clarification, this question reads "3/8 of the gas" and not "38 of the gas."
If Tom's car has 11 1/9 gallons of gas, and we want to know how much gas the car will have left if he uses 3/8 of that, we first need to find 3/8 of 11 1/9.
"Of" can usually be written as multiplication.
3/8 of 11 1/9 = 3/8 * 11 1/9 = 4 1/6
Next, we will use subtraction since he uses 4 1/6 gallons of gas.
11 1/9 - 4 1/6 = 6 17/18 gallons
HELP NEEDED FOR GEOMETRY PROOFS!!! I will give brainliest
The method used to prove the specified geometric relationship between the angles and sides of the triangles are as follows:
24. ΔDAE ≅ ΔBAC by SAS postulate, therefore
∠B ≅ ∠E CPCTC25. ΔACD ≅ ΔBCD by ASA postulate
∡A ≅ ∡B CPCTC26 ΔACD ≅ ΔBCD LH postulate.
∡A ≅ ∡B CPCTCWhat are the congruency postulates?The congruency postulates include, SSS, Side-Side-Side, AAS, Angle-Angle Side, SAS, Side-Angle-Side, HL, Hypotenuse Leg.
24. The two column proofs are presented as follows;
Statements Reasons
1. [tex]\overline{CD}[/tex] bisects [tex]\overline{BE}[/tex] 1. Given
2. [tex]\overline{BA}[/tex] = [tex]\overline{AE}[/tex] 2. Definition of bisected line
3. . [tex]\overline{BA}[/tex] ≅ [tex]\overline{AE}[/tex] 3.. Definition of congruency
4. [tex]\overline{CA}[/tex] = [tex]\overline{AD}[/tex] 4. Definition of bisection of line [tex]\overline{CD}[/tex]
5. [tex]\overline{CA}[/tex] ≅ [tex]\overline{AD}[/tex] 5. The definition of congruency
6. ∠DAE ≅ ∠BAC 6. Vertical angles theorem
7. ΔDAE ≅ ΔBAC 7. SAS congruency postulate
8. ∠B ≅ ∠E 8. CPCTC
The acronym, CPCTC represents Corresponding Parts of Congruent Triangles are Congruent
25. Statement Reasons
1. [tex]\overline{CD}[/tex] ⊥ [tex]\overline{AB}[/tex] 1. Given
2. [tex]\overline{CD}[/tex] bisects ∠ACB 2. Given
3. ∠3 = ∠4 = 90° 3. Definition of bisected lines
4. ∠1 ≅ ∠2 4. Definition of bisected angle ∡ACB
5. ΔACD ≅ ΔBCD 5. ASA congruency postulate
6. ∡A ≅ ∡B 6. CPCTC
26. Statement Reason
1. m∠1 = m∠2 = 90° 1. Given
2. ΔACD and ΔBCD are right triangles 2. Definition
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex] 3. Given
4. [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] 4. Reflexive property
5. ΔACD ≅ ΔBCD 5. LH Congruency postulate
6 ∡A ≅ ∡B 6. CPCTC
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For a particular rectangle, twice the width is 4 meters shorter than the length. The area of the rectangle is 126 square meters. What is the perimeter of the rectangle? ? meters
Let l be the length of the rectangle and w its width.
Then its area is given by:
a = l*w
Its perimeter is given by:
p = 2l + 2w
We also know that, for this specific triangle, we have:
2w = l - 4
l = 2w + 4
a = 126 m²
Applying this result in the area formula, we have:
w*l = 126
w(2w + 4) = 126
2w² +4w = 126
2w + 4w - 126 = 0
Therefore, w = 7 m and l = 2*7 + 4 = 10 m
Then, the perimeter is given by:
p = 2*18 + 2*7 = 36 + 14 = 50 m
Find the value of a. Enter a numeric answer only.
Solution
For this case we have the following, the sum of the angles needs to be 360 since we have a circumference:
10a-4 +6a-2 +8a+6=360
Regrouping we have:
10a +6a +8a -4 -2 +6= 360
24a= 360
a= 360/24= 15
12. Find the value of x.
+f
(7x+4) +(10x-11)=180 mid segment
The value of x is 11.
What is an equation?
Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.
We are given an equation (7x+4)+(10x-11)=180
We open brackets and simplify the equation by adding similar values we get
17x-7=180
17x=187
on dividing both sides by 17 we get
x=11
Hence the value of x is 11
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In the figure below, N lies between M and P.
Find the location of N so that the ratio of MN to NP is 7 to 2.
M
- 27
Location of N
N
?
X
→→
Ś
P
-9
The position of N on the line segment is at the -14 mark
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
How to determine the location of N?The complete question is added as an attachment
From the attachment, we have
The ratio is given as:
MN : NP = 7 : 2
Also, we have
Location of M = -27
Location of P = -9
The location of N is then calculated as
N = MN/(MN + NP) * (M - P)
Substitute the known values
N = 7/(7 + 2) * (-27 + 9)
Evaluate the sum
N = 7/9 * -18
Evaluate the product
N = -14
Hence, the location of point N is -14
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Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions?
Perimeter = 2 x Length + 2 x Width
Answer:
Step-by-step explanation:
Let L be the length and W the width
Perimeter of a rectangle is P = 2L + 2W
We are told that L = W + 14 (m) [the length is 14 meters more than the width]
Area of a rectangle is A = L*W
We learn that A = 96 m^2
L*W = 96
Since L = W + 14, we can substitute:
L*W = 96
(W + 14)*W = 96 m^2
W^2 + 14W = 96
W^2 + 14W - 96 = 0
The solution to W in the above equation is 5.04 m
This means L = 5.04 m + 14 m
L = 19.04 meters
Perimeter = 2W + 2L
Perimeter = 2(5.04) + 2(19.04) = 96 m^2