Graph the function h(x) = -2x– 3.
Answers
Answer:
look below
Step-by-step explanation:
To graph the function h(x) = -2x - 3, we can plot points on a coordinate plane using the equation and then connect the points to form the graph.
To find the points, we can choose different values of x and substitute them into the equation to calculate the corresponding values of h(x). Let's select a few values for x:
When x = -2:
h(-2) = -2(-2) - 3 = 4 - 3 = 1
So we have the point (-2, 1).
When x = 0:
h(0) = -2(0) - 3 = 0 - 3 = -3
So we have the point (0, -3).
When x = 2:
h(2) = -2(2) - 3 = -4 - 3 = -7
So we have the point (2, -7).
Now, we can plot these points on a coordinate plane and connect them to form the graph of the function h(x) = -2x - 3.
The graph will show a straight line that passes through the points (-2, 1), (0, -3), and (2, -7). The line will have a negative slope of -2, meaning it slopes downward from left to right.
Here's a rough representation of the graph:
|
|
-7 | .
|
-3 |
| .
1 |
|____________________
-2 0 2
Please note that this graph is just an approximation, and for a more accurate graph, you may use graphing software or a graphing calculator.
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Related Questions
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
Answers
9514 1404 393
Answer:
opposite: 4.88adjacent: 14.18Step-by-step explanation:
SOH CAH TOA is a mnemonic intended to remind you of the relevant trig relations.
Sin = Opposite/Hypotenuse ⇒ opposite = 15×sin(19°) ≈ 4.88 units
Cos = Adjacent/Hypotenuse ⇒ adjacent = 15×cos(19°) ≈ 14.18 units
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
relative extrema of f(x)=(x+3)/(x-2)
Answers
Answer:
[tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] has no relative extrema when the domain is [tex]\mathbb{R} \backslash \lbrace 2 \rbrace[/tex] (the set of all real numbers other than [tex]2[/tex].)
Step-by-step explanation:
Assume that the domain of [tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] is [tex]\mathbb{R} \backslash \lbrace 2 \rbrace[/tex] (the set of all real numbers other than [tex]2[/tex].)
Let [tex]f^{\prime}(x)[/tex] and [tex]f^{\prime\prime}(x)[/tex] denote the first and second derivative of this function at [tex]x[/tex].
Since this domain is an open interval, [tex]x = a[/tex] is a relative extremum of this function if and only if [tex]f^{\prime}(a) = 0[/tex] and [tex]f^{\prime\prime}(a) \ne 0[/tex].
Hence, if it could be shown that [tex]f^{\prime}(x) \ne 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex], one could conclude that it is impossible for [tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] to have any relative extrema over this domain- regardless of the value of [tex]f^{\prime\prime}(x)[/tex].
[tex]\displaystyle f(x) = \frac{x + 3}{x - 2} = (x + 3) \, (x - 2)^{-1}[/tex].
Apply the product rule and the power rule to find [tex]f^{\prime}(x)[/tex].
[tex]\begin{aligned}f^{\prime}(x) &= \frac{d}{dx} \left[ (x + 3) \, (x - 2)^{-1}\right] \\ &= \left(\frac{d}{dx}\, [(x + 3)]\right)\, (x - 2)^{-1} \\ &\quad\quad (x + 3)\, \left(\frac{d}{dx}\, [(x - 2)^{-1}]\right) \\ &= (x - 2)^{-1} \\ &\quad\quad+ (x + 3) \, \left[(-1)\, (x - 2)^{-2}\, \left(\frac{d}{dx}\, [(x - 2)]\right) \right] \\ &= \frac{1}{x - 2} + \frac{-(x+ 3)}{(x - 2)^{2}} \\ &= \frac{(x - 2) - (x + 3)}{(x - 2)^{2}} = \frac{-5}{(x - 2)^{2}}\end{aligned}[/tex].
In other words, [tex]\displaystyle f^{\prime}(x) = \frac{-5}{(x - 2)^{2}}[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex].
Since the numerator of this fraction is a non-zero constant, [tex]f^{\prime}(x) \ne 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex]. (To be precise, [tex]f^{\prime}(x) < 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace\![/tex].)
Hence, regardless of the value of [tex]f^{\prime\prime}(x)[/tex], the function [tex]f(x)[/tex] would have no relative extrema over the domain [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex].
A pizza is to be cut into fifths. Each of these fifths is to be cut into thirds. What fraction of the pizza is each of the final pieces?
Answers
3/5
Step-by-step explanation:
If a pizza was able to cut into fifths
each piece would count as 1/5
and for fifths to be cut into thirds it would be 1/15s
1/5 divided by 1/3 = 3/5
Hope this helps
Deandre can paint a small room in 6 hours. Deandre and Casey together can paint the same room in 4 hours. How long would it take for Casey to paint the room alone? Express your answer as a decimal. If necessary, round to the nearest tenth of hour.
Answers
Answer:
Step-by-step explanation:
If D can paint the room in 6 hours, in 1 hour she gets [tex]\frac{1}{6}[/tex] of the room painted;
If C can paint the room in x hours, in 1 hour she gets [tex]\frac{1}{x}[/tex] of the room painted.
It takes 4 hours to paint it together. Setting up the classic work equation gives us
[tex]\frac{1}{6}+\frac{1}{x}=\frac{1}{4}[/tex] and we need to solve for x. Multiply everything through by the LCM which is 12x:
[tex]12x(\frac{1}{6}+\frac{1}{x}=\frac{1}{4})[/tex] making our equation simplify to
2x + 12 = 3x and solve for x:
12 = x
C can paint the room alone in 12 hours.
2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is
10x + 4y - 18. Determine the length of the third side. Explain how you found your answer. (4 marks)
Answers
9514 1404 393
Answer:
2x +2y -8
Step-by-step explanation:
If the equal sides are 'a' and the third side is 'b', then the perimeter is ...
P = a +a +b = 2a +b
The length of the third side is then ...
b = P -2a . . . . . . subtract 2a from both sides
Substituting the given expressions, we find ...
b = (10x +4y -18) -2(4x +y -5)
b = 10x +4y -18 -8x -2y +10
b = 2x +2y -8 . . . . the length of the third side
The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath today
is 1/5. What is the probability I will take a bubble bath today, given that I took a nap?
Answers
Use Bayes Theorem to compute that probability. I will denote bath as [tex]B[/tex] and nap as [tex]N[/tex], the probability will be denoted as [tex]P(B)[/tex] or [tex]P(N)[/tex].
By Bayes Theorem
[tex]P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}[/tex]
Which reads,
"What is the probability of [tex]B[/tex] given [tex]N[/tex]".
We know that [tex]P(N\mid B)[/tex] is 1 because we already took a bath. So the formula simplifies to,
[tex]P(B\mid N)=\frac{P(B)}{P(N)}[/tex]
Now insert the data,
[tex]P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}[/tex]
So the probability that you will take a bath is [tex]0.25[/tex] after you have taken a nap.
Hope this helps. :)
Which of the following equations expresses the relationship between x and y in the table below ?
Answers
explanation : if you substitute the x in the equation for 0 and the y for 5 then solve/simplify. if you’re still not sure you can try the next one and substitute x for 2 and y for 11. you’ll see that y and x will equal each other. hope this helps:)
Answer:
y = 3x + 5
Step-by-step explanation:
just by going through the options and plugging in values from the chart, you can guess and check
y = 3x + 5 is the only answer that works
5 = 0 + 5
11 = 6 + 5
23 = 18 + 5
etc.
hope this helps!
Expand -11(5-p) can someone answer that please
Answers
Answer:
-55 +11p
Step-by-step explanation:
-11(5-p)
Distribute
-11*5 -11*(-p)
-55 +11p
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98 6°F Among other data, the researchers obtained the body temperatures of 109 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals is less than 98.6°F.
Required:
a. Determine the null hypothesis
b. Determine the alternative hypothesis
Answers
Answer:
H0 : μ ≥ 98.6
H1 : μ < 98.6
Step-by-step explanation:
The population mean temperature, μ = 98.6
The null hypothesis takes up the value of the population mean temperature as the initial truth ;
The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.
The hypothesis ;
Null hypothesis, H0 : μ ≥ 98.6
Alternative hypothesis ; H1 : μ < 98.6
2 angles in a triangle are 82 and 76. What is the measure of the 3rd angle.
A. 38
B. 22
C. 82
D. 76
Answers
Answer:
22
Step-by-step explanation:
The sum of the angles in a triangle are 180
Let the third angle be x
82+76+x = 180
158 +x = 180
x = 180-158
x =22
Now keep the,
Third unknown angle as y.
The formula we use,
→ Sum of all angles of triangle = 180°
Let's solve for y,
→ y + 82 + 76 = 180°
→ y + 158 = 180°
→ y = 180 - 158
→ [y = 22°]
Thus, option (B) is the answer.
If f(x) = x³ - 2, find f(3)
Answers
Answer:
25
Step-by-step explanation:
Assuming the equation is f(x) = x³ - 2
Plug in 3 for x
f(3) = 3³-2
= 27-2
=25
Answer:
25!
I hope it's helpful
Two camp counselors take 5 kids to the movies and sit in a row of 7 seats. if the counselors must sit in consecutive seats (in either order), how many seating arrangements are possible?
Answers
Answer:
the total number of arrangements possible is 1,440 ways
Step-by-step explanation:
Given;
total number of kids = 5
total number of counselors, = 2
Since the counselors must sit together in any order, first treat them as a single option. This gives 6! possible arrangements for all the participants.
Also, If they can sit in any order, then the total possible arrangements = 2(6!)
= 2( 6 x 5 x 4 x 3 x 2 x 1)
= 1,440 ways
Therefore, the total number of arrangements possible is 1,440 ways
Seating arrangement is unique way in which people can sit. The number of seating arrangements possible in this case is 2520
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
How to find the number of seating arrangements?In such situations, we need to model the situation with the view point which can be evaluated mathematically.
For give case, we can see that there are in total 7 seats. And 5 kids are to sit on them, with 2 camp counselors.
So 7 people have to sit on 7 seats.
But it is given that two counselors must sit together.
Now firstly, two counselors can choose 2 seats out of 7 seats in [tex]^7C_2 = \dfrac{7 \times 6}{2 \times 1} = 21[/tex] ways.
Then , in the rest of the 5 seats, 5 kids can arrange themselves in 5! ways(using permutations).
We have:
[tex]n! = n \times (n-1) \times (n-2) \times ... \times 2 \times 1\\\\5! =5\times 4\times 3\times 2\times 1 = 120[/tex]
Since each of this 120 arrangement is for each of 21 ways of counselors sitting, thus, there are 120 times 21 ways of those 7 people to sit (using rule of product), or total [tex]120 \times 21 = 2520[/tex]
Thus,
The number of seating arrangements possible in this case is 2520
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1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)
Answers
Answer:
0.6826 = 68.26% probability that you have values in this interval.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
X~N(8, 1.5)
This means that [tex]\mu = 8, \sigma = 1.5[/tex]
What is the probability that you have values between (6.5, 9.5)?
This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So
X = 9.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 8}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 6.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.5 - 8}{1.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability that you have values in this interval.
A test is divided into 4 sets of problems with the same number pf problems in each set. Alice correctly solves 35 problems. How many problems are on the test if Alice solved more than 60 percent of all the problems, but less than 65 percent of all problems? Give all possible answers.
Answers
Answer:
54, 55, 56, 57, 58
Step-by-step explanation:
Answer:
56 problems
Step-by-step explanation:
Set up an equation.
[tex]\frac{3}{5}x<35<\frac{13}{20}x[/tex]
Why do we do this? We are told that she solved MORE than 60%, or [tex]\frac{3}{5}[/tex], and LESS than 65%, or [tex]\frac{13}{20}[/tex]. Therefore, if we set the TOTAL number of problems to x, we have an equation we can solve.
[tex]\frac{3}{5}x<35<\frac{13}{20}x\\[/tex]
Multiply all parts of the inequality by 20 to get rid of the denominators.
[tex]20*\frac{3}{5}x<20*35<20*\frac{13}{20}x\\ \\12x<700<13x[/tex]
Now we can solve TWO individual inequalities to isolate the x variable.
[tex]12x<700\\x<\frac{700}{12}\\x < 175/3\\x<58[/tex]
We can approximate 175/3 to about 58 (rounding down). We will sometimes round down when we have to deal with whole numbers.
The second inequality is as follows.
[tex]13x>700\\x>700/13\\x>53[/tex]
Therefore, we can combine the two inequalities.
[tex]53<x<58[/tex]
There were in between 53 and 58 questions. Since the number of questions must be a whole number, there can be 54, 55, 56, 57, OR 58. Why does 58 also work? When you plug 58 back into the original equation, you get that it STILL works. This is due to the fact that inaccuracies in computations allow you to round UP.
However, the last thing to keep in mind is that there are four sections with an equal number of questions. Meaning, the final answer has to be a multiple of four. The only multiple of 4 is 56; therefore, the final answer is 56.
the following 3 shapes are made up of square, circles, and semi circles. Find the Area and perimeter of the shaded area. Write your answer as a completely simplified exact value in terms of pi
Answers
Answer:
Perimeter = 18 + 9pi
Area = 81 - 20.25*pi
Step-by-step explanation:
Perimeter = 9 + 9 + 2(2 pi r)/2 The twos cancel out.
Perimeter = 18 + 9*pi
Area of the square = 9 * 9 = 81 cm^2
Area of the 2 semicircles = 2 * pi * r^2/2
r = d/2
d = 9
r = 9/2 = 4.5
Area of the 2 semicircles = 2 (pi * 4.5^2)/2
Area of the 2 semicircles = 20.25 pi
Area of the blue figure = 81 - 20.25 pi
work out the surface area of this solid quarter cylinder in terms of pi. r 10cm.h 16
Answers
9514 1404 393
Answer:
(320 +130π) cm²
Step-by-step explanation:
The perimeter of the base will be the sum of two radii and the arc length of a quarter circle:
P = 2r +r(π/2) = r(2+π/2)
For a radius of 10 cm, the perimeter of the base is ...
P = (10 cm)(2+π/2) = (20+5π) cm
The lateral area of the quarter-cylinder is the product of this perimeter and the height:
LA = Ph = ((20 +5π) cm)(16 cm) = (320 +80π) cm²
__
The total base area is the area of a half-circle of radius 10 cm, so is ...
BA = 1/2πr² = (1/2)π(10 cm)² = 50π cm²
The total surface area is the sum of the base area and the lateral area:
SA = BA +LA = (50π +(320 +80π)) cm² = (320 +130π) cm²
Nicole was shopping at a local department store and had a budget of $60. She was
buying shorts (s) priced at $10 and t-shirts (t) priced at $8. She was heading to the
checkout stand when she saw a sign that said all t-shirts are 40% off. Write and simplify
an equation that Nicole could use to find the possible combinations of shorts and t-shirts
she could buy for $60.
Answers
Answe YEAH BOIIIIII!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter. To enter a−−√, type sqrt(a).
Part c: Is it possible for the company to make a profit of $15,000?
Answers
Answer:
The profit is maximum when x = 40.
Step-by-step explanation:
Cost function, C = 40 x + 300
Revenue function, R = 80 x - 0.5 x^2
The profit function is
[tex]P = R - C\\\\P = 80 x - 0.5 x^2 - 40 x - 300\\\\P = - 0.5 x^2 + 40 x - 300\\\\\frac{dP}{dx} = - x + 40\\\\So, \frac{dP}{dx} = 0\\\\-x + 40 = 0 \\\\x = 40[/tex]
So, the profit is maximum when x = 40 .
leave your answer in simplified radical form.
Answers
Answer:
The .jpeg file is the answer. Others are formulas that I use to solve.
How to divide 6,558 by 4 in long division
Answers
This is the solution to your question.
3|3x+4|-7=5 please help
Answers
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
[tex]3 |3x + 4| - 7 = 5[/tex]
Add 7[tex]3 |3x + 4 | = 12[/tex]
Divide by 3.[tex] |3x + 4| = 4[/tex]
Remove the absolute value signs and left with:[tex]3x + 4 = 4[/tex]
Subtract[tex]3x = 0[/tex]
[tex]x = 0[/tex]
SOMEONE HELP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Answers
cto cto cto cto cto cto cto cto cto cto
In the diagram attached, ΔABC has coordinates A(1,1), B(4,1), and C(4,5).
Given the function rule
f(x, y) → (x − 5, −y − 2)
Describe the transformation as completely as possible.
The diagram is attached-- Thanks in advance!
(No this is not homework, I was using a study guide I found online to study for a test.)
Answers
Answer:
Step-by-step explanation:
ΔABC has the vertices as A(1, 1), B(4, 1) and C(4, 5).
Rule for the transformation has been given as,
f(x, y) → (x - 5, -y - 2)
By this rule vertices of the transformed image will be,
A(1, 1) → A'(1 - 5, -1 - 2)
→ A'(-4, -3)
B(4, 1) → B'(4 - 5, -1 - 2)
→ B'(-1, -3)
C(4, 5) → C'(4 - 5, -5 - 2)
→ C'(-1, -7)
Dodi bicycles 14mph with no wind. Against the wind, Dodi bikes 10mi in the same time it takes to bike 20mi with the wind. What is the speed of the wind?
Answers
Answer:
4.67 mph
Step-by-step explanation:
Speed with no wind = 14 mph
Let wind speed = w mph
Thus;
Speed with wind = 14 + w
Speed against the wind = 14 - w
Now, we are told that against the wind he bikes 10 miles.
Thus, from; time = distance/speed, we have;
Time = 10/(14 - w)
Also, we are told he biked 20 miles with the wind. Thus;
Time = 20/(14 + w)
We are told the times he used in both cases are the same.
Thus;
10/(14 - w) = 20/(14 + w)
Divide both sides by 10 to get;
1/(14 - w) = 2/(14 + w)
Cross multiply to get:
1(14 + w) = 2(14 - w)
14 + w = 28 - 2w
w + 2w = 28 - 14
3w = 14
w = 14/3
w = 4.67 mph
I need help with this
Answers
Answer:
C
Step-by-step explanation:
In the graph given, we can expect the x axis to be horizontal and the y axis to be vertical. This means that the arm span represents y and the height represents x.
Therefore, if a girl on her team is 63 inches tall, we can say that y=x+2, and since height is x, y = 63 + 2 = 65
Integration 4t√t+adt
Answers
Answer:
Step-by-step explanation:
Integration (4t√t+a)dt
[tex]\int \left ( 4 t\sqrt t +a \right )dt\\\\=\int\left ( 4 t^{(\frac{3}{2})} +a\right ) dt\\\\= 4\times 2\times \frac{t^{\frac{5}{2}}}{5} + a t\\\\= 8 \frac{t^{\frac{5}{2}}}{5} + a t[/tex]
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.)
27,-9 ,3 ,-1 ,___
Answers
Divide by - 3
Step-by-step explanation:
The given list of numbers isn’t provided but the pattern will be divided by - 3
Which sets of values belong to the domain and range of a relation?
Answers
Answer:
Domain: input values, independent variables
Range: output vales, dependent variables
Step-by-step explanation:
Think of it like a graph: the domain are the x-values and the range is the y-values. if you're doing a problem with time, the time will go on the x-axis and cannot be influenced by the y-values, but the y-vales are depending on what the x-values are (independent/dependent). for the input/output, usually when solving equations on a graph, you plug in the x-value and find the y-value. you're INPUTTING the x-value to receive the OUPUT.
Domain = set of allowed inputs
The input x is the independent variable as it can do whatever it wants without relying on y.
-------------------------
Range = set of possible outputs
The output is the dependent variable. It depends on what the input x is. Often, we make y the output dependent variable.
-------------------------
For example, with y = 2x+5, we can plug in anything we want for x (it doesn't need to look to y for guidance or anything). Once we pick something for x, it will directly determine what y is.
Let's say we picked x = 10. That would mean y = 2x+5 = 2*10+5 = 25. The input x = 10 in the domain leads to y = 25 in the range. We see that the output y = 25 depends entirely on the independent input x = 10.
uppose cattle in a large herd have a mean weight of 1158lbs and a standard deviation of 92lbs. What is the probability that the mean weight of the sample of cows would differ from the population mean by less than 12lbs if 55 cows are sampled at random from the herd
Answers
Answer:
Hence the probability that the mean weight of the sample of 55 cows would differ from the population mean by less than 12 lbs is 0.66545.
Step-by-step explanation:
Work out the length x. 14 cm 7 cm Х
Answers
Answer:
If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.
Step-by-step explanation:
Area = length * width
Area = 14 cm * 7 cm
Area = 98 cm
