Finding Side Lengths in a Right Triangle
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The radioactive isotope has a final mass of 523 grams.

Herein we find the case of a radioactive isotope, whose mass is decreasing exponentially in time. Whose expression is described below:

m(x) = a · (1 - r / 100)ˣ

Where:

If we know that a = 1500, r = 10 and x = 10, then the mass of the radioactive isotope is:

m(10) = 1500 · 0.90¹⁰

m(10) = 523.018

The final mass of the radioactive isotope is equal to 523 grams.

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Answer:

thats 4th grade math... 0_0               but the answer is 414 ft².

Step-by-step explanation:

So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo

The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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Answer:

Step-by-step explanation:

4-10(9m-7)

4-90m+70

74-90m

56x+24/8

8(7x + 3)/8

7x + 3

24r + 16

8(3r + 2)

is 2m-3 same as 4(1/2m-3)

2m-3 = 2m-12

: no

-2(10-15x) same as 14x-20+16x

-20+30x = -20+30x

: yes

The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

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The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.

Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.

The total number of cards in the deck is:

Total number of cards = number of black cards + number of red cards = 33 + 77 = 110

The probability of drawing a black card is given by:

P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110

Therefore, the probability of drawing a black card is:

P(draw a black card) = 0.3 or 30%

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The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.

A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.

Let's solve each inequality separately:

4p + 1 < −11

Subtracting 1 from both sides, we get:

4p < -12

Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:

p > -3

So the solution to the first inequality is:

p > -3

Now let's look at the second inequality:

6p + 3 > 39

Subtracting 3 from both sides, we get:

6p > 36

Dividing both sides by 6, we get:

p > 6

So the solution to the second inequality is:

p > 6

Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:

p > 6 or p > -3

This can be written more simply as:

p > -3

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The number of packs of peanut m&m's did they sell that day is 378 packs.

The distance traveled by the plane is 1,008 miles.

The time taken by the plane is 7.78 hours.

Let

Number of peanut sold = x

Ratio of peanut to plain

7 : 10 = x : 540

7/10 = x/540

7 × 540 = x × 10

3,780 = 10x

divide both sides by 10

x = 3,780 / 10

x = 378

When t = 2.8 hours

d = 360t

d = 360(2.8)

d = 1,008 miles

Therefore, the time taken for the plane to fly 2800 miles is;

d = 360t

2800 = 360t

divide both sides by 360

t = 2,800/360

t = 7.78 hours

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The slope of the equation is 1/2 and the y-intercept is -5.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

Step 1:

The relationship between x and y can be expressed as:

y = (1/2)x - 5

This equation says that y is equal to half of x, with 5 subtracted from that value.

Step 2:

To graph this equation using the slope-intercept form (y = mx + b), we can identify the slope and y-intercept.

The slope of the equation is 1/2, which means that for every increase of 1 unit in x, y increases by 1/2 unit.

The y-intercept is -5, which is the point where the line crosses the y-axis.

To graph the equation, we can start by plotting the y-intercept, which is the point (0, -5).

Next, we can use the slope to find another point on the line. Since the slope is 1/2, we can move up 1 unit and right 2 units (since the slope is rise over run, or change in y over change in x). This gives us the point (2, -4).

We can now draw a line that connects these two points, which represents the relationship between x and y.

The two points are:

(0, -5)

(2, -4)

The graph of the equation is in the attached image.

Hence, The slope of the equation is 1/2 and the y-intercept is -5.

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Using curves, we can find that the value of y at the indicated point on the curve is √3.

What is the definition of curves?

A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.

Here in the question,

Given equation:

x = y² - 2

As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:

1 = y² - 2.

Adding 2 on both sides:

1 + 2 = y² - 2 + 2

⇒ 3 = y²

⇒ y = √3.

Therefore, the value of y at the indicated point on the curve is √3.

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The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.

In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.

Here we have

The table shows the age distribution of members of a gym.  

Age -            Under 21      21 -35     36 - 55   Over 55

percentage       12                42            32          14  

a) To find the probability that the selected member is 21 or more,

Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.

Probability (21 or more)

= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)

= 42% + 32% + 14%

= 88%

b) To find the probability that the selected member is 55 or less,  

Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.

Probability (55 or less)

= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)

= 12% + 42% + 32%

= 86%

c) To find the probability that the selected member is not in the 21 to 35 age group,

Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.

Probability (not in the 21 to 35 age group)

= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)

= 12% + 32% + 14%

= 58%

Therefore,

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

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a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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To find the constant k for this type of bacteria, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.

We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:

N(25) = 2 * N0

Substituting this into the formula, we get:

2 * N0 = N0 * e^(k*25)

Dividing both sides by N0 and simplifying, we get:

2 = e^(25k)

Taking the natural logarithm of both sides, we get:

ln(2) = 25k

Solving for k, we get:

k = ln(2)/25 ≈ 0.0278

Therefore, the equation for modeling the exponential growth of this type of bacteria is:

N(t) = N0 * e^(0.0278t)

*IG:whis.sama_ent

Answer:

-4 + 8 = 4

-2 + 6 = 4

-1 + 5 = 4

So the three pairs are -4 and 8; -2 and 6; and -1 and 5.

In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

The law of demand applies during online sales of shoes; that is when consumers rush to buy products at 50% discount.​

In Mathematics and Economics, the law of demand can be defined as an economic theory which states that there exist a negative relationship between the price of a product (good) and the quantity of the product (good) that is being demanded by consumers.

This ultimately implies that, holding all the other factors constant, there would be a significant decrease (fall or decline) in the demand for a product (good) and service when the price of a product (good) and service in the market increases (rises), and vice-versa in accordance with the law of demand.

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Complete Question:

The law of ___________applies during online sales of shoes; that is when consumers rush to buy products at 50% discount​

The cost of pizza with no toppings is $6. So correct option is C.

A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.

There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.

Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.

Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.

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The complete question is:

Answer:

1  17/30.

Step-by-step explanation:

you can find this out by seeing how many 30s go into 47 which is 1.

Then subtract to find how much is leftover still over 30.

47 - 30 = 17

So 1 and 17/30

Answer:The diagram shows the market demand and supply curves for the bread market. You know that there are 250 identical bakeries operating in the market

Step-by-step explanation:

The proof that AE is tangent to circle C is given below:

The angle addition postulate is a fundamental concept in geometry that states that the measure of an angle formed by two adjacent angles can be obtained by adding the measures of the two angles.

More specifically, given two adjacent angles with measures A and B, the measure of the angle formed by the two adjacent angles (denoted as AOB) can be found by adding the measures of the two angles:

A + B = AOB

This postulate is often used in geometric proofs and can be applied to any adjacent angles, including those formed by intersecting lines, parallel lines, or polygons.

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The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.

Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.

According to the given information:

A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).

To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.

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Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd