Answer:
[tex]x-8[/tex], smaller integer is 8.
Step-by-step explanation:
Given:
The product of two consecutive integers is 72.
The equation x(x+1)=72 represents the situation, where x represents the smaller integer.
Question asked:
Which equation can be factored and solved for the smaller integer ?
Solution:
[tex]x(x+1)=72\\\\ x^{2} +x=72\\ \\ By\ subtracting\ both\ sides\ by\ 72\\ \\ x^{2} +x-72=72-72\\ \\ x^{2} +x-72=0\\ \\ x^{2} +9x-8x-72=0\\ \\ Taking\ x+9\ as\ common \\ \\ x(x+9)-8(x+9)=0\\ \\ x+9=0,x-8=0\\ \\ x=-9,x=8[/tex]
[tex]x-8[/tex] can be factored and solved for the smaller integer, and that is 8.
Two consecutive integers are 8 and 9 and their product is 8 [tex]\times[/tex] 9 = 72
If 450 birds have to fit into 18 enclosures, & there are 3 enclosures in each section of the zoo, how many birds are in each section
There are 75 birds in each section
Step-by-step explanation:First, lets see how many in each enclosure so we have an amount to multiply by 3
450/18 = 25 birds per enclosure.
Now lets see how many birds would be in 3 enclosures i.e. a section
25 * 3 = 75
The fish population of a lake is decreasing each year. A study is conducted. But, unfortunately some data was lost. The researcher found in her notes that in year one the fish population was 18000 fish and in year three the fish population was 8000 fish. Assume a constant rate of decay. Find a formula F
Answer:
[tex]F(t) = 18000(0.6666)^{t}[/tex]
Step-by-step explanation:
The fish population after t years can be modeled by the following equation:
[tex]F(t) = F(0)(1-r)^{t}[/tex]
In which F(0) is the initial population and r is the constant rate of decay.
Year one the fish population was 18000
This means that [tex]F(0) = 18000[/tex]
In year three the fish population was 8000 fish.
Two years later, so [tex]F(2) = 8000[/tex]
[tex]F(t) = F(0)(1-r)^{t}[/tex]
[tex]8000 = 18000(1-r)^{2}[/tex]
[tex](1-r)^{2} = 0.4444[/tex]
[tex]\sqrt{(1-r)^{2}} = \sqrt{0.4444}[/tex]
[tex]1 - r = 0.6666[/tex]
[tex]r = 0.3334[/tex]
So
[tex]F(t) = 18000(0.6666)^{t}[/tex]
Oh freight elevator can hold a maximum weight of 3500 pounds and delivery man weighs 200 pounds is delivering curtains that each way 48 pounds he wants to know how many current you can safely put on the elevator at one time let's see represent the number of cartons write an inequality that represents the situation
Answer:
[tex]200+48n\leq 3500[/tex]
[tex]n\leq 66.7[/tex]
Step-by-step explanation:
The freight elevator can hold a maximum weight of 3500 poundsThe delivery man weighs 200 poundsEach carton weighs 48 poundsLet the number of cartons he can safely put on the elevator at one time=n
Total weight of Carton=48n
Since the weight of the man and the cartons combined must not be more than 3500 pounds,
Therefore,an inequality that represents the situation is:
[tex]200+48n\leq 3500[/tex]
We can solve for n if required
[tex]200-200+48n\leq 3500-200\\48n\leq 3200\\\text{Divide both sides by 48}\\n\leq66.7[/tex]
The delivery man can safely carry 66 Cartons.
Which expressions are equivalent to the one below click all that apply 21x/3x
After simplifying [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we find it equivalent to [tex]\(3^x\)[/tex], confirming options a, b, and f as correct.
To simplify the expression [tex]\(\frac{{21^x}}{{7^x}}\)[/tex], we can use the property of exponents which states that [tex]\(a^m/a^n = a^{m-n}\)[/tex]. Applying this property, we get:
[tex]\[\frac{{21^x}}{{7^x}} = \frac{{(7 \cdot 3)^x}}{{7^x}} = \frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\][/tex]
So, the simplified expression is [tex]\(3^x\).[/tex]
Now, let's check each option:
a. [tex]\(\frac{{7^x \cdot 3^x}}{{7^x}} = 3^x\)[/tex]. This expression is equivalent to the simplified form.
b. [tex]\((\frac{{21}}{{7}})^x = 3^x\)[/tex]. This expression is equivalent to the simplified form.
c. [tex]\(3\)[/tex]. This expression is not equivalent to the simplified form.
d. [tex]\((21 - 7)^x = 14^x\)[/tex]. This expression is not equivalent to the simplified form.
e. [tex]\(3^{x-7}\)[/tex]. This expression is not equivalent to the simplified form.
f. [tex]\(3^x\)[/tex]. This expression is equivalent to the simplified form.
Therefore, the expressions equivalent to [tex]\(\frac{{21^x}}{{7^x}}\)[/tex] are options a, b, and f.
The question probable maybe:
Given in the attachment
In one month, the median home price in the West fell from $203,400 to $192,300. Find the percent decrease.
Round your answer to the nearest tenth of a percent.
Answer:
94.5%
Step-by-step explanation:
Percent decrease can be represented as
[original price] * percentage = [new price]
When trying to find the percentage, you can manipulate the equation by dividing both sides by the original price to get:
percentage = [new price] / [original price]
In this case, this is represented by 192300/203400, or 94.5%
The median home price in the West fell from $203,400 to $192,300 then the percent decrease is 5.5%
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that In one month, the median home price in the West fell from $203,400 to $192,300.
We have to find the percent decrease.
Percent decrease =[ (difference in price)/(original price) ] ×(100)
=203,400-192,300/203,400 ×(100)
=11100/203,400 ×(100)
=5.457 %
Hence, the median home price in the West fell from $203,400 to $192,300 then the percent decrease is 5.5%
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Which graph represents the function y= 2/3x-2?
Answer:
third graph
Step-by-step explanation:
A spinner has 8 congruent sides, 1,9,5,3,2,16,11, and 8 if it spun 120 times what it's a reasonable prediction for the number of times it will land on an even number?
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
120 x 3/8 = 360/8 = 45
The answer would be 45 times.
You roll a pair of fair six-sided dice. The sample space of 36 possible outcomes is shown below. Based on this
information, answer the following questions.
What is P(A), the probability that the first die is a 5?
What is P(B), the probability that the second die is a 3?
What is P(A and B), the probability that the first die is a 5 and the second die is a 3?
What is PB
A), the conditional probability that the second die is a 3 given that the first die is a 5?
Is P(B A) = P(B)? Are the events A and B independent?
Choose all answers that apply:
The probabilities of interest when rolling a pair of fair six-sided dice are: P(A) the probability of the first die being a 5 is 1/6, P(B) the probability of the second die being a 3 is 1/6, P(A and B) the probability of both events occurring is 1/36, and P(B|A) the conditional probability of B given A is equal to P(B), indicating that events A and B are independent.
When rolling a pair of fair six-sided dice, each die is independent of the other. Therefore, the sample space consists of 6 x 6 = 36 equally likely outcomes. The probability that the first die is a 5, event A, is P(A) = 1/6 because there are 6 possible outcomes for the first die and only one of them is a 5.
The probability that the second die is a 3, event B, is also P(B) = 1/6 for the same reason as A, as there are 6 possible outcomes and only one of them is a 3. Now, the probability that the first die is a 5 and the second die is a 3, both events occurring simultaneously (A and B), is P(A and B) = P(A) times P(B) which equals 1/36.
The conditional probability that the second die is a 3 given that the first die is a 5, P(B|A), is simply the probability of B since events A and B are independent, so P(B|A) = P(B) = 1/6. This implies that knowing the outcome of the first die does not change the probability of the second die rolling a 3.
Given this independence, P(B|A) = P(B), and thus events A and B are indeed independent events.
[tex](a) \( P(A) = \frac{1}{6} \)\\(b) \( P(B) = \frac{1}{6} \)\\(c) \( P(A \text{ and } B) = \frac{1}{36} \)\\(d) \( P(B|A) = \frac{1}{6} \)\\(e) No, \( P(B|A) \neq P(B) \); events A and B are dependent.[/tex]
(a) P(A), the probability that the first die is a 5:
There are 6 outcomes where the first die is a 5.
[tex]\[ P(A) = \frac{\text{Number of outcomes where first die is a 5}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \][/tex]
(b) P(B), the probability that the second die is a 3:
There are 6 outcomes where the second die is a 3.
[tex]\[ P(B) = \frac{\text{Number of outcomes where second die is a 3}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \](c) \( P(A \text{ and } B) \), the probability that the first die is a 5 and the second die is a 3:[/tex]
There is only 1 outcome where the first die is a 5 and the second die is a 3, which is (5,3).
[tex]\[ P(A \text{ and } B) = \frac{\text{Number of outcomes where both A and B occur}}{\text{Total number of outcomes}} = \frac{1}{36} \][/tex]
(d) P(B|A) the conditional probability that the second die is a 3 given that the first die is a 5:
Given that the first die is a 5, there are 6 possible outcomes for the second die, and 1 of those outcomes is a 3 (the outcome (5,3)).
[tex]\[ P(B|A) = \frac{\text{Number of outcomes where B occurs given A}}{\text{Number of outcomes where A occurs}} = \frac{1}{6} \][/tex]
(e) [tex]\[ P(B|A) = \frac{1}{6} \neq \frac{1}{6} = P(B) \]\\Since \( P(B|A) \neq P(B) \), the events A and B are dependent, not independent.[/tex]
Destiny wants to buy a scarf for her mother.
The original price of the scarf $25.00, not including tax.
The scarf is on sale for 20% off the original price
What is the sale price of the scarf, not including tax?
$
The scarf is $20 without tax.
The scarf is 20% off of 25, 5 is 20% of 25 so all you have to do is 25 - 5 to get your answer.
25 - 5 = 20
The sale price of the scarf , not including the tax is $20.00.
What is sale price?A sale price is the discounted price at which goods or services are being sold.
Formula for finding the sale pricesale price = original price - discount price
According to the given question,
the original price of the scarf is $25.00
discount price = 20%of original price
⇒ discount price =[tex]\frac{20}{100}[/tex]×[tex]25[/tex]
⇒discount price = $5.00
Therefore,
sale price of scarf = $25.00-$5.00
Sale price of scarf = $20.00
Hence, the sale price of the scarf, not including tax is $20.00
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A high-speed bullet train accelerates and decelerates at the rate of 4 ft/s 2 . Its maximum cruising speed is 90 mi/h . (Round your answers to three decimal places.) (a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes
Answer:
22.9 miles
Step-by-step explanation:
We are given that
Acceleration=Deceleration=a=[tex]4ft/s^2[/tex]
Maximum cruising speed,v=[tex]90mi/h=90\times \frac{5280}{3600}=132ft/s[/tex]
1 hour=3600 s
1 mile=5280 feet
Time,t=15 minutes=[tex]15\times 60=900 s[/tex]
1 min=60 s
Initial speed,u=0
[tex]v=u+at[/tex]
Substitute the values
[tex]132=0+4t[/tex]
[tex]t=\frac{132}{4}=33 s[/tex]
[tex]s=u+\frac{1}{2}at^2=0+\frac{1}{2}(4)(33)^2=2178 ft[/tex]
Distance,d=[tex]speed\times time=vt=132\times 900=118800ft[/tex]
Total distance=s+d=2178+118800=120978ft
Total distance=[tex]\frac{120978}{5280}=22.9miles[/tex]
Hence, the maximum distance traveled by train =22.9 miles
The box plots show Rene’s scores in Spanish and in French. Spanish 2 box plots. The number line goes from 50 to 100. For Spanish, the whiskers range from 55 to 95, and the box ranges from 60 to 85. A line divides the box at 70. For French, the whiskers range from 55 to 90, and the box ranges from 65 to 80. A line divides the box at 75. French Which table correctly compares the measures of center and the measures of variability?
Answer:
The box plot below shows the total amount of time, in minutes, the students of a ... A vertical line is drawn inside the rectangle at the point 55. ... Part B: Calculate the interquartile range of the data, and explain in a ... (2 points) ... make the "whisker" portion longer and could potentially slightly shift the box.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.1. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship?
Answer: the minimum score required for the scholarship is 29.24
Step-by-step explanation:
Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = population standard deviation
Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91%(100 - 9 = 91).
Looking at the normal distribution table, the z score corresponding to the probability value of 0.91(91/100) is 1.35
From the information given,
µ = 21
σ = 6.1
Therefore,
1.35 = (x - 21)/6.1
6.1 × 1.35 = x - 21
8.235 = x - 21
x = 8.235 + 21 = 29.24
The minimum ACT Reading score required to be in the top 9% for a university scholarship is approximately 29.2, determined by using a z-score of 1.34, the mean score of 21, and the standard deviation of 6.1.
To determine the minimum ACT Reading score required to be in the top 9% of students, and hence eligible for a scholarship at a university, we utilize the concept of z-scores in a normal distribution. A z-score indicates how many standard deviations an element is from the mean.
First, we need to find the z-score that corresponds to the top 9% of the distribution. Standard z-score tables or calculators will show that the z-score for the top 9% is approximately 1.34. This z-score means the score is 1.34 standard deviations above the mean. Next, we apply the z-score formula:
Z = (X - μ) / σ
Where:
Z is the z-score (1.34 in this case),
X is the ACT score we want to find,
μ is the mean (21 for ACT Reading),
σ is the standard deviation (6.1 for ACT Reading).
We can rearrange the formula to solve for X (the ACT score):
X = Z * σ + μ
Substituting the values we have:
X = 1.34 * 6.1 + 21
X ≈ 29.214
The minimum ACT Reading score required for the scholarship is therefore approximately 29.2 when rounded to the nearest tenth.
What is closest to the difference between the means of the two dot plots?
Answer: The answer is B. 1.0
Step-by-step explanation:
That’s the closest mean
Answer:
A is 15.27 and B is 12.05
Step-by-step explanation:
I'll give points just please help(it's a little long sorry:( A student randomly selects some crayons from a large bag of crayons. He selects 10 brown
crayons, 5 blue crayons, 3 yellow crayons, 3 green crayons, 3 orange crayons, and 6 red
crayons. Answer the following questions based on this information. (You can write your
answer either as a fraction, decimal, or percent.) What is the estimate for the probability of selecting a blue crayon for the bag? What is the estimate for the probability of selecting a red crayon or a yellow crayon from the bag? Which color is most likely to be selected? If there are 300 crayons in the bag how many red crayons would you estimate to be in the bag?
Answer:
1/6 chance
Step-by-step explanation:
10+5+3+3+3+6=30 draws
out of 30 draws 5 blue
5/30 reduced is 1/6.
You randomly draw A marble from a bag, record it’s color, and then replace it. You draw a blue marble 11 out of 50 times. What is the experimental probability that the next marble will be blue?
Answer:
22/100 or 0.22 or 22%
Step-by-step explanation:
Out of the 50 times you drew a marble, you got 11 blue ones.
11/50
We can divide 11/50 and get 0.22, which is the same as 22/100 or 22%.
Hope this helps! ;-)
The required probability is,
[tex]P(B)=\frac{11}{50} [/tex]
The total number f marbles are 50
Now, the formula for finding the experimental probability is,
P(B)=Possible outcomes/ Number of outcomes
[tex]P(B)=\frac{11}{50} [/tex]
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Find the length of the radius in a circle if the diameter is 10 feet
Simplify the expression 2(-9+9v)
How many solution(s) are there
for this system?
6y=12x+36
15y=45x60
Final answer:
The given system of equations has one unique solution because the lines represented by the equations have different slopes, hence they intersect at exactly one point.
Explanation:
To answer how many solutions there are for the given system of equations:
6y=12x+36
15y=45x+60 (Assuming the '+60' was meant instead of '60', as '+60' makes it a linear equation)
We first simplify both equations to determine if they are identical, parallel, or intersecting.
For the first equation, we divide by 6:
y = 2x + 6
For the second equation, assuming a typo and it should be '+60', we divide by 15:
y = 3x + 4
Since the slopes (2 and 3) are different, the lines are not parallel and will intersect at exactly one point. Therefore, there is one unique solution to this system.
Please help!!!!!!!!!!!!!!!
Answer:
150
Step-by-step explanation:
1 box is 5 x 5 which=25 x 6 boxes=150
150 squared is your answer
Answer: 150
Step-by-step explanation:
The side of one cube is 5. 5 * 5 = 25 So 25 is the surface area of one cube side. A cube a 6 sides, and 25 * 6 = 150. Therefore, 150 is the surface area of the cube.
If the length of AC equals 30, what is the length of the midsegment DE? A) 10 B) 15 C) 20 D) 25
Answer:15
Step-by-step explanation:
I’m on USA test prep
In a triangle, the midsegment is always half the length of the base. Given that the length of AC is 30, the midsegment DE will be half of this which is 15. Thus, the answer is B) 15.
Explanation:
In geometry, a midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. For every triangle, the length of the midsegment is always half the length of the base of the triangle.
From your question, the length of AC (which is the base of the triangle) is 30. Therefore, the length of the midsegment DE would be half of 30, which is 15.
So the answer to your question is: B) 15.
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Can you guys help me out here?
Answer:
8906.4 feet
Step-by-step explanation:
The worker is walking around the park which is the circumference.
The equation for the circumference is diameter times (pi)
since the diameter is 975, you multiply 975 by pi which gives you 2968.8
Because the worker walks around the park 3 times you multiply the circumference by 3 which is 2968.8 times 3 which equals 8906.4
Therefore the worker walks 8906.4 feet a day
whats the greatest common factor for 150 and 250
Answer:
50
Step-by-step explanation:
The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The factors of 250 are: 1, 2, 5, 10, 25, 50, 125, 250
Then the greatest common factor is 50.
Hope this helped
:)
What is the solution to this system of equations?
x − 2y = 15
2x + 4y = -18
Answer:
The answer to your question is (3, -6)
Step-by-step explanation:
Data
x - 2y = 15 Equation l
2x + 4y = -18 Equation ll
Solve the system of equations by elimination
-Multiply equation l by 2
2x - 4y = 30
2x + 4y = -18
4x + 0 = 12
4x = 12
x = 12/4
x = 3
-Substitute x in equation l
3 - 2y = 15
-Solve for y
-2y = 15 - 3
- 2y = 12
y = 12/-2
y = -6
-Solution
(3, -6)
Answer:
C. x = 3, y = -6
Step-by-step explanation
Answer is correct from Plato
Solve the following system of equations please ASAP
Given:
The system of equation:
[tex]x+y = -4[/tex] -------- (1)
[tex]y = x^{2} -6x[/tex] --------- (2)
To find the values of x and y.
We will use substitution method.
From (1) we get,
[tex]y = -4-x[/tex]
We will put the value of y in (1) and we get,
[tex]-x-4 = x^{2} -6x[/tex]
or, [tex]x^{2} -5x+4= 0[/tex]
Now we will apply middle term factor method.
[tex]x^{2} -(4+1)x+4 = 0[/tex]
[tex]x^{2} -4x-x +4 = 0[/tex]
[tex]x(x-4)-1(x-4) = 0[/tex]
[tex](x-4)(x-1)= 0[/tex]
so, x = 4 and 1
Now,
Substitute x = 4 in (1) we get,
[tex]y = -4-4 = -8[/tex]
And putting x = 1 in (1) we get,
[tex]y = -4-1 = -5[/tex]
Hence, the solution of the given system of equation is (4,-8) and (1,-5)
Thus, Option A is the correct answer.
This week Andres will practice with his band for 1 1\2 hours monday , 1 3\4 hours on tuesday , and 2 hours wednesday . Next week andres will practice with his band for the same number of hours on monday tuesday wednesday . What was the total number of hours andres will practice with his band over these 6 days
Answer:
10.5 hours
Step-by-step explanation:
Given:
This week Andres will practice with his band for
[tex]1\frac{1}{2} \ means\ \frac{3}{2} \ hours[/tex] on Monday
[tex]1\frac{3}{4} \ means\ \frac{7}{4} \ hours[/tex] on Tuesday
2 hours Wednesday.
Next week Andres will practice with his band for the same number of hours on Monday, Tuesday, Wednesday.
Question asked:
What was the total number of hours Andres will practice with his band over these 6 days?
Solution:
As she practice for two weeks, three days of each week:
On two Monday, she will practice = [tex]\frac{3}{2} + \frac{3}{2} =\frac{3+3}{2} =\frac{6}{2} =3\ hours[/tex]
On two Tuesday, she will practice = [tex]\frac{7}{4} +\frac{7}{4}=\frac{7+7}{4} =\frac{14}{4} =\frac{7}{2} \ hours[/tex]
On two Wednesday, she will practice = [tex]2+2=4 \ hours[/tex]
Total hours, she will practice over 6 days [tex]=3+\frac{7}{2} +4[/tex]
[tex]=7+\frac{7}{2} \\ \\ =\frac{2\times7+7}{2} \\ \\ =\frac{21}{2} \\ \\ =10.5\ hours[/tex]
Thus, Andres will practice 10.5 hours with his band over these 6 days.
The total number of hours andres will practice with his band over these 6 days is 10 1/2 hours
Given:
Day 1 = 1 1/2 hours
Day 2 = 1 3/4 hours
Day 3 = 2 hours
The total number of hours for six days = 2(1 1/2) + 2(1 3/4) + 2(2)
= 2(3/2) + 2(7/4) + 4
= 6/2 + 14/4 + 4
= 3 + 14/4 + 4
= 7 + 14/4
= (28+14) / 4
= 42 / 4
= 10 2/4
= 10 1/2 hours
Therefore, the total number of hours andres will practice with his band over these 6 days is 10 1/2 hours
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Y = 60,209.47x - 207,150.70 How much do we predict a month with 9 sales people makes? Round to 2 decimal places. Do not put a dollar sign in your answer.
Answer:
The amount made in a month with 9 sales people = 334,734.53
Step-by-step explanation:
The amount, Y, made by a sales company in dollars is related to the number of sales people, x, at the company through the relation,
Y = 60,209.47x - 207,150.70
where Y = amount made in dollars
x = number of sales people
when x = 9, what is Y.
Y = 60,209.47x - 207,150.70
Y = (60,209.47×9) - 207,150.70
Y = 541,885.23 - 207,150.70
Y = 334,734.53
Hope this Helps!!!
What is the mode and range
What is the least common denominator for:
3/x and 2/4xy
Answer:
the least common denominator is 4xy
determine whether the vectors u and v are parallel, orthogonal, or neither. u=(9,0), v=(0,-9)
Answer:
orthogonal
Step-by-step explanation:
If the dot product of the two vectors is 0, then they must be orthogonal.
[tex]u*v=9(0)-9(0) = 0[/tex]
Answer: c
Step-by-step explanation: edge 2021
The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 28 feet and 6 feet long. It has an area of 34 square feet. What is the height of the cross section?
Answer:
The height of the cross section if 2 feet
Step-by-step explanation:
To solve this problem recall the formula for the area of a trapezoid of bases B (larger base) and b (smaller base) and height H:
[tex]Area = \frac{(B+b)\,H}{2}[/tex]
Therefore, for our case we have:
[tex]Area = \frac{(B+b)\,H}{2}\\34 \,ft^2 = \frac{(28\,ft+6\,ft)\,H}{2}\\34 \,ft^2 = \frac{(34 \,ft)\,H}{2}[/tex]
So, now we can solve for the height H:
[tex]34 \,ft^2 = \frac{(34 \,ft)\,H}{2}\\2\,*\,34 \,ft^2 =34\,ft\,* H\\H=\frac{2\,*\,34 \,ft^2}{34\,ft}\\ H=2\,ft[/tex]