Answers
Answer:
shape a is 20 cm squared
Step-by-step explanation:
shape a is a parallogram, A =b×h. 5x4=20
shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.
area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units
Related Questions
Dean's family goes on a road trip every summer. This scatter plot shows the number of days
they traveled and how far they went during their last 7 road trips.
What was the most common distance?(miles)
Answers
The most common distance in miles would be = 1,200 miles.
How to determine the most common distance that was travelled?To determine the distance that is most travelled the following is considered;
The total number of road trips = 7
On day 3 the distance travelled = 600 and 1,200 miles
On day 4 the distance travelled = 1,000,1,100 and 1,200 miles
On day 5 the distance travelled = 800 miles.
On day 6 the distance travelled = 1,300 miles
Therefore the most travelled distance = 1,200 miles.
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Doug is filing singly. his net taxable income is $80,575. every week, $304 is withheld from his earnings for income tax. based on the table below, what can doug expect when his taxes are due? between 80,550 and 80,600 dollars, for filing single, the amount of taxes is 16,539 dollars. a. doug will receive a refund of $123. b. doug will receive a refund of $2,977. c. doug will owe an additional $1,125. d. doug will owe an additional $731.
Answers
Doug is filing singly, and his net taxable income is $80,575. The tax amount for this income range is $16,539. Every week, $304 is withheld from his earnings for income tax. Doug can expect he will owe an additional $731. So option d is the correct answer.
Calculate the total amount withheld for the year.Doug has $304 withheld every week. There are 52 weeks in a year, so we multiply the weekly amount by 52:
$304 * 52 = $15,808.Compare the total amount withheld with the actual tax amount due.
The tax amount due for Doug's income is $16,539. We already calculated that the total amount withheld is $15,808.Determine if Doug will receive a refund or owe additional tax.
$16,539 (tax amount due) - $15,808 (total amount withheld) = $731.
Since the result is a positive number, Doug will owe an additional $731 when his taxes are due. Therefore, the correct answer is d. Doug will owe an additional $731.
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If KJ=10, find the length of arc HJ
Answers
Answer:
Step-by-step explanation:
The arc length formula is
[tex]L=\frac{\theta}{360}*2\pi r[/tex]
Theta is the angle that intersects arc HJ. That measure is 180-122 which is 58 degrees. We put that into the formula along with the radius measure of 10 to get:
[tex]L=\frac{58}{360}*2\pi (10)[/tex] which gives us, rounded to the nearest hundredth,
L = 10.12 units
a carpnter had a piece of wood that is 15 feet long. he cut the wood into pieces that are 1/4 of a foot long . how many pieces did he cut?
Answers
Therefore , the solution of the given problem of unitary method comes out to be the carpenter divided the wood into 60 pieces.
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
Divide the overall length of the wood by the length of each piece to get how many pieces the carpenter cut.
Each piece measures 0.25 feet, or 1/4 of a foot.
By dividing the overall length of the wood by the length of each component, we can determine the number of pieces:
=> Quantity = Length overall / Length of each element
=> Piece count is 15 feet divided by 0.25 feet. or 15/0.25
=> There are 60 parts total.
So, the carpenter divided the wood into 60 pieces.
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Town Hall is located 4. 3 miles directly east of the middle school. The fire station is located 1. 7 miles directly north of Town Hall.
Part A
What is the length of a straight line between the school and the fire station? Round to the nearest tenth. Enter your answer in the box.
Part B
The hospital is 3. 1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest
tenth. Enter your answer in the box.
Answers
Using Pythagorean theorem the distance between the school and the fire station is approximately 4.7 miles, while the distance between the school and the hospital is approximately 7.8 miles.
To solve this problem, we can use the Pythagorean theorem to find the distances and then add them up to get the total distance between the school and the fire station, and then between the school and the hospital.
Part A:
Let's call the middle school point A, Town Hall point B, and the fire station point C. We can draw a right triangle with AB as the base, BC as the height, and AC as the hypotenuse. Using the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
AC^2 = 4.3^2 + 1.7^2
AC^2 = 18.98 + 2.89
AC^2 = 21.87
AC ≈ 4.7 miles (rounded to the nearest tenth)
Therefore, the length of the straight line between the school and the fire station is approximately 4.7 miles.
Part B:
Let's call the hospital point D. We can draw another right triangle with CD as the base, BC as the height, and BD as the hypotenuse. Using the Pythagorean theorem, we have:
BD^2 = BC^2 + CD^2
BD^2 = 1.7^2 + 3.1^2
BD^2 = 2.89 + 9.61
BD^2 = 12.5
BD ≈ 3.5 miles (rounded to the nearest tenth)
Now, we can add the distance between A and B (4.3 miles) to the distance between B and D (3.5 miles) to get the total distance between A and D:
AD ≈ 7.8 miles (rounded to the nearest tenth)
Therefore, the length of the straight line between the school and the hospital is approximately 7.8 miles.
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For the class party, Josue and Pho each brought 1 3/5 liters of lemonade. How many liters of lemonade did they bring altogether?
Answers
Josue and Pho brought 3 1/5 liters of lemonade altogether
Josue and Pho brought 1 3/5 liters of lemonade each, so the total amount of lemonade they brought is:
1 3/5 + 1 3/5 = 3 1/5
To add the two mixed numbers, we first need to find a common denominator. In this case, the common denominator is 5. Then we convert both mixed numbers into fractions with a denominator of 5:
1 3/5 = (5 × 1 + 3) / 5 = 8/5
1 3/5 = (5 × 1 + 3) / 5 = 8/5
Now we can add the fractions:
8/5 + 8/5 = (8 + 8) / 5 = 16/5
Finally, we can convert the fraction back to a mixed number:
16/5 = 3 1/5
Therefore, Josue and Pho brought 3 1/5 liters of lemonade altogether.
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A license plate is made of three letters and three numbers, how many different license plates are possible?
Answers
There are 17,576,000 different license plates possible, considering 26 letters (A-Z) and 10 numbers (0-9).
There are 26 options for each of the three letters and 10 options for each of the three numbers. Therefore, using the multiplication principle, the total number of possible license plates is 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000.
Alternatively, we can use the permutation formula to calculate the number of arrangements: P(26,3) x P(10,3) = 15,600 x 720 = 11,251,200.
However, since order does not matter in a license plate, we need to divide by the number of permutations of three letters and three numbers, which is 3! x 3! = 36, resulting in 11,251,200 / 36 = 17,576,000 possible license plates.
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Rote tells the little monsters to do an overhead press every $12$ seconds and a squat every $30$ seconds. (For example, they should do their first squat $30$ seconds into the drill.)
How many times during the $200$ second drill should the little monsters do an overhead press and a squat at the same instant?
Answers
The number of times that the little monsters will do an overhead press and a squat at the same instant during the drill is: 3 times
How to solve Prime Factorization Problems?We are told that, Rote tells the little monsters to carry out an overhead press every 12 seconds and then also a squat every 30 seconds.
Thus, prime factorization of 12: 2² x 3.
Thus, prime factorization of 30: 2 x 3 x 5.
For us to get the least common multiple, we will have to find the highest power of each of the prime factors that show up in either factorization. Therefore, we can say that the smallest common multiple of 12 and 30 are: 2² x 3 x 5 = 60
This tells us that the little monsters will carry out an overhead press and then a squat at the same instant for every 60 seconds.
For us to find how many times this will occur during the 200-second drill, we will then divide 200 by 60:
200 ÷ 60 = 3 remainder 20
This tells us that there will exist 3 complete cycles of both of the exercises during the 200-second drill, with an additional 20 seconds left over.
Therefore, we can say that the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.
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The altitude (or height) of a triangle is increasing at a rate of 2.5cm/min while the area of the triangle is increasing at a rate of 3cm2/min. At what rate (in cm/min) is the base of the triangle changing when the altitude is 12cm and the area is 84cm2 Round your answer to three decimal places.
Answers
The base is decreasing at 1.917 cm/min when altitude is 12cm and area=84cm².
Let A be the area of the triangle, h be the height of the triangle, and b be the base of the triangle.
Then the formula for the area of a triangle is:
A = (1/2)bh
We are given that dh/dt = 2.5 cm/min (the height is increasing at a rate of 2.5cm/min), and dA/dt = 3 cm²/min (the area is increasing at a rate of 3cm²/min).
We want to find db/dt, the rate of change of the base of the triangle when h = 12 cm and A = 84 cm².
To solve this problem, we need to use the chain rule of differentiation.
We start by differentiating both sides of the formula for the area of a triangle with respect to time t:
dA/dt = (1/2) d/dt (bh)
Next, we can use the product rule of differentiation to find d/dt (bh):
d/dt (bh) = b dh/dt + h db/dt
Substituting this into the previous equation gives:
dA/dt = (1/2) [ b dh/dt + h db/dt ]
Now we can substitute the given values of dh/dt and dA/dt, as well as h = 12 cm and A = 84 cm².
To find db/dt:
3 cm²/min = (1/2) [ b (2.5 cm/min) + 12 cm db/dt ]
Simplifying this expression gives:
6 cm²/min = 2.5 b cm²/min + 12 cm db/dt
Substituting A = 84 cm² and h = 12 cm into the formula for the area of a triangle gives:
84 cm² = (1/2) b (12 cm)
Simplifying this expression gives:
b = 14 cm
Now we can substitute b = 14 cm into the previous equation to find db/dt:
6 cm²/min = 2.5 (14 cm) cm²/min + 12 cm db/dt
Simplifying this expression gives:
db/dt = (6 cm²/min - 35 cm²/min) / (12 cm)
db/dt = -1.917 cm/min (rounded to three decimal places)
Therefore, the base of the triangle is decreasing at a rate of 1.917 cm/min when the height is 12 cm and the area is 84 cm².
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For a science experiment Corrine is adding hydrochloric acid to distilled
water. The relationship between the amount of hydrochloric acid, x, and the
amount of distilled water, y, is graphed below. Which inequality best
represents this graph?
Answers
The best inequality that represents the relationship between the amount of hydrochloric acid (x) and the amount of distilled water (y) in the given graph is 3y - 2x > 0, option D is correct.
The graph shows a straight line with a negative slope passing through the origin. As the amount of hydrochloric acid, x, increases, the amount of distilled water, y, decreases
To see why, let's use a point on the line, such as (2, 3), and plug it into the inequality. We get:
3(3) - 2(2) > 0
9 - 4 > 0
This is true, so the point (2, 3) is a solution to the inequality. Any point on the line will also satisfy this inequality since it represents all possible combinations of x and y that Corrine can use in her experiment.
Alternatively, we can rewrite the inequality in slope-intercept form:
y < (2/3)x
This means that the y-values on the line are less than the corresponding values of (2/3)x. So as x increases, y must decrease to stay below the line. This confirms that 3y - 2x > 0 is the correct inequality.
Hence, option D is correct.
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The correct question is:
For a science experiment, Corrine is adding hydrochloric acid to distilled water. The relationship between the amount of hydrochloric acid, x, and the amount of distilled water, y, is graphed below. Which inequality best represents this graph?
A. 2y - 3x < 0
B. 3y - 2x < 0
C. 2y - 3x > 0
D. 3y - 2x > 0
The Worthington Family is applying for a loan to purchase a new home. In order to qualify they
must have a net worth greater than $100,000.
• Mr. Worthington is a dentist, so he has $85,400 in student loans to pay off.
•Mrs. Worthington earns $42,500 per year at her job.
•The Worthington family has a savings account with a balance of $18,800.
•They own two vehicles that are worth a combined total of $64,600.
• Mrs. Worthington owns an antique necklace valued at $6,200.
"Run.
• The Worthingtons have been saving for their children's college fund.
currently has a balance of $24,700
Answers
The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.
To calculate the net worth of the Worthington family, we need to add up all their assets and subtract their liabilities (debts). Let's start by listing them:
Assets:
- Savings account: $18,800
- Vehicles: $64,600
- Antique necklace: $6,200
- College fund: $24,700
Total assets: $114,300
Liabilities:
- Mr. Worthington's student loans: $85,400
Total liabilities: $85,400
To calculate the net worth, we subtract the liabilities from the assets:
Net worth = Total assets - Total liabilities
Net worth = $114,300 - $85,400
Net worth = $28,900
The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.
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I NEED HELPPPPPPPPPPPP
Answers
Answer: V = 2527.2 in^3
Step-by-step explanation:
V = Bh
that is, Volume = base area x height
the base area is the hexagon, and the height is given as 12.
Think of dividing the hexagon into 6 equal triangles, with height 7.8
so the area of all 6 triangles, (effectively the area of the hexagon), will be:
6(0.5 x 9 x 7.8) = 210.6 in^2
multiply this by the height to get the volume:
210.6 x 12 = 2527.2 in^3
thats it!
V = 2527.2 in^3
lmno is a parallelogram. if nm = x + 27 and ol = 3x + 9 find the value of x and then find nm and ol.
Answers
The length of NM and OL in the parallelogram LMNO are both 36 units.
How we find the value of x?Since LMNO is a parallelogram, we know that opposite sides are equal in length. Therefore, we can set NM and OL equal to each other:
NM = OL
We also know that NM = x + 27 and OL = 3x + 9, so we can substitute these expressions into the equation:
x + 27 = 3x + 9
Solving for x:
2x = 18
x = 9
Now that we know x, we can substitute it back into the expressions for NM and OL:
NM = x + 27 = 9 + 27 = 36
OL = 3x + 9 = 3(9) + 9 = 36
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Ms. Frank is going to wallpaper a living room with dimensions 24 feet long, 18 feet wide, and 8 feet high. How much wallpaper will Ms. Frank need if she is only putting it on the four walls?
Answers
Answer:
Step-by-step explanation:
you take 24 multiplied by 18 then by 8 and that'll equal
24 x 18 x 8 = 3456
Your brother traveled 115 miles in 2. 52 hours to come home for school break. What’s the average speed that he was traveling?
Answers
The average speed that your brother was traveling is approximately 45.63 miles per hour
The average speed is the total distance traveled divided by the total time taken. So we have:
Average speed = total distance ÷ total time
We are given the total distance as 115 miles and the total time as 2.52 hours. Therefore, the average speed is:
Average speed = 115 miles ÷ 2.52 hours
Average speed = 45.63 miles per hour
So, the average speed that your brother was traveling is approximately 45.63 miles per hour.
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Does anyone know the answer
Answers
Answer:
B) <FBG
Step-by-step explanation:
An adjacent angle is an angle that is right next to the given angle.
In this case, the given angle is <EBF.
We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.
Looking at the options, we can only see that <FBG is an option, making B the correct option.
Hope this helps :)
To the nearest whole cubic centimeter, what is the volume of the prism?
Answers
The volume of the prism in 120 cubic centimeter.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is a scalar quantity that characterizes the "size" or "capacity" of an object in three dimensions.
What is prism?A prism is a three-dimensional geometric shape that has two parallel and congruent bases connected by lateral faces that are typically rectangular or parallelogram-shaped. Prisms are classified based on the shape of their base, such as rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on. The lateral faces of a prism are perpendicular to the bases, and the bases are usually parallel to each other.
According to the given information:
Given the measures of prism is length = 8cm, breadth = 6 cm, height = 5 cm
The formula for volume of prism = 1/2 l*b*h
= 1/2 8*6*5
= 120 cubic centimeter
Hence the volume of prism is 120 cubic centimeter.
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How many solutions?
4x - y = 18 and -4x + y = -18
a. one
b. infinitely many
c. no solutions
Answers
The given equation 4x - y = 18 and -4x + y = -18 has b. infinitely many solutions.
To determine how many solutions there are for the system of equations 4x - y = 18 and -4x + y = -18, follow these steps:
Step 1: Notice that the second equation is just the negative of the first equation:
4x - y = 18
(-1)(4x - y) = (-1)(18)
-4x + y = -18
Step 2: Since the second equation is just the negative of the first, the two equations are dependent and represent the same line.
Step 3: When two equations represent the same line, there are infinitely many points where they intersect, as they overlap completely.
So, the answer is: b. infinitely many solutions.
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What are all the possible rectangle with the perimeter 16cm,20cm,and 14cm, find the area of each rectangle
Answers
The area of a rectangle can be found by multiplying its length and width.
For perimeter 16cm: 15 cm² and 16 cm²For perimeter 20cm: 24 cm² and 25 cm²For perimeter 14cm: 12 cm²How to find area of rectangles?To find the area of rectangles with different perimeters, we need to use the formula:
Area = length x width
Perimeter = 16 cmPossible dimensions:
Length = 5 cm, Width = 3 cm
Length = 4 cm, Width = 4 cm
Area of the first rectangle = 5 cm x 3 cm = 15 cm²
Area of the second rectangle = 4 cm x 4 cm = 16 cm²
Perimeter = 20 cmPossible dimensions:
Length = 6 cm, Width = 4 cm
Length = 5 cm, Width = 5 cm
Area of the first rectangle = 6 cm x 4 cm = 24 cm²
Area of the second rectangle = 5 cm x 5 cm = 25 cm²
Perimeter = 14 cmPossible dimensions:
Length = 4 cm, Width = 3 cm
Area of the rectangle = 4 cm x 3 cm = 12 cm²
Therefore, the areas of the possible rectangles with perimeters 16cm, 20cm, and 14cm are:
For perimeter 16cm: 15 cm² and 16 cm²
For perimeter 20cm: 24 cm² and 25 cm²
For perimeter 14cm: 12 cm²
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Molly has 250 trading cards. she gives n trading cards to her friend carol. marcus has 430 trading cards. he gives away three times as many cards as molly does. how many trading cards did molly give away if molly and marcus have the same number of trading cards left?
a.) 70 trading cards
b.) 80 trading cards
c.) 90 trading cards
d.) 180 trading cards
Answers
Molly gave away 90 trading cards, which is option (c).
Let's start by figuring out how many trading cards Marcus gave away. We know that Molly gave away n trading cards, so she has 250 - n cards left. Marcus gave away three times as many cards as Molly did, so he gave away 3n cards. That means he has 430 - 3n cards left.
We also know that Molly and Marcus have the same number of trading cards left, so:
250 - n = 430 - 3n
Simplifying and solving for n, we get:
2n = 180
n = 90
Therefore, Molly gave away 90 trading cards, which is option (c).
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Mollie drew mol and ted drew ted. they measured a few parts of their triangles
and found that ml = td, ol = ed, and l = d. what postulate can mollie and ted
use to justify why their triangles must be congruenta
Answers
Mollie and Ted can use the Side-Side-Side (SSS) postulate to justify why their triangles must be congruent.
According to the given information, the two triangles share three corresponding sides of equal length: ML = TD, OL = ED, and L = D.
The SSS postulate states that if three corresponding sides of two triangles are congruent, then the triangles are congruent. Therefore, because Mollie's triangle and Ted's triangle share three corresponding sides of equal length, they are congruent by the SSS postulate.
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express as a single simplified fraction. 3m^2-3n^2/m^2+mp divided by 6m-6n/p+m
Answers
The single simplified fraction is (m + n)(p + m) / 2m.
To simplify the expression
[tex](3m^2 - 3n^2) / (m^2 + mp)÷ (6m - 6n) / (p + m)[/tex]
we need to invert the second fraction and multiply by the first.
[tex](3m^2 - 3n^2) / (m^2 + mp) \times (p + m) / (6m - 6n)[/tex]
We can then factor out a 3 from the numerator and the denominator, and cancel out the (m - n) terms. 3(m + n)(m - n) / 3m(m - n) x (p + m) / 6(m - n)
Simplifying further, we can cancel out the 3's and the (m - n) terms. (m + n) / m x (p + m) / 2
The simplified expression is (m + n)(p + m) / 2m.
To simplify the given expression, we invert the second fraction and multiply it by the first. Then we factor out common terms and cancel out like terms. We simplify the expression to obtain the single fraction (m + n)(p + m) / 2m.
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Verónica jogged 10 3/16 miles in a one week, the next week she jogged 8 7/16 miles. how many more miles did she jog the first week? pls answer
Answers
Verónica jogged 7/4 or 1 and 3/4 more miles in the first week than in the second week.
Verónica jogged 10 3/16 miles in one week, next week she jogged 8 7/16 miles. how many miles did she jog the first week?Verónica jogged 10 3/16 miles in the first week and 8 7/16 miles in the second week. To find how many more miles she jogged in the first week, we need to subtract the distance she jogged in the second week from the distance she jogged in the first week:
10 3/16 miles - 8 7/16 miles
We need to first convert both mixed numbers to improper fractions:
10 3/16 = (10 x 16 + 3) / 16 = 163 / 16
8 7/16 = (8 x 16 + 7) / 16 = 135 / 16
Now we can subtract the two fractions:
163 / 16 - 135 / 16 = (163 - 135) / 16 = 28 / 16
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor (GCF), which is 4:
28 / 16 = (4 x 7) / (4 x 4) = 7 / 4
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Patricia bought 4 apples and 9 bananas for $12. 70 Jose bought 8 apples and I bananas for $17. 70 at the same grocery store What is the cost of one apple?
Answers
The cost of one apple is $2.15.
To find the cost of one apple, we can set up a system of equations with the given information. Let's use A for the cost of one apple and B for the cost of one banana:
1) 4A + 9B = $12.70
2) 8A + B = $17.70
Now, we can solve this system of equations. We can multiply equation 1 by 2 to match the number of apples in equation 2:
1) 8A + 18B = $25.40
Now subtract equation 2 from the modified equation 1:
(8A + 18B) - (8A + B) = $25.40 - $17.70
17B = $7.70
Now, divide by 17 to find the cost of one banana:
B = $7.70 / 17 = $0.45
Now that we know the cost of one banana, we can substitute B in equation 2 to find the cost of one apple:
8A + ($0.45) = $17.70
8A = $17.25
A = $17.25 / 8 = $2.15
So, the cost of one apple is $2.15.
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Please help!!! 10 points
Answers
The solution is, Options 1, 3, and, 5 are true.
The statements given are,
1.) The product of reciprocals is 1.
Let the fraction be a/b , and reciprocal be b/a ,
The product of the two will be 1.
Hence, the statement is true.
2.) To divide fractions, multiply the divisor by the reciprocal of the dividend.
Let the fraction be a/b , now,
a/b*1/a = a^2/b,
Hence, the statement is false.
3.) The reciprocal of a whole number is 1 over the number.
Let the number be 3, now,
The reciprocal of number 3 is 1/3 .
Hence, the statement is true.
4.) Reciprocals are used to multiply fractions.
The statement is false, Reciprocals are not used to multiply fractions.
5.) To find the reciprocal of a fraction, switch the numerator and denominator.
Let the fraction be a/b , then the reciprocal will be b/a .
Hence, the statement is true.
Therefore, Options 1, 3, and, 5 are true.
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complete question:
Select all that apply. Determine which of the following statements are true of reciprocals. Select all that apply. The product of reciprocals is 1 To divide fractions, multiply the divisor by the reciprocal of the dividend The reciprocal of a whole number is 1 over the number Reciprocals are used to multiply fractions To find the reciprocal of a fraction, switch the numerator and denominator
The angle of elevation between a fishing vessel and the top of a 50-meter-tall lighthouse is 12 degrees. What is the approximate distance between the fishing vessel and the base of the lighthouse?
A.
10. 6 meters
B.
48. 9 meters
C.
235. 2 meters
D.
240. 5 meters
Answers
We solve this problem using the angle of elevation, we can apply the tangent function from trigonometry. The approximate distance between the fishing vessel and the base of the lighthouse is 235.2 meters, which corresponds to option C. 235. 2 meters
Find the approximate distance between the fishing vessel and the base of the 50-meter-tall lighthouse when the angle of elevation is 12 degrees.
Set up the equation using tangent function.
tan(angle of elevation) = (height of lighthouse) / (distance between vessel and lighthouse base)
Plug in the values.
tan(12°) = 50 / distance
Solve for the distance.
distance = 50 / tan(12°)
Calculate the distance using a calculator.
distance ≈ 235.2 meters
So, the approximate distance between the fishing vessel and the base of the lighthouse is 235.2 meters, which corresponds to option C. 235. 2 meters
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Find the value of x
Hellpppp
Answers
Answer:
r = 14.60
Step-by-step explanation:
r²= 9²+(23/2)²
= 9²+11.5²
= 81+132.25
r² = 213.25
r = √213.25
= 14.60 to 2d.p
The sum of two numbers is 30. Determine the two numbers of their product is a maximum.
Answers
Answer:
Step-by-step explanation:
Let's call the two numbers x and y. We know that:
x + y = 30 (since the sum of the two numbers is 30)
We want to find the values of x and y that maximize their product, which is given by:
P = xy
To solve for x and y, we can use the fact that the sum of the two numbers is 30, so we can rewrite one of the numbers in terms of the other:
y = 30 - x
Substituting this into the equation for the product, we get:
P = x(30 - x)
Expanding this expression, we get:
P = 30x - x^2
To find the maximum value of P, we can take the derivative of this expression with respect to x and set it equal to zero:
dP/dx = 30 - 2x = 0
Solving for x, we get:
x = 15
So one of the numbers is x = 15, and the other is y = 30 - x = 15.
To confirm that this gives the maximum product, we can take the second derivative of P with respect to x:
d2P/dx2 = -2
Since the second derivative is negative, this means that the function P = 30x - x^2 has a maximum at x = 15.
Therefore, the two numbers are 15 and 15, and their product is maximized at P = 15 * 15 = 225.
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You are building a fence for your pasture. the length is three more than four times the width
Answers
The perimeter of the fence for the pasture is 10W + 6.
To find the perimeter of the fence, we need to add up the lengths of all four sides. Let's start by using the given information to find the length and width of the pasture.
Let's say the width of the pasture is W. Then, according to the problem, the length of the pasture is 3 more than 4 times the width, which can be expressed as:
Length = 4W + 3
Now that we have the length and width, we can find the perimeter by adding up all four sides:
Perimeter = 2(Length + Width)
Perimeter = 2(4W + 3 + W)
Perimeter = 2(5W + 3)
Perimeter = 10W + 6
Therefore, the perimeter of the fence is 10W + 6.
Note: The question is incomplete. The complete question probably is: You are building a fence for your pasture. The length is three more than four times the width. What is the perimeter of the fence.
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Austin spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -1.9°F. Between 9am and noon, the temperature rose 11.3°F. Between noon and 3pm, the temperature dropped 7.9°F. Between 3pm and 6pm, the temperature dropped 12.7°F. What was the temperature at 6pm?
Answers
To find the temperature at 6pm, we need to start with the temperature at 9am and then add or subtract the changes in temperature that occurred during the day.
We know that the temperature at 9am was -1.9°F. Between 9am and noon, the temperature rose 11.3°F, so at noon the temperature was:
-1.9 + 11.3 = 9.4°F
Between noon and 3pm, the temperature dropped 7.9°F, so at 3pm the temperature was:
9.4 - 7.9 = 1.5°F
Between 3pm and 6pm, the temperature dropped 12.7°F, so at 6pm the temperature was:
1.5 - 12.7 = -11.2°F
Therefore, the temperature at 6pm was -11.2°F.
