A surveyor makes the measures indicated in Fig. 19-71. For the figure, angle A = 34o and the Hypotenuse c = 159 ft. Note the angles are named with Capital Letters A, B, and C and the names or the sides opposite the angles are named with small letter
All parts of the triangle should be solved The parts of the triangle to include in the Problem Solution are: (1) degrees of all 3 angles A, B and C, (2) lengths of the two legs a, b , rounded to the nearest whole number, (3) length of the hypotenuse and (4) the area of the triangle with the proper units. That is 7 answers total.
Answers
The side lengths of the triangle are 89 ft, 132 ft and 159 ft
The angles of the triangle are 34 degrees, 56 degrees and 90 degreesThe area of the triangle is 5874 square unitsThe sides of the triangleThe given parameters are
Angle, A = 34 degrees
Hypotenuse = 159 ft
The length BC is calculated as
sin(A) = BC/Hypotenuse
So, we have
BC = Hypotenuse * sin(A)
This gives
BC = 159 * sin(34 degrees)
Evaluate
BC = 89 ft
The length AC is calculated as
cos(A) = AC/Hypotenuse
So, we have
AC = Hypotenuse * cos(A)
This gives
AC = 159 * cos(34 degrees)
Evaluate
AC = 132 ft
The angles for the triangleHere, we have
Angle, A = 34 degrees
Because the triangle is a right triangle, we have
Angle, C = 90 degrees
The sum of angles in a triangle is 180
So, we have
Angle B = 180 - 90 - 34
Angle B = 56
The area of the triangleThis is calculated as
Area = 0.5 * BC * AC
So, we have
Area = 0.5 * 89 * 132
Evaluate
Area = 5874
Hence, the area is 5874 square units
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Related Questions
Your car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol. How much of 69% percent ethanol fuel should you use so
that your tank is 40 percent ethanol?
Answers
Answer: 7.5
Step-by-step explanation:
the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent
.69 divided by 15 is .046
.13 divided by 15 is .008
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
What is mixture?A mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.Given is that a car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol.
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -
{x} = 69% of 15 - {40% of 15}
{x} = (69/100 x 15) - (40/100 x 15)
{x} = 10.35 - 6
{x} = 4.35
Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
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Explain why the slope(m) of this line is
2/6
Answers
The slope is 2/6 because the rise is 2 while the run is 6
rise 2
------- = -------
run 6
A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built
Answers
The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet
How to find the dimensions of the rectangle for the most economical fence?Given: Area = 1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot
In order to calculate the dimension of the fence
Let L and W represent the length and width of the fence respectively
Thus, the area of the fence can be represented as:
A = L × W = 1250 ---- (1)
L = 1250/W
Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot
C = 6×(2W + L) + 18×L
C = 12W + 24L ---- (2)
Substituting the value of L from equation 1 into equation 2 we have:
C = 12W + 24×(1250/W)
To minimize the cost we differentiate both sides with respect to W and equate the result to zero:
C = 12W + 24×(1250/W)
dC/dW = d/dW (12W + 30000/W)
0 = 12 - 30000/W²
12W² = 30000
W² = 2500
W = 50 feet
Since L = 1250/W
L = 1250/50
L = 25 feet
Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet
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a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number
Answers
Answer:
22
Step-by-step explanation:
12 + 19 + 7 + _?_ = 15
38 + _?_ = 15
-38 -38
-----------------------
? = 23
12 + 19 + 7 + 23 = 61
-1
12 + 19 + 7 + 22 = 60
60 ÷ 4 = 15
I hope this helps!
A student is using colored beads to make a model of magnesium hydroxide, Mg(OH)2. Magnesium atoms are
represented by orange beads, oxygen atoms by green beads, and hydrogen atoms by blue beads.
Model bead color key.
Magnesium orange beads O (orange)
Oxygen green beads O (green)
Hydrogen blue beads O (blue)
What combination of beads should the student use for the model?
Answers
The combination of beads that the student will use to make a model of magnesium hydroxide, Mg(OH)₂ is
Magnesium orange beads - 1Oxygen green beads - 2Hydrogen blue beads - 2What is model of molecule?Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.
These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules
Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.
The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:
Magnesium : Oxygen : Hydrogen = 1 : 2 : 2
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15 points!! Is the triangle a right triangle?
Answers
Answer: Yes.
Step-by-step explanation:
Answer:
yes, it is because the right side is the bigger side.
Step-by-step explanation:
See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.
How is solving a real-world problem with a system of equations similar to solving a real-world problem with a single equation in one variable? How is the process different?
Answers
Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
hope it helps
:)
what are steps to solving 30,002-28,596
Answers
Answer:
1,406
Step-by-step explanation:
Simplify Oa Ob Oc Od 10x² -32 4
Answers
Answer:
Step-by-step explanation:
Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 5x2 + 14x - 3 < 0 The solution set is O A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O A. В. + -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 7 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4. 7 8 C. + + + + + + + D. + -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 5 7 8 E. F. + + + + -7 -6 -3 -2 -1 1 2 3 6 -8 -7 -6 -5 -4 -3 -2 -1 1 3 5 6 7 8 OG. →O H.
Patrick is in a grocery store parking lot, 90meters away from his car. If he pushes his shopping cart at a constant velocity of 2meterspersecond toward his car, how much time will it take him to get one-third of the way to his car?
Write your answer as a whole number.
Answers
15 seconds of time will it take him to get one-third of the way to his car
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given,
Patrick is in a grocery store parking lot, 90meters away from his car
Patrick pushes his shopping cart at a constant velocity of 2meterspersecond toward his car.
We need to find time will it take him to get one-third of the way to his car
one-third of the way to his car means 1/3 of 90 which is 30 meters.
Speed =Distance/ Time
Time=Distance/speed
=30/2
=15 units.
Hence, 15 seconds of time will it take him to get one-third of the way to his car
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Given the function f (x)= x2 −5x + 6 , evaluate
Answers
Actually 20 is the answer
In your own words, tell me the difference between a geometric and an arithmetic sequence.
Answers
As several differences are there between them and is differentiated below.
What is Sequence?
A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.
Let a sequence's terms be a1, a2, a3,..., an,..., etc.
The term's position is indicated by the subscripts. That implies,
Initial phrase = a1
term two = a2
term three Equals a3
….
The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.
Geometric Sequence:
It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.Arithmetic Sequence:
It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,To learn more about Sequence, visit:
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Julie likes to make bead necklaces. She has 296 beads altogether, but has 32 more round beads than square beads. How much of each bead does she have?
Answers
Simplify this equation please
48
Answers
Answer:
Please look at the attached image, thank you so much! Hope this helps! :D
Step-by-step explanation:
Answer:
6.92820323028, rounded would be 6.92. Even more rounded would be 7.
Step-by-step explanation:
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Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.
Answers
Answer:
Step-by-step explanation:
If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.
Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.
Assume gas cost $3.70 a gallon. Write an equation representing the total amount you need to spend on the car for the trip, after paying for a one time tune-up of $100.
Answers
The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Also an equation is a set of variables that are constrained through a situation or case.
Given that the 1 gallon is $3.70
x gallons = $3.70x
So, C = 3.70x
This will be the cost of x gallons
Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".
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No
0.7
What’s the percentage
Answers
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2
Answers
24 units is the area of the shaded region if the "frame" is 2 units wide.
What is Area of Rectangle?The area of Rectangle is length times of width
We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:
width = 7 units
length = 12 units
Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).
So the measures for the shaded rectangle are:
width = 7 units - 4 units = 3 units
length = 12 units - 4 units = 8 units.
And the area of a rectangle is given by the product between the width and length, then we have:
A = (3 units)*(8 units) = 24 square units.
Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.
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Can somebody help me with this please?
Answers
Answer: -16.66
Reason: 10*-5/3=−16.66666667 or −50/3
In ARST, r = 71 cm, /T=48° and /R=37°. Find the length of t, to the nearest 10th of
a centimeter.
Answers
In the given triangle, the length of side t is 87.7 cm
Calculating the length of a side in a triangleFrom the question, we are to determine the length of t.
From the given information,
r = 71 cm
∠T = 48°
∠R = 37°
From the law of sines, we can write that
t / sin T = r / sin R
t / sin 48° = 71/sin 37°
t = (71 × sin 48°)/sin 37°
t = 87.6736
t ≈ 87.7 cm
Hence, the length of t is 87.7 cm
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Will mark brainliest
Answers
The solution is Option D.
The equation of the line is y = 28x
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the total distance traveled by the car y = 476 miles
Let the total amount of gasoline x = 17 gallons
So , the equation of line is given by
y = mx + c
where m is the slope
Slope m = y /x
Substituting the value for y and x in the equation , we get
Slope m = 476 / 17
= 28
Therefore , the equation of line is y = 28x and the graph is given below
Hence , The equation of the line is y = 28x
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A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is
Answers
The class width of the distribution is 4
What is class width?Class width is the difference between the Upper class limit and the Lower class limit of a class interval.
Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.
Similarly for a class interval of 75-79, the class width is 79-75= 4.
The upper class limit is 79 and the lower class limit is 75.
The class limit for all the frequency distribution is constant.
Therefore the class width of the distribution is 4
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The volume of a cube with side s is s3. Edna bought a cube-shaped jewelry box that has 7-inch sides. What is the volume of the jewelry box?
Answers
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The volume of a cube with side s = s³
And, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 x 7 x 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph
Answers
The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.
What is the rate of change function?
The pace at which one quantity changes in relation to another is known as the rate of change function.
Given, P = 0.015[tex]V^{3}[/tex]
Differentiating P with respect to V:
P′=(0.015)(3)[tex]V^{2}[/tex]
At V = 5.9 mph, then
P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph
Hence, the instantaneous rate of change of power is 1.6 W/mph.
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A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?
Answers
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The cost of each chair is $2.25.
The cost of each table is $8.25.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 4 = 5 is an equation.
We have,
Cost of each chair = x
Cost of each table = y
Now,
2x + 6y = 54 _____(1)
5x + 3y = 36 ______(2)
From (1) we get,
2x = 54 - 6y
x = (54 - 6y)/2 ______(3)
Now,
Putting (3) in (2) we get,
5(54 - 6y)/2 + 3y = 36
270/2 - 30y/2 + 3y = 36
135 - 15y + 3y = 36
99 = 12y
y = 99/12
y = 8.25 ______(4)
Now,
Putting 4 in (3) we get,
x = (54 - 6 x 8.25) / 2
x = 4.5/2
x = 2.25
Thus,
The cost of each chair is $2.25.
The cost of each table is $8.25.
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The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.
Answers
The length and width of the rectangle is 16 ft and 13 ft respectively.
What is the dimensions of the rectangle?The perimeter of a rectangle = 2(length + width)
Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ftThe perimeter of a rectangle = 2(length + width)
58 = 2{(w + 3) + w}
58 = 2(w + 3 + w)
58 = 2(3 + 2w)
open parenthesis
58 = 6 + 4w
subtract 6 from both sides
58 - 6 = 4w
52 = 4w
divide both sides by 4
w = 52/4
w = 13
Hence,
Width of the rectangle = w ft
= 13 ft
Length of the rectangle = (w + 3) ft
= 13 + 3
= 16 ft
Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively
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two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answers
Answer:
$33.25
1 package is $4.75
Step-by-step explanation:
9.5 divided by 2 is 4.75, that is how much one package costs.
4.75 times 7 is 33.25, that's seven packages worth.
A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe
for x hours. What is the cost of renting a canoe for twelve hours?
Answers
The graph of the equation y = 30x + 20 is shown below.
It would cost $380 for 12 hours.
How to Write and Graph an Equation?The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.
Therefore:
Slope/unit rate (m) = $30 per hour
Rental service charges is the y-intercept (b) = $20
To write the equation, substitute m = 30 and b = 20 into y = mx + b:
y = 30x + 20
See the attachment below for the graph of the equation.
Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:
y = 30(12) + 20
y = $380
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If the variance of the data values in a sample is 289, what is the standard
deviation of the data values?
O A. 17
OB. 19
OC. 18
O D. 16
Answers
Answer:
17
Step-by-step explanation: ..
I’m certain year, there were 86 female officials in congress, which comprised of the House of Representatives and the senate. If there were 58 more female me members of the House of Representatives than female senators, find the number of females in each house of congress
Answers
Answer:
58 members of the House of Representatives, and 28 members of the senate.
Step-by-step explanation:
We can find the answer to this by simply subtracting:
86 - 58 = 28
So, there are 58 members of the House of Representatives, and 28 members of the senate.
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