A triangle plot of land has one side along a straight road measuring 324 feet. A second side makes a 68Degree angle with the road and the third side makes a 54 degree angle with the road. How long are the other two sides?
Answers
The missing dimensions of the triangular plot of land are:
i. b = 2.45
ii. A = 69.5
iii. C = 75.5^o
What is a cosine rule?A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.
Cosine rule states that;
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B
To determine the missing values of the triangle in the attached diagram, we have;
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B
= 4^2 + 7^2 - 2(4*7)Cos35^o
= 16 + 49 -2(36*0.8192)
= 65 - 58.9824
= 6.0176
b = (6.0176)^1/2
= 2.4531
b = 2.45
From sine rule,
a/ Sin A = b/Sin B = c/ Sin C
a/ Sin A = b/Sin B
4/Sin A = 2.45/ Sin 35
Sin A = 4* Sin 35/ 2.45
= 0.9365
A = Sin^-1 0.9365
= 69.47
A = 69.5
So to determine the value of C, we have;
A + B + C = 180^o
69.5 + 35 + C = 180
104.5 + C = 180
C = 180 - 104.5
= 75.5
C = 75.5^o
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Related Questions
A recipe uses 3/4 teaspoon of cinnamon for every 4 cups of granola mix.
How many teaspoons are needed for 12 cups of granola mix?
Answers
Okay, here are the steps to solve this problem:
* The recipe calls for 3/4 teaspoon of cinnamon for every 4 cups of granola mix.
* So for 1 cup of granula mix, you need 3/4 / 4 = 3/12 teaspoon of cinnamon.
* For 12 cups of granula mix, you would need 12 * (3/12) = 3 teaspoons of cinnamon.
Therefore, for 12 cups of granola mix you would need 3 teaspoons of cinnamon.
Can you explain why you need to multiply x and y (and not add x and y) when you are adding
logarithms?
Answers
The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a positive actual number that is not exactly one.
What is a logarithm?A logarithm is the power to which a number must be raised in order to receive extra values. The simplest approach to express really large numbers is in this way. A number of important features of a logarithm demonstrate the fact that multiplication and division of logarithms can also be used to represent addition and subtraction logarithms.
The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a real number that is positive but not equal to one.
i.e., [tex]b^y=a[/tex] ⇔ [tex]log_b[/tex] a = y
In this case, "A" and "B" are two positive real numbers.
Y is an actual number.
Argument occurs inside the log as "a" by the name argument.
It is said that the base, or "b," is at the bottom of the log.
To put it another way, the logarithm provides a solution to the problem of "How many times is a number divided to get the other number?"
How numerous times must three be multiplied, for instance, to yield the number 27?
27 is the outcome of multiplying 3 times by 3.
Consequently, the logarithm is 3.
The logarithm form is written as follows:
[tex]log_3[/tex] (27) = 3 - equation 1
The base 3 logarithm of 27 is therefore 3.
It is also possible to write the above logarithm form as:
3x3x3 = 27
3³ = 27 - equation 2
Equations (1) and (2) are hence equivalent.
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URGENT PLEASE HELP !!!
Answers
The correlation coefficient for the data-set in this problem is given as follows:
r = 0.75.
How to obtain the correlation coefficient?To obtain the correlation coefficient of the data-set in this problem, we must insert the points of the data-set into a correlation coefficient calculator.
From the table, the points of the data-set are given as follows:
(0, 5.9), (0.8, 8.6), (1.3, 15.5), (1.6, 17.3), (13.3, 21.5).
Inserting these points into a calculator, the correlation coefficient is given as follows:
r = 0.75.
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Does each of these graphs have an Euler circuit? If so, find it.
Answers
Only first figure of graph have an Euler circuit.
We have to given that;
There are 3 graphs are shown in figure.
Since, A graph has an Euler circuit if and only if the degree of every vertex is even.
Hence, In first graph,
Every vertex have even degree with 2 or 4.
Thus, It shows an Euler circuit.
In second graph,
Some vertex have odd degree with 3.
Hence, It does not shown an Euler circuit.
In third graph,
Some vertex have odd degree with 3.
Hence, It does not shown an Euler circuit.
Thus, Only first figure of graph have an Euler circuit.
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An amount of $290,000 is borrowed for a periad of 25 years loan is below. Payments of $1, 530.73 are made monthly Payment # Payment Interest Debt Payment 1 1,530.73 966.67 564.06 N 1,530.73 964.79 565.94 3 1,530.73 962.90 567.83 4 5 rest rate of 4%. The amortization schedule for this Balance 289, 435.94 288, 870.00 288,302.17 Calculate 2, the balance on the loan at the end of month 4. Give your answer to the nearest dollar. Do not include com or the dollar sign in your answer.
Answers
The balance on the loan at the end of month 4 is approximately $289,836.23.
We are given that;
Amount borrowed= $290,000
Time 25 years
Payment= $1, 530.73
Now,
To calculate the balance on the loan at the end of month 4, we can use the following formula2:
Balance = (Loan amount - Debt payment) * (1 + Interest rate / 12) - Debt payment
Where:
Loan amount is the original amount borrowed ($290,000)
Debt payment is the amount of principal paid in each monthly payment ($564.06 for the first month and $565.94 for the second month)
Interest rate is the annual interest rate divided by 100 (0.04)
Plugging in the values, we get:
Balance = ($290,000 - $564.06) * (1 + 0.04 / 12) - $565.94 Balance = $289,435.94 * 1.003333 - $565.94 Balance = $290,402.17 - $565.94 Balance = $289,836.23
Therefore, by the interest the answer will be $289,836.23.
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Janeesa lives 247.5 miles away from her grandmother, and the speed limit on that stretch of
highway is 55 miles per hour. Today, she only has 4 hours to get to her grandmother's birthday
lunch on time!
How much faster over the speed limit does Janeesa need to drive to make it on time? Round to the
tenths place if your answer isn't a whole number.
mph.
Answers
distance = rate x time
In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 247.5 / 4 = 61.875
So Janeesa needs to travel at an average speed of 61.875 miles per hour to make it to her grandmother's birthday lunch on time. Since the speed limit is 55 miles per hour, she would need to drive 6.875 miles per hour faster than the speed limit. Rounding to the tenths place, that's about 6.9 miles per hour over the speed limit. However, it's important to remember that speeding is dangerous and can result in serious accidents. It's always better to leave earlier and plan ahead to avoid the need to speed.
Janeesa needs to drive about 6.9 mph faster than the speed limit to make it on time.
What is the speed limit
To find out how fast Janeesa needs to drive to make it on time, one can use the formula:
distance = rate x time
In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 247.5 / 4 = 61.875
To know how much faster Janeesa needs to drive, one has to subtract the speed limit from the required speed:
Speed Difference = Required Speed - Speed Limit
= 61.875 mph - 55 mph
= 6.875 mph
Therefore, Janeesa needs to drive approximately 6.9 mph faster than the speed limit to make it on time.
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The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?
Answers
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, the length of side WX is 13 mm.
If the scale factor of figure STUV to figure WXYZ is 3:1, it means that every length in figure STUV is three times longer than the corresponding length in figure WXYZ.
To find the length of side WX, we need to first identify the corresponding sides of the two figures. We know that ST is three times longer than W, and SV is three times longer than Y. So, we can set up the following proportion:
ST/WX = SV/YZ
Substituting the given values, we get:
39/WX = 51/YZ
We need to find the value of WX, so we can solve for it by cross-multiplying the proportion:
39 * YZ = 51 * WX
Since we don't know the value of YZ, we need to find it in terms of WX. We can use the scale factor of 3:1 to relate the lengths in the two figures:
ST = 3 * W
SV = 3 * Y
Substituting the first equation, we get:
W = ST/3 = 39/3 = 13 mm
Substituting the second equation, we get:
Y = SV/3 = 51/3 = 17 mm
Now we can substitute these values into the proportion:
39/WX = 51/17
Solving for WX, we get:
WX = (39 * 17) / 51 = 13 mm
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Complete question is:
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WX?
Help asap math homework
Answers
u need to find the measure of arc GK to get arc HGJ. add all the given numbers and minus it from 360; a full circle. u would get 50, so then add HG, GK, and KJ which is 155+50+70 to get 275
Can someone please explain this to me?
Answers
[tex]\textit{since we know that }\triangle FGH \cong \triangle CDE \\\\[-0.35em] ~\dotfill\\\\ HF=EC\implies -3s+44=-3t+50 \\\\\\ HG=ED\implies 6s=t+43\implies \boxed{6s-43=t} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{-3s+44=-3(6s-43)+50}\implies -3s+44=-18s+129+50 \\\\\\ 15s+44=129+50\implies 15s+44=179\implies 15s=135 \\\\\\ s=\cfrac{135}{15}\implies \boxed{s=9}\hspace{9em}\stackrel{ 6(9)-43 }{\boxed{t=11}}[/tex]
Find the tangent of each angle that is not the right angle.
Drag and drop the numbers into the boxes to show the tangent of each angle.
Answers
The solution is, the tangent of each angle that is not the right angle is:
angle tan A = 1.33
angle tan B = 0.75
Here, we have,
Given:
ABC is a right triangle.
angle ACB = 90
To find:
tan A
tan B
We know that tangent of an angle is given by the ratio
= opposite / adjacent
The opposite side and adjacent side is taken with respect to the angle for which the tangent is to be found.
tan A = BC/ AC
= 8/6
= 4/3
= 1.33
and, tan B = AC/BC
= 6/8
=0.75
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Base twelve needs twelve digits, so we use t for ten and e for eleven and our usual ten digits. What base ten number does 1t5e twelve represent?
Answers
Therefore, 1t5e twelve represents the number 3239 in base ten.
what is system of equations?
A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is a set of values for the variables that satisfy all the equations in the system simultaneously.
For example, consider the following system of two equations:
x + y = 5
2x - y = 3
This is a system of two equations with two variables, x and y. The solution to this system is the values of x and y that make both equations true at the same time. In this case, the solution is x = 2 and y = 3, because when we substitute these values into the equations.
In base twelve, the place values increase by a factor of twelve at each position, starting from the rightmost position. The rightmost position has a place value of 1, the next position to the left has a place value of 12, the next position to the left has a place value of 12^2 = 144, and so on.
To convert the number 1t5e in base twelve to base ten, we need to multiply each digit by its corresponding place value, and then add up the results:
1t5e (base twelve) = 1 * 12^3 + 10 * 12^2 + 5 * 12^1 + 11 * 12^0
= 1 * 1728 + 10 * 144 + 5 * 12 + 11 * 1
= 1728 + 1440 + 60 + 11
= 3239
Therefore, 1t5e twelve represents the number 3239 in base ten.
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What are the values of w and x?
Answers
The angle measures of w and x are given as follows:
w = 51º.x = 78º.How to obtain the angle measures?In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.
The congruent side lengths are given as follows:
SR and RQ.
Hence the congruent angle measures are given as follows:
w -> opposite to SR.51º -> opposite to RT.Hence angle w is given as follows:
w = 51º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:
x + 2 x 51 = 180
x = 180 - 102
x = 78º.
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Select the statement that is not true.
A. The translation of a line is a pair
of parallel lines.
B. The rotation of a pair of parallel lines is a pair of parallel lines.
C. The reflection of a line is a line.
D. The rotation of a line is a line.
Answers
Answer: B. The rotation of a pair of parallel lines is a pair of parallel lines.
Explanation: A translation of a line is a displacement of the line, or a transformation which moves all points of the line, without changing its shape or orientation. This means that a pair of parallel lines will remain parallel after a translation.
A rotation of a line is a transformation in which all points of the line are rotated around a pivot point, and the line will change its orientation.
A reflection of a line is a transformation in which all points of the line are reflected across a single axis. This means that a line will remain a line after a reflection.
Therefore, the statement that is not true is B. The rotation of a pair of parallel lines is a pair of parallel lines.
An urn contains 10 red balls, 20 yellow balls, and 60 orange balls. If you reach into the urn and select a single ball at random, what is the probability of selecting a orange ball?
Answers
Answer:
2/3 or 67%
Step-by-step explanation:
To find the exact probability for you to reach into the orange balls you'll have to do a data table on which you'll include how many orange balls are by the total amount of balls that are within the urn.
For example:
The urn contains:
* 10 red balls
* 20 yellow balls
* 60 orange balls
Total amount of balls that you have on the urn is 90, you'll get this result by doing a simple addition of the table of content.
Afterwards, we have to find the probability, so you will have to take the amount of orange balls (which is 60) and divide it by 90 (Which is the total amount of balls you have on the urn).
60/90
A quick tip for you to do this on a simplified manner is by dividing the numerator and the denominator by their greatest common divisor (Which in this case is 30) (30x2 = 60) (30x3 = 90)
60/90 = (60 divided 30) / (90 divided 30) = 2/3
To resolve this problem, we get that the probability of selecting an orange ball is 2/3 or approximately 0.67 which we'll simplify to 67%
I hope this helped you
Which angles are adjacent to AGC? Select all that apply.
Answers
A roller for construction work is 5 feet in diameter. When the roller has made one turn, how far has it
traveled?
Answers
Answer:
Approximately 15.7 ft
Step-by-step explanation:
We want to find the circumference of the circle
C = pi * diameter
C = pi *5
C = 5pi ft or approximately 15.7 ft
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
We are given that the diameter of the roller is 5 feet. The radius of the roller is half of the diameter, which is:
r = d/2 = 5/2 = 2.5 feet
Substituting this value in the formula for the circumference, we get:
C = 2πr = 2π(2.5) = 5π
Therefore, when the roller has made one turn, it has traveled a distance equal to 5π feet (approximately 15.7 feet).
Find the volume of the right cone below. Round your answer to the nearest tenth if necessary.
16
7
Answers
The volume of the given right cone is approximately 597.9 cubic units.
In this problem, we are going to find the volume of a right cone. A cone is a three-dimensional object that has a circular base and tapers to a point. The term "right" means that the axis of the cone is perpendicular to its base. The formula for the volume of a right cone is V = (1/3)πr²h, where V is the volume, r is the radius of the circular base, and h is the height of the cone.
Now, let's apply this formula to the given cone. We are given that the radius of the circular base is 16 and the height of the cone is 7. So, we can substitute these values into the formula to get:
V = (1/3)π(16)²(7) V = (1/3)π(256)(7) V = (1/3)(1,792π) V ≈ 597.9
We round our answer to the nearest tenth as requested. So, the final answer is V ≈ 597.9.
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A 9v battery produces a current of 18 amps. What is the resistance
Answers
If a 9v battery produces a current of 18 amps then the resistance of the circuit element is 0.5 ohms.
We can use Ohm's law to determine the resistance (R) of a circuit element
Given the voltage (V) and current (I) through it:
R = V / I
In this case, the voltage (V) is 9 volts and the current (I) is 18 amps. Substituting these values into the formula, we get:
R = 9 V / 18 A
Simplifying the expression on the right-hand side, we get:
R = 0.5 Ω
Therefore, the resistance of the circuit element is 0.5 ohms.
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• What is the cost price of a bag if it was sold for Rs 500 at a loss of 5%?
Answers
Answer:
526.32
Step-by-step explanation:
Let's assume that the cost price of the bag is "C".
Selling Price = Cost Price - Loss
We get:
500 = C - 0.05C
500 = 0.95C
C = 500/0.95
C ≈ 526.32
Therefore, the cost price of the bag was approximately Rs 526.32.
We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Answers
Answer: The answer to your question is C. Brainliest?
Step-by-step explanation:
For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:
2/12 = (2 x 5) / (12 x 5) = 10/60
For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:
2/15 = (2 x 4) / (15 x 4) = 8/60
Now, we can add the two fractions:
10/60 + 8/60 = 18/60
Simplifying this fraction by dividing both numerator and denominator by 6, we get:
18/60 = 3/10
Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.
The answer is C. 0.3.
Marcus and Tony work for Lombardo's Pipe and Concrete. Mr. Lombardo is preparing an estimate for a customer. He knows that Marcus lays a slab of concrete in 9 hours. Tony lays the same size slab in 3 hours. If both work on the job and the cost of labor is $48.00 per hour, decide what the labor estimate should be.
Answers
If both Tony and Marcus work on the job and the cost of labor is $48.00 per hour then labor estimate for the job is $576.00.
Marcus: 1 slab / 9 hours = 1/9 slab per hour
Tony: 1 slab / 3 hours = 1/3 slab per hour
The total amount of work they can do in one hour is the sum of their individual rates:
Marcus and Tony: 1/9 + 1/3 = 4/9 slab per hour
So together, Marcus and Tony can lay 4/9 of a slab per hour.
time = work / rate
time = 1 / (4/9) = 2.25 hours
total labor cost = hours worked x cost per hour
The total number of hours worked is the sum of the hours worked by Marcus and Tony:
total hours worked = 9 hours + 3 hours = 12 hours
The cost per hour is $48.00, so the labor estimate for the job is:
total labor cost = 12 hours x $48.00/hour
= $576.00
Therefore, the labor estimate for the job is $576.00.
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solve for x input numerical value only!! solve asap!!! for brainlist
Answers
The value of x in the rectangle is,
⇒ x = 6
We have to given that;
Corresponding angles are,
⇒ (8x + 19)° and (21x - 13)°
Hence, We can say that;
⇒ (8x + 19)° + (21x - 13)° = 180°
⇒ 29x + 6 = 180
⇒ 29x = 174
⇒ x = 174/29
⇒ x = 6
Thus, The value of x in the rectangle is,
⇒ x = 6
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Why do you think influences exchange rates?
(Subject: Economics)
Answers
how many square killometers
Answers
Answer:
120 km²
Step-by-step explanation:
You just need to add all areas, (3×5) + (9×3) + (13×6) = 15 + 27 + 78 = 120
Help on Part A and B
Answers
Answer:
The Correct answer is B
Step-by-step explanation:
WHAT IS THE 3 KINDS OF SYSTEM OF LINEAR EQUATION ACOORDING TO THE No. OF SOLUTIONS BRAINLY
Answers
The types of systems of linear equations are as follows:
Dependent: The system has infinitely many solutions. The graphs of the equations represent the same lines. Example:
. The system has infinitely many solutions.
Independent: The system has exactly one solution. The graphs of the equations intersect at a single point.
Inconsistent: The system has no solution. The graphs of the equations are parallel lines.
a cable technician working fo the local cable company needs to lay down cable down through the neighborhood below. He is unsure how much cable cable he needs, though. Use the pythagorean theorem to help him find the length in feet of cable he needs to fufill his duty
Answers
Let's say the distance he needs to cover is 1000 feet and there is a height difference of 200 feet between the two points.
Using the Pythagorean theorem, we can find the length of cable he needs:
c² = a² + b²
where c is the length of the cable, a is the distance he needs to cover, and b is the height difference between the two points.
Plugging in the values we have:
c² = 1000² + 200²
c² = 1,040,000
c = √1,040,000
c ≈ 1,020.62
Therefore, the technician needs approximately 1,020.62 feet of cable to fulfill his duty.
Precision manufacturing: A process manufactures ball
bearings with diameters that are normally distributed
with mean 25.1 millimeters and standard deviation
0.08 millimeter.
a. Find the 60th percentile of the diameters.
b. Find the 32nd percentile of the diameters.
c. A hole is to be designed so that 1% of the ball bearings will
fit through it. The bearings that fit through the hole will be
melted down and remade. What should the diameter of the
hole be?
Answers
z = invNorm(0.6) = 0.2533
Now we can use the formula z = (x - mu) / sigma to find the diameter x that corresponds to this z-score:
0.2533 = (x - 25.1) / 0.08
x - 25.1 = 0.020264
x = 25.120264
Therefore, the 60th percentile of the diameters is 25.120264 millimeters.
b. To find the 32nd percentile of the diameters, we need to find the diameter that separates the smallest 32% of the diameters from the largest 68%. We can use a standard normal distribution table to find the z-score that corresponds to the 32nd percentile:
z = invNorm(0.32) = -0.4472
Now we can use the formula z = (x - mu) / sigma to find the diameter x that corresponds to this z-score:
-0.4472 = (x - 25.1) / 0.08
x - 25.1 = -0.035776
x = 25.064224
Therefore, the 32nd percentile of the diameters is 25.064224 millimeters.
c. To find the diameter of the hole, we need to find the diameter that separates the smallest 1% of the diameters from the largest 99%. We can use a standard normal distribution table to find the z-score that corresponds to the 1st percentile:
z = invNorm(0.01) = -2.3263
Now we can use the formula z = (x - mu) / sigma to find the diameter x that corresponds to this z-score:
-2.3263 = (x - 25.1) / 0.08
x - 25.1 = -0.186104
x = 24.913896
Therefore, the diameter of the hole should be 24.913896 millimeters.
Help now quickly will give brainlist
Answers
Answer:
x = - 12
Step-by-step explanation:
the central angle subtended by the arc with measure 45° are congruent, that is central angle is 45°
the 3 angles on the diameter then sum to 180° , that is
45 + 65 + x + 82 = 180
x + 192 = 180 ( subtract 192 from both sides )
x = - 12
Estimate, correct to three decimal places, all the zeros of the following polynomials. (Enter your answers as comma-separated lists.)
(a) P(x) = 4x³5x² - 2x + 1
X=
(b) P(x) = 5x³+x² - 7x-2
X=
(c) P(x) = 2x³-6x² - 5x + 4
X=
(d) P(x)=x² - 4x³ + 5x - 1
X=
Answers
The zeros of P(x) are approximately -1.160, -0.086, and 0.246.
(b) P(x) = 5x³ + x² - 7x - 2
The zeros of P(x) are approximately -1.518, -0.471, and 0.660.
(c) P(x) = 2x³ - 6x² - 5x + 4
The zeros of P(x) are approximately -1.343, 0.515, and 1.828.
(d) P(x) = x² - 4x³ + 5x - 1
The zeros of P(x) are approximately -0.408 and 1.225.