The values of ∠A=44° , b=42.1 units and c=46.1 units for the triangle ABC in which ∠B=60° , ∠C=76° and a=33 is given was found using sine-law.
What is sine law?
Any triangle with a side and its opposite angle known can be solved using the sine rule (not just right-angled triangles). The sine rule is given by \(\frac{Sin A}{a} =\frac{sin B}{B} =\frac{Sin C}{C}\) . The other version of this is \(\frac{a}{Sin A} =\frac{b}{Sin B} =\frac{c}{Sin C}\). Use the Sine Rule version where the lengths are on top if you need to determine the length of a side. Use the Sine Rule version where the lengths are on top if you need to determine the length of a side.
Here given values of ΔABC, ∠B=60° , ∠C=76° and a= 33
We know that by angle sum property, ∠A + ∠B + ∠C =180°
∴∠A + ∠B + ∠C =180°
∠A + 60° + 76° =180°
∠A = 180 - 60 - 76
∠A=44°
According to Sine law, \(\frac{a}{Sin A} =\frac{b}{Sin B} =\frac{c}{Sin C}\)
Taking \(\frac{a}{Sin A} =\frac{b}{Sin B}\) , we can find side b.
\(\frac{a}{Sin A} =\frac{b}{Sin B}\)
\(\frac{33}{Sin 44} =\frac{b}{Sin 60}\)
\(\frac{33}{0.6946} = \frac{b}{0.866}\)
b = \(\frac{33}{0.6946} x 0.866\)
=42.143 units
On rounding off to nearest tenths value of b=42.1 units
Taking \(\frac{a}{Sin A} =\frac{c}{Sin C}\) , we can find side c.
\(\frac{a}{Sin A} =\frac{c}{Sin C}\)
\(\frac{33}{Sin 44}= \frac{c}{Sin 76}\)
\(\frac{33}{0.6946} =\frac{c}{0.970}\)
c = \(\frac{33}{0.6946} x 0.970\)
c = 46.084
On rounding off to nearest tenths value of c=46.1 units
The values are ∠A=44° , b=42.1 units and c=46.1 units.
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20 Points to who gets this. :)
Find the area of the triangle below.
Answer:
Well t find the area of a triangle, you need to multiple Base x height. That gives you 43.56. Now you divide by 2. So the end product will give you 21.78. Those same rules apply to every time you are finding the area of a triangle.
Step-by-step explanation:
Answer: A
Step-by-step explanation: 7.8 x 4.4= 34.32 x .5= 17.16 = A
PLZ HELP (20 points)
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
Group of answer choices
Only A
Only B
Both A and B
Neither A nor B
Answer:Neither A nor B
Answer: neither A nor B
The Hendricksons are in charge of bringing treats for 505050 football players. They brought 333 coolers of popsicles and 222 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat
If the Hendricksons are in charge of bringing treats for 505050 football players. The statement that best predicts how many football players will get a popsicle is: C. There will be exactly 30 football players who get a popsicle.
How to find the football players that will get a popsicle?First step is to find the total cooler
Total cooler = 3+2
Total cooler = 5
Since play we have 3:2 type of color
Hence,
Number of player with popsicles = 3/5 × 50
Number of player with popsicles = 30
Number of player with sandwiches = 2/5 × 50
Number of player with sandwiches = 20
Therefore the correct option is C.
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The complete question is:
The Hendricksons are in charge of bringing treats for 50 football players. They brought 3 coolers of popsicles and 2 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat. Which statement best predicts how many football players will get a popsicle? Choose 1 answer:
A. There will be exactly 20 football players who get a popsicle.
B. There will be close to 20 football players but not exactly 20 who get a popsicle.
C. There will be exactly 30 football players who get a popsicle.
D. There will be close to 30 football players who get a popsicle but not exactly 30 who get a popsicle
Im give qs for my lil sis so she wants 16 x 5
Answer:
80
Step-by-step explanation:
16x5=80
The table shows the last holiday destination of 60 people.Holiday
destinations
Frequency | Angle in º
France
25
Spain
18
Greece
15
Other
2
Complete the table and draw a pie chart
to represent this information.
Note: Please draw your pie chart in a 'clockwise' direction from the line already drawn
and follow the order from the table (France, then Spain etc...).
The required answer are according to the following order,
a) France;
25/60 × 360/1 = 150°
b) Spain;
18/60 × 360/1 = 108°
c) Greece;
15/60 × 360/1 = 90°
d) Other;
2/60 × 360/1 = 12°
What do you mean by sum of angles?
We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:
The angle subtended is obtained from number of people that chose a particular location.
a) France;
25/60 × 360/1 = 150°
b) Spain;
18/60 × 360/1 = 108°
c) Greece;
15/60 × 360/1 = 90°
d) Other;
2/60 × 360/1 = 12°
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CAN SOMEONE HELP ME PLZ NO LINKS
Answer:
length = 2w - 3
l = length
w = width
2(length) + 2(width) = perimeter
2(2w - 3) + 2(w) = 60
6w -6 =60
w = 11
len = 2(11) - 3
Step-by-step explanation:
A line passes through (9,2) and (12,-4). Write the equation of the line in standard form.
A. 2x + y = 20
B. 2x - y = 5
C. 2x - y = 16
D. 2x + y = 16
For the 1st equation,
2x + y = 20Putting x = 9, y = 2or, 2 (9) + 2 = 20or, 18 + 2 = 20or, LHS = RHSNow, putting x = 12, y = -4 in the above equation, we have2(12) + (-4) = 20or, 24 - 4 = 20or, LHS = RHS.So we can see that the first equation is the equation of the line.This is given in the graph in the picture.Like this way, if we check with other equations, we see that they are not the required equation of the line.Answer:
A. 2x + y = 20
Hope you could get an idea from here.
Doubt clarification - use comment section.
Meagan has a bag with 8 red cubes, 3 yellow cubes, and 5 green cubes. What is the probability of
hat she will pick a red cube, keep it, and then pick another red cube?
A.8/17
B.7/30
C.7/32
D.8/18
Answer:
B. 7/30
Step-by-step explanation:
1st time to pick red is 8/16 8 red cubes out of 16 are red
2nd time to pick red is 7/15 7 red cubes out of 15 are red,
*if one red is picked already
8/16 x 7/15 = 7/30
Let f(x)=sinx and g(x)=cosx. Find the value of (f−g)(45∘) (f−g)(45∘)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression
The value of (f-g)(45°) is √2/2 - √2/2 = 0.
To find the value of (f-g)(45°), we need to substitute the angle 45° into the expressions for f(x) and g(x) and then subtract the two functions.
Given f(x) = sin(x) and g(x) = cos(x), we can evaluate f(45°) and g(45°).
Using the angle sum formula for sine and cosine, we know that sin(45°) = cos(45°) = √2/2. Therefore, f(45°) = √2/2 and g(45°) = √2/2
Substituting these values into the expression (f-g)(45°), we have (√2/2) - (√2/2).
Since the two terms have the same value, but with opposite signs, their difference is 0. Therefore, (f-g)(45°) simplifies to 0.
Hence, the value of (f-g)(45°) is 0.
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Find an angle
θ
θ coterminal to
−
2
2
∘
−22
∘
, where
0
∘
≤
θ
<
36
0
∘
0
∘
≤θ<360
∘
.
Answer:
ģģgggggģgghjjhhhhhhh8i8ivvvvvbvgddddgkkki8ijffhiii
plz helppp
Analyze the diagram below and complete the instructions that follow. Find the value of x and the value of y
A. x=15, y= 10 √3
B. x=20, y= 10 √3
C. x=20 √3, y= 5 √3
D. x=15, y= 5 √3
Answer:
Use the SOH CAH TOA
Step-by-step explanation:
Angle = 60°
x = opposite o
y = adjacent a
10√ 3 = hypotenuse h
To find x we use SOH {sineø = o/h}
Sin 60° = x/10√ 3
x=10√ 3 * sin 60
X=15
You can use Pythagoras theorem or CAH{cosø = a/h}
Cos 60°= y/10√ 3
y=Cos 60° * 10√ 3
y=5√ 3
A human bone is made up of water 1/4 and 9/20 minerals, and the rest is living tissue. What decimal represents the amount of a human bone that is living tissue?
Answer:
0.3
Step-by-step explanation:
First you need to add 1/4 and 9/20, and you would get 7/10. That only leaves 3/10, which as a decimal is 0.3.
The decimal that represents the amount of a human bone that is living tissue is 0.3
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that human bone is made up of water 1/4 and 9/20 minerals, and the rest is living tissue.
First we need to add 1/4 and 9/20,
Thus we would get 7/10.
That only leaves 3/10, which as a decimal is 0.3.
The decimal that represents the amount of a human bone that is living tissue is 0.3
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what is the output of the following code snippet? public static void main(string[] args) { int value = 3; value ; system.out.println(value); }
The output obtained after executing the java code snippet,
public static void main(string[] args)
{
int value = 3;
value++;
system.out.println(value);
}
will be 4.
As per the question statement, we are provided with a java code snippet, which goes as:
public static void main(string[] args)
{
int value = 3;
value++;
system.out.println(value);
}
We are required to determine the output, that we will obtain on executing the above mentioned code.
That is, on executing the code
public static void main(string[] args)
{
int value = 3;
value++;
system.out.println(value);
}
We will obtain an output of 4, as "++" is the post increment function.
Java: Java is a general-purpose, class-based, object-oriented programming language designed for having lesser implementation dependencies, where all programs are made of entities representing concepts or physical things known as “objects”Output: Output is the result of any action.To learn more about Java Code snippets and their Outputs, click on the link below
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15p+69=93.
solve for both variables
Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. This week, she posted 1/3 of the remaining fliers. How many fliers has she still not posted?
The number of fliers that she has still not broadcasted will be 48 fliers.
What is Algebra?Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.
Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,
⇒ (1 - 1/5) x 90
⇒ (4/5) x 90
⇒ 72 fliers
This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,
⇒ (1 - 1/3) x 72
⇒ (2/3) x 72
⇒ 48 fliers
The number of fliers that she has still not broadcasted will be 48 fliers.
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Put this equation into slope-
intercept form.
5x – 4y = 12
An arts academy requires there to be 5 teachers for every 95 students and 4 tutors for every 40 students how many students does the academy have per teacher? Per tutor
Answer:
19 students per teacher and 10 students per tutor
Step-by-step explanation:
To find the amount of students per teacher and per tutor you have to divide
95 students /5 teachers
19 students per teacher
40 students /4 tutors
10 studetns pet tutor
how many seconds does it take to deposit of on a decorative drawer handle when is passed through a solution? round your answer to significant figures.
The time it takes to deposit a coating on a decorative drawer handle through a solution depends on various factors, such as the type and concentration of the solution used, the size and shape of the handle, and the method of deposition.
The time it takes to deposit a coating on a decorative drawer handle through a solution depends on various factors, such as the type and concentration of the solution used, the size and shape of the handle, and the method of deposition. In general, the process of depositing a coating through a solution involves immersing the handle in the solution, allowing the coating to adhere to the surface, and then removing the handle and allowing it to dry. This process can take anywhere from a few seconds to several minutes, depending on the variables mentioned above.
To get a more accurate answer to your question, you may need to provide more specific details about the type of solution and coating you are using and the method of deposition. Additionally, you may want to consult with an expert in the field of surface coatings or material science to get a more precise estimate.
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Which points are the vertices of the ellipse?
points G and H
points J and K
O
points L and N
• points M and N
Answer:
your answer is point g and h
a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected
The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.
We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.
The total depth range is:
35 m - 5 m = 30 m
The distance between each sample is 3 m, so the number of samples is:
(30 m) / (3 m/sample) + 1 = 10 + 1 = 11
Therefore, the diver collected a total of 11 water samples.
find the critical value za/2 that corresponds to a 80 confidence level
the critical value zα/2 that corresponds to an 80% confidence level is approximately 1.2816.
To find the critical value zα/2 that corresponds to an 80% confidence level, we need to determine the value of α/2.
A confidence level of 80% implies that the remaining area under the standard normal distribution curve is (1 - 0.80) = 0.20.
Since the standard normal distribution is symmetric, we divide this remaining area equally between the two tails, resulting in
α/2 = 0.10.
To find the corresponding critical value, we look up the z-score that corresponds to an area of 0.10 in the standard normal distribution table (also known as the z-table) or use a statistical calculator.
The critical value zα/2 for α/2 = 0.10 is approximately 1.2816.
Therefore, the critical value zα/2 that corresponds to an 80% confidence level is approximately 1.2816.
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If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is?
If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.
What is probability?
Probability can be regarded as a measure of the likelihood of an event that can take place.
It should be noted that Many events cannot be predicted with total certainty, hence , If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.
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find the distance between the points (9, 8) and (9, 3)
Answer: √
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Substitute the actual values of the points into the distance formula.
√
(
9
−
9
)
2
+
(
3
−
8
)
2
Step-by-step explanati i hope you under stand
Wirte hey worth problem that could be olved by writing and olving multitep equation then olve your problem
On solving the provided question, we can say that - by solving the equation, jake is of 21 years
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign.
Given that Rita is 17 years old and Jack is 4 years older, what is Jack's age
Solution,
Let Jack's age be x.
The answer to the query is
\(x = 1 7 + 4\\x = 21\)
Jack is therefore 17 years old.
As a result, the answer to the question and its explanation are provided above.
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Solve the following compound inequality: x≥−2 or x<1
A. −2≤x<1
B. no solution
C. x≥−2
D. all real numbers
Answer:
d
Step-by-step explanation:
I did the test ! --_-
How would you define a pair of parallel lines?
Answer:
We say that two lines (on the same plane) are parallel to each other if they never intersect each other, ragardless of how far they are extended on either side. Pictorially, parallel lines run along each other like the tracks of a train.
Hope this helps <3
f(x1, x2) 421 +222 3x² +213 5x11² (√₁+√₂)² 10ln(₁) (x₁+x₂)(x² + x3) min(3r1, 10√2) max{5x1,2r2} MP1(x1, x₂) MP2(X1, X₂) TRS(x1, x₂) Output (2,4)
The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.
The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:
1. The first term is 421 + 222, which equals 643.
2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.
3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.
4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.
5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.
6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.
7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.
8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.
9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.
Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:
- 421 + 222 = 643
- 3x² + 213 = 225
- 5x11² = 1210
- (√₁+√₂)² = 9
- 10ln(₁) ≈ 6.9314718
- (x₁+x₂)(x² + x3) = 408
The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.
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four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the $gure above. if the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?
The perimeter of the octagon is 64 centimeters. To find the perimeter of the octagon, we need to determine the length of one side and then multiply it by 8 since an octagon has 8 equal sides.
Let's denote the side length of the octagon as "x". Since the four triangles are removed from a square piece of sheet metal, the remaining shape is also a square.
The area of the square is equal to the side length squared, so the area of the square piece of sheet metal is x^2. We are given that the total area of the removed material is 196 square centimeters. Since there are four triangles, the area of each triangle is 196/4 = 49 square centimeters.
The area of a triangle is equal to (base * height) / 2. In this case, the base and height of each triangle are equal to x, so we can write the equation as (x * x) / 2 = 49.
Simplifying the equation, we have x^2 = 98.
Taking the square root of both sides, we find x = √98 = √(49 * 2) = 7√2.
Finally, multiplying the side length by 8, we get the perimeter of the octagon: 8 * (7√2) = 56√2, which is approximately 79.4 centimeters.
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The point (-6, 4) is reflected over the x-axis. Find the point of reflection.
Answer:
-6, -4
Step-by-step explanation: