i tried the cosine rule and the sine rule but i dont get why the answer is wrong.
Answers
Answer:
93.2° (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
From inspection of the given triangle:
B = 38°b = 9 cmc = 11 cmSubstitute the values into the sine rule to find the measure of angle C:
[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]
[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]
[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]
[tex]\implies C=48.80523914...^{\circ}[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]
[tex]\implies A=93.19476086...^{\circ}[/tex]
Therefore, the size of angle A is 93.2° (nearest tenth).
Related Questions
Find the y-intercept of the line y=1/3x–1.
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answers
Answer:
-1
Step-by-step explanation:
This line is already in slope, intercept form of y = mx + b <===='b' is the y-axis intercept = -1
PLEASE HELP! What can you conclude about the triangles? *Hint: What is congruent and how can you prove it?
Answers
The triangle's conclusion is that the two triangles are equal because they are congruent.
What are Congruent triangles?If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.The two triangles generated in the illustration are triangles GHJ and GKM.To substantiate the triangle GHJ = GKMAngle JGH=Angle KGM ( opposite angles)angle K equals angle H (alternating angles)Angle H = thus Angle JWe can say that the triangles are congruent because the three angles of each triangle are equal.To Learn more About triangle's conclusion refer To:
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Help please will mark brainiest!
Answers
Answer:
A = 12cm^2 B = 18cm^2 C = 54cm^2
Step-by-step explanation:
area = side 1 x side 2
12 ( 3/4 - 2x) Ue the ditributive property to remove the parenthee. Simplify your anwer a much a poible
Answers
Answer:
9 - 24x
Step-by-step explanation:
When using the distributive property, the number outside the parentheses (12) is "distributed" to each of the values inside the parentheses. In other words, 12 will be multiplied by 3/4 and 2x:
12(3/4 - 2x)
12(3/4) - 12(2x) <----- so now we successfully got rid of the parenthesis. Next, simplify
12(3/4) = 9
12(2x) = 24x
9 - 24x <----this is the final answer since it can't be simplified further
I need some serious help
Answers
Answer: y=7x-23
Step-by-step explanation:
y-y1=m(x-x1)
Plug them in:
-2-12=m(-2-5)
-14=m(-7)
m=7
y=7x+b
Plug in a coordinate:
12=7(5)+b
12=35+b
-23=b
y=7x-23
Karen was trying to factor 6x^2+106x 2 +106, x, squared, plus, 10. She found that the greatest common factor of these terms was 222 and made an area model:.
Answers
The width of area model is 2x units
What is area ?Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.
According to the given information :
The given expression is [tex]6x^{2}+106x[/tex]
We need to find the width of area model , so The above expression represents the area of rectangle A
By making the factors of the above expression
A = [tex]6x^{2}+106x[/tex]
= [tex]2x( 3x + 53 )[/tex]
Area of rectangle is defined as
A = l × b
where l is length and b is width
In the above expression
b = 2x
l = 3x + 53
So , The width of area model is 2x units
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Drag each label to the correct location in the equation. sakeem is a landscape architect. when he creates a lawn, his supplier charges $0.43 per square foot for sod. sakeem charges his customers $2.00 per square foot to lay the sod. the profit sakeem makes when creating a lawn varies directly as the number of square feet of sod he lays. create an equation to show sakeem’s profit when laying sod, where y is the profit and x is the number of square feet of sod. recall that profit is the difference of the amount earned and the amount spent.
Answers
The formula is Y=kx.
What is profit?the financial gain experienced when the income from a commercial activity is greater than the costs, taxes, and other costs associated with maintaining the activity in question.
When laying sod, the equation to determine sakeem's profit is Y= KX, where y represents profit, x is the number of square feet of sod, and k is a constant.
His supplier bills him $0.43 per square foot for sod when he builds a lawn.
For laying the sod, Sakeem's costs his clients $2.00 per square foot.
The amount of sod used to create a lawn directly affects how much money Sakeem's makes.
The profit will then be
Earnings = 2 - 0.43 ,Earnings = $1.57 per square foot
The formula is Y=KX.
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Charmaine wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (incm^2 ) versus the length (in cm).
Find the range and domain of the functions
Answers
The Range of the length of a rectangle having fixed width and area increasing linearly is = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers,
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
The width of the rectangle is fixed, and the length is changing.
The line is formed when connected through the graph.
The area of the rectangle = [tex]length\times width[/tex]
So when the width is fixed, the area would increase linearly and directly proportional to length.
Calculate the range of function y = cx,
y = area as shown in the graph, x is the length, and width is constant c.
Range = {y ∈ R : c ≠ 0 or y ≠ 0}
Calculate the domain,
It can be any real number, as the area can't be negative.
Domain = All real numbers.
Therefore, Range = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 km/h faster than the other. If the two buses are 1722 kilometers apart after 7 hours, what is the rate of each bus?
Answers
Answer:
66mph i belive
Step-by-step explanation:
Both question A and B please
Answers
The coordinates of P and Q are
P (-1/2, 3/2) Q (-4, -3/2)PQ have equal slope with BC so they are parallel
How to find the coordinates of P and QThe coordinates of P and Q is found using the midpoint formula
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
solving for P (X, Y) Using points A(2, -1), B(-3, 4)
(X, Y) = ((2 + -3)/2, (-1 + 4)/2)
= (-1/2, 3/2)
solving for Q (X, Y) points A(2, -1), C(-5,-7)
(X, Y) = ((2 + -5)/2, (-1 + -7)/2)
= (-3/2, -4)
Parallel lines have equal slopes
Using BC = (4 - -7) / (-3 - -5) = 11/2
Using PQ = (-4 - 3/2) / (-3/2 - -1/2) = (-11/2) / (-1) = 11/2
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Juan had $3. 50. Julian had 2 1/2 time a much a juan how much money did julian have
Answers
We know that Julian has $8.75 using mathematical operations.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.
The five basic operations in mathematics are addition, subtraction, multiplication, division, and modular forms.
So, we know that:
Juan has $3.50.
Julian has 2½ times Juan.
So, the money Julian has is:
First, calculate 2½:
2½
4+1/2
5/2
2.5 times
The money Julian has is:
3.50 * 2.5
$8.75
Therefore, we know that Julian has $8.75 using mathematical operations.
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Population The expression n 25 gives the population (in thousands) of an animal after 5 years, where n is the starting population in thousands. Find the populatio
5 years if the starting population is 3,000
Answers
The population after 5 years if the starting population is 3000 is 75,000.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The population after 5 years.
= n x 25
Where n is the starting population in thousands.
The expression can be considered as.
= nx²
Where x is the number of years.
Now,
n = 3000
The population after 5 years.
= 3000 x 25
= 75,000
Thus,
The population is 75,000.
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The flasks are in the shape of cones.
The smaller flask has a base radius of
8
cm and a vertical height of
20
cm.
The larger flask has a base radius of
14
cm.
The larger flask is now partly filled with liquid up to a vertical height of
15
cm.
Calculate the volume of liquid in the flask.
Give your answer in terms of π
Answers
The volume of the liquid in the conical flask is 980 π cm³
What is a Cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Given data ,
Let the two cones be A and B
Now , the smaller cone be A
The larger cone be B
The radius of the smaller cone is r = 8 cm
The height of the smaller cone is h = 20 cm
Now , the volume of the smaller cone V = ( 1/3 ) πr²h
Substituting the values in the equation , we get
Volume of cone A = ( 1/3 ) πr²h
Volume of cone A = ( 1/3 ) π x 8 x 8 x 20
Volume of cone A = 426.67 π cm³
Now ,
The larger flask is filled with height H = 20 cm
The radius of the larger cone is R = 14 cm
The height of the larger cone is H = 15 cm
Now , the volume of the smaller cone V = ( 1/3 ) πR²H
Substituting the values in the equation , we get
Volume of cone B = ( 1/3 ) πR²H
Volume of cone B = ( 1/3 ) π x 14 x 14 x 15
Volume of cone B = 980 π cm³
Therefore , the volume of the larger cone B is 980 π cm³
Hence , The volume of the liquid in the conical flask is 980 π cm³
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The half-life of Radium-223 is 11.43 years. What is the annual decay rate? Express the result to four decimal places.
Express the annual decay rate as a percentage to two decimal places.
%
Answers
Answer:
Below
Step-by-step explanation:
e^(-kt) = 1/2 when t = 11.43
so k = .060642797
e^ (- .060642797 * 1) = .9411 <==== is left after one year
which means the decay in one year is
1 - .9411 = .05884 = 5.88% per year
Graph the line that has a slope of -7/6 and includes the point (0, 1)
Answers
Answer: (6,-6),(0,1) plot these 2 points
Step-by-step explanation:
According to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. How many of those households owned a pet? Round to the nearest whole number.
Answers
If according to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. The number of those households that owned a pet is: 200,588.
How to find the number of household who owned a pet?We would be making use of the given data to find the number of household that owned a pet.
Using this formula
Number of household with pet = Percentage of household × Number of household
Let plug in the formula
Number of household with pet = 72% × 278,595
Number of household with pet = 200,588 household
Therefore the Number of household with pet is 200,588.
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The stereo normally priced at $299 is on sale for 15%off. Find the discount and the sale price.
Answers
299 * 0.15 = 44,85
To get the price after discount:
299 - 44,85 = 254,15
Answer: Sale price: $254.15 , Discount: $44.85
Step-by-step explanation:
15% off indicates that the stereo will now cost 85% of what it did originally:
$299(100% – 15%) = $299(85%)
Decimalizing the percentage results in = $299(0.85) = $254.15
Discount= $299 - $254.15 = 44.85
I NEED HELP 87 POINTS + BRAINLIEST
Answers
a) The Volume of space that is not occupied is; 13.80 in³
b) The length, are and volume have distinct final units.
c) The Volume of the composite shape is the sum of the Volume of Cone, Volume of Cylinder and Volume of Hemisphere
How to find the volume of a composite object?a) Tennis ball is usually considered to be a sphere. The formula for volume of sphere is;
V = ⁴/₃πr³
where r is radius.
Since diameter = 2.6 inches, then radius; r = 2.6/2 = 1.3 inches
Thus;
Volume of each tennis ball;
V = ⁴/₃π(1.3)³
For the three tennis balls;
V₃ = 3(⁴/₃π(1.3)³)
V₃ = 8.788π
Volume of the cylindrical container = πr²h
h is height = 3(2.6) = 7.8 inches
V_cyl = π(1.3² * 7.8)
V_cyl = 13.182π
Volume of space not occupied = 13.182π - 8.788π
Volume of space not occupied = 13.80 in³
b) For length, the unit will be singular
For Area, the unit will be squared
For Volume, the unit will be cubed
c) There are three objects that make up the composite object namely; Cone, Cylinder, hemisphere. Thus;
Volume of composite shape = Volume of Cone + Volume of Cylinder + Volume of Hemisphere
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What is the quotient? 8^2-81/(x-3)(x-9)
Answers
The quotient of the given division is (x + 9).
What is synthetic division?
Synthetic division is a technique for performing manual Euclidean division of polynomials in algebra that requires less writing and calculation than long division. Although it is typically taught for division by monic linear polynomials, the technique can be applied to division by any polynomial.
Given: x^2 - 81 / (x - 9)
We have to find the quotient for the given division.
We can find the quotient using synthetic division.
x + 9
[tex]\sqrt[x-9]{x^2-81}[/tex]
- x^2 - 9x
_______________
9x - 81
- 9x - 81
_____________
0
Hence, the quotient of the given division is (x + 9).
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COMPLETE THE PROOF! MY FINAL IS TMRW AT 8 AM!!!!
Given: segment QP is congruent to segment RS and segment QP is parallel to segment RS.
Prove: segment QR is parallel to segment PS.
Answers
A two-column method be that can used to prove that segment QR is parallel to segment PS is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{QP}[/tex] ≅ [tex]\overline{RS}[/tex] 1. Given
2. [tex]\overline{QP}[/tex] ║ [tex]\overline{RS}[/tex] [tex]{}[/tex] 2. Given
3. ∠PRQ ≅ ∠RPS [tex]{}[/tex] 3. Alt. int. angles theorem
∠QPR ≅ ∠PRS [tex]{}[/tex]
4. ∠PRQ = ∠RPS [tex]{}[/tex] 4. Definition of congruency
∠QPR = ∠PRS
5. ∠QRS = ∠PRQ + ∠PRS [tex]{}[/tex] 5. Angle addition postulate
∠QPS = ∠QPR + ∠RPS
6. ∠PRQ + ∠PRS = ∠QPR + ∠RPS [tex]{}[/tex] 6. Substitution property
7. ∠QRP = ∠QPS [tex]{}[/tex] 7. Transitive property
8. [tex]\overline{PR}[/tex] ≅ [tex]\overline{PR}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. Reflexive property
9. ΔQRP ≅ ΔSPR [tex]{}[/tex] 9. ASA congruency rule
10. ∠PQR ≅ ∠PSR [tex]{}[/tex] 10. CPCTC
11. ∠PQR = ∠PSR [tex]{}[/tex] 11. Definition of congruency
12. QRSP is a parallelogram [tex]{}[/tex] 12. Parallelogram opp. int. ∠s theorem
13. [tex]\overline{QR}[/tex] ║ [tex]\overline{PS}[/tex] [tex]{}[/tex] 13. Properties of a parallelogram
What is a parallelogram?A parallelogram is a quadrilateral that has opposite parallel sides.
The details of the reasons used to prove that the segment [tex]\overline{QR}[/tex] is parallel to segment [tex]\overline{PS}[/tex] are as follows;
Alt. int. angles theorem
The alternate interior angles theorem states that the alternate interior angles formed between two parallel lines and their common transversal are congruent
Definition of congruency
Two geometric figures are congruent if they have the same measurements.
Angle addition postulate
The angle addition postulate states that the measure of an angle ∠A, which is formed by two adjacent angles ∠B and ∠C, is the same as the sum of the measures of the two angles, ∠A = ∠B + ∠C
Substitution property
The substitution property of equality states that if a variable, a = another variable, b, a = b, then b can be plugged into expressions and equations to substitute for a and the values of the expressions and sides of equations remain the same.
Transitive property
The transitive property of equality states that if a = b, and b = c, then a = c
Reflexive property
The reflexive property of congruency states that a geometric figure is congruent to its self
ASA congruency rule
The Angle-Side-Angle congruency rule states that if two angles and the included side of one triangle are congruent to the two angles and included side of another triangle, then the two triangles are congruent.
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent
Parallelogram opp. int. ∠s theorem
The parallelogram opposite interior angles theorem states that the opposite interior angles of a parallelogram are congruent.
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a basketball player has made 66% of his foul shots during the season. assuming the shots are independent, find the probability that in tonight's game he misses for the first time on his 6th attempt?
Answers
The probability that in tonight's game he misses for the first time on his 6th attempt = 0.2244
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The Probability that the basketball player made a foul shot = 0.66 or 60%
Then the probability of good shot is = 1-0.66
= 0.34
probability that in tonight's game he misses for the first time on his 6th attempt = (1-p) 5(p)
= ( 1- 0.34)⁵ (0.34)
= 0.2244
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Need help with part A
Answers
Answer: 0.4
Step-by-step explanation:
The question is asking for the probability to own a dog.
40% own a dog.
If you add all of the percentages you get 100%
40/100
=0.4
The probability is 0.4 times to randomly select a resident that only owns a dog.
Question is in picture
Answers
The length of line segment LB is equal by definition of bisector to 6 feet.
How to determine the missing length of a geometric system of two right triangles
In this question we find a geometric system with two right triangles generated by bisector AL, that is, a side that divides line segment CL into two segments of equal length. Then, the length of line segment LB is equal to:
CL = LB
Where CL and LB are measured in feet.
If we know that CL = 6 ft, then the length of line segment LB is 6 feet.
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Which of the following will be perpendicular to the line y = -1/4x + 10? Select all that apply. Please explain your answer choices.
a. y = 4x + 2
b. y = 1/4x - 9
c. y = -4x + 10
d. y = 4x - 5
Answers
Perpendicular lines have slopes that are opposite signs and reciprocals.
Since the line y = -1/4x + 10 has a slope of -1/4, the slope of the perpendicular line will be + 4/1 or 4. So any line with a slope of 4 will be perpendicular to y = -1/4x + 10.
This means A and D will be your answers.
if your school uses Desmos pls respond
50 points
Answers
Answer:
I use desmos!
Step-by-step explanation:
100 POINTS ILL GIVE BRAINLIEST PLEASEE
Answers
The required proof is completed by proving that triangle FCA and triangle DBE are congruent hence sides FA ≅ ED
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLIn the problem, since FG can safely be extended to FC also EG to EB so that
FC ≅ EB this is one side of the triangle
Similarly, AB can be extended to AC and DC to DB such that
AC ≅ DB another side of the triangle
Given that < C ≅ < B the required sides for congruency by the SAS rule is completed and thus FA = ED
The SAS rule have it that when two sides and the included angle of angle of a triangle is equal to that of another triangle then all the sides and the angels are equal therefore they are congruent triangles
since ΔFCA ≅ ΔEBD the corresponding sides are equal to each other
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2. The Linton family has a circular swimming pool. The radius of the pool is 15 feet_
circumference of the pool? Use 3.17 for
Answers
The required circumference of the pool is given as 95.1 feet.
What is the perimeter?Perimeter is the measure of the figure on its circumference. where the circumference of the circle is given as 2πr.
Here,
The Linton family has a swimming pool as of the circular profile.
The radius of the circular swimming pool is 15 feet
π = 3.17
Now,
Circumference of the swimming pool is given as,
= 2πr
Substitute the value in the above formula,
Circumference of the swimming pool = 2 × 3.17 × 15
= 95.1 feet.
Thus, the circumference is 95.1 feet.
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i have no idea how to do this pls help
Answers
Answer:
2
Step-by-step explanation:
How many 1/4 cups fit in a 1/2 cup?
This is a division problem.
We need to divide 1/2 by 1/4.
1/2 ÷ 1/4 =
= 1/2 × 4/1
= 4/2
= 2
Answer: 2
PLEASE I NEED HELP!!!!
Answers
Step-by-step explanation:
as you wrote correctly, proportional relationships are in the form
y = mx
that means the line has to go through the origin (0, 0). otherwise it is in the form
y = mx + b
which is still linear but not proportional.
1a.
the rate of change is between 2 points A and B
(Yb - Ya)/(b - a)
in our case e.g. (4, 5.52) and (8, 11.04)
(11.04 - 5.52)/(8 - 4) = 5.52 / 4 = 1.38
when we use other points we get the same result. we see e.g. that when we double x (pounds), then also y (cost) is doubled.
the rate of change is 1.38.
this is also called the slope of the line.
b.
as mentioned in a., when we multiply x by a factor, then y is multiplied by the same factor. it also means that the function contains (0, 0) : for 0 pounds we pay $0.
c.
y = 1.38x
2a.
the slope is (as it is the same as the rate of change) the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another.
we try to find points with integer coordinates to do that.
I see e.g. (3, 4) and (6, 8).
x changes by +3 (from 3 to 6).
y changes by +4 (from 4 to 8).
so, the slope is +4/+3 = 4/3.
b.
the simplest indicator is that the line goes through the origin (0, 0), which it does.
c.
y = (4/3)x
..
gujhtuvvvfgvbbhtdxccgyujjgttggg
Answers
Answer:
do you need help with anything if not hello
Step-by-step explanation: