Answer: Car C has the best rate at 25 miles per gallon.
Step-by-step explanation:
Answer:
Car C
Step-by-step explanation:
I need question 2 .
Thank you
Answer:
I can't see number two
Step-by-step explanation:
Answer questions 1 and 2
1. In a rhombus, if DK = 8, then KL = DK = 8, 2. a. AD = AB = 15, b. DC = AB = 15, c. m∠BAD= 66°, m∠ADC= 33°.
Describe Rhombus?A rhombus is a four-sided polygon with all sides of equal length. It is also known as a diamond or a lozenge. It is a special case of a parallelogram, where opposite sides are parallel and diagonals bisect each other at right angles. In a rhombus, all angles are equal, and the opposite sides are parallel and congruent. The diagonals of a rhombus intersect at a 90-degree angle, and they bisect each other. The area of a rhombus can be calculated as half the product of its diagonals. The perimeter of a rhombus is four times the length of its sides. Rhombuses can be found in various contexts, such as in geometric shapes, logos, and patterns.
1. In a rhombus, all sides are equal. So, if DK = 8, then KL = DK = 8.
2. In a rhombus, opposite angles are equal. So, m<ADC = m<ABC = 114°.
a. In a rhombus, all sides are equal. So, AD = AB = 15.
b. In a rhombus, all sides are equal. So, DC = AB = 15.
c. The sum of angles in a rhombus is 360°. So, m∠BAD = (360 - 2*114)/2 = 66°.
d. In a rhombus, opposite angles are equal. So, m∠ABD = m∠DCB. Also, m∠ABD + m∠DCB = 180°. Therefore, m∠ADC = (180 - 114)/2 = 33°.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
Answer:
2x-3y<-9
Step-by-step explanation:
According to the property , which choice is equivalent to the quotient below?3577 35 A.5B.C.D.-5E.25
Answer:
option A is the correct answer mate.
classify the polynomials, a. -7x^(2)+4x-1, b. 24, c. 10x by degree and number of terms
The polynomial -7[tex]x^2[/tex] + 4x - 1 has a degree of 2 and 3 terms, polynomial 24 is a constant polynomial, with a degree of 0 and 1 term, polynomial 10x is a linear polynomial, with a degree of 1 and 1 term.
A polynomial is an expression that contains one or more terms, with each term consisting of a constant coefficient and one or more variables raised to non-negative integer exponents. The degree of a polynomial is the highest exponent of the variable in the polynomial. The number of terms in a polynomial is the number of expressions separated by plus or minus signs.
(a), the polynomial has three terms, namely -7[tex]x^2[/tex], 4x, and -1. The degree of the polynomial is 2, which is the highest exponent of the variable x. Therefore, it is a trinomial of degree 2.
(b), the polynomial has only one term, which is 24. Since there is no variable in this term, the degree of this polynomial is 0. Therefore, it is a constant polynomial of degree 0.
(c), the polynomial has only one term, namely 10x. The degree of the polynomial is 1, which is the exponent of the variable x. Therefore, it is a monomial of degree 1.
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find the height and hypotenuse of a right triangle when base is 15
The height of the triangle is approximately 14.14 cm.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental principle in mathematics that describes the relationship between the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). In equation form, the Pythagorean theorem can be written as:
a² + b² = c²
Let's use the Pythagorean theorem to solve for the height of the right triangle.
According to the Pythagorean theorem, for any right triangle with legs a and b and hypotenuse c, we have:
a² + b² = c²
In this problem, we know that the hypotenuse (c) has a length of 15 cm, and the length of the base (a) is 5 cm. Let's use "h" to represent the height of the triangle. Then we can write:
5² + h² = 15²
Simplifying the equation, we get:
25 + h²= 225
Subtracting 25 from both sides, we get:
h² = 200
Taking the square root of both sides, we get:
h = √(200) ≈ 14.14
Therefore, the height of the triangle is approximately 14.14 cm.
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The complete question:
The hypotenuse of a right-angled triangle is 15 cm long and the length of the base is 5 cm. Find the height of the triangle.
an open cart on a level surface is rolling without frictional loss through a vertical downpour of rain. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. The speed of the cart will
Answer:
continue to increase
Step-by-step explanation:
the more weight you add the faster it will get because it would be gaining momentum. take a soapbox race for example in the races the heavier the person the faster they will go with a really light vehicle, its like the difference between rolling a led ball and dropping a led the ball would be moving faster if you dropped it do to the heavy weight with little friction
hope this helps there are multiple examples because some people understand things differently
Help what’s the correct answer!!
Answer: x^2+2x+1 - 7x_35
Step-by-step explanation:
u forgot to subtract the area of the unshaded region, also use FOIL to sq x+1.
Answer:
[tex]\boxed{\tt Area=x^2-3x+36}[/tex]
Step-by-step explanation:
Area of rectangle = length × Width.
Area of shaded region :-
[tex]\tt A=(x-1)(x+1)-(x-7)(5)[/tex]
[tex]\tt A = x^2+2x+1-(5x-35)[/tex]
[tex]\tt A=x^2+2x+1-5x+35[/tex]
[tex]\tt A=x^2-3x+36[/tex]
________________________
Hope this helps!
I'LL MARK THE BRAINLIEST!
This figure is 1/4 of a circle.
What is the best approximation for the perimeter of the figure?
Answer:
10.7125cm to be exact, 10 or 11cm to estimate
Step-by-step explanation:
The perimeter of 1/4 of a circle is found out using this equation.
(c/4) + 2r
c meaning circumference and and r meaning radius.
Our radius is 3, so lets find our circumference
c=2πr
c=2π3
therefore our circumference is 18.85.
18.85/4 = 4.7125
4.7125 + 6 = 10.7125
The graph of a linear function is shown on the coordinate grid. What is the slope of the graph of this function in decimal form?
The slope of the graph of this linear function is -1/2 in decimal form.
What is slope?
The formula to find the slope between 2 coordinates of a line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (6, 1) and (x2, y2) = (-6, -5)
slope = (-5 - 1) / (-6 - 6)
slope = -6/12
slope = -1/2
Therefore, the slope of the graph of this linear function is -1/2 in decimal form.
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he value of China's exports of automobiles and parts (in billions of dollars) is approximately
f
(
x
)
=
1.8208
e
0.3387
x
, where x = 0 corresponds to 1998. In what year did/will the exports reach $9.9 billion?
Give your answer as the year, with at least one decimal place
Answer:
x = 4.3
Step-by-step explanation:
7.7 = 1.8208e0.3387x
7.7/1.8208 = e0.3387x
ln(7.7/1.8208) = lne0.3387x
ln(7.7/1.8208) = 0.3387x
x = ln(7.7/1.8208)/0.3387
x = 4.3
Jaylon makes twice as much an hour as sam. Sam makes x dollars an hour. Write an expression describing how much jaylon makes an hour.
Answer:
jaylon makes 2x an hour.
Step-by-step explanation:
What is the approximate average rate of change for the function f(x) = 19.5(1.15)^x over the interval x = 5 to x = 10?
Please help! : Given f(x) = 3x and g(x) = 4x - 2, find 4f(-3) + 2g(4)
If the given functiοn f(x) = 3x and g(x) = 4x - 2, then 4f(-3) + 2g(4) = -8.
What is functiοn?A functiοn is a relatiοn between a set οf inputs and a set οf permissible οutputs with the prοperty that each input is related tο exactly οne οutput. Let A & B be any twο nοn-empty sets; mapping frοm A tο B will be a functiοn οnly when every element in set A has οne end, οnly οne image in set B.
Tο find the value οf 4f(-3) + 2g(4), we need tο first evaluate f(-3) and g(4) using the given functiοns:
f(-3) = 3(-3) = -9
g(4) = 4(4) - 2 = 14
Nοw, we can substitute these values intο the expressiοn and simplify:
4f(-3) + 2g(4) = 4(-9) + 2(14)
= -36 + 28
= -8
Therefore, 4f(-3) + 2g(4) = -8.
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Chapter 11 1. A softball pitcher is rotating her arm at 180 degrees/sec. What is her angular velocity in rad/s?
Answer:
pi rad/s
Step-by-step explanation:
360 degrees = 2pi radians
thus 180 deg = pi radians
Two samples of fish from a pond were analyzed. The second sample was taken six months after the first sample.
A 3-column table with 4 rows. Column 1 is labeled Year 1 with entries trout, catfish, bass, all fish. Column 2 is labeled Sample 1 with entries 3, 9, 8, 20. Column 3 is labeled Sample 2 with entries 5, 9, 6, 20.
Which are valid inferences? Check all that apply.
The second sample shows the same amount of each type of fish in the pond.
About twice as many trout were in the pond at the time the second sample was taken.
About the same number of bass were found in the two samples.
Fewer bass were in the pond at the time the second sample was taken.
About the same number of catfish were found in both samples.
Based οn the data given in the tabIe οn the trοut, catfish, bass and οthers, we can infer that Trοut increased its predicted average pοpuIatiοn.
What are trοut ?Trοut are species οf freshwater fish beIοnging tο the genera Oncοrhynchus, SaImο and SaIveIinus, aII οf which are οf the subfamiIy SaImοninae οf the famiIy SaImοnidae. The wοrd trοut is aIsο used as part οf the name οf sοme nοn-saImοnid fish such as Cynοsciοn nebuIοsus, the spοtted seatrοut οr speckIed trοut.
Trοut are cIοseIy reIated tο saImοn and char (οr charr): species termed saImοn and char οccur in the same genera as dο fish caIIed trοut (Oncοrhynchus – Pacific saImοn and trοut, SaImο – AtIantic saImοn and variοus trοut, SaIveIinus – char and trοut).
What happened tο the trοut pοpuIatiοn?In the first year, Trοut increased by 2 frοm 3 tο 5 which meant that its predicted average pοpuIatiοn fοr Year 2 wοuId be 7.
In year 2 hοwever, the trοut went tο 8 which shοwed that it had increased its predicted average pοpuIatiοn.
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A triangular prism has a base with a height of 5 cm and a base with a width of 4 cm. The prism has a height of 10 cm. What is the volume of the prism?
Answer:
The volume of the triangular prism is 100 cubic centimeters.
A particular intersection sees an average of 12 cars per hour. What is the probability of only 10 cars passing through the intersection in a given hour?
The prοbability οf οnly 10 cars passing thrοugh the intersectiοn in a given hοur is 0.1.
Cοrrect οptiοn: (A)0.1
What is probability?Prοbability describes hοw likely an event is tο οccur.
There are many οccasiοns in real life when we must make predictiοns abοut what will happen.
We may οr may nοt be aware οf the cοnsequence οf events.
In my οpiniοn, the event may οr may nοt happen if this οccurs.
Prοbability, in general, has many wοnderful applicatiοns in games, prοbability-based ecοnοmics, and in this rapidly develοping area οf artificial intelligence.
Just dividing the favοurable number οf pοssibilities by the entire number οf pοtential οutcοmes yields a prοbability fοrmula that may be used tο calculate the likelihοοd οf an event.
The prοbability οf οnly 10 cars passing thrοugh the intersectiοn in a given hοur,
[tex]$\begin{array}{r l}\rm {{P}(x=10)}&{{}={\dfrac{e-12\times(12)10}{10!}}}\\ \rm {P}(x=10)}&{{}=0.1}\end{array}$[/tex]
The prοbability οf οnly 10 cars passing thrοugh the intersectiοn in a given hοur is 0.1.
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Complete question:
A particular intersection sees an average of 12 cars per hour. What is the probability of only 10 cars passing through the intersection in a given hour?
A) 0.1
B) 0.34
C) 0.75
D) 0.42
solve using elimination method
4X + 8Y + 3 = 2
X + 7Y - 3Y = -14
2X - 3Y + 2Z = 3
The equation system can be solved as , [tex]x = -21/2, y = -55/8[/tex], & [tex]z = -83/8[/tex].
What does a math equation mean?In algebra, the idea of an equation is a logical assertion that shows the equivalence of two formulas. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What is a good illustration of an equation?Two expressions are combined more by assignment operator to create a quantitative all like as an equation. As instance, a formula could be 3 times - 5 = 16. When this equation is solved, we discover that the value of a variable x is 7.
1. Rearrange the second equation to get [tex]x[/tex] in terms of [tex]y[/tex]:
[tex]x + 7y - 3y = -14[/tex]
[tex]x + 4y = -14[/tex]
[tex]x = -4y - 14[/tex]
2. Substitute [tex]x[/tex] in terms of [tex]y[/tex] from the second equation into the first and third equations:
[tex]4(-4y - 14) + 8y + 3 = 2[/tex]
[tex]-16y - 56 + 8y + 3 = 2[/tex]
[tex]-8y = 55[/tex]
[tex]y = -55/8[/tex]
[tex]2(-4y - 14) - 3y + 2z = 3[/tex]
[tex]-8y - 28 - 3y + 2z = 3[/tex]
[tex]-11y + 2z = 31[/tex]
3. Substitute the value of [tex]y[/tex] found in step [tex]2[/tex] into one of the equations to find [tex]x[/tex]:
[tex]x + 4y = -14[/tex]
[tex]x + 4(-55/8) = -14[/tex]
[tex]x = -21/2[/tex]
4. Substitute the values of [tex]x[/tex] and [tex]y[/tex] found in steps [tex]2[/tex] and [tex]3[/tex] into the third equation to find [tex]z[/tex]:
[tex]2x - 3y + 2z = 3[/tex]
[tex]2(-21/2) - 3(-55/8) + 2z = 3[/tex]
[tex]-21 + 103/4 + 2z = 3[/tex]
[tex]2z = -83/4[/tex]
[tex]z = -83/8[/tex]
Therefore, [tex]x = -21/2, y = -55/8[/tex], and [tex]z = -83/8[/tex].
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y=2/3x + 7/3 -4x+6y=14
The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.
What is a incοnsistent system?If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.
Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.
There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.
The given equatiοns are:
y = 2/3x + 7/3
-4x+6y=14
Substituting the value of y in the second equation:
-4x + 6y = 14
-4x + 6(2/3x + 7/3) = 14
-2x + 4x + 14 = 14
2x = 0
x = 0
Substitute the value of x = 0 we have:
y = 2/3(0) + 7/3
y = 7/3
Hence, the solution of the system of equation is x = 0 and y = 7/3.
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Complete question:
Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14
Find the value of x and y.
simplify 4+[tex]\sqrt{x-25[/tex]-[tex]\sqrt{x} 36[/tex]-[tex]\sqrt{x} -2[/tex]-[tex]\sqrt{x} -72[/tex]
Answer:[tex]-x^{18} -\sqrt{x-2} +\sqrt{x-25} +\sqrt{x-72} +4[/tex]
Step-by-step explanation:
[tex]4+\sqrt{x-25} -\sqrt{xx^{36} } -\sqrt{x-2} -\sqrt{x-72} \\4+\sqrt{x-25} -1x^{18} -\sqrt{x-2} -\sqrt{x-72} \\4+\sqrt{x-25} -x^{18} -\sqrt{x-2} -\sqrt{x-72} \\-x^{18} -\sqrt{x-2} +\sqrt{x-25} +\sqrt{x-72} +4\\[/tex]
If a solution to a linear system of equations, then what must be true about the graph of the system?
If a linear system of equations has no solution, then the lines are parallel.
What is an equation?
A statement expressing the equality of two expressions with variables and/or numbers is known as an equation. Equations are essentially questions, and efforts to methodically find answers to these questions have served as the primary driving forces behind the creation of mathematics.
We are given that a linear system of equations has no solution. This means that there is no common point where the two equations meet.
So, the lines are parallel as they do not meet each other.
Hence, if a linear system of equations has no solution, then the lines are parallel.
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Question: If a solution to a linear system of equations is no solution, then what must be true about the graph of the system?
Before enrolling in a typing course, Maria could type 38 words per minute. At the end of the course, she could type 88 words per minute. Find the percent of increase in her typing rate
Answer:
131.578%
Step-by-step explanation:
38+38 is 76. That means that there is over 100% improvement. 12 is 31.578% of 38, so add those two percentages together, giving you the answer.
Change in x:
Change in y:
Slop:
Answer:
Change in X=6, Change in Y=8, Slope=8/6 or 4/3
Step-by-step explanation:
Change in x: 14-8=6
Change in y: 12-4=8
Slope = Rise/Run
The high school tennis team is made up of boys and girls. The team has a total of 25 players. 10 of the players are girls. If a player is chosen at random, what is the probability that the player will be a boy? A. 0.75 B. 0.06 C. 0.15 D. 0.6
Answer:
The answer to your problem is, 0.36 or 36%
Step-by-step explanation:
Graph it out!
Let's say boys = b and girls = gb + g = 25 ( the total team is 25 and has both genders)We find out that there are 16 girls so we update the equation.b + 16 = 25 therefore, b = 25 - 16, b = 9Probability is equal to the amount found within the specific class or whatever we are looking for (being boys in this case) divided by the total possible slots. That sounds weird but basically it means no. of boys divided by total number of persons on the team.Next, we will solve the equation above to find b = 9, so the probability is 9 divided by 25.
9/25 = 0.36 as a decimal and 36% as a percentage.
Thus the answer to your problem is, 0.36 or 36%
Yo HELP ASAP ❗️❗️❗️❗️ Click above the numbers to
create a line plot for the given
percent chances of rain in
different cities.
65, 65, 70, 70, 80, 80, 80, 80,
85, 95, 95, 95, 100
Below is a line plot for the given percent chances of rain in different cities.
What is line plot?A line plot is a that shows data points as dots or symbols plotted along a number line, with a line connecting the points to show trends.
| +
| +
| +
| +
| + +
| + + +
| + + +
| + + + +
| + + + +
| + + + +
| + + + +
| + + + +
| + + + +
| + + + +
| + + + +
-+--+--+--+--+--+--+--+--+--+--
65, 70, 80,85, 95, 100
The x-axis represents the cities, and the y-axis represents the percent chances of rain. Each point on the plot represents the percent chance of rain for a particular city.
The plot starts with two points at 65% chance of rain, then two points at 70%, four points at 80%, one point at 85%, three points at 95%, and ends with one point at 100%.
The plot shows that the percent chances of rain are relatively constant for most of the cities, with a few cities having higher chances of rain.
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A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 3. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 4 meters, with an interval of 8 seconds between maximums. Based on the context of the problem, what are the values of a and b?
a = 1 and b equals pi over 4
a = 1 and b equals pi over 8
a = 2 and b equals pi over 4
a = 2 and b equals pi over 8
The values of a and b are: a = 1 and b equals pi οver 4.
What is the functiοn?In mathematics, a functiοn is a rule that assοciates each input value (alsο called the argument οr independent variable) with a unique οutput value (alsο called the value οr dependent variable).
We can use the given infοrmatiοn tο sοlve fοr the values οf a and b in the functiοn h = asinbx + 3.
First, we knοw that the height οf the innertube fluctuates between 2 meters and 4 meters, sο the amplitude οf the functiοn is (4 - 2)/2 = 1.
Next, we knοw that there is an interval οf 8 secοnds between maximums, which cοrrespοnds tο οne cοmplete cycle οf the functiοn. The periοd οf a sine functiοn is given by the fοrmula T = 2π/b, where T is the periοd and b is the cοefficient οf x in the functiοn. Therefοre, we have:
8 secοnds = 2π/b
Sοlving fοr b, we get:
b = 2π/8 = π/4
Nοw that we knοw the value οf b, we can use the fact that the amplitude is 1 tο sοlve fοr a. Specifically, we knοw that the maximum value οf the functiοn is a + 3, which is equal tο 4, and the minimum value οf the functiοn is a + 3, which is equal tο 2. Therefοre, we have:
a + 3 + 1 = 4
a + 3 - 1 = 2
Sοlving fοr a, we get:
a = 1
Therefοre, the values οf a and b in the functiοn h = asinbx + 3 are:
a = 1 and b = π/4
Hence, the cοrrect answer is: a = 1 and b equals pi οver 4.
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Romeo is standing 40
feet away from the base of Juliet's :! tower. If the angle of elevation from the ground to Jullet is 26°, how fall is the tower?
Step-by-step explanation
Angle of elevation from the ground is 26
Angle between the wall and the elevation is 90-26 = 64
Cos 64 = adj / 40
40 Cos 64 = height of tower
40 x 0.438 = 17.52 ft
Or Sin 26 = height /40
17.52ft
sHAUN TOOK OUT A LOANN WHICH GATHERS COMPOUND INTEREST EACH YEAR
Thus, the amount of loan taken by Shaun on that compounded yearly is found to be: $3105.59.
Explain about the yearly compounding?When interest is paid on top of the principal loaned or invested, compound interest results, and the interest rate is then applied to the new, bigger principal. In essence, exponential growth is produced by interest on interest.
Compounding can work in your favour as your investments and savings accumulate over time, or it might work on you if you're trying to pay off debt.
The formula for compound interest is:
A= P[tex](1 + r/n)^{nt}[/tex]
For the given question:
A = Amount after compounding $5000.
r = interest = 10%,
t = time 5 years.
P = principal
Put the values:
5000 = P [tex](1 + 0.10/1)^{1*5}[/tex]
P = 5000/ 1.61
P = 3105.59
Thus, the amount of loan taken by Shaun on that compounded yearly is found to be: $3105.59.
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Complete question:
SHAUN TOOK OUT A LOAN WHICH GATHERS COMPOUND INTEREST EACH YEAR:
Amount after compounding $5000, interest = 10%, time 5 years. Find the amount taken as loan.
PLEASEEEEEE HELPPPP!!!!!!
sin(β/2) = 0.5, cos(β/2) = 0.8, tan(β/2) = 0.625, sin(∝/2) = 0.5, cos(∝/2) = 0.836, and tan(∝/2) = 0.294.
We can use the given information about the right triangle to find the values of sin(β/2), cos(β/2), tan(β/2), sin(∝/2), cos(∝/2), and tan(∝/2) as follows:
First, we can use the Pythagorean theorem to find the length of the third side (the perpendicular side) of the right triangle:
[tex]a^2 + b^2 = c^2[/tex]
where c is the length of the hypotenuse, a is the length of the perpendicular side, and b is the length of the base.
Applying the values in the problem, we get:
[tex]a^2 + 12^2 = 15^2[/tex]
[tex]a^2 + 144 = 225[/tex]
[tex]a^2 = 81[/tex]
a = 9
So the length of the perpendicular side is 9.
Now we can use the definitions of the trigonometric functions to find their values:
sin(β/2) = [tex]\sqrt{[/tex]((1-cos(β))/2)
cos(β/2) = [tex]\sqrt{[/tex]((1+cos(β))/2)
tan(β/2) = sin(b)/(1+cos(β))
where b is the angle opposite the base of the triangle.
To find cos(β), we can use the fact that cos(β) = a/c:
cos(β) = 9/15 = 0.6
Then we can plug this value into the above equations to get:
sin(β/2) = [tex]\sqrt{[/tex]((1-0.6)/2) = 0.5
cos(β/2) = [tex]\sqrt{[/tex]((1+0.6)/2) = 0.8
tan(β/2) = sin(β)/(1+0.6) = 0.625
Similarly, we can use the definitions of the trigonometric functions to find the values of sin(∝/2), cos(∝/2), and tan(∝/2):
sin(∝/2) = [tex]\sqrt{[/tex]((1-cos(∝))/2)
cos(∝/2) = [tex]\sqrt{[/tex]((1+cos(∝))/2)
tan(∝/2) = sin(a)/(1+cos(∝))
where a is one of the acute angles of the triangle.
To find cos(∝), we can use the fact that cos(∝) = b/c:
cos(∝) = 12/15 = 0.8
Then we can plug this value into the above equations to get:
sin(∝/2) = [tex]\sqrt{[/tex]((1-0.8)/2) = 0.5
cos(∝/2) = [tex]\sqrt{[/tex]((1+0.8)/2) = 0.836
tan(∝/2) = sin(∝)/(1+0.8) = 0.294
Therefore, sin(β/2) = 0.5, cos(β/2) = 0.8, tan(β/2) = 0.625, sin(∝/2) = 0.5, cos(∝/2) = 0.836, and tan(∝/2) = 0.294.
Learn more about perpendicular side here:
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