Solve the following. List all possible possible solutions for the ambiguous case. #7
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The sum of the interior angles of any triangle is always 180º:
[tex]A+B+C=180[/tex]Use the equation above and the given data to find C:
[tex]\begin{gathered} C=180º-A-B \\ C=180º-38º-72º \\ C=70º \end{gathered}[/tex]Law of sines:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]Use the pair of ratios for a and b to solve a:
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB} \\ \\ a=sinA*\frac{b}{sinB} \\ \\ a=sin38º*\frac{12}{sin72º} \\ \\ a=7.8 \end{gathered}[/tex]Use the pair of ratios for b and c to solve c:
[tex]\begin{gathered} \frac{c}{sinC}=\frac{b}{sinB} \\ \\ c=sinC*\frac{b}{sinB} \\ \\ c=sin70º*\frac{12}{sin72º} \\ \\ c=11.9 \end{gathered}[/tex]Thenm, the solution for the given triangle is:A=38ºB=72ºC=70ºa=7.8b=12c=11.9
Related Questions
A total of $7000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if the annual interest is $510?
Answers
The total invested = $7000
Part of the money at 7% and the reminder at 15%
Let the part at 7% = x
So, the part at 15% = 7000 - x
Given the annual interest = $510
so,
7% of x + 15% of ( 7000 - x ) = 510
0.07 * x + 0.15 * ( 7000 - x ) = 510
0.07 x + 0.15 * 7000 - 0.15 x = 510
0.07 x + 1050 - 0.15x = 510
0.07 x - 0.15 x = 510 - 1050
-0.08 x = - 540
divide both sides by -0.08
x = -540/-0.08 = 6,750
7000 - x = 7000 - 6750 = 250
So, the part that is invested at a rate of 7% = $6,750
And the part that invested at a rate of 15% = $250
question will be in picture
Answers
ANSWER:
C. 50 fewer people will attend for every dollar the admission price increases.
STEP-BY-STEP EXPLANATION:
The equation in its slope and y-intercept form is as follows
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We have the following equation
[tex]n=800-50p[/tex]We can see that in this case the slope is - 50, therefore the answer would be 50 fewer people will attend for every dollar the admission price increases.
If ∆ABC is congruent to ∆PQR, find the length of QR.
Answers
If ∆ABC is congruent to ∆PQR, find the length of QR.
Given that If ∆ABC is congruent to ∆PQR:
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.
When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.
From the triangle ABC, the side BC = 4,
Hence the PQR, the side QR = 4 since they are congruent
A triangle has side lengths measuring 10m, 24m, and 26m. Explain how you use Pythagorean Theorem to determine whether or not the triangle is a right triangle.
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Hello there. To solve this question, we'll have to remember some properties about the pythagorean theorem and right triangles.
Given a triangle with side lengths 10 m, 24 m and 26 m, we have to determine whether this is a right triangle or not.
First, let's assume these are the sides lengths of a right triangle, as follows:
Notice in this case we choose the largest side to be the hypotenuse. We know that the largest side of a triangle has to be less than the sum of the legs and any combination would do, but since we'll apply the Pythagorean theorem, we already know that the hypotenuse has to be the largest side of the triangle.
For a right triangle with legs a, b and hypotenuse c, the Pythagorean theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, that is
[tex]a^2+b^2=c^2[/tex]Hence we plug a = 10, b = 24 and c = 26.
We have to see if this equality will hold for the values;
[tex]10^2+24^2=26^2[/tex]On the right hand side, square the number
[tex]676[/tex]On the left hand side, square and add the numbers
[tex]100+576=676[/tex]Notice we got the same answer, then we say that these values satisfy the Pythagorean theorem.
Therefore, this is a right triangle.
Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30N, and the other east and at an angle of 30 degrees northward and a tension force of 40 N. Find the components of the net force on the cart. Show all work.
Answers
The net force on the cart is 62N
and the vertical component =36.64 N
the horizontal component= 50N
What is revolution of vector?
The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component
30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.
40N tension isN 30° E which means
the vertical component= 40 sin60=36.64N
Horizontal component= 40 cos 60= 20N
sum of vertical = 36.64N +0= 36.64N
sum of horizontal= 30N+20N= 50N
60° was used for tension 40N because the angle of vector must always lie on the horizontal axis
therefore the net force F is obtained by using Pythagoras theorem
F= √(50^2+36.64^2)
= 62N to the nearest whole number.
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Analyze the graph of the function f(x)=4|x+7|+8 compared to the graph of the absolute value function g(x)=|x| .
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Given:
The functions
[tex]\begin{gathered} g(x)=|x| \\ f(x)=4|x+7|+8 \end{gathered}[/tex]Required:
Determine changes made in g(x) to get f(x).
Explanation:
The steps are:
[tex]\begin{gathered} f(x)=4|x+7|+8 \\ Shift\text{ the graph to the left }7\text{ units.} \\ Shift\text{ the graph upwards }8\text{ units.} \\ Apply\text{ a vertical stretch of }4\text{ units.} \end{gathered}[/tex]So. fourth option is describing the f(x).
The graph
Answer:
Completed the answer.
The functions rands are defined as follows.r(x)=32-4s(x) = -2x+4Find the value of s(r(-5)).s(r(-5)) = 00/0
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With the use of factorization, we can state that s and r have values of -2 and 3, respectively.
What is factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a POLYNOMIAL) into a product of another entity, Or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring.The given values are
r(x)= 3x-4 s(x)= -2x+4Solving with the help of factotisation.
s(r(-5))(2x-4)(3x-4-5)2x+4(3x-9)6x² - 6x - 36Dividing the eqn by 6
x²-x-6taking common factors= x(x-3) + 2(x-3)(x+2)(x-3)x= -2,3hence,from above solving we can say that values of s and r are: 2,3
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solve the system of equations using elimination (1/2)x+(1/3)y=4(1/3)x+y=-2
Answers
EXPLANATION
Let's consider the system of equations:
(1) (1/2)x + (1/3)y = 4
(2) (1/3)x +
I really need a clear, step-by-step explanation
Answers
1) 1/6
3) -7/6
what is the difference between rational and fractional numbers?Any number with the formula a/b, where both "a" and "b" are whole numbers, and where "b" ≠ 0, is a fraction. A rational number is one that has the pattern p/q, where p and q are both integers, and q≠0.Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators. Later, include and simplify.To learn more about : fractional numbers
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What is g(f(x)) if f(x) = 3x + 2 and g(x) = -2x + 4?
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⇒g(f(x)) means that in the function g(x) insert/plug in what f(x) is equal to in the place of x. f(x)= 3x+2 meaning in the place of x in g(x) insert 3x+2 and simplify.
[tex]g(f(x))=-2(3x+2)+4\\g(f(x))=-6x-4+4\\g(f(x))=-6x[/tex]
Attached is the solution of what g(f(x)) is equal to.
Use the graph of the function below to answer the questions.i just need help with b and c
Answers
Answer:
a) Yes
b) -3, 0, 2
c) [-1, -3], [3, -4], [5, -1]
Explanation:
a) From the graph, we can see that f(3) = -4.
Therefore, f(3) is negative
b) From the graph, we can see that the values of x for which f(x) = 0 are -3, 0, and 2.
c) From the graph, we can see that the values of x for which f(x) < 0 are -1, 3, and 5.
Using the interval notation, we'll have [-1, -3], [3, -4], [5, -1]
which representation shows y as a function of x?if you can't see c, is says: -1,0 -1,5-1,10-1,15
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At first ,we should know that :
The relation between x and y will be a function when each value of x appeared one time
We will check the options:
A. for the figure of option A, each value of x connected one time to a value of y
B . there are 2 arrows from 0 and 1
C. the values of x = -1 , connected four times to the value of y
So, the answer is option A
discriminant of the equation x squared minus 5x equals -2 is
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Recall that the "discriminat" of a quadratic equation of the form:
a x^2 + b x + c = 0
is given by the formula: b^2 - 4 a c
So for our equation:
x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:
x^2 - 5 x + 2 = 0
Now we recognize:
a = 1
b = - 5
c = 2
and write the discriminant
b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17
Then, the discriminat of the equation is: 17.
Ben has a 6 3/5 pound bag of granola. He wants to give his friends 3/4 pound of granola each. To how many friends can Ben
give granola?
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Answer:21 to each of his 3 friends
Step-by-step explanation:
5LATR이S20What is the value of sinEnter an exact value or round to the nearest hundredth.(5)
Answers
Sine:
[tex]\sin (x)=\frac{opposite}{hypotenus}[/tex]Using the calculator (in radians), we can get the value:
[tex]\sin (\frac{\pi}{3})\approx0.87[/tex]PLS HELP ME WITH THIS
Answers
Equation of the line in slope-intercept form = y = 8x − 1
How to calculate the equation of the line?
Given:
Co-ordinates of the first line (x, y)=(0,-1), (1,7), (2,15), (3,23),(4,31)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{7+1}{1-0}\\\\=8[/tex]
The slope - intercept form of a line is given by,
y = mx + b ---(1)
Let us substitute ( x, y )= (0, -1) in (1)
-1 =(8)*0+b
-1= b
b = - 1 ----(2)
Let us substitute m and b in the slope-intercept equation (1)
y = 8x − 1
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Sammy is 5 years younger than twice Lizzy's age. Sammy os 15 years old. How old is Lizzy?
Answers
Answer:
Lizzy is 40
Step-by-step explanation:
15 + 5 + 20
20 x 2 = 40
Answer:
35
Step-by-step explanation:
15 x 2= 30 + 5=35
the five is because he is 5 years younger than lizzy
adding to her age
Find two different ways to show that one third+ one fourth is not equal to 3/7. You can use numbers words and labels sketches.
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We can show that one third + one fourth is not equal to 3/7 by following two ways.
By Calculation.By Analysis. By Calculation.We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.
let's Consider we have value as 1.
∴ one third of value will be [tex] \frac{1}{3} [/tex]
∴ one forth of value will be [tex] \frac{1}{4} [/tex]
∴ three of seven of value will be [tex] \frac{3}{7} [/tex]
Now we can do the mathematic calculation on one third and one forth of the value.
As given we have to calculate the addition of one third and one forth of the value
∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]
= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make base same )
= [tex] \frac{4\ + 3}{12}[/tex]
= [tex] \frac{7}{12}[/tex]
∴ By the calculation we clearly got that the addition of one third and one forth of the value is equal to the seven of twelve of the value.
We can also prove it by analysis as follows ;
Proof by analysis:-Consider a number say 120.
∴ 1/3 of 120 will be 40
∴ 1/4 of 120 will be 30
∴ 3/7 of 120 will be 51.42
Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = 70
Comparing it with 3/7 i.e 51.42 ≠ 70
Hence proved 1/3 + 1/4 ≠ 3/7 .
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evaluate(if possible) the sine,cosine, and the tangent of the real number
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find the radius of the circle given the central angle and the area of the Shaded sector
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we have the following formula for the area of a sector of a circle:
[tex]A_s=\frac{\theta\cdot\pi}{360}\cdot r^2_{}[/tex]In this case, we have the following information:
[tex]\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}[/tex]then, using the formula and solving for r, we get the following:
[tex]\begin{gathered} 60\pi=\frac{24\cdot\pi}{360}\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=\frac{21600\pi}{24\pi}=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}[/tex]therefore, the measure of the radius is r = 30
Determine the distance between M(4, 0) and N(-2, -3).
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Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Step 2
let
P1=M(4,0)
P2=N(-2,-3)
replace
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}[/tex]I hope this helps you
I need to know the answer for this question?
Answers
The probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So,
Red socks: 10White socks: 6Blue socks: 8Total number of socks: 10 + 8 + 6 = 24
Formula: P = favourable events/Total number of events
Probability of picking a blue sock first:
P = 8/24P = 1/3Probability of picking a white sock at second:
P = 6/24P = 1/4Therefore, the probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
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Calculate the total loss after 4 years if 299000 is reduced by 4% per annum
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The total loss after 4 years is $47840.
How to calculate the value?From the information, we want to calculate the total loss after 4 years of 299000 is reduced by 4% per annum.
It should be noted that this simply means the calculation using the interest formula. In this case, the total loss will be gotten by knowing the interest.
In this case, the interest formula can be illustrated as:
Interest = PRT / 100
where P = Principal = 299000
R = Rate = 4%
T = Time = 4 years
Interest = (299000 × 4 × 4) / 100
Interest = 4784000 / 100
Interest = 47840
In this case, the calculation of the interest is the loss that the person gets.
Therefore, the loss is $47840.
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I need a run down on how to do multi step equations.Number 3 only
Answers
Answer:
x=-7
Explanation:
Given the equation:
[tex]8x-2=-9+7x[/tex]To solve equations of this form, the goal is to try to bring all the terms containing the variable (letter x or any letter) to one side of the equation and the constants to the other side.
First, subtract 7x from both sides.
[tex]\begin{gathered} 8x\textcolor{red}{-7x}-2=-9+7x\textcolor{red}{-7x} \\ x-2=-9 \end{gathered}[/tex]Next, add 2 to both sides.
[tex]\begin{gathered} x-2+2=-9+2 \\ x+0=-7 \\ \implies x=-7 \end{gathered}[/tex]The value of x is -7.
5
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2
If log₁/2x = -1, then the value of x is
a) 2
b) 1/2
c)-1
Answers
The value of the variable 'x' in logarithmic expression is: 2
What is logarithm?
In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.
According to the question, the given logarithmic expression are as follows:
[tex]log_{1/2}x = -1[/tex]
Using standard logarithmic property, we get
x = (1/2)^-1
⇒x = 2
Hence, the logarithmic value of the variable 'x' is: 2
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If there is more then one element in the set, separate them with commas
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Answer:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
Explanation:
The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Then, the outcome for the event that the select number is 2 is
Event that the number chosen is 2 = {2A, 2B, 2C}
Therefore, the answers are:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
my questions is about. latitude and longitude
Answers
Answer
Option B is correct.
The latitude and longitude of the point X is 42.5°N, 77.5°W
Hope this Helps!!!
Find the cos equation given amplitude: 6, period: 2π, vertical shift: 0, and horizontal shift:OA. y = 6 cos 0 + 2OB. y = 6 cos 0 - 2OC. y = 6 cos (0+²)OD. y = 6 cos (0-3)Reset Selection2T3
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Given: A cosine function with amplitude: 6, period: 2 pie, vertical shift: 0, and horizontal shift-
[tex]\frac{2\pi}{3}[/tex]Required: To determine the function.
Explanation: The cosine function is defined as-
[tex]y=Acos(Bx-C)+D[/tex]where
[tex]\begin{gathered} A=Amplitude \\ \frac{2\pi}{B}=Period \\ \frac{C}{B}=Phase\text{ shift} \\ D=Verical\text{ shift} \end{gathered}[/tex]Hence, the required function is-
[tex]y=6cos(x-\frac{2\pi}{3})+0[/tex]Final Answer: The function is-
[tex]y=6cos(x-\frac{2\pi}{3})[/tex]Hence, Option D is correct.
PLEASE HELP URGENT:
Graph the following function:
y=3sin(2x−π/2)−2
Drag the black dot to shift your graph in the desired direction. Use the blue draggable dot to change the period. Drag the orange dot to change the amplitude and/or reflect with respect to the x-axis. The horizontal distance between the vertical dotted green lines corresponds to one period.
Answers
A graph of this sine wave function y = 3sin( 2x + π/2) - 2.
A sine wave, also known as a sinusoidal wave or simply a sinusoid in mathematics, is a basic waveform that is frequently employed to describe periodic oscillations, with each interval's displacement amplitude being directly proportional to the sine of the displacement's phase angle.
This mathematical expression can be used to model or depict a sine wave mathematically:
y = asinbx
Where a represents the amplitude of a sine wave, b represents the periodicity.
After that, we would use the lowest common denominator (LCM) to solve the sine wave function given:
y = 3sin( 2x - π/2 ) - 2
y = 3sin( ( 2(2x) - π)/2) - 2
y = 3sin( ( 4x - π)/2 ) - 2
In conclusion, this sine wave function has an amplitude of 3 and a periodicity is 2.
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Find the linear equation of the plane through the point (1, 3, 10) and parallel to the plane x+6y+2z+4=0
Answers
The most appropriate choice for equation of plane will be given by-
Required equation of plane is [tex]x + 6y +2z=39[/tex]
What is a plane?
A surface which is spanned by two linearly independent vectors is called a plane.
The general equation of plane is [tex]ax + by + c =d[/tex] where
[tex](a,b,c)[/tex] are the components of normal vectors.
Equation of the plane parallel to [tex]x + 6y +2z=-4[/tex] is
[tex]x +6y+2z=c[/tex] [As the perpendicular vector of two parallel planes are same]
The required plane passes through (1, 3, 10)
Putting [tex]x=1, y=3,z=10[/tex] in [tex]x + 6y+2z=c[/tex]
[tex]1 + 6 \times 3 + 2\times 10 = c\\1 + 18+20=c\\c=39[/tex]
So, Required equation of plane is [tex]x + 6y +2z=39[/tex]
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