By applying the Sine Law and rearranging the equation, we can determine the missing parts of the triangle and solve for angles and sides.
We will draw a triangle based on the given measures and then use the Sine Law to solve for the other parts. The Sine Law relates the measures of angles and sides in a triangle.
Let's assume we have a triangle with sides a, b, and c, and angles A, B, and C, respectively. To solve for the other parts using the Sine Law, we need at least one side and its corresponding angle.
Suppose we are given side A and angle A. We can draw the triangle accordingly. The side opposite angle A will be labeled "a," and angle A will be opposite side a.
Next, we can use the Sine Law, which states that the ratio of a side length to the sine of its opposite angle is constant. The Sine Law can be expressed as:
a/sin(A) = b/sin(B) = c/sin(C)
With this information, we can solve for the other parts of the triangle. If we are given side A and angle A, we can use the Sine Law to find the ratios of the other sides to their corresponding angles.
By rearranging the Sine Law equation, we can solve for the unknown sides or angles. For example, to find side b, we have:
b = (a * sin(B)) / sin(A)
Similarly, we can find side c using:
c = (a * sin(C)) / sin(A)
And we can find the other angles using the inverse sine function:
B = sin^(-1)((b * sin(A)) / a)
C = sin^(-1)((c * sin(A)) / a)
By applying the Sine Law and rearranging the equation, we can determine the missing parts of the triangle and solve for angles and sides.
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Why is 1 + (−5) equal to −4? (1 point)
a) Because it is 5 units to the right of 1 on a horizontal number line
b) Because it is 5 units to the left of 0 on a horizontal number line
c) Because it is 5 units to the right of 0 on a horizontal number line
d) Because it is 5 units to the left of 1 on a horizontal number line
I'm pretty sure it's D
Filler to post
Answer: The Answer is (D)
Step-by-step explanation: Because the positive number is before the negative number and all you got to do is go 1 positive number to the right and there is your Answer.
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Need this answered.
Please Show work, Thanks! :)
Answer:
A
Step-by-step explanation:
i use the foil method
you can find more information on yt
MATH QUESTION ON SLOPESSSSSSS
Given: m = 3/2 and b = -1
The slope and y-intercept for a linear equation are given. Which graph matches this information?
the graph of f(x) is shown below. what are the values of a, b, c, and d in the definition of f(x) below? (graph and definition of f(x) shown in attached image)
Answer:
Step-by-step explanation:
For the given piecewise function,
Let the equation of the segment AB is,
y = ax + 7 where x < -2
Since a point (-2, 3) lies on the given line,
3 = a(-2) + 7
3 - 7 = -2a
a = 2
Therefore, f(x) = 2x + 7 when x < -2
For the segment BC,
f(x) = 3 where -2 ≤ x ≤ 2
For the segment CD,
f(x) = bx + 9
Since a point (2, 3) lies on this segment,
f(2) = 2b + 9 = 3
2b = 3 - 9
b = -3
Therefore, equation of segment CD will be,
f(x) = (-3)x + 9 where x > 2
what number would “x” be ?
Answer:
11
Step-by-step explanation:
To divide these terms we should subtract x from 7
19^7/19^x = 19^-4
19^7-x = 19^-4
7 - x = -4
-x = -4 -7
x = 11
help pls...........................
Answer:
220%,2.2,√5,2.25
Step-by-step explanation:
220%=2.2
√5=2.23
If X= 24, and b = 20
what does x²+b²-123 equal
Answer:
853
Step-by-step explanation: hope this helps
Answer:
853
Step-by-step explanation:
Hope this helps!
24^2 = 976
20^2 = 400
976+400-123= 853
Carmen suele ir a la biblioteca de su barrio cada 28 días, Rafael cada 25 y Teresa cada 22. El día 12 de septiembre se encuentran los 3 amigos. ¿Qué día volverán a coincidir?
Responder:
7.700
Explicación paso a paso:
Dado que:
Carmen va a la biblioteca cada 28 días
Rafael va a la biblioteca cada 25
Theresa cada 22 días.
Si todos se reunieron el 12 de septiembre, ¿cuándo volverán a reunirse?
Para obtener la fecha de su próxima reunión, multa el mínimo común múltiplo de los diferentes días en que Theresa, Rafael y Carmen van a la biblioteca
____28__25__22
__2_14__25___11
__2_7__25___11
__5_7__5____11
__5_7__1____11
__7_1__1____11
_ 11_1__1 ____1
Por lo tanto, el múltiplo común más bajo:
(2 * 2 * 5 * 5 * 7 * 11) = 7700
Por lo tanto, todos se volverán a encontrar en el nido 7.700 días
Mr. and Mrs. Rainer took out a $240,000 loan to purchase their home. If the interest rate on the loan is 1.2% compounded bimonthly, how much interest will they have paid after 30 years?
I NEED HELP ASAP (Picture is attached) IF YOU ANSWER YOU A REAL ONE! (WORD PROBLEM)
Which expression is equivalent to 5m + m + 2m?
Answer:
8m
Step-by-step explanation:
?11 re raising money for their class trip by having a bake sale. If they sell okies at $0.30 apiece, then the total
number of dollars ed by the expression .7p + .3k. The class expects to The eighth graders a p cupcakes at
$0.70 apiece and kco raised at the bake sale is represent sell 110 cupcakes and 150 cookies.
The class expects to raise $122 from selling 110 cupcakes and 150 cookies at the given prices.
It seems like there is some incomplete or unclear information in your statement. However, I can provide you with some interpretation based on the information provided.
If the eighth graders sell cupcakes at $0.70 apiece and cookies at $0.30 apiece, the total amount of money raised can be represented by the expression 0.7p + 0.3k, where p represents the number of cupcakes sold and k represents the number of cookies sold.
The class expects to sell 110 cupcakes and 150 cookies. Plugging these values into the expression, we can calculate the total amount raised:
Total amount raised = (0.7 * 110) + (0.3 * 150)
= 77 + 45
= $122
Therefore, the class expects to raise $122 from selling 110 cupcakes and 150 cookies at the given prices.
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1. What is the value of x in the equation ? 2x -12 = ?
3
Answer:
15/2
Step-by-step explanation:
Consider a rabbits population p(t) of a country satisfies the differential equations dp/dt=kp(400-p) with k constant, if population in 1960 was 100 million and was then growing at the rate of 2 million per year. Predict this country's population for the year 2010 ?
Answer:
Step-by-step explanation:
Given the differentials equation
dp/dt=kp(400-p)
dp/p(400-p) = kdt
Integrating both sides
1/200(lnp - ln(400-p)) = kt+C
(lnp - ln(400-p)) = 200kt+C
ln(p/400-p) = 200kt+C
p/400-p = Ce^200kt
At t = 0, P(t) = 100
On substituting
100/400-100 = Ce^200k(0)
100/300 = C
C = 1/3
Since the population is growing at 2 million per year, then at t = 1, p(t) = 102
1 = kp(400-p)
1 = k(102)(400-102)
1 = k(102)(298)
1 = 30396k
k = 1/30396
Next is to predict the population by 2010.
From 1960 to 2010, there are 50years
Using the expression
p/400-p = Ce^200kt.
p(50)/400-p(50) = 1/3e^200(50)/30396
p(50)/400-p(50) = 1/3e^10000/30396.
p(50)/400-p(50) = 1/3e^0.3289
p(50)/400-p(50) = 0.4631
P = (400-p)0.4631
p = 185.26-0.4631p
1.4631p = 185.26
p = 185.26/1.463
p = 126.63
Hence the country's population by 2010 is approximately 127million
3 f(x)=4x−3, find f ( − 5 ) f(−5)
Answer:
Step-by-step explanation:
f(-5)= 4(-5) - 3 = -20-3 = -23
The height of a golf ball hit in the air is modeled by the equation H(t)=-16t²+48t, where H represents the height, in feet , and t represents the number of seconds that have passed since the ball was hit What is the height of the ball after 2 seconds?
The ball is at a height of _________ feet after 2 seconds
*hint, 2 seconds is the time. Plug in the 2 for t to find the height h(t) using the order of operations.
T is time, so replace t with 2 seconds and solve:
-16(2)^2 + 48(2)
-16(4) + 96
-64 + 96 = 32
The ball is 32 feet high in 2 seconds
Answer:
The ball is 32 feet high in 2 seconds
Step-by-step explanation:
T is time, so replace t with 2 seconds and solve:
-16(2)^2 + 48(2)
-16(4) + 96
-64 + 96 = 32
The ball is 32 feet high in 2 seconds
Which factor could be part of the function so that f (x) decreases as x approaches infinity and as x approaches negative infinity? Select all that apply. f(x) = (3x + 1)(2x - 5)(x + 9)(?) Select all that apply: -4
-2/3x
5x2 (3x-7) -(x + 4)
The factor that could be part of the function so that f (x) decreases as x approaches infinity and as x approaches negative infinity is -(x + 4).
The function f(x) decreases as x approaches infinity and as x approaches negative infinity if and only if the degree of the polynomial in the denominator is greater than the degree of the polynomial in the numerator. This means that the factor that completes the function f(x) = (3x + 1)(2x - 5)(x + 9)
Let us analyze each of the factors:
(3x + 1) is a linear factor that does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
(2x - 5) is also a linear factor that does not help in decreasing function as x approaches infinity and as x approaches negative infinity.
(x + 9) is a linear factor that does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
(-4) is a constant term that does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
(-2/3x) is a linear factor that does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
5x² is a quadratic factor that is of degree 2 and thus does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
(3x-7) is also a quadratic factor that is of degree 2 and thus does not help in decreasing the function as x approaches infinity and as x approaches negative infinity.
-(x + 4) is a linear factor of degree 1 and it helps in decreasing the function as x approaches infinity and as x approaches negative infinity.
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The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0). The focus of the reflector is 6 feet above the vertex. The reflector extends 5.5 feet to either side of the vertex. What is the depth of the reflector? Round your answer to the nearest hundredth.
The depth of the reflector is about _____
feet.
Answer:
1.26 feets
Step-by-step explanation:
Given the following :
Vertex (0, 0)
Focus of reflector = 6 feets
Extension = 5.5 feets
Equation to obtain conic section of a parabola:
(x - h)² = 4p(y - k)
Vertex (0, 0)
h =0 ; k = 0, p = 6, x = 5.5
(5.5 - 0)² = 4*6(y - 0)
30.25 - 0 = 24(y - 0)
30.25 = 24y
y = 30.25 / 24
y = 1.26
Hence, depth of reflector = 1.26 feets
If the degree in the numerator is smaller than the degree in the denominator and there is no vertical
shift, then there is a vertical horizontal at y = 0.
O True
O False
Step-by-step explanation:
what do u think ?
not always true so the answer is false
Propositional Logic a) If P is the statement that 2 > 1 and Q is the statement that 32 = 4, write out in English (without simplification!) the statement (P A Q) V (-Q). Is this statement true? Can you see a simpler logically equivalent statement? b) You have encountered a person who is known to either always lie or always tell the truth. She tells you that "If either P or not P, then both P and not P." You do not know the truth value of P, but can you tell whether this person is a truth teller or a liar?
A simpler logically equivalent statement is "2 > 1 or not 32 = 4." This statement is true because 2 is greater than 1, regardless of whether or not 32 equals 4.
If P is the statement that 2 > 1 and Q is the statement that 32 = 4, then the statement (P A Q) V (-Q) is **"2 > 1 and 32 = 4 or not 32 = 4."**
If you encounter a person who is known to either always lie or always tell the truth, and she tells you that "If either P or not P, then both P and not P," then you can tell that she is **a liar.**
This is because the statement "If either P or not P, then both P and not P" is a **contradiction**. A contradiction is a statement that is always false. In this case, the statement is false because it is impossible for both P and not P to be true at the same time.
Since the person is known to either always lie or always tell the truth, and she has just told you a contradiction, you can conclude that she is a liar.
Here is a table showing the truth values of the statement "If either P or not P, then both P and not P" for different truth values of P:
| P | Not P | "If either P or not P, then both P and not P" |
|---|---|---|
| True | False | False |
| False | True | False |
| True | True | False |
| False | False | True |
As you can see, the statement is false regardless of the truth value of P. This means that the person who told you this statement must be a liar.
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Given g(x) equal -3x-4 find g (1)
Answer:
g(1) = -7
Step-by-step explanation:
Step 1: Define
g(x) = -3x - 4
g(1) is x = 1
Step 2: Substitute and Evaluate
g(1) = -3(1) - 4
g(1) = -3 - 4
g(1) = -7
Answer:
-7
Step-by-step explanation:
-3x-4
-3(1)-4
-3-4
-7
Hope this helps and can I have brainliest!
Jordan missed 10% of the problems on the test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Jordan missed?
Answer:
13
Step-by-step explanation:
10 % of 125 is 12.5 which is approximately 13
Q is th midpoint of pr.if pq = x+8 and qr =9x, what is the qr
Answer:
Step-by-step explanation:
7x5=35 i hope this helps
As Q is the midpoint of pr the value of qr will be 9 units
What is midpoint of line segment?
The midpoint divides the line segment into two equal parts.
Here in the question It is given that q is the midpoint of pr which implies q will divide pq into two equal parts that is pq (x+8) equals qr (9x). now calculating x value first :
[tex]\begin{aligned}pq&=qr\\x+8&=9x\\8x&=8\\x&=1\end{aligned}[/tex]
Now, qr will be [tex]9x=9\cdot1=9[/tex]
Therefore, As Q is the midpoint of pr the value of qr will be 9 units
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Determine if the equation has ONE solution, NO solution, or INFINITE solutions. 6x+3+2x=8x+7-10 O intimate solutions O ONE solution. O NO solutions
Answer:
No solution
Step-by-step explanation:
It is no solution because if they simplify it gets 3=7-10 which is not possible so it is no solutions
Answer:
Infinite solutions.
Step-by-step explanation:
First, you want to combine like terms. (combine 6x and 2x, and combine 7 and -10.)
8x + 3 = 8x - 3
Next, you want to move + 3 to the other side.
8x = 8x + 3 - 3
After that, you want to subtract 3 - 3.
8x = 8x + 0
Now, you move the 8x to the other side.
8x - 8x = 0
Next, you subtract 8x - 8x.
0 = 0
0 = 0 means that all real numbers are solutions. The equation also is an identity. So, the answer to this problem is infinite solutions.
Hope this helps! <3
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 4: zeros: O 3-5i, 4i
O 3+5i, 4-i O -3-5i,-4
We have all the zeros of the polynomial. Therefore, there are no remaining zeros of f(x). The given polynomial f(x) is a degree 4 polynomial. The given zeros of f(x) are `3-5i`, `4i`, `3+5i` and `4-i`.
We have to find the remaining zeros of f.
The remaining zeros of f are the solutions of f(x) = 0 which are not given in the question. Degree of polynomial = 4
We are given all the four zeros of the given polynomial.
So, we can write the expression for f(x) by using all these zeros.
f(x) = a(x - 3 + 5i)(x - 3 - 5i)(x - 4i)(x - 4 + i) [Using the zero factor property]
Now, we have to find the remaining zeros.
Let's find it out :f(x) = a(x - 3 + 5i)(x - 3 - 5i)(x - 4i)(x - 4 + i)f(x)
= a[(x - 3)² - (5i)²][(x - 4)² - (i)²]
(Using a² - b² = (a + b)(a - b))f(x)
= a[(x - 3)² + 25][(x - 4)² + 1] (Since i² = -1)f(x)
= a(x² - 6x + 34)(x² - 8x + 17)f(x)
= a[x⁴ - 14x² + 33x + 612] (Expanding the above expression)
The polynomial f(x) is a degree 4 polynomial.
Hence, we have all the zeros of the polynomial. Therefore, there are no remaining zeros of f(x).
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Find the length of the side of an equilateral triangle whose area is 9√3 cm2
Please help for 10 points
Answer:
s = 6 cm
Step-by-step explanation:
The area (A) of an equilateral triangle is calculated as
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is the length of side )
Here A = 9[tex]\sqrt{3}[/tex] , thus
[tex]\frac{s^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] ( multiply both sides by 4 to clear the fraction )
s²[tex]\sqrt{3}[/tex] = 36[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
s² = 36 ( take the square root of both sides )
s = [tex]\sqrt{36}[/tex] = 6
I need help plz 10 points
Answer:
The fraction in simplest form is: 25/3
Simplify as much as possible (5^3)^-2
Answer:
1/15625
Step by Step Explanation:
Its the right answer
1 if 10n+5= -5 what is -7n
2.if -3p + 8=26 what is -23+p
Step-by-step explanation:
10n= -5-5
10n= -10
n=-10/10
n=-1
then putting value of n in -7n
-7(-1)
7
2
-3p+8=26
-3p=26-8
-3p=18
p=18/-3
p=-6
putting value of p in -23+p
-23+(-6)
-29
Alonzo's suitcase can weigh no more than 20 kilograms if he wants to take it on the airplane without paying a fee. His suitcase weighs 220 hectograms. How much weight will Alanzo have to take out of his suitcase to meet the weight limit?
Given: Alonzo's suitcase can weigh no more than 20 kilograms if he wants to take it on the airplane without paying a fee.
Let x denote the weight of suitcase, then
We know that 1 kg =10 hg
Therefore, 20kg=
⇒
Since, the weight of his suitcase is 220 hg.
The amount of weight will Alanzo have to take out of his suitcase to meet the weight limit will be :-
Hence, 20 hg of weight have to take out of his suitcase to meet the weight limit.
Answer:
20 hectograms
Step-by-step explanation:
Hope this helps!
