Answer:
The values of x that satisfy the given equation are:
x1 = 1.183 + nπ
x2 = -1.183 + nπ
Step-by-step explanation:
Given tan²x - sin²x/sin²x = 5
Simplifying this, we have
tan²x - 1 = 5
Adding 1 to both sides, we have
tan²x = 6
Because tan²x = (tanx)², we can write as
(tanx)² = 6
Taking square roots of both sides, we have.
tanx = ±√6
x = arctan(±√6) + nπ
≈ 1.183 + nπ or -1.183 + nπ
The question asks to find a trigonometric value for x given a trigonometric equation. Clear solution steps cannot be provided due to ambiguity in the equation's presentation. Normally, one would use trigonometric identities or methods like Newton's method to find x.
Explanation:The question requires us to find a numerical value of one trigonometric function of x given the equation tan2x - sin2x/sin2x = 5. Although the provided reference text contains various trigonometric contexts, it lacks direct relation to solving the given equation.
In order to solve for x, one would typically aim to manipulate the equation into a standard trigonometric identity or apply techniques such as Newton's method if handling a more complex algebraic expression involving trigonometric functions.
To tackle the given trigonometric equation, we would ideally express tan2x in terms of sin2x and cos2x using the identity tan2x = sin2x/cos2x, thus simplifying the equation and allowing us to isolate and solve for x.
Unfortunately, there is an ambiguity in the equation presented in the question (lack of clear parentheses), and so a definitive solution cannot be provided without clarification.
a plane averaged 400 mph on a trip going east, but only 280 mph on the return trip. The total flying time in both directions was 8.5 hours. what was the one-way distance?
Answer:
1400 miles
Step-by-step explanation:
Speed is the time rate of change of distance. It is the ratio of distance to time and is given by the equation:
[tex]Speed(S) = \frac{distance(d)}{time(t)}\\ S=\frac{d}{t}[/tex]
plane averaged 400 mph on a trip going east, but only 280 mph on the return trip.
The time spent (t₁) in going east is given by:
[tex]S=\frac{d}{t_1}\\ t_1=\frac{d}{S} =\frac{d}{400mph}[/tex]
The time spent (t₂) in going east is given by:
[tex]S=\frac{d}{t_2}\\ t_2=\frac{d}{S} =\frac{d}{280mph}[/tex]
The total time (t) = t₁ + t₂
t = t₁ + t₂ = 8.5 hours
[tex]\frac{d}{400}+\frac{d}{280} =8.5\\280d+400d=952000\\680d=952000\\d=1400miles\\[/tex]
Therefore the one way distance is 1400 miles
Khloe ran around the track 7 times at the same rate of speed. It took her 21 minutes to run. Zachary took 4 minutes to run around the track once. Which student ran faster? Explain.
Zachary ran faster with 4 minutes per lap compared to Khloe's 3 minutes per lap.
To compare the speeds of Khloe and Zachary, we need to find their respective speeds in terms of minutes per lap.
Khloe ran around the track 7 times in 21 minutes, so her speed is [tex]\( \frac{21}{7} = 3 \)[/tex] minutes per lap.
Zachary took 4 minutes to run around the track once, so his speed is [tex]\( 4 \)[/tex] minutes per lap.
Comparing their speeds, Zachary's speed is faster at 4 minutes per lap, whereas Khloe's speed is 3 minutes per lap.
In summary, Zachary ran faster than Khloe because he completed each lap in 4 minutes compared to Khloe's 3 minutes per lap.
Help please will give B
-1/-3 positive rational number or negative rational number
+1/-3 positive rational number or negative rational number
-2/+3 positive rational number or negative rational number
+1/+3 positive rational number or negative rational number
+2/-3 positive rational number or negative rational number
-1/+3 positive rational number or negative rational number
-2/-3 positive rational number or negative rational number
+2/+3 positive rational number or negative rational number
Hi there! Hopefully this helps!
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Remember: When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number.
(-1/-3) Positive Rational Number.
(+1/-3) Negative Rational Number.
(-2/+3) Negative Rational Number.
(+1/+3) Positive Rational Number.
(+2/-3) Negative Rational Number.
(-1/+3) Negative Rational Number.
(-2/-3) Positive Rational Number.
(+2/+3) Positive Rational Number.
In mathematics, the sign of a rational number is determined by the signs of the numerator and the denominator. If both the numerator and the denominator are of same sign (either positive or negative), the rational number is positive. If they have different signs (one positive, one negative), the rational number is negative.
Explanation:According to the rules of mathematics, the sign of a rational number is determined by the signs of the numerator and the denominator. If both are positive or both are negative, the resulting number is positive. If one is positive and the other is negative, the result is negative.
-1/-3: This can be interpreted as negative divided by negative. When we divide negative by negative, the result is a positive rational number.+1/-3: This is positive divided by negative, giving a negative rational number.-2/+3: This means negative divided by positive, resulting in a negative rational number.+1/+3: Both positive, hence the result is a positive rational number.+2/-3: Stands for positive divided by negative which gives a negative rational number.-1/+3: Interpreted as negative divided by positive, giving a negative rational number.-2/-3: Both are negative, so the result is a positive rational number.+2/+3: Both are positive. Hence, the result is a positive rational number.Learn more about Rational Numbers here:https://brainly.com/question/24398433
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You take a 10 question multiple choice test. Each question has 4 choices and you guess on all of them. What is the probability you get 7, 8, 9, and 10 questions right. Explain your work
Answer:
Probability of getting 7 correctly = 0.0030899
Probability of getting 8 correctly = 0.00038624
Probability of getting 9 correctly = 0.00002861
Probability of getting 10 correctly = 0.00000095367
Probability of Getty at least 7 questions correctly = 0.0035057
Step-by-step explanation:
Please kindly check the attached files for more explanation.
Please help!!!!
Find the sum of the series
15
1
(2 1)
n
n
. Show your work.
Answer:
225
Step-by-step explanation:
Using the basic components of summation ∑
∑n = [tex]\frac{1}{2}[/tex] n(n + 1) and ∑1 = n
Thus
∑ (2n - 1) ← for n = 1 to 15
= ∑2n - ∑1
= 2∑n - ∑1
= 2 ([tex]\frac{1}{2}[/tex] n(n + 1)) - n
= n(n + 1) - n ← Evaluate for n = 15 ( the upper value )
= 15 × 16 - 15
= 240 - 15
= 225
Answer:
255
Step-by-step explanation:
What is the radius and diameter of the following circle 24cm
Answer:
radius is 12 cm
diameter 24 cm
Answer: Radius= 12cm Diameter= 24cm
Step-by-step explanation:
Keisha and David each found the same value for cosine theta, as shown below, given Sine theta = Negative StartFraction 8 Over 17 EndFraction. Keisha’s Solution David’s Solution Tangent squared theta + 1 = secant squared theta. StartFraction sine squared theta Over cosine squared theta EndFraction + 1 = StartFraction 1 Over cosine squared theta EndFraction. StartFraction (eight-seventeenths) squared Over cosine squared theta EndFraction + 1 = StartFraction 1 Over cosine squared theta EndFraction. (eight-seventeenths) squared + cosine squared theta = 1. cosine theta = plus-or-minus StartRoot 1 minus StartFraction 64 Over 289 EndFraction EndRoot. cosine theta = plus-or-minus Fifteen-seventeenths sine squared theta + cosine squared theta = 1. cosine squared theta = 1 minus (negative eight-seventeenths) squared. cosine theta = plus-or-minus StartRoot StartFraction 225 Over 289 EndFraction EndRoot. Cosine theta = plus-or-minus fifteen-seventeenths Whose procedure is correct? Keisha’s procedure is correct. David’s procedure is correct. Both procedures are correct. Neither procedure is correct.
Answer:
C) Both procedures are correct
Step-by-step explanation:
1 + tan²(theta) = sec²(theta)
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Answer:
c) both are correct
Step-by-step explanation:
Which equation has x = 4 as the solution?
olog,(3x+4)= 2
log, (2x-5) = 2
log, 64=4
log, 16 =4
The equation that has the solution x = 4 is [tex]log_ 4 (3x+4) = 2[/tex].
Option A is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To find which equation has x = 4 as the solution,
We can substitute x = 4 into each equation and see which one gives a true statement.
Now,
[tex]log_4 (3x+4) = 2\\log_3 (2x-5) = 2\\log_x 64 = 4\\log_x 16 = 4[/tex]
We can write it as,
4² = 3x + 4
16 = 3x + 4
16 - 4 = 3x
3x = 12
x = 4
3² = 2x - 5
9 = 2x - 5
9 + 5 = 2x
14 = 2x
x = 7
[tex]x^4[/tex] = 64
x = [tex]64^{1/4}[/tex]
[tex]x^4[/tex] = 16
x = 16[tex]16^{1/4}[/tex]
x = 2
Thus,
[tex]log_ 4 (3x+4) = 2[/tex] has the solution x = 4.
Learn more about solutions of equations here:
https://brainly.com/question/545403
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The complete question:
Which equation has x = 4 as the solution?
[tex]log_4 (3x+4) = 2\\log_3 (2x-5) = 2\\log_x 64 = 4\\log_x 16 = 4[/tex]
5 ½ x 3=
2 ⅓ x 4 ¾=
-2 ⅖ x 3 ¼=
1. Solve and show your work for each question.(a) What is 0.36 expressed as a fraction in simplest form?(b) What is 0.36 expressed as a fraction in simplest form? (c) What is 0.36 expressed as a fraction in simplest form?<br />Answer: ( For question A there is a line over 36). ( For question B there is a line over 6). ( For question C there is no line over 0.36).
Answer:
9/25
Step-by-step explanation:
0.36
36/100
18/50
9/25
Answer:
Step-by-step explanation:
____
a) 0.36 = 0.3636........
x = 0.363636.......
{After decimal two digits are there and both are repeated. So, multiply both side by 100}
100x = 36.3636....... equ(i)
x = 0.3636...... equ(ii) {Now, subtract equ (ii) form (i)
99x = 36
x = 36/99
x = 4/11
0.3636...... = 4/11
B) __
0.36 = 0.366666.....
{After decimal point two digits are there but only one digit, 6 is repeated. so first multiply both sides of equation [x=0.366...] by 100 and mark it as equation (i) and then multiply both sides of the equation [x=0.366...] by 10 and mark it as (ii) equation }
x = 0.3666....
100x = 36.66666..... ---------- (i)
10x = 3.66666...... ---------(ii) {Now subtract (ii) from (i)}
90x = 33
x = 33/90
x = 11/30
0.36666..... = 11/30
c)
[tex]0.36=\frac{36}{100}\\\\= \frac{9}{25}[/tex]
The volume of the cylinder above is 2314.25units3 , and the radius of the base is 8.9 units. Find the volume of the cone.
Answer:
771.4 units^3
Step-by-step explanation:
Formula for volume of a cylinder = V=πr^2h
Plug in the numbers to solve for the height (note: the height of an oblique or slanted cylinder is the same as a regular right cylinder)
2314.25 = π(8.9)^2 h
h=9.3
Then plug the height into the formula for a pyramid
V = 1/3πr^2
V = 1/3 π (8.9)^2 (9.3)
V = 771.4 units ^3
2.) Find the length of RQ.
Answer:
the length of angle R Q is 4
Which graph represents a function with an initial value of One-half?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.08), (0, 0.4), (1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.4), (0, 0.2), (1, 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.12), (0, 0.6), (1, 3).
Mark this and return
Answer:
The answer is B) On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5).
Step-by-step explanation:
The initial value is the y-intercept and b has a y-intercept of 0.5
Hope this helps :)))
Answer:
B edge 2020
Step-by-step explanation:
Work out the size of angle x
Answer:
23° is the right answer brother !
3 – (–3) + 7 – 4 =
Question 12 options:
A)
14
B)
9
C)
2
D)
12
Answer:
=9
Step-by-step explanation:
3–(–3)+7–4=
=3+3+7-4
=6+7-4
=13-4
=9
I hope this helps!
Answer:
3−(−3)+7−4
=9
Answer is B
evaluate the expression shown 6(14+8)12
Answer:
1584
Step-by-step explanation:
2(2x +1) = 3(x-8) =
how do you solve this
Answer:
x=-26
Step-by-step explanation:
Distributive property first (both sides)
you would get
4x+2 = 3x-24
next you will subtract 3x from both sides
1x+2=-24
add 24 to both sides
1x+26=0
move 26 to the other side but since you flipped it you have to make it negative
x=-26
Factor completely 14g^5 - 21g^7
Answer:
7g^2 (2 - 3g^2
Step-by-step explanation:
First, you have to factor out the GCF
in this case, factor out 7g^5 to get
7g^2 (2 - 3g^2)
At this point you can't factor anymore, so you get
7g^2 (2 - 3g^2)
Look at the image to answer.
Maria subtracted 10x instead of adding it on step 4
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Line 4 has the problem:
[tex]12x-10x=44-10x+10x[/tex]
The correct way to put it is:
[tex]12x+10x=44-10x+10x[/tex]
which comes out to:
[tex]12x+10x=44-10x+10x\\22x=44\\x=2[/tex]
How many games did they play
The number of games played is 9
Let the number of games played = g
Amount of bet per game = $2
Number of games won by Marty = 4
Number of games won by Wendy will be;
g - 4Amount won by Wendy = $10
This means ;
cost per bet × number of games won by Wendy = 10
2(g - 4) = 10
2g - 8 = 10
2g = 18
g = 9
Hence, They played 9 games.
Students in 10th and 11th grade were asked whether they have a job. The raw data was converted to relative frequencies and recorded in the table below.
A 4-column table with 3 rows. The first column has no label with entries job, no job, total. The second column is labeled tenth grade with entries 0.14, 0.86, 1. The third column is labeled eleventh grade with entries 0.25, 0.75, 1. The fourth column is labeled total with entries 0.20, 0.80, 1.
Given the conditional relative frequency table by column, what does the 0.14 represent?
Given that a student is a 10th grader, there is a 14% chance he or she has a job.
Given that a student has a job, there is a 14% chance he or she is a 10th grader.
14% of the students surveyed are 10th graders who have a job.
14% of the students are 10th graders.
Answer:
A.
Given that a student is a 10th grader, there is a 14% chance he or she has a job.
TOOK ONE FOR THE TEAM
Answer:
A) Given that a student is a 10th grader, there is a 14% chance he or she has a job.
Step-by-step explanation:
What is the relationship between the sides x and y in the given figure?
Need help plz thank you
Answer:
20000
Step-by-step explanation:
1 km = 1000 m. 20 km = 20000, basically # of km times 100
Answer: 20,000 meters or 12.4 miles (Didn't know which one you meant)
Step-by-step explanation:
To get miles all you have to do is divide it by 1.6.
To get the meters all you have to do is to multiple it by 1000.
(Hope this helps)
Does 6 have a greater absolute value than -8
Answer:
No
Step-by-step explanation:
The absolute value of -8 is 8,and 6<8.
Mark me brainliest if I helped:D
-3/5n=2/5 pls help me
Answer:
the answer is the expression, 5n-3
Step-by-step explanation:
Answer:
The value of n is -3/2.
Step-by-step explanation:
In order to solve x, you have to use the Cross-Multiplication :
[tex] \frac{ - 3}{5n} = \frac{2}{5} [/tex]
[tex] - 3(5) = 2(5n)[/tex]
[tex] - 15 = 10n[/tex]
[tex]10n \div 10 = - 15 \div 10[/tex]
[tex]n = \frac{ - 15}{10} [/tex]
[tex]n = \frac{ - 3}{2} [/tex]
PLEASE HELP ME ASAP..................................
Answer:
2, 4, 5
Step-by-step explanation:
Answer:
5x+3x AND 8x
(10b-10b) And 0
y-9(3) AND -27
Step-by-step explanation:
please give me brainliest
5x + 2y = 7
y=x+1
What is the solution set of the given system?
{(5/7, 1217)
{(9/7,16/7)
{(1217,5/7)
{(16/7.9/7)]
(5/7, 12/7) <- I think you meant to type that. Its the first one
Step-by-step explanation:Step 1: Substitute y=x+1 in for y in 5x + 2y = 7
5x + 2(x+1) = 7
Step 2: Solve it
5x + 2x + 2 = 7
7x + 2 = 7
- 2 - 2
7x = 5
--- ---
7 7
x = 5/7
Step 3; Plug x into y=x+1
y = 5/7 + 1
y = 12/7
Answer:
{(5/7 , 12/7)}
Step-by-step explanation:
First plug y into one of the x's
5x + 2(x + 1) = 7
Now solve for X
5x + 2x + 2 = 7
Combine like terms
7x + 2 = 7
Subtract 2 from each side
7x = 5
Divide to get x by itself
x = 5/7
Now plug that into the second equation for x
y = 5/7 + 1
now just solve it
y = 12/7 if they want it simplified then it's 1 5/7
Hope this helped!
Second try PLEASE HELP ME ASAP i always give brainliests and thanks +20 points!
(if you can please explain too how to find the discriminant i am very bad at it)
Answer:
The discriminant is positive
Step-by-step explanation:
You can find that because on the graph, the top of the curve is on Y and its positive. Its at positive 4 so its positive......sorry im not good at explaning hope this helped.....also you can check google images or videos and it explanes.
Answer:
Positive
Step-by-step explanation:
In order to answer this question, we need to figure out the equation of the quadratic.
We see that the vertex is at (0, 4) and that the points (1, 3) and (2, 0) are on the graph. The generic quadratic is: ax^2 + bx + c, so we can just plug in these three points to find a, b, and c:
4 = 0 + 0 + c ⇒ c = 4
3 = a + b + c = a + b + 4 ⇒ a + b = -1
0 = 4a + 2b + c = 4a + 2b + 4 ⇒ 4a + 2b = -4
We now have two linear equations (a + b = -1 and 4a + 2b = -4) so multiply the first one by 2 and subtract it from the second:
4a + 2b = -4 ⇒ 4a + 2b = -4
- 2(a + b) = (-1) * 2 ⇒ - 2a + 2b = -2
______________ ⇒ ______________
Our difference is 2a = -2, so a = -1. Plug this back in to find b: a + b = -1.
-1 + b = -1
b = 0
So our equation is -x^2 + 4 = 0.
The discriminant is just b^2 - 4ac. Here, it is: 0^2 - 4 * (-1) * (4) = 16.
So the discriminant is positive.
Hope this helps!
Select the three ratios that represent the number of blue marbles to red marbles.
Answer: Either 2:3 or 3:2
Simplify this exponent
10^7
We can simplify the exponent by multiplying 10 to itself 7 times.
= 10 * 10 * 10 * 10 * 10 * 10 * 10
= 100 * 10 * 10 * 10 * 10 * 10
= 1000 * 10 * 10 * 10 * 10
= 10000 * 10 * 10 * 10
= 100000 * 10 * 10
= 1000000 * 10
= 10000000
10^7 = 10,000,000
~Good luck