This relationship is not true.
[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]
and
[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]
Rewrite the equation in terms of only tangent.
[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]
Factorize the left side.
[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]
Solve for [tex]\tan(x)[/tex].
[tex]\tan^2(x) - 1 = 0[/tex]
[tex]\tan^2(x) = 1[/tex]
[tex]\tan(x) = \pm 1[/tex]
[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]
where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.
Over the last baseball season, Billy averaged 28 hits per 100 turns to bat, while Carl averaged one hit for every 2.5 turns. At these rates, which player would have more hits in 500 turns to bat, and how many more?
Using proportions, it is found that Carl would have 60 more hits in 500 turns.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Billy's proportion is of 28/100, hence his amount of hits in 500 turns is:
500 x 28/100 = 140 hits.
Carl's proportion is of 1/2.5, hence his amount of hits in 500 turns is:
500 x 1/2.5 = 200 hits.
The difference is:
200 - 140 = 60 hits.
Carl would have 60 more hits in 500 turns.
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Is there a difference between [tex]-\frac{x}{y}[/tex] and [tex]\frac{-x}{-y}[/tex] ?
Do they mean different things?
There is a difference between the expressions -x/y and -x/-y
How to determine if there is a difference between the expression?The expressions are given as:
-x/y and -x/-y
When the expression -x/-y is evaluated, we have:
-x/-y = x/y
This means that
-x/y = -x/y
-x/-y = x/y
When the above expressions are compared, we can see that both expressions are not equal
Hence, there is a difference between the expressions -x/y and -x/-y
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The regular pentagon shown is rotated clockwise about center point P.
●P
Choose all degrees of rotation that will carry the regular pentagon onto itself.
A. 72°
B. 90°
C. 108°
D. 144°
E. 216°
Answer:
A. 72°
D. 144°
E. 216°
Step-by-step explanation:
are you tempted to calculate the internal angles ?
that is, I guess, the trap set by your teacher here, and it would be the wrong approach.
nevertheless, quickly just as a reminder :
the sum of all internal angles in a polygon is
(n - 2)×180°
n being the number of sides.
in our case that is
(5 - 2)×180 = 3×180 = 540°
so, each internal angle is 540/5 = 108°.
but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.
we are running each vertex along a circle arc. the center of that circle being P.
after every 1/5 of the circle arc there is a vertex of the pentagon.
and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.
so, instead of a full circle rotation we need only 1/5 of that :
360 / 5 = 72°
and with every additional 1/5 of the circle arc (or 72°) we get it again.
that means at
72°
144°
216°
288°
360°
the pentagon carries onto itself.
therefore, A, D and E are correct.
???????????????????????
Using the scale found on the number line, how would the number 1 be best represented?
A 0/8. B 4/8. C 8/1. D 7/8. E 8/8
PLEASE I NEED HELP
Based on the given scale, the number, 1, on the number line would best be represented by the number A. 8/8.
What is the scale?Based on the first number given which is 1/8, we know that the scale is such that the denominator would be 8.
The best way to write 1 would therefore be to express it in terms of a ratio with 8 being the denominator.
That would mean that 1 would be 8/8 which results in 1.
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PLS HELP THANK YOU VERY MUCH
Given AB, explain how to construct a square with sides of length AB.
Answer:
because it is a square, you just need to make a square with the side lenghts all being a or b
Step-by-step explanation:
What are the solutions to the inequality (x-3)(x+5) ≤0?
O {x| 3≤x≤5}
O {xl-5≤x≤-3}
O x1-5≤x≤ 3}
O {xl-3≤x≤5}
Answer: -5<=x≤3 ==> 3rd option
Step-by-step explanation:
(x-3)(x+5)≤0
x-3>=0 and x+5≤0
x>=3 and x≤-5 ==> Not possible since a number subtracted by 3 can't be greater than the same number added by 5.
x-3≤0 and x+5>=0
x≤3 and x>=-5 ==> -5<=x≤3 ==> 3rd option
The solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is (x-3)(x+5) ≤0
To solve this inequality, we first find the critical points by setting the expression inside the inequality to zero:
(x-3)(x+5) = 0
This gives us two critical points: x=3 and x=-5.
We want to find where the expression is less than or equal to zero, so we include the endpoints of the intervals where the expression is zero or negative.
Hence, the solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.
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2. Find the 200th term of
the sequence:
3. 7. 11, 15, 19....
Answer:
our initial is 3
a1=3
difference or d = 4
The general formula is an = a1+(n-1)*d
an= 3+(200-1)*4
an=3+199*4
an=3+396
an = 399
therefore the 200th item is 399
Step-by-step explanation:
a =3 d=4 n=200
apply the general formula for the nth term
Help!!
Find the after-tax return to a corporation that buys a share of preferred stock at $49, sells it at year-end at $49, and receives a $4 year-end dividend. The firm is in the 21% tax bracket.
This is what I got so far:
Before-tax:
(49-49)+4 = 4,
4/49 = 0.0816,
After-tax:
0.0816 (1-021) = 0.06448 or 6.45%
Based on the calculation below, the after-tax return to the corporation is $3.16 per share or 6.44% if expressed in percentage.
How do we calculate the after-tax return?The after-tax return can be calculated using the following formula:
After-tax return = Total return * ( 100% - tax rate) .............. (1)
Where:
Total return Received = Dividend received + Change in price = $4 + ($49 - $49 ) = $4 + $0 = $4
Tax rate = 21%
Substituting the values into equation (1), we have:
After tax return = $4 * ( 100% - 21%)
After-tax return = $3.16 per share
The after-tax return can also be expressed in percentages as follows:
After-tax return in percentage = After-tax return / Share price = $3.16 / $49 = 0.06444897 = 6.44%
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At a large university it is known that 30% of the students live on campus. The director of student life is going to take a random sample of 500 students. Which of the following is most likely to occur?
Using point estimation, the sample proportion falls between 0.2 and 0.4.
What is point estimation?The sample distribution offers details on the point estimator to choose. If the distribution's mean matches the actual value of the population parameter, the estimator is considered to be impartial. As a result, the population percentage p and the sample proportion p ought to be quite similar.
The correct option is C, because the average of 0.2 and 0.4 is 0.3
Complete Question is -At a large university it is known that 30% of the students live on campus. The director of student life is going to take a random sample of 500 students. Which of the following is most likely to occur?
a.) The sample proportion falls between 0.3 and 0.5.
b.) The sample proportion falls between 0.1 and 0.3.
c.) The sample proportion falls between 0.2 and 0.4.
d.) The sample proportion falls between 0.25 and 0.35.
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Under his cell phone plan, Gavin pays a flat cost of $62.50 per month and $5 per gigabyte. He wants to keep his bill at $86.50 per month. How many gigabytes of data can he use while staying within his budget?
Answer: 4.8 this is on a school site so i know this because i used the other persons answer and it marked me wrong.
1. Factor by grouping
a² + ab - 56b²
Answer: (a-7b)(a+8b)
Step-by-step explanation:
a² + ab - 56b²=
a² + 8ab -7ab - 56b²=
a(a+8b) -7b(a+8b)=(a-7b)(a+8b)
Evaluate the expression when m= -4
m2 +6m +9
Answer:
41
Step-by-step explanation:
because if m=-4 that means (-4)2+6(-4)+9=41
I need help on question 1-6
Will be mark brainlist
Answer:Look
Step-by-step explanation: Look and solve its not that hard
Un poste mide 150 centímetros y está pintado de azul, rojo y amarillo. La parte pintada de azul es 2/5 del poste, la parte pintada de rojo es 1/2 de la pintada de azul, y lo que resta está pintado de amarillo ¿cuánto mide cada parte?
A 150 cm post is painted in shades of azure, red, and amber. The blue portion of the post is two-fifths of the way up, the red portion is one-half of the blue portion, and the remaining portion is painted in amarillo. What does each part weigh?
71 forms
First, we'll determine how many different ways the five cubes may be arranged in a column using the multiplicand rule:
5 * 4 * 3 * 2 * 1 = 120
We have five cubes to place at the base of the column, four for the second position, three for the third position, and so on until all the cubes are organized.
Then we'll calculate how many different ways we may arrange the five cubes so that they'reBlue cubos twirl around one another. In this case, we would count the two blue cubes as though they were only one, which means that we would only have "4 cubes" and be able to arrange them in 24 different ways:
4 * 3 * 2 * 1 = 24
On the other hand, the two blue cubes can be arranged in one of two different ways: first the clear, then the dark, or first the dark, then the clear.
That is to say, there are 24 different ways to arrange the cubes so that the light comes on first and the dark follows, and there are 24 different ways to arrange the cubes so that the dark comes on first and the light follows.
This means that 48 of the 120 ways to organize the five cubes contain the cubes. 72 (120-48) formas los dos cubos azules no se tocan entre sí.
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Guided Practice #1
Damaya is baking pies. For every 2 cups of flour, she uses 3
cups of sugar. How many cups of sugar will she need if she
uses 12 cups of flour? Model your answer on the double
number lines below.
0
O.
G
E
Answer:
18 cups of sugar
Step-by-step explanation:
I don't see any answer choices in your post but assuming it she has to use 3 cups of sugar for every 2 cups of flour, then that would mean she has to use 3/2 cups of sugar for every 1 cup of flour.
So if she uses 12 cups of flour she will have to use (3/2) x 12 = 18 cups of sugar
Which graph shows a function where f(2)=4?
Answer:
The correct option is 1.
Step-by-step explanation:
We have to find a function where f(2)=4. It means the value of function is 4 at x=2.
In graph 1, the value of function is 4 at x=2, therefore option 1 is correct.
In graph 2, the value of function is -4 at x=2, therefore option 2 is incorrect.
In graph 3, the value of function is not shown in the graph at x=2, therefore option 3 is incorrect.
In graph 4, the value of function is not shown in the graph at x=2, therefore option 4 is incorrect.
Thus, correct option is 1.
Two adjacent angles are in the ratio 5 ratio 3 and they together form an angle of 128 degree find these angles
Answer:
The angles are 80° and 48°.==============================
Let the angles be x and y.
Their ratio is 5/3:
x/y = 5/3Their sum is 128:
x + y = 128Solve the system by substitution:
x = 5y/3x + y = 1285y/3 + y = 1288y/3 = 128y = 3*128/8y = 48Find x:
x = 128 - 48 = 80The perimeter of a rectangle is 28 cm. Which of the following express the area of the rectangle in terms of the width x?
Answer:
14x−x
2
Step-by-step explanation:
Perimeter is 2x + 2y = 28 (y is the length BTW)
To find y, transfer equations
28-2x=2y
Divide both sides by 2
14-x = y
Now you have your length in terms of x
Multiplt length and width
x(14-x)
14x - x {}^{2}14x−x
2
9×8 no using cocalator
Answer:
9x8=72
Step-by-step explanation:
I didn't use a calculator I memorized it?
Nine hundred ninety two hundred thousandths wrote in decimal form
Answer:
I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!
step-by-step explanation:
Yessenia simplified an expression as shown below:
Answer:
Step 1
Step-by-step explanation:
Yessenia should have distributed 3 to (x+4) as her first step.
her steps should have been as follows:
x+6+3(x+4)
x+6+3x+12
re write: x+3x+6+12
4x+18
The length of a rectangle is twice its width.
If the perimeter of the rectangle is 48 ft, find its length and width.
Formula we use,
→ P = 2(L + W)
Then the value of L and W is,
→ P = 2(L + W)
→ 48 = 2(2x + x)
→ 2(3x) = 48
→ x = 48/6
→ [ x = 8 ]
Then the width will be,
→ W = x = 8 ft
Hence, the width is 8 ft.
Now the length will be,
→ L = 2x = 2(8) = 16 ft
Therefore, the length is 16 ft.
mathematics [tex]what is the product of 17 and 41?[/tex]
Answer: 697
Step-by-step explanation:
17 * 41=
17 * (40+1)=
17 * 40 + 17 * 1=
17 * 10 * 4 + 17=
170 * 4 + 17=
680+17=697
Write the symbolic statement in words. Use p, q, r, s, t, and u as defined below.
p: The tour goes to Italy.
q: The tour goes to Spain.
r: We go to Venice.
s: We go to Florence.
t: The hotel fees are included.
u: The meals are not included.
r → ~s
We go to Florence and we do not go to Venice.
We go to Venice if and only if we do not go to Florence.
We go to Venice and we do not go to Florence.
If we do not go to Florence, then we will go to Venice.
If we go to Venice, then we will not go to Florence.
The definition of the symbolic statement r → ~s is:
If we go to Venice, then we will not go to Florence.
What is the definition of the given symbolic statement?First, we have to look at the definition of the events.
Event r means that the person goes to Venice.Event s means that the person goes to Florence, hence event ~s means that the person does not go to Florence.The operation → is a implication operation, hence a → b is: if a then b.In this problem, the statement is:
If r then not s.
Considering events r and s, the correct option is:
If we go to Venice, then we will not go to Florence.
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Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive
integer value.
x²=8(x-5)
Answer:
See below
Step-by-step explanation:
Expand to get x^2 - 8x + 40 = 0
a = 1 b = -8 c = 40
expressions that are equivalent to k/2
A: k-2
B: 2/k
C: 1/2 k
D: k/2
E: k+k
The correct option is D: k/2 is the expression that is equivalent to the expression, K/2.
What is defined as the equivalent expressions?Two equations are equivalent unless and until they produce the same result for all matching variable values. As a result, we can determine whether 2 expressions seem to be equivalent by putting in many distinct corresponding values of the variables to ensure that each expression returns the same value in every instance.If we enter matching variable values into two mathematical expressions and get a different result from each expression, the two expressions really not equivalent.In response to the question;
We must determine the expression that is equivalent to k/2.
Among the options, Option D: k/2 is same as expression K/2.
Choice C, when written as (1/2)k, is equivalent to k/2 since they both imply half of k.
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x^x = 2^2048
solve for x
x=256
[tex] {256}^{256} = ( { {2}^{8} })^{256} = {2}^{8 \times 256} = {2}^{2048} [/tex]
4.
A standard glass of wine is 5 oz. How many full glasses of wine can you get from a typical 750 ml bottle?
full 5-oz glasses of wine.
Answer:
5
Step-by-step explanation:
750ml= 25 fluid oz each glass is 5oz
5/25=5oz
Find the measures of complementary angles with measures 9x+6 and 3x degress
Step-by-step explanation:
As we know that the value of Complementary angle is always 90°
9x° + 6° + 3x° = 90°
12x° + 6° = 90°
12x° = 90° - 6
12x° = 84°
[tex]x° = \frac{84°}{12°} \\ [/tex]
x° = 7°
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