Answers
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
How to prove a trigonometric equivalence
In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:
[tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}[/tex]
[tex]\tan \alpha + 1 + \cot \alpha[/tex]
[tex]\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1[/tex]
[tex]\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\frac{1}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\sec \alpha \cdot \csc \alpha + 1[/tex]
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
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Related Questions
help me please please please!!!
What formula should be used to calculate an unknown side of a right angled triangle
when the hypotenuse (c) and one other side (b) are known?
a) Oa^2 = b^2-c^2
b) Oa^2 = c^2 + b^2
c) Oa^2 = c^2-b^2
d) Oc^2 = a^2 - b^2
e) Oc^2 = b^2- a^2
Answers
because it would be the hypotenuse c squared minus the side b squared
The sum of a squared plus b squared equals c squared
Answer:
c) Oa^2 = c^2-b^2
Step-by-step explanation:
the formula of finding hypotenuse (c) is
c^2 = a^2 + b^2
that means c^2 - b^2 = a^2
a^2 = c^2 - b^2.
Help please!
A vocational school admits 4 out of every
10 people who apply for admission. One
year, 640 students were admitted. How
many people applied for admission?
Answers
Answer:
319
Step-by-step explanation:
i am really not sure but i believe so i hope it is the right answer
Answer:
1600 people
Step-by-step explanation:
This is a ratio problem. We can set up the proportion by letting x be the number of people who applied for admission:
[tex]\frac{4}{10}=\frac{640}{x}[/tex]
Since we know that 4 people get in for every 10 people that apply, we can set up an equation like the one above and solve for x by cross multiplying:
[tex]6400=4x\\x=1600[/tex]
This means that 1600 people applied for admission to the vocational school.
una fracción de reducción a su mínima expresión en igual a 1/8. si la suma de sus terminos es 72. hallar la diferencia entre ellos
Answers
Por lo tanto el número es p/q = 8/64.
¿Qué es una fracción?Fracción es un número que se puede representar en forma de p/q, donde q no es igual a cero.
It is given that :
En su forma más simple, el número es 1/8
Sea el número p/q
p + q = 72 (dado)
p/q = 1/8
q = 8p
p+8p = 72
9p = 72
p = 8
q = 8p
q = 8 * 8 = 64
Por lo tanto el número es p/q = 8/64.
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Question
(01.02 MC)
For which of the following distributions is the mean most likely to be less than the median?
Answers
The distribution where the mean is most likely to be less than the median is the third histogram.
How to illustrate the information?It should be noted that when the histogram shows the day is left skewed, it means the mean is less than the median.
If it right skewed, the mean is greater than the median.
When they're equal, the data is symmetric.
In this case, based on the information, the distribution where the mean is most likely to be less than the median is the third histogram.
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Geometry question Need help with #10
Answers
Answer:
x = 6
Step-by-step explanation:
Line segment SU is a bisector of angle <TSV which means it divided the angle into two equal parts:
The measure of <TSV = 62 in this case the measure of <VSU = 62/2 = 31
we can write the following equation to find the value of x
5x + 1 = 31 subtract 1 from both sides
5x = 30 divide both sides by 5
x = 6
John swims 2.5 miles and sees a total of 12 fishes if he swims 8 miles how many fish will he see
Answers
Answer:
Step-by-step explanation:
2.5 miles = 12 fishes
Therefore,
8 miles = 12*8/2.5=96/2.5= 960/25=38.4 fishes
on the first day the apple iphone 5 was released, the local store had 200 in stock. by 8:00 pm, the store had sold 3/5 of their stock. how many phone were left in the store’s stock?
Answers
Answer:
120 Phones
Step-by-step explanation:
3/5 of 200
Step 1: Divide 200 by 5
200 ÷ 5 = 40
Step 2: Multiply 40 by 3
40 · 3 = 120
Answer: 3/5 of 200 = 120
Tip: When finding a fraction of a whole, divided the whole by the denominator, then multiply the quotient you got by dividing the whole by the denominator by the numerator
Example: 1/2 of 80
80 ÷ 2 = 40
40 · 1 =40
1/2 of 80 = 40
What is b and c in this expression?
[tex]\sqrt[4]{15^7} }[/tex]
Answers
The value of b and c is 4 and 7.
What is algebra?Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.
Elementary algebra: elementary algebra, branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business.
From the given question,
[tex]\sqrt[4]{15^7}[/tex] This expression can also be written in the form of [tex]a^\frac{b}{c}[/tex]
We will convert [tex]\sqrt[4]{15^7}[/tex] to the required form:
[tex](15^\frac{7c}{4b} )\left \{ {{a=15^\frac{7c}{4b} } \atop {b=b} , c = c} \right.[/tex]
Hence,
From the above equation we get the value of b and c is 4 and 7.
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On a coordinate plane, a quadrilateral has points E (negative 2, 0), D (0, 4), G (4, 2), and F (0, 0).
Which are true if figure DEFG is reflected across the x-axis? Check all that apply.
D(0, 4) → D'(0, –4)
E(–2, 0) → E'(–2, 0)
The perpendicular distance from G' to the x-axis will equal 2 units.
The perpendicular distance from D' to the x-axis will equal 8 units.
The orientation will be preserved.
Answers
By applying the reflection rule across the x-axis to quadrilateral DEFG, we obtain the following true statements:
D(0, 4) → D'(0, -4)E(-2, 0) → E'(-2, 0)The perpendicular distance from G' to the x-axis will be equal to 2 units.The reflection of a quadrilateral.In Geometry, the x-axis would remain the same if a quadrilateral is reflected across the x-axis and the sign on the y-axis would change either from positive to negative and vice-versa.
By applying the reflection rule across the x-axis (x, y) → (x, -y), we obtain the following true statements:
D(0, 4) → D'(0, -4)E(-2, 0) → E'(-2, 0)The perpendicular distance from G' to the x-axis will be equal to 2 units.Read more on reflection here: https://brainly.com/question/10929277
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Answer:
A
B
C
Are the right answer
Step-by-step explanation:
6) A basket contains 5 yellow, 3 blue and 2 white balls. If a ball is drawn randomly from the basket, find the probability of not getting a blue ball.
Answers
Answer: 70%
Step-by-step explanation:
A basket contains:
5 yellow balls
3 blue balls
2 white balls
What would be the probability of randomly picking a ball and the ball not being blue?
So, we can find the probability of picking up a blue ball. Let's do that first.
To calculate the probability of getting a blue ball, we need to divide the number of blue balls by the number of possible balls.
The number of blue balls = 3
The total number of balls = 2 + 3 + 5 = 10 balls
3 blue balls divided by 10 balls = 0.3.
If you multiply 0.3 by 100%, it will give you a probability of finding a blue ball equal to 30%
Now, we just need to find the probability of NOT finding a blue ball. Because we have 30% of finding a blue ball, we just need to subtract 30% from 100%.
100 - 30$ = 70%
The probability of not getting a blue ball is equal to 70%.
Hope I Helped!
[tex]|\Omega|=5+3+2=10\\|A|=5+2=7\\\\P(A)=\dfrac{7}{10}=70\%[/tex]
The figure shown is a regular octagon. The measure of
What is the measure of
Answers
Answer:
135°
Step-by-step explanation:
X is also 135° as is S , T U , V, W and Y
Answer:
b)135°
Step-by-step explanation:
The value of an interior angle of 135° is appreciated
In a regular polygon all interior angles are equal
Angle x = 135°
Hope this helps
I WILL MARK BRAINLIEST A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 20 child bikes and 6 adult bikes in a week.
Answers
Using a system of equations, it is found that since 20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable c: number of child bikes.Variable a: number of adult bikes.Each child bike requires 4 hours to build, as do each adult bike. The company has 100 hours of testing, hence:
4c + 4a = 100.
c + a = 25.
With 20 child bikes and 6 adult bikes in a week, we have that c = 20, a = 26, hence:
c + a = 26
20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.
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find the product (2y - 2nb) (y+4nb)
Answers
Answer: 2y^2+6bny-8n^2b^2
Step-by-step explanation: I hope this helps!
Using a phone to drive people to Web-based survey instruments is known as a(n) online focus group. online theater system. hybrid survey. cybertracking tactic.
Answers
Answer:
Using a phone to drive people to web-based survey instruments is known as a hybrid survey.
suppose it costs $45 to attend a concert where the band plays for 1.5 hours.
a. what was the cost to attend the concert per hour?
b. what was the cost to attend to the concert per minute
make sure to show your work
Answers
Answer
$30 minutes per hour
$0.5 per minute
Step-by-step explanation:
45/1.5=30
45/90=0.5
fill in the blank 2 x 3/4 = _ + 3/4
Answers
According to multiplication you can use repeated addition to get the same product of the given equation.
Ex: 5x2= 2+2+2+2+2 ( 5 groups of 2)
Both will give you same answer (10).
Hence 2 x 3/4 = 3/4 + 3/4
Answer:
2 x 3/4 = 3/4 + 3/4
Step-by-step explanation:
if t is 25% of u, then what percent of 4t is 2u?
Answers
Step-by-step explanation:
t = .25u (given)
4 t = 4 (.25u) = u
then u = 50% of 2 u
4t = 4(0.25u) =
u
Then u is 50 percent of 2u.
Hope this helps, please mark brainliest if possible :)
can you help me im stuck here
Answers
Answer:
its dependent varaible
Answer:
Step-by-step explanation:
NOW WATSH ME WIP WAHS E NYA NAY
Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.
Select the four true statements regarding the side lengths Mrs. Ibarra chose.
15 + 36 greater-than 41, so the side lengths will form a triangle.
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Answers
Answer:
See below.
Step-by-step explanation:
Sides: 15, 36, 41
True: 15 + 36 greater-than 41, so the side lengths will form a triangle.
True: 15 squared + 36 squared = 1,521
True: 41 squared = 1,681
True: Since a squared + b squared not-equals c squared, it will not be a right triangle.
Answer:
A) 15 + 36 greater-than 41, so the side lengths will form a triangle.
C) 15 squared + 36 squared = 1,521
D) 41 squared = 1,681
E) Since a squared + b squared not-equals c squared, it will not be a right triangle.
Proof:
(LOOK AT IMAGE)
EG is a tangent to the circle below at point F.
Calculate the size of angle x.
Give reasons for your answer.
Answers
[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)
[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)
Help me help me help me help me help me please
Answers
Answer:
x = 1, 4
Step-by-step explanation:
We assume the graph is of the relation y = f(x). The desired values of x are those that correspond to points where the y-value is -2.
Reading the graphWe are only interested in the x-coordinates of points that lie on the horizontal line where y = -2. Those points are (1, -2) and (4, -2).
The values of x such that f(x) = -2 are x=1 and x=4.
Kara wants to make a histogram of the number of students who wear blue shirts in her class throughout the week. She gathered the following information:
Day 1 4 students
Day 2 9 students
Day 3 5 students
Day 4 7 students
Day 5 6 students
What data would be on the horizontal axis?
names of the students wearing the blue shirts
the exact color of the blue shirt
school day
number of students wearing blue shirts
Answers
Answer:
school day
Step-by-step explanation:
When drawing a chart or a graph:
x-axis: Independent variabley-axis: Dependent variableThe two given variables are:
number of students who wear blue shirtsdays of the weekTherefore, in this scenario the independent variable is the school day and the dependent variable is the number of students since the former effects the latter.
So the data on the horizontal axis (x-axis) is: school day
1. One group (A) contains 180 people.
One-fourth of the people in group A will be
selected to win free tickets to a concert.
There is another group (B) in a nearby town
that will receive the same number of tickets,
but there are 292 people in that group.
What will be the ratio of non-winners in
2
group A to non-winners in group B after the
selections are made?
Answers
Answer:
135:147
Step-by-step explanation:
180/4=45
180-45=135
292-45=247
135:247
what is the area of the shaded region?
Answers
To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.
For this triangle, we will need to know the formula to find the area of a triangle:
[tex]A=\dfrac{1}{2}bh[/tex]
Solving the QuestionThe given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:
Find the area of the large triangleFind the area of the little triangleSubtract the area of the little triangle from the large triangleArea of the Large Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2[/tex]
Area of the Small Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2[/tex]
Subtract the Area of the Small Triangle from the Area of the Large Triangle[tex]30 mm^2-6mm^2\\=24mm^2[/tex]
AnswerThe area of the shaded region is [tex]24mm^2[/tex].
You should be able to find this
without a calculator.
cos(cos-¹ 0.3) = [?]
Answers
Hello:
Let's consider this problem in steps:
Let's gather some information:
cosine and arccosine cancel each other out in this caseNow let's apply our knowledge to solve the problem:
[tex]\rm \hookrightarrow cos(cos^{-1}0.3) = 0.3[/tex]
Answer: 0.3
Hopefully that helps!
[tex]\frak{Hi!}[/tex]
[tex]\large\text{Related Concept-:}[/tex]
[tex]\boxed{\begin{minipage}{10cm} \sf{If\;you\;take\;the\;inverse\;cosine}\\ \;of\;a\;number,\;and\;then\;take\; its\;cosine,\;don't\;you\;get\;the\;number \\ you started with? \end{minipage}}[/tex]
ClarificationThe inverse cosine and the cosine are operations that undo each other.
This being said, let's solve our problem.
[tex]\bf{cos(cos^{-1}\;0.3)=0.3[/tex], based on what I said above
[tex]\cal{CALLIGRAPHY}[/tex]
A construction company prepares an
estimate to install a new pool for a home-
owner. The estimate includes h hours of
labor, where h>80. The company's goal
is for the estimate to be within 8 hours
of the actual number of hours of labor. If
the company meets the goal and it takes
a hours of actual labor, which inequality
represents the relationship between the
estimated number of hours of labor and
the actual number of hours of labor?
A) a+h≤8
B) a2h+8
C) ash-8
D) -8≤a-h≤8
Answers
The equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is D. -8≤a-h≤8.
How to illustrate the equation?From the information given, the estimate includes h hours of labor, where h>80 and the company's goal is for the estimate to be within 8 hours of the actual number of hours of labor.
Here, the equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is -8≤a-h≤8.
In conclusion, the correct option is D.
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In the following exercises, multiply the binomials. Use any method.
258. (5x − y)(x − 4)
Answers
Answer:
Hence the expression [tex]$$(5x-y)(x-4)=5x^2-xy-20x+4y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (5 x-y)(x-4).We have to multiply the given expression.Multiply the (5 x-y) by -4, multiply the (5 x-y) by x then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 5x & - & y \\ \times & {} & {} & {} & x & - & 4 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 20x & + & 4y \\ 5{{x}^2} & - & xy & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}5{{x}^2} & - & xy & - & 20x & + & 4y \\ \end{matrix}$$[/tex]
Which conditional and its converse form a true biconditional?
If x = 19, then 2x – 3 = 35.
If x = 3, then x2 = 9.
If x2 = 4, then x = 2.
If x > 0, then > 0.
Answers
The conditional and its converse that form a true biconditional is; Option A; If x = 19, then 2x – 3 = 35.
How to Interpret Biconditional Statements?
A) If x = 19, then 2x – 3 = 35.
Thus, 2(19) - 3 = 35. Thus, this is a true biconditional.
B) If x = 3, then x²= 9.
This is not a true biconditional because x could also be -3.
C) If x² = 4, then x = 2
This is not a true biconditional because x could also be -2.
D) If x > 0, then |x| > 0.
This is not a true biconditional because x could also be negative which less than zero.
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Please help me its due soon! :(
Select all the correct answers.
Consider the graph of the function : f(x)=logx
Which are features of function g if g(x)= 4log(x)+4
Answers
The features of the function g(x) = 4log(x) + 4 are
(b) range (-∞, ∞)(d) x-intercept (0.1, 0)(e) Vertical asymptote, x = 0How to determine the features of g(x)?The function is given as;
g(x) = 4log(x) + 4
The intercept
A logarithmic function has no y-intercept.
Set g(x) to 0, to determine the x-intercept
4log(x) + 4 = 0
Divide through by 4
log(x) + 1 = 0
This gives
log(x) = -1
Take the inverse of both sides
x = 10^-1
Evaluate
x = 0.1
The x-intercept is (0.1, 0)
The vertical asymptote
Recall that:
A logarithmic function has no y-intercept.
This is so because it is undefined at x = 0
So, the vertical asymptote is x = 0
The domain and the range
A logarithmic function cannot take a negative input or 0 input
So, the domain is x > 0
However, the range is all set of real numbers i.e (-∞, ∞)
Hence, the features of g(x) are (b), (d) and (e)
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Write root of fourth 81x³y4z8 with rational exponents
Answers
The fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
How to find the fourth root of ⁴√(81x³y⁴z⁸)To find the fourth root of ⁴√(81x³y⁴z⁸) with rational exponents, we use the root rule of indices which states that [tex]\sqrt[n]{a} = a^{\frac{1}{n} }[/tex]
So, ⁴√(81x³y⁴z⁸) = ⁴√(81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸)
We now apply the
So, ⁴√(81x³y⁴z⁸) = ⁴√81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸
[tex]= 3 X x^{\frac{3}{4} } X y^{\frac{4}{4} } X z^{\frac{8}{4} } \\= 3 X x^{\frac{3}{4} } X y^{1} X z^{2} \\= 3x^{\frac{3}{4} }yz^{2}[/tex]
So, the fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
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