Answers
Let's prove that (sec x)(csc x) is equal to cot x + tan x
[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]
[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]
Hence student A did correctly prove the identity properly.
Also Looking at student B's work, he verified the identity properly.
So, Both are correct in their own way.
Part BIdentities used:
[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex] (appeared in step 3)
[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex] (appeared in step 6)
[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex] (appeared in step 6)
Related Questions
Question 9 of 10
For what value of x is the rational expression below equal to zero?
3x + 15
6-x
OA. -5
OB. 5
O C. 6
OD. -6
UBMIT
Answers
Answer:
A. -5
Explanation:
For (3x + 15)/(6 - x) to be equal to zero. Set the equation to 0.
Doing so:
(3x + 15)/(6 - x) = 0
3x + 15 = 0(6 - x)
3x + 15 = 0
3x = -15
x = -15/3
x = -5
Therefore, the value of x is -5 to equal to zero.
Competitive firms that earn a loss in the short run should
Answers
Competitive business firms that earn a loss in the short-run should shutdown if price (P) is lesser than average variable cost (AVC).
What is an average variable cost?An average variable cost (AVC) can be defined as the cost of production per unit item incurred by a business firm and divided by total output of production. Thus, it's calculated by dividing total variable cost (TVC) by total output of production.
As a general rule in Economics, competitive business firms that earn a loss in the short-run are advised to shutdown their production when price (P) is lesser than average variable cost (AVC).
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What are the zeros of the quadratic function f(x)=6x^2+12x-7?
(Please pick from one of the options in the photo)
Answers
The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.
The missing options are given below.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function is given below.
f(x) = 6x² + 12x – 7
Then the zeroes of the quadratic function will be
[tex]\rm x = \dfrac{-12\pm \sqrt{12^2 - 4 * 6 * (-7)}}{2 * 6}\\\\\\\rm x = \dfrac{-12\pm \sqrt{312}}{12}\\\\\\\rm x = -1 \pm \sqrt{\dfrac{13}{6}}\\\\\\x = -1 - \sqrt{\dfrac{13}{6}} , -1 + \sqrt{\dfrac{13}{6}}[/tex]
Then the correct option is A.
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Item at position 9
The lifetimes of 20,000 light bulbs are normally distributed. The mean lifetime is 230 days. The standard deviation is 40 days. Find the values defined by standard deviation in a normal distribution for 3 standard deviations.
Answers
Using the normal distribution, the values within 3 standard deviations of the mean are given 110 to 350.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 230, \sigma = 40[/tex].
The bounds of the values within 3 standard deviations of the mean are given by X when Z = -3 and X when Z = 3, hence:
Z = -3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-3 = \frac{X - 230}{40}[/tex]
X - 230 = -3(40)
X = 110.
Z = 3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]3 = \frac{X - 230}{40}[/tex]
X - 230 = 3(40)
X = 350.
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Please answer BOTH the questions xoxo <3
Answers
Answer:
First Image: Choice B
Second Image: Choice B
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
First Image:
In our equation, y = 0.1x + 1,
we see that the y-intercept of the line is 1 and the slope is 0.1
We can simple plug in the x values to test if the table is true:
x = -1
y = 0.1x + 1 → y = 0.1(-1) + 1 → y = -0.1 + 1 → y = 0.9
This proves choices A and C are INCORRECT
The next point is at x = 10
y = 0.1x + 1 → y = 0.1(10) + 1 → y = 1 + 1 → y = 2
Making choice D INCORRECT
Hence, you've selected the correct choice (B)!
Second Image:
In our equation, y = 3x + 2,
we see that the y-intercept of the line is 2 and the slope is 3
Choice A is INCORRECT due to (0,0) not logical as the y-intercept is 2
Choice B is CORRECT due to (1/3, 3) not logical as that 3 = 3(1/3) + 2
6 = 3(4/3) + 2 → 6 = 4 + 2. → 6 = 6
3 = 3(1/3) + 2 → → 3 = 1 + 2. → 3 = 3
20 = 3(6) + 2 → 20 = 18 + 2. → 20 = 20
Choice C is INCORRECT due to (-6, 20) not logical as that 20 = 3(-6) + 2
Choice D is INCORRECT due to (10, 4) not logical as that 10 = 3(4) + 2
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10,000,000,000 is which power of ten? 21 -1 10 100
Answers
Answer:
10
Step-by-step explanation:
There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]
The length of a rectangle is 44 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
Answers
Answer:
18 inches by 80 inches
Step-by-step explanation:
The given relations can be used in conjunction with the Pythagorean theorem to find the rectangle dimensions.
__
setupLet x and y represent the width and length of the rectangle, respectively. One of the relations is that between length and width:
y = 2x +44 . . . . . length is 44 more than twice the width
The other relation is described by the Pythagorean theorem. The square of the diagonal is the sum of the squares of the length and width:
x² +y² = (y +2)²
__
solutionExpanding the second equation, and subtracting y², we find ...
x² +y² = y² +4y +4
x² = 4y +4
Substituting for y using the first equation gives the quadratic ...
x² = 4(2x +44) +4
x² = 8x +180 . . . . . . . eliminate parentheses
x² -8x +16 = 196 . . . . add 16 -8x to make perfect squares
(x -4)² = 14²
We're only interested in the positive solution, so ...
x = 4 +14 = 18 . . . . . . . . square root, add 4
y = 2(18) +44 = 80
The dimensions of the rectangle are 18 inches wide by 80 inches long.
_____
Check
The diagonal is √(18² +80²) = √6724 = 82.
8(w-5)=16 solve for w please give working out
Answers
find the value of x. round to the nearest tenth
Answers
Answer:
*79.40*
Step-by-step explanation:
using sine rule..
a/sinA = b/sinB
42/sin19= x/sin142
x= sin142*42/sin19
= 79.42356..
to the nearest tenth = 79.40.
Answer:
Step-by-step explanation:
a/sinA = b/sinB
(42/sin19) = (x/sin142)
x = (sin142 *42 / sin19)
Round to the nearest tenth -> 79.4
Simplify
24x²y
6x
for all x = 0.
Answers
Step-by-step explanation:
[tex] = \frac{24 {x}^{2} y}{6x} [/tex]
[tex] = \frac{24}{6} . \frac{ {x}^{2}y }{x} [/tex]
[tex] = 4.xy[/tex]
[tex] = 4xy[/tex]
[tex] \: [/tex]
• Substitute the value of x.
[tex] = 4xy[/tex]
[tex] = 4 \times 0y[/tex]
[tex] = 0[/tex]
If a widget factory as a fixed operating cost of $2,500 per day plus a cost of $1.50 per widget produced. If a widget sells fro $5.00, what is the least number of widgets that must be sold per day to make a profit?
Answers
At least 714 numbers of widgets must be sold per day to make a profit.
Given fixed operating cost = $2,500 per day cost of widget =$ 1.50
widget sells = $ 5.00
Cost function = C(X)=1.50x+2500
Revenue function = R(X)=5 x
At Break Even point R (X) = C (X)5
X= 1.50X+25003.5
X =2500X =714
hence to reach break even point or make profit 714 no to be sold.R(714)= 3571.
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Para administrar 500 ml de suero fisiológico (SF) al 0,9% en el período de 8 horas a las 20 horas, se debe planear un goteo, en gotas/min. Igual a:
Answers
Si administran 500 ml. La tasa de goteo requerida en gotas por minuto es de 21 gtt/min.
Tasa de goteo requeridaUsando esta fórmula
Tasa de goteo requerida=(ml administrado×gotas/mL)÷ (Número de horas×Número de minutos por hora)
Vamos a conectar la fórmula
Tasa de goteo requerida =(500 mL x 20 gtt/mL) ÷ (8 hrs. x 60 min)
Tasa de goteo requerida =10,000÷480
Tasa de goteo requerida = 20.8
Tasa de goteo requerida =21 gtt/min (Aproximadamente)
Por lo tanto, la tasa de goteo requerida en gotas por minuto es de 21 gtt/min.
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A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price for an adult ticket was $17.00. The register confirms that $9,587.50 was taken in. How many student tickets and adult tickets were sold?
Answers
The number of student tickets is 175 and the number of adult tickets is 425.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price for an adult ticket was $17.00. The register confirms that $9,587.50 was taken inSuppose the number of the student ticket is St and adult are At.
St + At = 600
St = 600 - At
Another expression for the total amount will be given as:-
13.5St + 17At = 9587.50
Put the value of St in the equation to find the value of At.
13.5( 600 - At) + 17At = 9587.50
8100 - 13.5At +17At = 9587.5
17At - 13.5 At = 9587. 5 - 8100
3.5 At = 1487.5
At = 425
St + At = 600
St = 600 - At = 600 - 425 = 175
Therefore the number of student tickets is 175 and the number of adult tickets is 425.
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Boxes of tins are delivered to a shop. There are 37 boxes. Each box contains 25 tins. How many tins are there?
Answers
Answer:
Step-by-step explanation:
it equal 925 tins in total when you multiply 37 times 25. Hope that helps
Use a real number line to define la.
Choose the correct answer below.
OA. |a| = -a for any real number a.
B. The midpoint of the origin and a is la for any real number a.
OC. The distance from the origin to a is la for any real number a.
D. The distance from a to a is |a| for any real number a.
Answers
A number line is just that – a straight, horizontal line with numbers placed at even increments. The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
As we know that in the given function |a|, when any value is given to a, then the value that the function is written is equal to a.
Let a=-5, then the value that the function will return is 5. Which is the distance borigin and a, on the number line.
Hence, The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.
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If f(x) = 3x + 10 and g(x) = 2x - 4, find (f- g)(x).
Answers
Step-by-step explanation:
please mark me as brainlest
An object is dropped from 39 feet below the tip of the pinnacle atop a 715-ft tall building. The height of the object after seconds is given by the equation . h=16T^2+676.Find how many seconds pass before the object reaches the ground.
Answers
Answer:
6.5 seconds
Step-by-step explanation:
Ok so the equation you gave is -16T^2 + 676 in the comments which is what I'll be using for this problem. The problem is really just asking you to find the zeroes of the equation excluding any negative solutions since that doesn't really represent anything in this context since T is time.
So the first step is to set the equation equal to 0
[tex]0 = -16t^2 + 676[/tex].
Subtract 676 from both equations.
[tex]-676 = -16t^2[/tex]
Divide both sides by -16
[tex]42.25 = t^2[/tex]
Take the square root of both sides
[tex]\pm6.5 = t[/tex]
Ignore the negative and take only the positive solution, since in this context it doesn't make much sense. So after 6.5 seconds the height is 0, meaning it hits the ground after 6.5 seconds.
I need help pronto!!
Answers
Answer:
There were 42 fewer students who chose Football than Hockey.
Step-by-step explanation:
Fraction of students who chose Hockey
= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] units = 21
1 unit = 42
No. of students who chose Football
= 2 units ([tex]\frac{2}{6}[/tex])
= 84 students
No. of students who chose Hockey
= 3 units ([tex]\frac{3}{6}[/tex])
= 126 students
Difference between no. of students who chose Football and Hockey
= 126 - 84
= 42 students
∴There were 42 fewer students who chose Football than Hockey.
a farmer uses 1/6 of his land to plant pineapples, 5/9 to plant durians and the remaining 48.5 acres to plant vegetables. calculate the area of land used to plant pineapples and durians
Answers
Step-by-step explanation:
x = total area of land
x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6
6x - x - 30/9 × x = 291
5x - 30/9 × x = 291 | multitude both sides by 9
45x - 30x = 2,619
15x = 2,619
x = 174.6 acres
pineapples were planted on 174.6 × 1/6 = 29.1 acres.
durians were planted on 174.6 × 5/9 = 97 acres.
If a soup recipe yields 20 gallons, how many 5 fluid ounce portions will the recipe yield?
Answers
The total number of 512 portions will be made the recipe that contains 5 fluid ounces each.
The soup recipe gives 20 gallons.
As we know one gallon produces 128 fluid ounces.
There are 20 gallons produced.
So the number of fluid ounces produced will be 20*128= 2560
Given in the question each portion contains 5 fluid ounces.
Then there is a total of 2560 numbers of fluid ounces.
So the number of portions will be = number of fluid ounces/ number of fluid ounces in each portion= 2560/5= 512
Therefore the total number of 512 portions will be made the recipe that contains 5 fluid ounces each.
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-5x-5<15
Solve the inequality and graph solution set. Write solution set in (a) set builder notation and (b) interval notation
Answers
-5x-5<15 [given]-5x<20 [add 5 to both sides]x>-4 [divide both sides by -5, don't forget to flip the inequality sign]
(a) [tex]\{x: x > -4 \}[/tex]
(b) [tex](-4, \infty)[/tex]
A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32.
a. Compute the value of the test statistic
Answers
The value of the z test statistic will be 2.55.
What is the z test statistic?The z test statistic is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z test statistics is given as
z = (x – μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A sample of 25 provided a sample mean μ = 14 and a sample standard deviation σ = 4.32.
Then the value of the z test statistic will be
z = (x – μ) / σ
z = (25 - 14) / 4.32
z = 11 / 4.32
z = 2.546 ≈ 2.55
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The graph of the parent function f(x) = x3 is translated to form g(x) = (x – 7)3 + 9. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answers
Step-by-step explanation:
let's write this properly :
f(x) = x³
g(x) = (x - 7)³ + 9
this translation means that every point of f(x) is shifted up by 9 units (by the "+ 9" term), and shifted right by 7 units (the " x - 7" term means that for every x the original result of x-7 happens, so, 7 units "later" or more to the right than originally).
so, the original (0, 0) point corresponds to (7, 9).
Question 19 of 40
Which of the following is the correct definition of an angle?
OA. A shape formed by two intersecting lines or rays
B. A shape formed by the intersection of two lines
C. A shape formed by two intersecting rays
D. A shape formed by two intersecting lines from a common point
Answers
The correct definition of an angle is D: A shape formed by two intersecting lines from a common point.
What is a line segment?A line segment is extended infinitely in both directions whereas a 'ray' is a line segment that has one endpoint and extends infinitely in the other direction.
Now, an 'angle' is formed by two rays having a common end-point.
As the angle has a common endpoint,
Therefore it is not possible to form an angle by intersecting two rays having different endpoints.
Hence, option D is correct.
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Need help, can't figure this one out:
Find the perimeter of the following rectilinear figure.
Answers
The perimeter of the following rectilinear figure is 54 units.
What is Perimeter ?Perimeter of a figure is the distance covered when a person walk one round across its edges .
The given figure is in the form of a rectangle ,
The perimeter is equal to the sum of all sides ,
The bottom base is 13 includes (base of the small extended figure )
The left side is 14(includes left side of the small extended figure)
The right side is 10+5+4 (includes right side of the small extended figure)
The top is 8
Therefore the perimeter is 13+14+10+5+4+8 = 54 units
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Find the area.
help pls
Answers
Answer:
30 square feet
Step-by-step explanation:
The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.
A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2, how wide is the walkway?
Answers
========================================================
Explanation:
x = width of the walkway in feet
This is some positive real number.
The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x
Refer to the diagram below.
The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft
The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.
-----------
Area = length*width
1056 = (20+2x)*(40+2x)
1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule
1056 = 800 + 40x + 80x + 4x^2
0 = 4x^2 + 40x + 80x + 800 - 1056
0 = 4x^2 + 120x - 256
4x^2 + 120x - 256 = 0
4(x^2 + 30x - 64) = 0
x^2 + 30x - 64 = 0
Let's use the quadratic formula to finish solving for x.
Plug in a = 1, b = 30, c = -64
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]
Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.
The only practical solution is x = 2
Therefore, the walkway is 2 feet wide
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 0.7 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years?
Round answer to three decimal places
Answers
The probability of 6 years or more, so we want the complement,
1 - 0.98533 = 0.01467 1.467% chance, not very likely.
What is Z-score?A z score is a type of statistical measurement that gives an idea of how far a raw score is from the mean of a distribution. A z score is used in a z test for hypothesis testing.
Here, Because you are looking for the mean of a group of 7.8, the standard deviation will shrink by a factor of √6
Old standard deviation = 0.7,
new standard deviation = 0.7/√6 = 0.64254
You need to find a z-score and then convert your z-score to a probability.
z-score = (your score - average)/ std dev
z-score = (7.8 - 6)/0.64254
z-score = 2.1789
To convert a z-score either look it up on a table or use a calculator.
But z-tables are designed to shade to the left, which means this is the probability that the mean life is 6 years or less. We want the probability of 6 years or more, so we want the complement, 1 - 0.98533 = 0.01467
1.467% chance, not very likely.
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I will give BRAINLIEST! ANSWER FOR 30 Points !!!!
Pleasee look at picture
What is the frequency of the tangent function represented in the graph below?
Answer CHOICES:
1 , 4 , 3 , 2
Answers
Answer:
The answer is 3
Step-by-step explanation:
You can see that it recurs faster than usual for a tan curve so 1 is eliminated and it cant be 2 or 4 because it isnt recurring equally.
Please give brainliestWhich of the following is another name for a proof by contradiction?
Answers
There are a few possibilities:
Indirect proofreductio ad absurdumThe second term refers to the idea of simplifying a claim down to an impossible absurd one.
