Answer:
Tan(x)
Step-by-step explanation:
JUST TOOK THE TEST
tan(x) is equivalent to 1/sin2x - cos2x/sin2x. Option a is correct.
To determine equivalent 1/sin2x - cos2x/sin2x.
tan(x) is tangent of x here, tan is trigonometric operator.
Here,
= 1/sin2x - cos2x/sin2x
= (1-cos2x)/sin2x
= (2sin²x)/2sinxcosx
= sin(x)/cos(x)
= tan(x)
Thus, tan(x) is equivalent to 1/sin2x - cos2x/sin2x.
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Given a point A(-3,-1), it is dilated by some scale
factor to A' (-9,-3). If the same dilation is applied
to B(-1,-5), what are the coordinates of B'?
Answer:
[tex]B' = (-3, -15)[/tex]
Step-by-step explanation:
Given
[tex]A = (-3,-1)[/tex]
[tex]A' = (-9,-3)[/tex]
[tex]B = (-1,-5)[/tex]
Required
Determine the coordinates of B'
Since A' is the image of A; we need to first calculate the scale factor using
[tex]A' = A * Scale\ factor[/tex]
Make Scale Factor the subject
[tex]Scale\ Factor = \frac{A'}{A}[/tex]
Substitute values for A' and A
[tex]Scale\ Factor = \frac{(-9,-3)}{(-3, -1)}[/tex]
Factorize the numerator
[tex]Scale\ Factor = \frac{3 * (-3,-1)}{(-3, -1)}[/tex]
[tex]Scale\ Factor = \frac{3 * 1}{1}[/tex]
[tex]Scale\ Factor = 3[/tex]
The coordinates of B' is then calculated as follows:
[tex]B' = B * Scale\ Factor[/tex]
Substitute values for B and Scale Factor
[tex]B' = (-1,-5) * 3[/tex]
[tex]B' = (-3, -15)[/tex]
The roof of the Westin Tower (officially called the Westin Peachtree Plaza Hotel) in Atlanta is located at a height of 723 ft. Assume a stone is dropped from this roof. (Note: Round numerical answers to two decimal places, if necessary.)
Required:
a. Find the distance of the stone above the ground at any time t (before it hits the ground).
b. How long does it take the stone to reach the ground?
c. With what velocity does it reach the ground?
Answer:
a) The stone takes approximately 6.704 second to reach the ground.
b) The stone takes approximately 6.704 second to reach the ground.
c) The stone hits the ground at a velocity of -215.695 meters per second.
Step-by-step explanation:
a) The stone experiments a free fall, which is a uniform accelerated motion due to gravity and in which effects from air friction and Earth's rotation are negliglble. Then, the vertical distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = y_{o}+v_{o}\cdot t +\frac{1}{2}\cdot g\cdot t^{2}[/tex] (1)
Where:
[tex]y_{o}[/tex] - Initial height of the stone, measured in meters.
[tex]v_{o}[/tex] - Initial velocity of the stone, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If we know that [tex]y_{o} = 723\,ft[/tex], [tex]v_{o} = 0\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the distance of the stone above the ground at any time [tex]t[/tex] is represented by the following model:
[tex]y = 723 -16.087\cdot t^{2}[/tex] (2)
b) If we know that [tex]y = 0[/tex], then the time taken by the stone to reach the ground is:
[tex]723-16.087\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{723}{16.087} }\,s[/tex]
[tex]t \approx 6.704\,s[/tex]
The stone takes approximately 6.704 second to reach the ground.
c) The function velocity is found by differentiating (2) once:
[tex]v = -32.174\cdot t[/tex] (3)
If we know that [tex]t \approx 6.704\,s[/tex], then the velocity when it hits the ground is:
[tex]v = -32.174\cdot (6.704)[/tex]
[tex]v = -215.695\,\frac{m}{s}[/tex]
The stone hits the ground at a velocity of -215.695 meters per second.
Which set of numbers represents a Pythagorean triple?
Answer:
52 , 165 , 173 is Pythagorean triple.
Step-by-step explanation:
Pythagorean triple;
a² + b² = c²
Computation:
88² + 105² ≠ 139²
39² + 80² ≠ 119²
38² + 198² ≠ 202²
52² + 165² = 173²
So,
52 , 165 , 173 is Pythagorean triple.
please help me will mark brainliest
How can you use an inequality to describe the dimensions of a figure?
A scalene triangle can be identified by the inequality of the lengths of its sides and size of its angles.
Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western)
Answer:
p₁ - p₂ = ( -0,28 . 0 )
Step-by-step explanation:
Eastern gray squirrel
Sample size n₁ = 60
p₁ = 22 % p₁ = 0,22 then q₁ = 1 - 0,22 q₁ = 0,88
Western gray squirrel
Sample size n₂ = 120
p₂ = 36% p₂ = 0,36 Then q₂ = 1 - 0,36 q₂ = 0,64
p (s) = ( p₁ - p₂ ) /√ (p₁*q₁ ) / n₁ + (p₂*q₂/ n₂)
p(s) = ( 0,22 - 0,36 ) /√ (0,22*0,88)/60 + ( 0,36*0,64)/120
p(s) = -0,14 /0,071
p(s) = - 1,9718
Then
CI = ( p₁ - p₂ ) ± p(s) *EED
EED = /√ (p₁*q₁ ) / n₁ + (p₂*q₂/ n₂) = 0,071
CI = ( - 0,14 ± 1,9718 * 0,071 )
CI = ( - 0,14 ± 0,14 )
CI = ( - 0,28 ; 0 )
we will find with 95% of confidence the mean of the sampling distribution of the difference in sample proportion in the interval ( -0,28 , 0 )
p₁ - p₂ = ( -0,28 . 0 )
The sampling distribution of the difference in the proportions between proportion is given by possible values of the difference.
The mean of the difference in sample proportion is; (E) 0.22 - 0.36
Reasons:
The given information are;
Percentage of eastern gray squirrel population weighing over 0.5 kg = 22%
Percentage of western gray squirrel population weighing over 0.5 kg = 36%
Sample size of the eastern gray squirrels = 60
Sample size of the western gray squirrels = 120
Required:
The mean of the sampling distribution of the difference in sample proportions (eastern minus western)
The mean of the difference is given by the difference of the mean.
The mean of the sampling distribution of the difference in the sampling proportion from two populations is; Mean = p₁ - p₂
Where;
p₁ = The proportion of the eastern gray squirrel = 22% = 0.22
p₂ = The proportion of the western gray squirrel = 36% = 0.36
Therefore;
Mean = p₁ - p₂ = 0.22 - 0.36
The correct option is (E) 0.22 - 0.36
Learn more here:
The possible question options obtained online includes;
[tex](A) \ \sqrt{\dfrac{0.22 \cdot (0.78)}{120} + \dfrac{0.36\cdot (0.64)}{60} }[/tex]
[tex](B) \ \sqrt{\dfrac{0.22 \cdot (0.78)}{60} + \dfrac{0.36\cdot (0.64)}{120} }[/tex]
(C) 60·(0.22) - 120·(0.36)
(D) 0.36 - 0.22
(E) 0.22 - 0.36
You bought 5 chocolate bars and 8 blow pops for $23.25. Your sister bought 2 chocolate bars and 13 blow pops for $21.55. How much did each chocolate bar cost?
Answer:
$2.65Step-by-step explanation:
Let chocolate bar cost = c and blow pops cost = b
As per given we have equations below:
5c + 8b = 23.25 2c + 13b = 21.5513 times the first equation minus 8 times the second to eliminate b and find c:
13(5c + 8b) - 8(2c + 13b) = 13(23.25) - 8(21.55) 65c - 16c = 129.85 49c = 129.85 c = 129.85/49 c = 2.65Each chocolate bar costs $2.65
hard 9th grade work pls help
3 x1/4 =
Please help me
Answer:
3/4
Step-by-step explanation:
please mark me as brainliest
Answer:
3/4
Step-by-step explanation:
You just multiply the whole number by the numerator.
Find the 75th term of the following arithmetic sequence.
12, 21, 30, 39,
9514 1404 393
Answer:
678
Step-by-step explanation:
The sequence has a first term of 12 and a common difference of 21-12 = 9. The explicit formula for the n-th term is ...
an = a1 +d(n -1)
For a1 = 12 and d = 9, this is ...
an = 12 + 9(n -1)
Using 75 for the value of n, we have ...
a75 = 12 + 9(75 -1) = 12 + 666 = 678
The 75th term is 678.
Solve the following equation for f. Be sure to take into account
whether a letter is capitalized or not.
9 = Gf
Answer:
f is equal to 3 which means g is also equal to 3
Step-by-step explanation:
Tawfiq Trading Company plans to supply 50,000 cartons of oil in January 2021 with the carton selling for $ 20.
It is predicted that the imported oil will fall by 20,000 if the price of a carton of oil falls by 20%.
develop the Supply Equation formula?
Answer:
[tex]\displaystyle s=5,000p-50,000[/tex]
Step-by-step explanation:
Linear Model
The supply of cartons of oil in January 2021 is predicted to reach 50,000 cartons for Tawfiq Trading Company with the carton selling for $20.
If we call s the supply of cartons and p the price, the ordered pair (p,s) for this condition is (20 ; 50,000).
It's predicted that the supply will fall by 20,000 if the price falls by 20%. The new supply will be 50,000-20,000=30,000 and the new price will be 0.8*$20=$16. This gives us the second point (16 ; 30,000)
The equation of a line passing through points (p1,s1) and (p2,s2) can be found as follows:
[tex]\displaystyle s-s_1=\frac{s_2-s_1}{p_2-p_1}(p-p_1)[/tex]
Substituting the given points:
[tex]\displaystyle s-50,000=\frac{30,000-50,000}{16-20}(p-20)[/tex]
Calculating:
[tex]\displaystyle s-50,000=\frac{-20,000}{-4}(p-20)[/tex]
[tex]\displaystyle s-50,000=5000(p-20)[/tex]
Operating and simplifying:
[tex]\displaystyle s-50,000=5,000p-100,000[/tex]
[tex]\mathbf{\displaystyle s=5,000p-50,000}[/tex]
HELLLPPP I WILL MARK BRAINLIEST
Answer:part, whole
Step-by-step explanation:
Part, whole
the difference of the
ages of two brothers is 4 years 5 years ago if the product of their ages was 96 find their present ages
Answer:
OB - Older Brother
YB - Younger Brother
A) OB -YB = 4
B) OB * YB = 96
B) OB = 96 / YB
Multiplying A) by -1
A) -OB + YB = -4 then we add B)
B) OB = 96 / YB
YB = -4 + 96 / YB
Multiplying both sides by YB
YB^2 = -4YB +96 then re-arranging
YB^2 + 4YB -96 = 0 solving by quadratic equation
AS OF 5 years AGO:
Younger Brother's age = 8
Older Brother's age = 12
NOW THEIR AGES ARE:
8 + 4 = 12 YB and
12 + 4 = 16 OB
Step-by-step explanation:
2x (3x+20) find the value of X
Answer:
6x^2+40x
Step-by-step explanation:
2x(3x+20)
6x^2 +40x
That's your answer. you won't be able to find x
Solve for L.........
Answer:
L = P/2 - W
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
P = 2L + 2W
Step 2: Solve for L
Subtract 2W on both sides: P - 2W = 2LDivide 2 on both sides: (P - 2W)/2 = LDistribute division: P/2 - W = LRewrite: L = P/2 - WIf the total value of the coins is 36¢, what is the missing coin?
Answer:
1 penny 3 nickels 2 dimes = 36 cents
quarter
Step-by-step explanation:
30% of the presents under the
tree were for Tammy. If there
were 20 presents under the
tree, how many presents did
Tammy get?
Answer:
6
Step-by-step explanation:
Karen is solving the quadratic equation shown below x2+12x-1=0 x2+12x-1+1=0+1
The solutions to the quadratic equation x² + 12x - 1 = 0 are given by:
[tex]x = -6 \pm \sqrt{37}[/tex]
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are given as follows:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation is given by:
x² + 12x - 1 = 0.
The coefficients are:
a = 1, b = 12, c = -1.
Hence:
[tex]\Delta = 12^2 - 4(1)(-1) = 148[/tex][tex]x_1 = \frac{-12 + \sqrt{148}}{2}[/tex][tex]x_2 = \frac{-12 - \sqrt{148}}{2}[/tex]Since [tex]\sqrt{148} = 2\sqrt{37}[/tex], the solutions are given as follows, simplifying by 2:
[tex]x = -6 \pm \sqrt{37}[/tex]
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Mahammad Yunus is the founder of the Grameen Bank and a recipient of the Nobel Peace Prize for his work to find solutions to extreme poverty. The Grameen Bank issues microcredit loans and is the world's original microlending organization. Microcredit loans are one way to help people move out of extreme poverty. The loans involve lending very poor people small amounts of money to start a new business or to expand an existing one. 1. Malik wants to open a bicycle repair shop in India. He will need 800 rupees to buy the tools and equipment necessary to start his business. After that, he will need 1,400 rupees per month to keep his business running a. Copy and complete the table below for Malik's total costs. Number of Months in Business Total Costs to Operate (in rupees) 1 2 3 6 n
Answer:
sorry didnt get to find the anwser
Step-by-step explanation:
Given triangle GHJ, the measure of angle G equals 110°, the measure of angle J equals 40°, and the measure of angle H equals 30°. Complete the following statements. Since angle G is angle, the opposite side, JH, is . The order of the side lengths from longest to shortest is .
Answer:
Since angle G is
✔ the largest
angle, the opposite side, JH, is
✔ the longest side
. The order of the side lengths from longest to shortest is
✔ HJ, GH, and GJ
.
Step-by-step explanation:
Answer: the answers are
-the largest
-the longest side
-HJ, GH, and GJ
Step-by-step explanation: put them in edge 2020, got them right Hope this helps :)
Help 6th grade math thanks
Answer:
8.75
Step-by-step explanation:
In order to find the unit rate, you need to divide the variable by the independent variable. In this case, your dependent variable would be $122.50 because the cost depends on how much you are buying; you're independent variable will be 14 because it doesn't depend on the other.
Divide 122.5 by 14 and your answer would be 8.75
Hope this helps!!! :)
Also, please give me brainliest if you don't mind. :)
If you don't want to, then it's okay.
8.75 hope this answers your question.
whats the answer? if you know it
Answer:
Step-by-step explanation:
360
The coordinate grid shows three points P, Q, and R:
A four-quadrant coordinate grid from negative 10 to positive 10 in increments of 2 is drawn. Point P is plotted on the ordered pair negative 6, negative 2. Point Q is plotted on the ordered pair negative 6, negative 6. Point R is plotted on the ordered pair 4, negative 6.
The distance between Q and R is ______ units.
Numerical Answers Expected!
Answer for Blank 1:
Answer:
10 unitsStep-by-step explanation:
Given:
Point Q = (-6, -6)Point R = (4, -6)The segment QR is horizontal as both have same y- coordinate of -6.
The distance between Q and R is the distance between x- coordinates:
4 - ( -6) = 10 unitsAnswer:
10
Step-by-step explanation:
i took the test flvs right segmant exam
HELP ASAP QUESTION IN PHOTO
is 6(4j - 6) and 24 - 36j equivalent
Answer:
no because its supposed to be 24j-36
Step-by-step explanation:
so basically im trying to say is that they did the problem wrong.
A box contains 4 red pens, 3 blue pens, and 5 black pens. A pen is selected at random, not replaced, and then a second pen is selected. Find probability of: P(red, then blue)
Answer:
bbbbbb
Step-by-step explanation:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbb
What I don’t get this someone help
Answer:
1 3/4 gallon or 1.75
Step-by-step explanation:
1 (1/4) = 5/7
5/4 = 5/7
5/4 = 1.25
1.25/x = 5/7
7(1.25) = 5x
5x = 8.75
x = 1 3/4
Best answer gets brainiest. On Wednesday at camp, Diana went for a hike at 5:35 A.M. The hike took 1 hour and 30 minutes. As soon as she got back from the hike, Diana played volleyball for 55 minutes. What time did Diana finish playing volleyball?
Include A.M. or P.M. in your answer.
Answer:
Diana finshed playing volleyball at 8am
Step-by-step explanation:
So we know she started at 5:35 AM
And she hiked for an hour and 30 minutes
so 5:35+1 hour is 6:35
and 6:35+35 is 7:05
So before playing volley ball, the time is 7:05 am
Now volley ball was 55 minutes
so 7:05+55 is 8
So 8am
Answer:
She finish playing valleyball at 8:00 am
Step-by-step explanation:
Hike at 5:30 => 1h 30 min => 7:05
valleyball at 7:05 => 55 min => 8:00
solve for x 4(x-3)-8=16
Answer:
x=9
Step-by-step explanation:
4(x-3)-8=16
1. Distribute
(4x) - (4*3) - 8 =16
4x-12-8=16
Combine the 12 and the 8
4x-20=16
Add 20 to both sides
4x-20+20=16+20
4x=36
Divide by 4.
x=9
Hope this helps plz hit the crown :D
Find the slope of the line that passes through (10, 8) and (9, 13)