Answer:
Trigonometric identities
[tex]\sec^2(\alpha)=1+\tan^2(\alpha)[/tex]
[tex]\csc^2(\alpha)=1+\cot^2(\alpha)[/tex]
[tex]\cot^2(\alpha)=\dfrac{1}{\tan^2(\alpha)}[/tex]
Solution[tex]\begin{aligned}\sec^2(\alpha) \cdot \csc^2(\alpha) & = (1+\tan^2(\alpha))(1+\cot^2(\alpha))\\\\ & =1+\cot^2(\alpha)+\tan^2(\alpha)+tan^2(\alpha)\cot^2(\alpha)\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+\tan^2(\alpha) \cdot \dfrac{1}{\tan^2(\alpha)}\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+ \dfrac{\tan^2(\alpha)}{\tan^2(\alpha)}\\\\& = 1+\cot^2(\alpha)+\tan^2(\alpha)+1\\\\& = \tan^2(\alpha)+\cot^2(\alpha)+2\end{aligned}[/tex]
Answer:
See below ~
Step-by-step explanation:
Trigonometric Identies (needed)
sec²a = 1 + tan²a cosec²a = 1 + cot²acot²a = 1/tan²aSolving
Expanding the LHS
sec²a * cosec²a(1 + tan²a) * (1 + cot²a)1 + tan²a + cot²a + (tan²a * cot²a)1 + tan²a + cot²a + 1tan²a + cot²a + 2⇒ RHS∴ Hence, we have proved the left hand side of the equation is equal to the right hand side.
What is 0.75 written as a fraction?
A-1/75
B-10/75
C-75/100
D-7/5
E-75-10
Answer:
[C] 75/100
Step-by-step explanation:
0.75 as a fraction is 75/100.
Steps:
0.75 over 1
0.75/1
Multiply both the numerator and denominator by 100
75/100
Hence, the answer is [C] 75/100
[RevyBreeze]
Answer:
[C] 75/100
Step-by-step explanation:
Given:
What is 0.75 written as a fraction?
Solution:
0.75 = Decimal
Rewriting the decimal number as a fraction with 1 in the denominator
[tex]0.75=\frac{0.75}1[/tex]
Now, multiply to remove the 2 decimal places. So, you multiply top and bottom by 10² = 100
10² is the same thing as 100 because 10² = 10 × 10 and 10 × 10 = 100
[tex]\frac{0.75}{1}\times\frac{100}{100}=\frac{75}{100}[/tex]
Thus, the answer is [C] 75/100
Kavinsky
11 by 12 minus 7 by 15
27
using bodmas rule:
[tex]\sf b - bracket, o - order, d - division, m - multiplication, a - addtion, s - subtraction[/tex]
=================
Solve:
11 x 12 - 7 x 15 (carry out multiplication first)
132 - 105 (subtract)
27 (final answer)
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{11}{12}-\dfrac{7}{15}[/tex]
Take LCM (60}[tex]\\ \rm\Rrightarrow \dfrac{11(5)-7(4)}{60}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{55-28}{60}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{27}{60}[/tex]
Write -7i as complex number
Step-by-step explanation:
z = 0 -7i ....................
Read the following numbers and write them in expanded form 443 092 101
What is 2038 x 28? Giving Brainliest
Answer:
57064
Step-by-step explanation:
Apples were sold at 9 for $5. Carol bought a total of 27 apples. If Carol paid the cashier using two $10 bills, how much change did she recive?
Answer:
She received $5 back
Step-by-step explanation:
Answer:
170
Step-by-step
Add 5 27 times count by 5s and you will get the answer.
simplify 1/2 / 5/8 + 1/4
Answer: 1 1/20
Step-by-step explanation:
1/2 / 5/8 + 1/4
=8/10 +1/4
=21/20
=1 1/20
1. What is the sum of the four 30 degrees angles in the wheel? Show your work.
Answer:
120 degrees
Step-by-step explanation:
30 * 4 = 120
Answer:
Step-by-step explanation:
30 + 30 + 30 + 30 = 30 x 4 = 120 degrees
If triangleABC is a right angle triangle at C.then what is the value of cos(A+B)
Answer:
Hi there!
As we know that the sum of all three angles of a triangle is 180°.
If ∆ABC is right angled at C
C = 90°
=> [tex]\:\mathsf\red{∠A\: +\:∠B\: +\: ∠C\:=\:180°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: +\: 90°\:=\:180°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: =\:180°\:-\:90°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: =\:90°}[/tex]
Multiplying cos both sides. We get,
=> [tex]\:\sf{cos\:(∠A\: +\:∠B)\: =\:cos\:90°}[/tex]
We know cos 90° = 0, by trigonometric ratio.
=> [tex]\:\sf{cos\:90°\:=\:0}[/tex]
So,
[tex]\:\mathsf{cos(∠A\: +\:∠B)=\:cos\:90°\:=\:0}[/tex]
=> [tex]\:\sf\purple{cos\:(∠A\:+\:∠B)\:=\:0}[/tex]
[tex]\:\mathsf\blue{Hope\:this\:helps\:you!\:}[/tex]
WHY IS NOBODY HELP ME I GOT 2 OTHER QUESTIONS POSTED AND NOBODY ANSWERED ME
Answer:
B. F(0) = 4
Step-by-step explanation:
Im unsure about the C tho.
I NEED THIS ANSWER ASAP
base twelve needs 12 digits so we use "t" for ten and "e" for eleven and our usual ten digits.* what base ten number does 1t5e represent?
Answer:
65
Step-by-step explanation:
t = 10
e = 11
10 + (11*5)
65
X+3=2X+6(x+4)
Please Answer!
What is the answer to this?…
Answer:
0.5n
Step-by-step explanation:
n/2 is equal to n * 1/2. 1/2 is equal to 0.5, so n * 1/2 = n * 0.5 = 0.5n.
The diameter of a circle is 11 cm. Find its circumference in terms of .
Answer:
C= 34.56 cm
Step-by-step explanation:
Using the formulas
C=2πr
d=2r
Solving for C
C= πd = π·11 ≈ 34.55752cm
(d) Sandy’s gross annual income is $51,350. She is paid biweekly and has 5% deducted from her paycheck for her 403(b). Her employer matches her deduction, up to 4%. How much is deposited into Sandy’s 403(b) each payday?
Based on the annual income, the payment period, and the amount deducted for the 403(b), the amount deposited into Sandy's 403(b) is $220.
How much is deposited into Sandy's 403(b)?First find the biweekly income:
= 51,350 / (52 weeks / 2 )
= 51,350 / 21 weeks
= $2,445.24
5% is deducted from her wages and the employer matches 4% of the salary. The amount deposited is:
= (5% + 4%) x 2,445.24
= $220
Find out more on 403(b) at https://brainly.com/question/2908111.
a mountain bike is on sale for 25% off. The regular price is $123.50. About how much is the discount
Matthew collected data about the ages of the actors in two different community theater groups. He drew a box plot for one of the sets of data and made a table of the other set of data.Ages of Actors is the Southside Players
For the Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players : the median is 26, the range is 12 and the IQR is 12.
What is median?The median is regarded as the middle number among a series of sorted numbers that are placed in ascending or descending order.
Note that from the image attached, the northside ages are 22, 25, 28, 29, 29, 36, 36, 41, 49, 49, 54.
The median northside ages therefore is 36
For Range = Highest number - Lowest number
54-22 = 32
IQR = Q₃ - Q₁
Note that first quartile Q1 is said to be the median of the n lowest values and third quartile Q3 is the median of the n highest values.
Lowest value is 22 + 25/2 = 28.5.
Highest value is 49 + 44/ 2= 46.5.
Therefore, IQR = Q₃ - Q₁
46.5 - 28.5 =
IQR = 36
Note, for Southside Players;
If the Ages of Actors is the Southside Players are 20 22 24 26 28 30 32 34.
Then the median is = 26
Range is = 34-22 = 12
IQR = Q₃ - Q₁
Lowest = 20 + 22/ 2 = 21
Highest is 32 + 34 / 2 = 33
33 - 21
IQR = 12
Therefore, for the Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players : the median is 26, the range is 12 and the IQR is 12.
Learn more about Range from
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Ben spent 1/6 of his money on a burger, fries, and a drink. Then he spent half of the money he had left: $5 on a magazine, $8.25 on a bookmark, and $10.50 on a book. How much money did he have to begin with?
Please answer asap and please explain your answer.
The amount of money Ben had to begin with after spending 1/6 and 1/2 of it is 57 dollars.
How to find the how much money he had with an equation?let
x = amount he had to begin with
He spent 1/6 of his money on a burger, fries, and a drink. Therefore,
amount spent on burger, fries, and a drink = 1 / 6 x
Hence,
amount he had left = x - 1 / 6 x =6x - x /6 = 5 / 6 x
Then he spent half of the money he had left.
1 / 2(5 /6 x) = 5 + 8.25 + 10.50
5 / 12 x = 23.75
cross multiply
5x = 23.75 × 12
5x = 285
divide both sides by 5
x = 285 / 5
x = 57
Therefore, the amount of money he have to begin with is $57.
learn more on equation here: https://brainly.com/question/5718696
Answer:
$57
Step-by-step explanation:
10.50 - 7.50 = 3
3 x 19 =57
$57
The length of one of the sides of a regular hexagon is 7.8cm, find the perimeter of this polygon
Answer:
46.8 cm
Step-by-step explanation:
A hexagon has six sides. If it is a regular hexagon, then it is equilateral, meaning that each side is the same length. If one side is 7.8cm, then all sides will be 7.8cm. You can find the perimeter by adding 7.8 six times, or multiplying 7.8 by six.
7.8 · 6 = 46.8
hope this helps!
On Friday, Jessica babysat for 3 hours and earned $27. On Saturday, Jessica babysat for 6 hours and earned $54. On Friday, Jessica babysat for 7 hours and earned $63. Write an equation to represent her earnings if x represents hours and y represents earnings
Answer:
y = 9x
Step-by-step explanation:
We can make the x-values represent how many hours Jessica babysat, and the y-values represent how much money she earned each day.
We have these points:
(3, 27)(6, 54)(7, 63)The days of the week she worked do not matter in this problem. We are just trying to find the association between hours worked and money earned.
We can start by finding the slope of the line by using two of the points. I will be using (3, 27) and (6, 54).
The slope formula is [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex].
Substitute these two points into the formula:
[tex]\displaystyle m = \frac{54-27}{6-3}[/tex] [tex]\displaystyle m = \frac{27}{3}[/tex][tex]m=9[/tex]The slope of the line is m = 9.
Now, we can use the point-slope equation to find the equation of the line that represents Jessica's earnings.
Point-slope equation: [tex]y-y_1=m(x-x_1)[/tex].
Substitute the slope m = 9 and the point (3, 27) into the equation.
[tex]y-(27)=9(x-(3))[/tex] [tex]y-27=9(x-3)[/tex] [tex]y-27=9x-27[/tex][tex]y=9x[/tex]The equation y = 9x represents Jessica's earnings, where x represents hours and y represents earnings.
Patty has a flower box in the shape of a rectangular prism with interior dimensions that are 15 inches in length, 8 inches in width, and 6 inches in height. Patty will fill the flower box 3/4 full of soil. How many cubic inches of soil will be in the flower box?
Answer:
540 cubic inches.
Step-by-step explanation:
Stacey has 30 hamburgers. 4/6 of them have cheese on them. The rest are plain. How many burgers have cheese on them?
Answer:
20 burgers
Step-by-step explanation:
4/6×30 = 2/3 ×30 = 60/3 = 20
Given parallelogram EFGH, find the values of x and y.
Answer:
y = 40, x = 9
Step-by-step explanation:
2(3y)+2(2y-20)=360
y = 40
2x=18
x = 9
You are designing a triangular pennant for your school. If you have only 117 square inches of fabric and you want the pennant, when suspended from its base, to hang down 18 inches, what must the length of the
base be?
Answer:
13 inches
Step-by-step explanation:
Area of fabric : 117 square inchesHeight : 18 inchesBase x Height x 1/2 = Area (Fabric)Base x 18 x 1/2 = 117Base x 9 = 117Base = 13 inchesAnswer:
The base must be 13 inches
Step-by-step explanation:
Step 1: Determine the length of the base
[tex]A = 1/2 * b * h[/tex]
[tex]117\ in^2 = 1/2 * b * 18\ in[/tex]
[tex]117\ in^2 = 9\ in * b[/tex]
[tex]\frac{117\ in^2}{9\ in} = \frac{9\ in * b}{9\ in}[/tex]
[tex]13\ in = b[/tex]
Answer: The base must be 13 inches
If a_1=4a 1 =4 and a_{n+1}=3a_n-3a n+1 =3a n −3 then find the value of a_3a 3
Answer:
Step-by-step explanation:
Solve for t. Please help asap!
Answer:
The answer is B.
[tex]t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a}[/tex]
Step-by-step explanation:
[tex]d=3+at^2\\\\d-3=at^2\\\\\frac{d-3}{a}=t^2\\\\ t=+\sqrt{\frac{d-3}{a} } , -\sqrt{\frac{d-3}{a} }[/tex]
I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.
Ex: 12^3 = (x^4)*(y^3)*(z^6)
Can anyone explain how to make that a logarithmic equation?
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]12^3~~ = ~~x^4 y^3 z^6\implies \log_{12}(x^4 y^3 z^6)=3 \\\\\\ \log_{12}(x^4)~~ + ~~\log_{12}(y^3)~~ + ~~\log_{12}(z^6)~~ = ~~3 \\\\\\ 4\log_{12}(x)~~ + ~~3\log_{12}(y)~~ + ~~6\log_{12}(z)~~ = ~~3[/tex]
A game lasts 5/8 hours. Rachel played 4 of these games. For how long did she play in total? Write your answer in the simplest form.
Answer:
5/2 or 2 1/2 hours
Step-by-step explanation:
Multiply 5/8 by 4, which is 20/8, then you simply from there so 5/2=2 1/2
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 28 ft/s. The ball's height h (in feet) after 1 seconds is given by the following:
h = 3 +28t-16t^2
Find all values of 1 for which the ball's height is 11 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
1 seconds
DO
х
?
initial
height
ground
The value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
Given that the height of the ball at time t is given by the function,
[tex]h(t) = 3+ 28t -16t^2[/tex]
where t is in seconds and h is in feet.
Now, the height of the ball is given to be 11 feet, therefore, substituting the value of h in the function as 11,
[tex]h(t) = 3+ 28t -16t^2\\\\11 = 3+ 28t -16t^2\\\\-16t^2 + 28t +3 -11 = 0\\\\-16t^2 + 28t -8 = 0[/tex]
Now, solving the given quadratic equation, we will get,
[tex]x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-(28)\pm \sqrt{(28)^2-4(-16)(-8)}}{2(-16)}\\\\t= 0.36\ or\ 1.39[/tex]
Hence, the value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
Learn more about Quadratic Equations:
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Use appropriate property and find -1/6×4/7+1/2-3/7×1/6
Answer:
1/3
Step-by-step explanation:
Multiply left to right, so you start with -1/6*4/7=-2/21
Then you apply the fraction rule so -1/6*4
and 4 can be expressed by 4/1 so -1/6*4/1=-2/3
Then after solving you will get -4/6
then you factor 4=2*2 what will be -2*2/6
Then you cancel the common factors what are 2
so you bring back the 7 so -2/3/7 and 7 can be expressed as 7/1 and then you apply the fraction rule and flip it to 1/7 what will be solved as -2/21
so then it will be -2/21+1/2-1/14-3/7*1/6
Then you will have to solve -3/7*1/6 what is 1/14
so -2/21+1/2-1/14=1/3 final equation
Answer:
⅓Step-by-step explanation:
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