Answer:
See below
Step-by-step explanation:
[tex]A=\theta[/tex]
[tex]$\sin(90\º - \theta) \cos(90\º - \theta) = \frac{ \tan(\theta)}{1+ \tan^2(\theta)}$[/tex]
According to cofunctions identities:
[tex]\boxed{\sin(90\º - \theta)=\cos(\theta)}[/tex]
[tex]\boxed{\cos(90\º - \theta)=\sin(\theta)}[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{ \tan(\theta)}{1+ \tan^2(\theta)}$[/tex]
Once
[tex]$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)} $[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{ \frac{\sin(\theta)}{\cos(\theta)}}{1+ \frac{\sin^2(\theta)}{\cos^2(\theta)}}$[/tex]
Take
[tex]$1+\frac{\sin^2(\theta)}{\cos^2(\theta)}}=\frac{\sin^2(\theta) + \cos^2(\theta)}{\cos^2(\theta)} $[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{ \frac{\sin(\theta)}{\cos(\theta)}}{\frac{\sin^2(\theta) + \cos^2(\theta)}{\cos^2(\theta)} }}$[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \cdot \frac{\cos^2(\theta)}{\sin^2(\theta) + \cos^2(\theta)} }$[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \cdot \frac{\cos^2(\theta)}{\sin^2(\theta) + \cos^2(\theta)} }$[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{\sin(\theta)\cos(\theta)}{\sin^2(\theta) + \cos^2(\theta)} }$[/tex]
Once
[tex]\boxed{\sin^2(\theta) + \cos^2(\theta)=1}[/tex]
[tex]$\cos(\theta) \sin(\theta) = \frac{\sin(\theta)\cos(\theta)}{1 }$[/tex]
[tex]$\cos(\theta) \sin(\theta) = \sin(\theta)\cos(\theta)$[/tex]
[tex]$\therefore \sin(90\º - \theta) \cos(90\º - \theta) = \frac{ \tan(\theta)}{1+ \tan^2(\theta)}$[/tex]
22. Find three consecutive odd numbers such that the sum of five times the smaller number and twice
the larger number is 33 more than six times the median number.
Answer:
The numbers are 37, 39 and 41.
Step-by-step explanation:
Let the smallest number be [tex]x\\[/tex].
Then the other numbers will be [tex]x+2, x+4[/tex] (as they are consecutive odd numbers, their difference will be 2).
As per the given statement:
LHS(Left Hand Side) : Sum of five times the smaller number and twice the larger number.
i.e. five times the smaller number = [tex]5\times x[/tex]
twice the larger number = [tex]2 \times (x+4)[/tex]
Their sum:
The Left Hand Side becomes:
[tex]5x+2(x+4)[/tex]
RHS(Right Hand Side):
33 more than six times the median number:
i.e. [tex]6\times(x+2) +33[/tex]
Equating LHS and RHS:
[tex]5x+2(x+4) = 6x+12 +33\\\Rightarrow 7x+8=6x+47\\\Rightarrow \bold{x =37}[/tex]
Therefore, the numbers are 37, 39 and 41.
an algebraic expression that may contain numbers, variables, and exponents.
Answer:
3x^2 + 7xy + 5
Step-by-step explanation:
5^4-x^2+x-2 divided by x - 2
Answer: x −x 3 +x 2 +623x−2
Step-by-step explanation:
Meg makes paper flowers. She makes 15 flowers each hour.
She makes flowers for 5 hours each day, on 5 days of the week.
The flowers are packed in boxes. 6 flowers are packed into each box.
How many boxes are needed for all the flowers Meg makes in a week?
Answer:
62.5is what I got but i think you round it
Step-by-step explanation:
Find a decimal estimate for square root of 12
Answer:
3.464
Step-by-step explanation:
PLEASE HELP its urgent
Answer:
y = -1
Step-by-step explanation:
1y + 14 = -4y + 9
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Add 4y and subtract 14 from both sides:
1y (+4y) + 14 (-14) = -4y (+4y) + 9 (-14)
1y + 4y = 9 - 14
5y = -5
Divide 5 from both sides:
(5y)/5 = (-5)/5
y = -5/5 = -1
-1 is your answer for y.
~
Please help me! Thanks.
Answer:
129 is yr ANSWER........
Answer:
[tex]\huge \boxed{\mathrm{129\° }}[/tex]
Step-by-step explanation:
Adjacent angles in a parallelogram add up to 180 degrees.
[tex]\mathrm{m \angle A + m \angle B=180}[/tex]
Solving for [tex]\mathrm{m \angle B}[/tex].
[tex]\mathrm{m \angle B=180-m \angle A}[/tex]
[tex]\mathrm{m \angle B}=180-51[/tex]
[tex]\mathrm{m \angle B=129}[/tex]
which expression is equivalent to 4/9x7?
Is there an answer key?
Answer:
3.11111111
Step-by-step explanation:
solved all the equations and simplified the original problem. The answer for the third one was the same as the original problem.
If y is directly proportional to x and y = 5 when x = 2, find the value of y when
x=7.
Answer:
y = 17.5
Step-by-step explanation:
y is directly proportional to x means that
y = k.x
when y=5, x=2 --> k = y/x = 5/2
when x=7
y = k.x = 5/2 . 7 = 35/2 = 17.5
If y is directly proportional to x and y = 5 when x = 2 the value of y is 17.5
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that y is directly proportional to x
y = 5 when x = 2
We need to find the value of y when x is 7
To find the value of y when x is 7 we have to construct a proportional formula as below
2/5=7/y
Apply cross multiplication
2y=35
Divide both sides by 2
y=35/2
y=17.5
Hence, If y is directly proportional to x and y = 5 when x = 2 the value of y is 17.5
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In the figure given below, ∠DBC=90° and ∠DBE is one-third of ∠ABE.
Answer:
CBE = 112.5 degrees
find m∠1 if m∠1 = 6x and m∠CAB = 11x+9
NEED HELP ASAP PLEASE!
Answer:
<1 = 54
Step-by-step explanation:
< CAB = <1 + <2
We have to assume that AP is a perpendicular bisector or we cannot solve the problem.
That would mean that <1 = <2
11x+9 = 6x+6x
11x+9 = 12x
Subtract 11x from each side
9 = 12x-11x
9 =x
We want <1
<1= 6x
<1 = 6*9
<1 = 54
Question 8. PV = nRT, solve for T please?
Question 10. C= Wtc÷1000, solve for W, please?
Answers:
[tex]\huge \boxed{T= \frac{P V}{n R} } \\ \\ \\ \\ \huge \boxed{W= \displaystyle \frac{1000C }{tc}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
8.[tex]P \cdot V = n \cdot R \cdot T[/tex]
Dividing both sides by n · R:
[tex]\displaystyle \frac{P \cdot V}{n \cdot R} =T[/tex]
9.[tex]\displaystyle C=\frac{Wtc }{1000}[/tex]
Multiplying both sides by 1000:
[tex]1000C=Wtc[/tex]
Dividing both sides by tc:
[tex]\displaystyle \frac{1000C }{tc}=W[/tex]
[tex]\rule[225]{225}{2}[/tex]
PLEASE HELP! We can translate ()=2|−2|−5 to the right 3 units and up 5 units to create (). Write the equation for function g.
Answer:
[tex]g(x)=2\,|x-5|[/tex]
Step-by-step explanation:
Recall that a horizontal translation (shift) in 3 units to the right involves directly subtracting 3 from the variable x (horizontal axis variable) , and that moving the function up 5 units involves adding to the whole function 5 units. That is:
[tex]g(x)=2\,|x-3-2|- 5+ 5\\g(x)=2\,|x-5|+0\\g(x)=2\,|x-5|[/tex]
3 + 4n + n = 2n + 15.
Answer:
n = 4
Step-by-step explanation:
3 + 4n + n = 2n +15
3 + 5n = 2n + 15
5n - 2n = 15 - 3
3n = 12
n = 12 / 3
= 4
Answer:
N=4
Step-by-step explanation:
Simplifying
3 + 4n + n = 2n + 15
Combine like terms: 4n + n = 5n
3 + 5n = 2n + 15
Reorder the terms:
3 + 5n = 15 + 2n
Solving
3 + 5n = 15 + 2n
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '-2n' to each side of the equation.
3 + 5n + -2n = 15 + 2n + -2n
Combine like terms: 5n + -2n = 3n
3 + 3n = 15 + 2n + -2n
Combine like terms: 2n + -2n = 0
3 + 3n = 15 + 0
3 + 3n = 15
Add '-3' to each side of the equation.
3 + -3 + 3n = 15 + -3
Combine like terms: 3 + -3 = 0
0 + 3n = 15 + -3
3n = 15 + -3
Combine like terms: 15 + -3 = 12
3n = 12
Divide each side by '3'.
n = 4
Simplifying
n = 4
A rectangle has an area of 60 cm2. Its width is 7 cm less than its length. (a) Let x cm be the length of the rectangle. Write an equation using the rectangle's area. (b) Solve your equation for x (c) Find the dimensions of the rectangle.
Answer: (a) [tex]A = x^{2}-7x[/tex]
(b) x = 12 or x = -5
(c) Length = 12cm
Width = 5cm
Step-by-step explanation: Area of a rectangle is calculated as:
A = length*width
(a) If length = x,
width = x - 7
Then, equation is:
A = x(x - 7)
[tex]A = x^{2} - 7x[/tex]
(b) Solving for x:
[tex]A = x^{2} - 7x[/tex]
[tex]x^{2} - 7x = 60[/tex]
[tex]x^{2} - 7x - 60=0[/tex]
Using Bhaskara to solve equation:
[tex]x = \frac{7+\sqrt{(-7)^{2}-4.1.(-60)} }{2}[/tex]
[tex]x =\frac{7+\sqrt{289} }{2}[/tex]
[tex]x =\frac{7+17}{2}[/tex]
[tex]x_{1} = \frac{7+17}{2}[/tex] = 12
[tex]x_{2}=\frac{7-17}{2}[/tex] = -5
The quadratic equation gives two values for x: x = 12 or x = -5
(c) Dimensions are positive numbers, so the value of x used is x = 12.
As length is x:
length = 12cm
Width is 7 less than length:
width = x - 7
width = 5cm
The rectangle has length of 12cm and width of 5cm.
which of the following is equivalent to sqrt-75
A. -sqrt75
B. 3isqrt5
C. 25sqrt3
D. 5isqrt3
Answer:
D.
Step-by-step explanation:
[tex] \sqrt{-75} = \sqrt{-1 \times 75} = \sqrt{-1 \times 25 \times 3} = 5i\sqrt{3} [/tex]
The square root of the given number is 5i√3. Therefore, option D is the correct answer.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
The given number is √(-75).
Here, √(-75) can be written as √(-25×3)
= 5i√3
Therefore, option D is the correct answer.
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(10x + бу + 5)
Over 2
Answer:
5x+3y+5/2(5 over 2)
Step-by-step explanation:
Divide 10 by 2
divide 6 by 2
divide 5 by 2 and you stay at 5/2
Answer: 5x+3y+2.5
Step-by-step explanation: 10x+6y+5/2
10/2=5
6/2=3
5/2=2.5
Identify the set of numbers that best describes every situation. Select all that apply. The height of an airplane as it descends to an airport runway. a Integers b Irrational c Rational d Whole Numbers e Real
Answer:
a, c, d, e could all be used to describe this
Step-by-step explanation:
If a plane is defending it is so many feet from the ground and feet are in whole numbers. integers, rational numbers, real numbers, and whole numbers are all whole
can someone plz help?
Answer:
Division property of equality
Step-by-step explanation:
What she did was ;
[tex]\frac{-3x}{-3} =\frac{3}{-3} \\\\x =-1[/tex]
How do you do this? I'll give brainliest, please help.
Answer:
Domain is all values of X or (-∞,∞)
Range is all the possible values of Y. Since it goes up to 3, and then it goes down, it's all values less than or equal to y, or (-∞,3] or y ≤ 3 (depending on how you need to enter the response.
Step-by-step explanation:
Simplify 3x + 9(X+6) =
help please
Answer:
12x +54
Step-by-step explanation:
3x + 9(X+6) =
Distribute
3x+9x +54
12x +54
Answer:
[tex] 12x + 54[/tex]
Step-by-step explanation:
[tex]3x + 9(x + 6) \\ 3x + 9x + 54 \\ = 12x + 54[/tex]
Write the equation of a line with a slope of 3 and a y-intercept of 1.
Take a look at the image below.
sum1 plz help me & explain it ! thank you :)
Answer:
D
Step-by-step explanation: 2 x square root of 2 is 2.8284.......
Point M is located at (9,0) What is located 4 units from point M?
Answer:
which way it could be (9,4) (9,-4) (13,0) (5,0)
Step-by-step explanation:
Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett is Max?
Answer:
Max is 9 feet above Brett.
Step-by-step explanation:
If you subtract how far Max is below the surface to how far Brett is below the surface you find the difference of how much more above Brett Max is.
This would be the mathematical process:
34-25=9
Max is 9 feet above Brett.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that Brett is 34 feet below the surface and Max is 25 feet below the surface.
Max is more than twice as deep below the surface as Brett,
Thus we can determine this difference by subtracting Max's depth from Brett's.
The mathematical solution would be as follows:
⇒ 34 - 25
⇒ 9
Hence, Max is 9 feet above Brett.
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Find P(1), if p(x)=(x-1) (x+1)
Answer:
0
Step-by-step explanation:
So we have the function:
[tex]p(x)=(x-1)(x+1)[/tex]
To find p(1), substitute x for 1:
[tex]p(1)=((1)-1)((1)+1)\\[/tex]
Simplify:
[tex]p(1)=(0)(2)\\p(1)=0[/tex]
Thus, p(1) is 0.
What is da answer?Brainlest to the best answer
Answer:
g(-6)=-13
Step-by-step explanation:
[tex]g(x)=3x+5\\\\x=-6\\\\g(-6)=3(-6)+5\\\\g(-6)=-18+5\\\\g(-6)=-13[/tex]
when the problem says find g(120) and they give you g(x) you just have to put instead of x put 120
so in this case instead of x we put - 6
Calculate the mean and median of each data set and determine what type of distribution it has data set 1 : 5 8 9 6 3 2 10 8 5 4 3 Data set 2: 8 7 3 2 4 6 2 7 4 9 6
Answer:
Data Set 1:
Mean= 5.73
Median= 5
Shape of distribution: skewed right
Data Set 2:
Mean: 5.27
Median: 6
Shape of distribution: Skewed left
Step-by-step explanation: Edmentum
The mean of Data set 1 is approximately 5.727 and the median is 5.
The mean of Data set 2 is approximately 5.273 and the median is 6.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
For Data set 1:
The sum of all values in the dataset is:
5 + 8 + 9 + 6 + 3 + 2 + 10 + 8 + 5 + 4 + 3 = 63
The number of values in the dataset is 11.
The mean of the dataset is:
63 / 11 = 5.727 approx.
Sort the values in ascending order:
2, 3, 3, 4, 5, 5, 6, 8, 8, 9, 10
Since there are 11 values, the median is the middle value, which is 5.
Therefore, the mean of Data set 1 is approximately 5.727 and the median is 5.
The distribution of the dataset seems to be slightly skewed to the right.
For Data set 2:
The sum of all values in the dataset is:
8 + 7 + 3 + 2 + 4 + 6 + 2 + 7 + 4 + 9 + 6 = 58
The number of values in the dataset is 11.
The mean of the dataset is:
58 / 11 = 5.273 approx.
Sort the values in ascending order:
2, 2, 3, 4, 4, 6, 6, 7, 7, 8, 9
Since there are 11 values, the median is the middle value, which is 6.
Therefore, the mean of Data set 2 is approximately 5.273 and the median is 6.
The distribution of the dataset seems to be slightly skewed to the left.
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Comelia and Christopher are arguing about Real Number (R) Sets. Comelia says that all Whole (W) numbers are Rational (Q) and Christopher
says that all Rational (Q) numbers are Whole (W). Who is correct and explain why?
Answer:
Comelia is correct.
Step-by-step explanation:
Rational numbers are those whole can be represented as a fraction.
=> Every fraction is a rational number.
Comelia Says:
All Whole Numbers are Rational Numbers
=> Example: 3 = rational number
=> 3 can be represented as a fraction
=> 30/10 = 300/100
So, Comelia's statement is correct.
Christopher Says:
All Rational Numbers are Whole Numbers
=> Example: 1/2 = Whole Number
=> 1/2 is a fraction
=> 1/2 = .5
=> .5 is not a whole number.
Whole numbers don't have numbers after the decimal point.
So, Christopher's statement is incorrect.
Andi bakes and sells cupcakes. She charges $24 per
dozen cupcakes. You can have them delivered for an
extra fee of $0.20 per mile. If Andi delivers 5 dozen
cupcakes to a customer and drives 18 miles to their
house, how much did she charge the customer?
Answer:
123.60$
Step-by-step explanation:
Step 1: 24 x 5 = $120
step 2: 18 x .20 = $3.60
step 3: $120 + $3.60 = $123.60
$123.6
Step-by-step explanation:
5 dozen= 5×$24=$120
18 miles=18×$0.20=$3.6
$120+$3.6=$123.6
thus, she charged the customer $123.6