Consider an angle with a measure of θ=225∘.
Sketch a diagram representing the situation.
Determine the measure of the reference angle for this angle.
_______°
Now, determine the exact values of the following expressions. Your answers should include fractions and square roots, and not decimal values.
cos(θ)=
sin(θ)=
tan(θ)=
Answers
Answer:
cos 225° = [tex]-\frac{\sqrt{2} }{2}[/tex]
sin 225° = [tex]-\frac{\sqrt{2} }{2}[/tex]
tan 225° = 1
Step-by-step explanation:
I cannot sketch a diagram, but a 225° angle is a 3rd quadrant angle and the reference angle is 45° (225 - 180 = 45)
cos and sin are negative in the 3rd quadrant and the tan is positive
cos 225° = - cos 45° = [tex]-\frac{\sqrt{2} }{2}[/tex]
sin 225° = -sin 45° = [tex]-\frac{\sqrt{2} }{2}[/tex]
tan 225° = tan 45° = 1
Related Questions
Suppose 7x-5 M=- 3 x-8 and NE 2 2 x - 5 x - 50 X - 14 x +40 and you want to add the fractions M and N, in other words you want to compute 7x-5 3 x - 8 2 x - 5 x - 50 x - 14 x + 40 and simplify the result. We know that, before you can add the fractions, you must find a common denominator and rewrite each fraction so it has that common denominator. Once the rewritten fractions have the same denominator, you can add them and simplify the result.
There are four text boxes below. In the first text box, enter a common denominator for the two fractions. In the second text box, rewrite M so that it possesses the common denominator you found. Note that your entry in this text box should equal M, however it should have the common denominator you found. In the third text box, rewrite N so that it possesses the common denominator you found. In the last text box, compute your simplified answer for M N . Make sure that your answer is simplified; the numerator and denominator of your answer for M N should not have common factors. Note that your entry for the common denominator should be a polynomial with integer coefficients. Your other three entries should be fractions that contain polynomials. All of your answers should contain no letters other than the variables that appear in M and N. Do not include an equals sign with any of your answers. All of your expressions should be mathematically correct and not contain non-mathematical symbols. After entering your answers, click the Save Answer button. Your computer will display how your answers were interpreted, and you will have the opportunity to accept these answers or modify them.
Enter a common denominator for M and N here:
Enter M rewritten here:
Enter N rewritten here:
Enter your simplified result here:
Answers
Answer:
[tex](a)[/tex] [tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
[tex](b)[/tex] [tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
[tex](c)[/tex] [tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
[tex](d)[/tex] [tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Step-by-step explanation:
Given
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Solving (a): A common denominator of M and N.
To do this, we simply get the LCM of both denominators
[tex]M = x^2 - 5x - 50[/tex]
[tex]N = x^2 - 14x + 40[/tex]
Factorize both:
[tex]M = (x - 10)(x + 5)[/tex]
[tex]N = (x- 10)(x - 4)[/tex]
The LCM is
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
Hence, the common denominator is:
[tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
Solving (b): Rewrite M
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
Factor the denominator:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of M by (x - 4)
The expression becomes:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)} * \frac{x - 4}{x-4}[/tex]
[tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
Solving (c): Rewrite N
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Factor the denominator:
[tex]N = \frac{3x - 8}{(x-4)(x-10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of N by (x + 5)
The expression becomes:
[tex]N = \frac{3x - 8}{(x-4)(x-10)} * \frac{x + 5}{x + 5}[/tex]
[tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
(d) Solve M + N
[tex]M + N = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)} + \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
Take LCM
[tex]M + N = \frac{(7x - 5)(x-4) + (3x - 8)(x + 5)}{(x+5)(x - 10)(x-4)}[/tex]
Open brackets
[tex]M + N = \frac{7x^2 - 28x - 5x + 20 + 3x^2 + 15x - 8x - 40}{(x+5)(x - 10)(x-4)}[/tex]
Collect Like Terms
[tex]M + N = \frac{7x^2 + 3x^2- 28x - 5x + 15x - 8x + 20 - 40}{(x+5)(x - 10)(x-4)}[/tex]
[tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answers
Answer:
comparing both equations
-2x-1=3x+4
or, -1-4 =3x+2x
or, -5=5x
or, X= -1
Y= -2x-1
or, Y= -2(-1)-1
or, Y=1
hence, ( -1,1)
.A town fair charges $6 for general
admission and $1.50 for each ride. Use
the pattern in the table to find the cost of 7
rides and 10 rides. Then write an equation
for the pattern.
Answers
Answer: $1.50r + $6
Step-by-step explanation:
1.50 times 7 is $10.5 without admission
1.50 times 10 is $15 without admission
(R for rides)
so $1.50r + $6 is the equation
A 90° rotation about the origin maps APQR to ALMN. Are the
triangles congruent?
Answers
Answer:
No
Step-by-step explanation:
25 divided by the difference of 12 and 7
Answers
Answer:
5
Step-by-step explanation:
25 / ( 12-7) = 25 / 5 = 5
I hope im right!!
A rectangular flag has an area of 3/8 square foot. The width is 3/4 foot. What is the length of the flag?
Answers
Answer:
1/2
Step-by-step explanation:
Area= 3/8
Width=3/4
Length=?
3/8=0.375
3/4x1/2=3/8 (0.375)
Find the area of the kite.
Answers
Answer:
Step-by-step explanation:
width of kite=2[√(17²-15²)]=2√(289-225)=2√64=2×8=16
area of kite=(22×16)/2=176 sq. units
Which of the following expressions are equivalent to 256^x? Select all that apply.
a. 8^2x
b. 4^4x
c. (64^x)^2
d. (16^x)^2
e. 2^8x
Answers
Answer:
d
Step-by-step explanation:
i did it on eduhguenity
The solutions which satisfy the equation A = 256ˣ are
Option B. 4⁴ˣ
Option D. 16²ˣ
Option E. 2⁸ˣ
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by A = 256ˣ
a)
The value of equation B = 8^2x
B = 8²ˣ
On simplifying the equation , we get
B = 8²⁽ˣ⁾
B = 64ˣ
And the value of B ≠ A
b)
The value of equation B = 4^4x
B = 4⁴ˣ
On simplifying the equation , we get
B = 4⁴⁽ˣ⁾
B = 256ˣ
And the value of B = A
c)
The value of equation B = (64^x)^2
B = (64ˣ)²
On simplifying the equation , we get
B = 64²⁽ˣ⁾
B = 4096ˣ
And the value of B ≠ A
d)
The value of equation B = (16^x)^2
B = (16ˣ)²
On simplifying the equation , we get
B = 16²⁽ˣ⁾
B = 256ˣ
And the value of B = A
e)
The value of equation B = 2^8x
B = (2⁸)ˣ
On simplifying the equation , we get
B = 256⁽ˣ⁾
And the value of B = A
Hence , the equations which satisfy are
Option B. 4⁴ˣ
Option D. 16²ˣ
Option E. 2⁸ˣ
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y у
45°
x 100°
y = [?
Answers
The value of y is 55°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
x and 100° together form a straight angle.
x + 100 = 180
x = 180 - 100
x = 80
Now,
45° + x + y = 180
45 + 80 + y = 180
y = 180 - 125
y = 55°
Thus,
y = 55°.
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PLEASE HELP!! The AHS Football team did a weigh in at the start of training camp. The weights of the players were distributed normally with a mean of 98kg and a standard deviation of 6kg. Which of the following curves represents the data? A,B, Or C??
Answers
Answer: Choice C
=========================================================
Explanation:
The mean is 98, so that's the center of the distribution. This is where the highest point occurs because the most people are clustered around here. This rules out choice A and the answer is between B or C.
One standard deviation above the mean is 98+6 = 104. All we do is add on the standard deviation (6) to the mean (98) to get 104.
One standard deviation below the mean is 98-6 = 92
The graph that has tickmarks at 92 and 104 indicate we are exactly 1 standard deviation from the mean (98)
Similarly, 2 standard deviations above the mean is at 98+2*6 = 98+12 = 110. Or you could say 104+6 = 110.
2 standard deviations below the mean would get us to 98-2*6 = 98-12 = 86
The same idea applies to 3 standard deviations as well.
All of this matches with graph C. We can eliminate graph B by noticing that something like 95 is not a result of 98-6.
Suppose that Upper X has a discrete uniform distribution f left-parenthesis x right-parenthesis equals StartLayout left-brace1st Row 1st Column 1 divided by 3, 2nd Column x equals 1,2,3 2nd Row 1st Column 0, 2nd Column otherwise EndLayout A random sample of n equals 33 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.4. Express the final answer to four decimal places (e.g. 0.9876).
Answers
Answer:
the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444
Step-by-step explanation:
Given the data in the question;
x f(x) xp(x) x²p(x)
1 1/3 0.33333 0.33333
2 1/3 0.66667 1.33333
3 1/3 1.00000 3.0000
∑ 2.0000 4.6667
∑(xp(x)) = 2
∑(x²p(x)) = 4.6667
Variance σ² = ∑(x²) - ∑(x)² = 4.6667 - (2)² = 4.6667 - 4 = 0.6667
standard deviation σ = √variance = √0.6667 = 0.8165
Now since, n = 33 which is greater than 30, we can use normal approximation
for normal distribution z score ( x-μ)/σ
mean μ = 2
standard deviation = 0.817
sample size n = 33
standard of error σₓ = σ/√n = 0.817/√33 = 0.1422
so probability will be;
p( 2.1 < X < 2.4 ) = p(( 2.1-2)/0.1422) < x"-μ/σₓ < p(( 2.4-2)/0.1422)
= 0.70 < Z < 2.81
= 1 - ( 0.703 < Z < 2.812 )
FROM Z-SC0RE TABLE
= 1 - ( 0.25804 + 0.49752 )
= 1 - 0.75556
p( 2.1 < X < 2.4 ) = 0.2444
Therefore, the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444
Are 12/102 and 18/153 equivalent ratios?
Answers
Answer:
there are 2 ways:
[tex]\frac{12}{102}[/tex] ?= [tex]\frac{18}{153}[/tex]
1) try to simplify
[tex]\frac{12}{102}[/tex] (divide the numerator and denominator by 6) ?= [tex]\frac{18}{153}[/tex] (divide the numerator and denominator by 9)
2/17 = 2/17 so yes they are equivalent
2) use cross products
102x18 ?= 12x153
1836 = 1836 so yes they are equivalent
A $240.00 item is marked down by 25%.
What is the new cost of the item?
Round to two decimals if needed.
$
Answers
Explanation:
240 X 0.25 = 60
240 - 60 = 180
Paulo missed three out of 15 questions on a quiz, or 3/15. Write the fraction of questions Paula answered correctly as a decimal. What is the answer??
Answers
Step-by-step explanation:
12/15 in a calculator
0.8
Convert 65 millimeters to centimeters
Pls use step by step pls
Answers
Answer:
65 mili= 6.5cm
Step-by-step explanation:
divide the length value by 10
Divide 65 by 10 to get the number of centimetres:
65mm/10mm=6.5cm
Hope this helps!!
A farmer sells 8.9 kilograms of pears and apples at the farmer's market. 1 4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answers
Answer:
7.5 kilograms of apples
Step-by-step explanation:
Take the total amount and subtract the amount of pears.
8.9-1.4=7.5
Answer:
If 2/5 are apples, 2/5 x 8.9 kilos = 0.4 x 8.9 = 3.56 kilos of apples
pears = 8.9 - 3.56 = 5.34 kilos
if apples are 2/5, then pears are 3/5. 3/5 x 8.9 = .6 x 8.9 = 5.34 kilos of pears
Select the equation that represents the question.
0.8% of 150 is what number?
O 0.008 = a × 150
O a = 0.008 X 150
O 150 = a × 0.008
13
O 0.008 = 150 x a
Solve the equation.
a
Answers
Answer:
[tex]a = 0.008 * 150[/tex]
Step-by-step explanation:
Given
[tex]0.8\% * 150[/tex]
Required
Represent as an equation
Let a be the result of the equation.
So, we have:
[tex]0.8\% * 150 = a[/tex]
Express 0.8% as decimal
[tex]0.008 * 150 = a[/tex]
Rewrite
[tex]a = 0.008 * 150[/tex]
Prove (triangle)ABC is congruent to (triangle) DEF using ASA
Answers
Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Answer:
Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Step-by-step explanation:
Please help me on this
Answers
And 5 times 7 = 35 for the big box
And the top are 2 little boxes of an area of 4
35+8=43
Answer:
Step-by-step explanation:
please help asap! It’s due today
Answers
Toni gives a cashier a $20 bill he is buying an item for $4.79 how much money should tony get back
Answers
Answer:
$15.21
Step-by-step explanation:
Answer:
15.21
Step-by-step explanation:
20−4.79
Subtract 4.79 from 20 to get 15.21.
15.21
24j - 9 Factor the following expression using GCF
Answers
Answer:
See it and do it
Follow please
The radius of the circle is 2.5 cm. - Find the circumference of the circle. Round your answer to the nearest centimeter
2.5 cm
8 cm
O 16 cm
O 79 cm
O 157 cm
Answers
Answer:
I would say A but i am not sure i did not take the test
Step-by-step explanation:
help please!!!! don't understand
Answers
23-17=6
4x=6
6/4=1.5
X=1.5
Hope this helps
Answer:
1.5
Step-by-step explanation:
23-17=6
6/4= 1.5
Keith is riding his bicycle. He rides at a speed of 13 kilometers per hour for 32.5 kilometers. For how many hours does he ride?
Answers
Answer:
422.50
Step-by-step explanation:
just multiply 13 × 32.5=422.50
Convert 65 millimeters to centimeters
Pls help me on this question
Answers
Answer:
Its 6.5
Step-by-step explanation:
Erin Thompson agreed to purchase a house for 97,900
Answers
Answer:
wow
Step-by-step explanation:
no way bro that's brazy
In a survey of 300 students 24 students said that social studies was their favorite subject. What percentage of the students asked, said that social studies was their favorite subject?
Answers
Answer:
Step-by-step explanation:
24/300 = 0.08 = 8%
The figures below show the front view and top view of a rectangular prism that is packed with unit cubes. What is the volume of the prism if there are no gaps or overlaps in the unit cubes? ____ cubic unit
Answers
Answer:
60 cubic units
Step-by-step explanation:
The figure is 5 tall, so just add 5 for each square on the top view.
The volume of the rectangular prism is 60 cubic units
What is the Volume of a Rectangle?
The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular prism be represented as V
Now , the equation will be
The length of the rectangular prism = 3 units
The width of the rectangular prism = 4 units
The height of the rectangular prism = 5 units
Now , the volume is calculated by
Volume of Rectangle = Length x Width x Height
Substituting the values in the equation , we get
Volume of Rectangle V = 3 x 4 x 5
On simplifying the equation , we get
Volume of Rectangle V = 60 cubic units
Therefore , the value of V is 60 cubic units
Hence , the volume of the rectangular prism is 60 cubic units
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Olivia sold water bottles over four days. Create a graph to determine if
the quantities of bottles and number of days are proportional If the
quantities are proportional, what is the constant of proportionality?
Answers
Answer:
sorry I cannot help
Step-by-step explanation:
I will try after some time to help u....LOL
enjoy