Step-by-step explanation:
[tex] \sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
Use the identity
[tex] \sin^2 \theta = \dfrac{1 - \cos 2\theta}{2} [/tex]
on the left side.
[tex] \dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
[tex] \dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
Now use the identity
[tex] \sin \theta = \cos(\frac{\pi}{2} - \theta) [/tex]
on the left side.
[tex] \dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
[tex] \frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
which is not solution to the folloeing linear equality
A. (-2, 1)
B. (0, 0)
C. (2, -1)
D. (-9, -9)
Answer:
B
Step-by-step explanation:
Find the value of x. Use the photo I uploaded to help plz.
A. X=2
B. X=3
C. X=33
D. X=52
A flagpole that is 28 feet tall casts a 15-foot shadow. At the same time, a nearby tree casts a 21 foot shadow. Find the height of the tree.
Round to the nearest tenth.
Answer:
7.5 ft tall
Step-by-step explanation:
We can find the height of the tree if you provide the actual length of the trees shadow.
Not really sure what a "toilet for a shadow" means.
Example: If the tree cast a shadow that was 4 feet long we would use a ratio:
Height/shadow = Height/Shadow
28/15 = x/4 cross multiply
15x = 4(28)
x = 4(28)/15 ≅ 7.47 ft
Rounding I would call the tree 7.5 ft tall
Hope this helps.
Answer:
39.2 feet
Step-by-step explanation:
In case of flagpole:
[tex] tan \theta = \frac {28}{15}..... (1)[/tex]
Since, a nearby tree casts a 21 foot shadow at the same time. So the angle formed will be equal.
Let the height of the tree be x feet.
Therefore,
[tex] tan \theta = \frac {x}{21}.....(2)[/tex]
From equations (1) & (2)
[tex] \frac {28}{15} = \frac {x}{21}.....(2)\\\\
x = \frac{28\times {21} }{{15} }\\\\
x = \frac{588}{{15} }\\\\
x = 39.2 \\\\
[/tex]
The measure of an angle is 26°. What is the measure of its complementary angle?
Answer:
64
Step-by-step explanation:
Complementary angles have to add up to 90.
90-26=64.
Answer:
64°
Step-by-step explanation:
Complementary angle means it add up to 90°
26° + x = 90°
x = 64°
The graph shows a proportional relationship between y (price) and x (number of pounds of rice).
What is the unit rate, expressed in price per pound?
Answer:
0.80
Step-by-step explanation:
I just took the test I wrote the $1.67 it was wrong.
y = -2x + 13 when x = 6
Answer: 1
Work: After plugging in the 6 in the X, the new equation is -2(6) + 13. After doing the multiplication of -2 and 6, you get -12. Add -12 + 13, and the answer (Or y) equals 1.
I hope this helps, and Happy Holidays! :)
Find the area of the rhombus! Please help!
Answer:
100m
Step-by-step explanation:
First, find the area of one triangle. Use l*w/2 to do that.
10*5=50
50/2=25
Multiply this by 4 to get the total area
25*4=100
Have a good day!
please help i’ll give brainliest! thank you!
Answer:
no correlation
Step-by-step explanation:
the dots are scattered randomly and not in a positive or negative correlation
Jonathan wants to the new baseball game for his game console. The game costs $45.99. If sales tax is 6%, write an equation to find the total cost of the game, represented as P.
Answer:
45.99x.94=P
Step-by-step explanation:
Suppose that a bond has a face value of ₱ 100,000 and its maturity date is 10 years from now. The coupon rate is 5% payable semi-annually. Find the price of the bond, assuming that the required yield is 4%.
Answer:
Bond Price= $108,175.71
Step-by-step explanation:
Giving the following information:
Face value= $100,000
Coupon rate= 0.05/2= 0.025
YTM= 0.04/2= 0.02
Time period= 10*2= 20 semesters
To calculate the price of the bond, we need to use the following formula:
Bond Price= cupon*{[1 - (1+i)^-n] / i} + [face value/(1+i)^n]
Bond Price= 2,500*{[1 - (1.02^-20)] / 0.02} + [100,000/(1.02^20)]
Bond Price= 40,878.58 + 67,297.13
Bond Price= $108,175.71
In this exercise we have to use the knowledge of finance to calculate the stipulated value through the percentages, thus we find that:
Bond Price will be [tex]\$108,175.71[/tex]
From the information given in the text we found that:
Face value: [tex]\$100,000[/tex] Coupon rate: [tex]0.05/2= 0.025[/tex] YTM: [tex]0.04/2= 0.02[/tex] Time period: [tex]20 \ semesters[/tex]
To calculate the price of the bond, we need to use the following formula:
[tex]Bond\ Price = cupon*{[1 - (1+i)^{-n}] / i} + [face \ value/(1+i)^n][/tex]
So with the formula already informed we will replace the values given in the text find what we want.
[tex]Bond \ Price = 2,500*{[1 - (1.02^{-20})] / 0.02} + [100,000/(1.02^{20})]\\Bond Price= 40,878.58 + 67,297.13\\Bond Price= \$108,175.71[/tex]
See more about finances at: brainly.com/question/10024737
BRANLIEST AND 50 POINTS
What is the prime factorization of 135?
3 × 5 × 9
3 × 5 3
3 2 × 5 2
3 3 × 5
Answer:
3×5×9
Step-by-step explanation:
It's the only answer that can be applied
But you have to expand it farther
2×5×9
2×3×3×5
Note:if you want the answer from your options the answer is 2×5×9
Otherwise 2×3×3×5
Fay opens a credit card with an APR of 15.25% compounded monthly. How much is charged in interest this month if her balance is $1,300? (4 points)
Answer:
total charge = $ 16.52
refer to the Attachment please :)
hope this helps you ^^"
One litre of paint covers 1.5 square meters. How many litres must I buy so that I have enough to paint a wall 6 m long and 3 m high ?
Answer:
12 litres
Step-by-step explanation:
The area to be covered is
A = 6 × 3 = 18 m²
Divide the area by 1.5 for required amount of paint, that is
18 ÷ 1.5 = 12 litres
8. You deposit $2000 in an account that
earns 5% annual interest. Find the balance
after 1 year if the interest is compounded
quarterly.
A. $2,100
B. $2,101.89
C. $2,102.32
D. $2,102.49
Answer: A, $2,100
Step-by-step explanation:
2000x1.05=2,100
JK has endpoints located at J(15, - 13) and K(-9, 27). What are the coordinates of the midpoint of JK?
Answer:
[tex](3,7)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point J (15, -13)
Point K (-9, 27)
Step 2: Find Midpoint
Simply plug in your coordinates into the midpoint formula to find midpoint.
Substitute [MP]: [tex](\frac{15-9}{2},\frac{-13+27}{2})[/tex]Subtract/Add: [tex](\frac{6}{2},\frac{14}{2})[/tex]Divide: [tex](3,7)[/tex]33+36 is the same as Blank +29
Below is the graph of linear equation F(x)-2x-4
AL
1. Which point represents the grach's yntercept?
A. Part A C. Point
B. Parte D. Point
2 Which point represents the grach's recept?
A. Porta C. Point
B. Part 3
D. Ponto
1 Which ont represents the grach's 2007
A. Part C. Ponto
B Parts D. Point
Answer:
1. B. point B.
2. C. point C.
3. C. point C.
Step-by-step explanation:
1. In order to find the graph's y-intercept, we need to locate the point where the line crosses the y-axis. This will always happen at x=0, therefore, the y-intercept is located at point B (0,-4)
2. In order to find the x-intercept, we need to find the point where the line crosses the x-axis. This will generally happen when y=0, so that will be point C (2,0)
3. In order to find the graph's zero, we need to find the point where y=0. In other words, the graph's zero is the point where the function is equal to zero (the x-intercept) so this will br point C again (2,0)
11. The chance of a woman getting breast cancer in her lifetime is 1 out of 8. At this rate, how many
women in classroom of 32 women would be expected to come down with breast cancer in her lifetime?
Answer:4
Step-by-step explanation:8x4=32
Since it is 1 out of 8, 32/8=4
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
108 is 36% of what number? Write and solve a proportion to solve the problem.
Answer: 300
Step-by-step explanation:
Let the number be represented by x.
Therefore, based on the information given in the question, this can be expressed as:
36% of x = 108
36/100 × x = 108
0.36 × x = 108
0.36x = 108
x = 108/0.36
x = 300
Therefore, the number is 300
Find the value of X and Y
Answer:
Answer: x=4, y=10
Step-by-step explanation:
Lines and Angles
When lines cross, the angles formed in the intersections meet certain properties that help us to solve some geometry problems.
We must recall the so-called linear angles, defined as the adjacent angles formed in the point where two lines cross.
Linear angles always add up to 180°
We can see line m intersects with the horizontal (unnamed) line forming two pair of linear angles, thus:
29x - 3 + 15x + 7 = 180
Simplifying:
44x +4 = 180
Subtracting 4:
44x = 176
Dividing by 44:
x = 176/44
x = 4
Now below the horizontal line, we find other pair of linear angles, thus:
13y - 17 + 15x + 7 = 180
Substituting x=4:
13y - 17 + 60 + 7 = 180
Simplifying:
13y + 50 = 180
Subtracting 50:
13y = 180 - 50 = 130
Dividing by 13:
y = 130/13 = 10
y = 10
Answer: x=4, y=10
can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)
Answer:
Yes it is proportional
Step-by-step explanation:
Notice how when x goes up 1 y goes up by 1.6. There is a pattern, if there is no pattern then you would see that numbers either go up or down with no pattern.
If RSTU is translated by the rule (x,y) > (x+2, y-10) , in which quadrant will the image R'S'T'U be located ?
Answer:
D) Quadrant 3
Step-by-step explanation:
ok so lets get a random point and try it out i see -10 is a big number so i will use R and see where it is and then t
R(-8,3) so add 2 to x and minus 10 y
R'(-6,-7)
Now t
T(-4,9)
(+2,-10)
T'(2,-1)
It is Quadrant 3
If RSTU is translated by the rule (x, y) ⇒ (x + 2, y - 10) the image R'S'T'U be located at the D. Third quadrant.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
From the given diagram, the coordinate of the vertex(T) is (- 4, 10).
Let, T' be the vertex when the quadrilateral is translated by the rule
(x, y) ⇒ (x + 2, y - 10).
Therefore, The translated coordinate of the vertex(T') is,
(- 4 + 2, 10 - 10).
= (- 2, 0).
So, The quadrilateral will lie in the third quadrant.
learn more about quadrilaterals here :
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B
1
N
4
5
5
(4x+6)
(5x -5)
7
00
0
A
С
(3x + 8)
The value of x is
and the length of the base is
Answer: (2x + 3) • (x-1)
Step-by-step explanation:
1 Pull out like factors :
4x + 6 = 2 • (2x + 3)
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
(5x - 5) = 5 • (x - 1)
A camper leaves camp and travels 4 miles west and 3 miles north. How far is the camper from his original starting point?
Answer:
5 miles
Step-by-step explanation:
To answer this question, use the following:
According to pythagorean theorem, the hypotenuse of the triangle, c, with legs a and b, can be found with the following equation:
[tex]a^2+b^2=c^2[/tex]
Thus plugging in 3 for a and 4 for b:
[tex]c^2 = 25[/tex]
[tex]c=5[/tex]
In the context of this graph, what do the slope and y-intercept mean?
Help me for a brainliest
please help with 1-3
HURRY PLZZZ I WIL MARK LOTS OF POINTS Which pattern does not follow the rule subtract 8, multiply by 2, subtract 8,
multiply by 2, .?
A)15,7, 14,6, 12,..
B)20, 12, 24, 16, 30, ...
C)17,9, 18, 10, 20, .
D)24, 16, 32, 24, 48
Answer:
B)20,12,24,16,30
Step-by-step explanation:
A) 15,7,14,6,12
15 to 7: subtract 8
7 to 14: multiply by 2
14 to 6: subtract 8
6 to 12: multiply 2
B) 20,12,24,16,30
20 to 12: subtract 8
12 to 24: multiple 2
24 to 16: subtract 8
16 to 30: add 14
C)17,9,18,10,20
17 to 9: subtract 8
9 to 18: Multiply 2
18 to 10: subtract 8
10 to 20: multiply 2
D)24,16,32,24,48
24 to 16: subtract 8
16 to 32: multiply 2
32 to 24: subtract 8
24 to 48: multiply 2
You can clearly see that all of them follow the pattern except B, making B the answer.
Don't be afraid to reach out if you need any more help. I hope that helps you!
Answer:
B
Step-by-step explanation:
B becasue 30 isn't 16 times 2. It would have to be 32.
is 3x+11/x-4 = 4/x(x-4)
Answer:
x= -5
Step-by-step explanation:
please help me get the question right away
Answer:
true
Step-by-step explanation:
hopefully this helps :)
Can someone help with this I’ll mark u as brainlist
Answer:i don’t really k ow but i need points to ask questions
Step-by-step explanation: