I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,
[tex]\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)[/tex]
and I assume you're supposed to establish an identity.
Recall the double angle identities for cos and sin :
cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1
sin(2α) = 2 sin(α) cos(α)
Now expand the left side as
(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)
Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :
… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]
Cancel the factors of 1 + 2 cos(α) :
… = sin(α) / cos(α)
which is equivalent to
… = tan(α)
by definition of tan.
Adam wishes to have $21 comma 000
available in 22
years to purchase a new car for his son as a gift for his college
graduation. To accomplish this goal, how much should Adam invest now in a CD that pays 1.78
%
interest compounded semiannually
? round to the nearest cent as needed
Answer:
la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
59.904 simplified. (help)
Answer:
59 113/125
Step-by-step explanation:
“if there are 12 boys and 48 girls in a room, fill out all of the possible ratios of boys to girls that could be made.”
Answer:
1 boy 4 girls, 2 boys 8 girls, 3 boys 12 girls, 4 boys 16 girls
What is the measure of the angle at the tail end of the kite?
Answer:
58°
Step-by-step explanation:
measure of the angle at the tail end of the kite
= 360° - (122° + 90° + 90°)
= 360° - 302°
= 58°
4/9x6= (write in simplest form)
Answer:
24/7
Step-by-step explanation:
Answer:
8/3
Step-by-step explanation:
4 * 6 = 24 8
9 9 3
Is 2.5 : 8 and 7.5 : 24 equivalent?
Answer:
Yes
Step-by-step explanation:
[tex]\frac{2.5}{8} = \frac{7.5}{24} = \frac{5}{16}[/tex]
Answer:
yes it is equivalent
because when we multiple 3
to both 2.5 and 8
then it will. 7.5:24
so, answer is yes
hope it helps
Jada’s babysitter is four times Jada’s current age. In 5 years, Jada will be half her babysitter’s current age.
Answer:
24
Step-by-step explanation:
We can deduce that Jada's current age from her babysitter's age is 6 years.
Word problems in algebra?Word problems in algebra involve our ability to discern abstract concepts and define variables that can be used to solve them algebraically. We do so by writing out an equation using variables and solving the equation.
From the given problem;
If Jada's current age = xThen Jada Babysitter = 4xSo, x + 4x = 1
In five years' time;
Jada Babysitter's age = 5(4x)Jada current age [tex]\mathbf{=\dfrac{5(4x)}{2}}[/tex]So, we can have the equation:
[tex]\mathbf{\rightarrow \ 5(4x) + \dfrac{5(4x)}{2} = 5}[/tex]
20x + 10x = 5
30x = 5
x = 0.6
Therefore, Jada's current age is [tex]\mathbf{=\dfrac{5(4(0.6))}{2} = 6 years }[/tex]
Learn more about word problems in algebra here:
https://brainly.com/question/21405634
Which equation is represented by the line
Write the slope of a line parallel to the given line. y=8x+3
Answer:
8
Step-by-step explanation:
Slope of parallel lines are equal
In the equation y=8x+3,
8 stands for the slope
Have an amazing day :)
Will give brainlst! Pls help
Answer:
C. As the Test Score increases, the Social media time decreases
Step-by-step explanation:
D. Yes, linear because if I were to draw a line on the graph most of the points on the scatter plots would match?
Answer:
C. As the Social media time increases, the Test score decreases.
D. Yes, I think the relationship between the test scores and social media time appears liner, because linear lines tend to be straight, and has a constant rate of change. In this case, there is a constant rate of change, and the plot points aren't all over the place.
Explanation (sort of):
Look at the graph going from left to right; You will see that the plot points continue to "fall" closer to the x-axis. This is why "Test scores" are decreasing instead of "Social media time", unlike what someone else answered with.
Quadrilateral ABCD at A(-2,2),B(-2,4),C(2,4), and D(2,2). The quadrilateral is then transformed using the rule(x-2,y+8) to form the image A'B'C'D'. What are the new coordinates of A',B',C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.
PLZ Help! Using the chain link rule, how to find f'(5)
given f(x)=(g(x))^3 and
g(5)=-3 and g'(5)=6
Please show steps, I will award 5 stars
Answer:FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"
READ PROMPT
Step-by-step explanation:
5. Examine the expression below. Select the answer that correctly completes each statement below. * Enter your answer for all parts below.
Sample Answer: C, B, C
5x+2y+7
a The term 5x could be read as:
A the sum of 5 and x
B. the product of 5 and x
C. the quotient of 5 and x
b. In the expression, 7 is a:
A coefficient
B. constant
C. variable
c. In the expression, 2 is a:
A coefficient
B. constant
C. variable
Answer:
B, B, A.
Step-by-step explanation:
5x means 5 multiplied by x, so is it A, B or C? the product, because that means multiplied. a is B.
For b, we can see that 7 is a constant, because it isn't being multiplied by anything.
For c, 2y is 2 multiplied by y. Y would be the variable, and 2 would be the coefficient.
PLEASE WILL MARK BRAINIEST!!!!!! Jameson and Quincy each deposit $7,000 into accounts that earn 6% interest, but Jameson earns annual simple interest while Quincy earns annual compound interest. Assuming neither one of them makes any deposits or withdrawals for 5 years, which of the following is a true statement?
Jameson will have about $9,367.58 less in his account than Quincy.
Jameson will have about $267.58 less in his account than Quincy.
Jameson will have about $2,367.58 more in his account than Quincy.
Jameson will have about $2,100 more in his account than Quincy.
Jameson will have about $267.58 less in his account than Quincy.
What is Compound Interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Here, Jameson deposit Principal = $ 7000
Duration = 5 years
Rate of interest = 6 % SI per annum.
For simple Interest, Amount = P(1+RT)
Total amount in Jameson at the end of 5 years = 7000 ( 1 + 0.06 X 5)
= 7000 X 1.3
= $ 9100
Quincy deposit Principal = $ 7000
Duration = 5 years
Rate of interest = 6 % CI per annum.
For Compound Interest, Amount = P(1+R)ⁿ
Total amount in Quincy at the end of 5 years = 7000 ( 1 + 0.06)⁵
= 7000 X 1.34
= $ 9367.58
Thus, Jameson will have about $267.58 less in his account than Quincy.
Learn more about Compound Interest from:
https://brainly.com/question/14295570
#SPJ1
ez math help -thanks
Answer:
use photo math.....
1) -8
2)9
3)18
evaluate -3 x +2x-1 if x=-5
100 POINTS IF YOU ANSWER WITH WHHSHSHSS OR SOMTJING GETTING REPORTED AND IT WILL TAKE YOUR POINTS. Math Properties of Equality, Part 2
For each expression, write an equivalent expression to show the
mathematical properties of equality.
Distributive Property:
6(m +4) = ?
Associative Property:
2 + (m + x) = ?
Commutative Property:
x + 3 = ?
Distributive Property:
3(2y - 6) = ?
Distributive Property:
m(y + 5) = ?
Answer:
Distributive Property:
6m+24
Associative Property:
m+x+2
Distributive Property:
6y-18
Distributive Property:
my+5m
The first term of an arithmetic sequence is -5, and the tenth term is 13.
Find the common difference.
2
1.8
8/9
Answer:
Step-by-step explanation:
Let d be the common difference.
a₁₀ = a₁ + (10-1)d
13 = -5 + 9d
d = 2
HELPPPPPP math please only correct answer i beg you
Answer:
the area is 15
Step-by-step explanation:
if you split this shape into a triangle and a square, the triangle would measure with a legnth og 4 and a with of 3, which = 12 and then you divide by 2 to = the triangles area(6) then you add tht to the area of the square 3*3=9. so the answer would be 15
The daily budget of $40, to be spent entirely on coffee and comic books. Each comic book is priced at $8 and each
cup of coffee is priced at $4. To maximize utility, how many cups of coffee and how many comic books should I buy How many total utils will i enjoy?
Answer:
3 comic books and 4 cups of coffee
Step-by-step explanation:
8 × 3 = 24
4 × 4 = 16
16 + 24 = 40
help please i beg you
Answer:
4800
Step-by-step explanation:
Answer:
108
Step-by-step explanation:
if u need step by step explanation please comment
what is 2X500 pls!!!!!
Answer:
1000
Step-by-step explanation:
2×500=1000
hope it helps
What is the length of side s of the square shown below?
45
8
90°
S
O A. 413
B. 2
O C. 1
D. 6
E. 4
O F. 8-12
Answer:
A. 4√2..........................
A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what is the fair
price for a ticket?
Answer:
$5
Step-by-step explanation:
1000/200=5
Answer:
20 cents.
Step-by-step explanation:
A fair price would be 200/1000 = 1/5 of a dollar which is 20 cents. But this does not allow for the people putting on the raffle to make any money for doing it. It would be better if the raffle went for a dollar. Most people would think that is fair and would not begrudge a dollar.
-3 > t+5/-1
can someone plz solve this inequality
The table shows the width and length of different pictures
Answer:
There is no table? try taking a screenshot
Step-by-step explanation:
find the quotient 1 7/8 / 5 5/8
Which statement about the solution to the system and its justification is true? Please help!!
Answer:
c i think
Step-by-step explanation:
Solve for s. 5s = -5s + 8(2s + 6)
what is s value?
Answer:
5s = -5s + 8(2s + 6)
5 s = 11 s + 48
s = -8
so the Solution: S = -8
HOPE THIS HELPS <3 HAVE A NIVE DAYY :)
10 points AND BRAINLIEST EASY QUESTION MUST BE DONE IN 10 MIN OR LESS. NO TROLL ANSWERS
Answer:
Initial Value=15
Rate of change=15/10=1.5
Equation: y=1.5x+15
Step-by-step explanation:
y=ax+b
y=1.5x+b
15=1.5(0)+b
b=15