The product of sin 30 and sin 60 is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees .
The product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
Sine and cosine of complementary anglesFrom the complementary angle theorem, we have that
sinθ = cos (90° - θ)
and
cosθ = sin (90° - θ)
By applying the theorem,
sin 30° = cos (90° - 30°)
∴ sin 30° = cos 60°
Also,
sin 60° = cos (90° - 60°)
∴ sin 60° = cos 30°
Thus, sin 30° = cos 60° and sin 60° = cos 30°
Hence, the product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
Learn more on Sine and cosine of complementary angles here: https://brainly.com/question/16127404
Distributive Property Assignment
1/6(3/5x+18)=
Leave answer as a fraction.
Answer:
1/10x+3
Step-by-step explanation:
1/6(3/5x+18)
Multiply 3/5x and 18 by 1/6
1/10x+3
prove that sin 60° = 2 tan 30°/1+ tan² 30°
◈ LHS :
[tex]:\implies\tt\:sin60\degree[/tex]
[tex]:\implies\bf\:\dfrac{\sqrt{3}}{2}[/tex]
◈ RHS :
[tex]:\implies\tt\:\dfrac{2tan30\degree}{1+tan^230\degree}[/tex]
[tex]:\implies\tt\:\dfrac{2\times \dfrac{1}{\sqrt{3}}}{1+{\large(}\dfrac{1}{{\sqrt{3}}}{\large)}^2}[/tex]
[tex]:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{3+1}[/tex]
[tex]:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{4}[/tex]
[tex]:\implies\bf\:\dfrac{\sqrt{3}}{2}[/tex]
Hence Proved !!
The New Horizons space probe passed the moon 8 hours and 35 minutes after launch. Write this number as a fraction and reduce. Choose the correct answer. Use 60 as your denominator, not 100, because there are 60 minutes in one hour. A. 9 3/7 hours B. 8 hours C. 8 1/2 hours D. 8 7/12 hours
Answer:
D
Step-by-step explanation:
8 hours and 35 minutes can be rewritten as the mixed fraction 8 35/60.
You can reduce this fraction by dividing the numerator and denominator by 5.
35/5 = 7
60/5 = 12
So, 35/60 = 7/12
Now add 8 to your reduced fraction.
8 + 7/12 = 8 7/12
Hope this helped!
What is the domain of the function y=x/x?
Answer:
-infinity < x < +infinity
Step-by-step explanation:
the domain of a cube root function is the set of all real numbers. unlike a square root function which is limited to non-negative numbers, a cube root can use all real numbers because it is possible for three negatives to equal a negative.
Answer:
A
Step-by-step explanation:
Edge 2021
(-7.4)+e=9.11 what is e
Greetings from Brasil...
Solving this equation
-7.4 + E = 9.11E = 16.51Please help me with this math
Share is 4 times as old as Marcos. If the sum of their age is 45, which equation could best be used to find their ages?
Answer:
5x = 45
Step-by-step explanation:
x represents marcos
4x represents Share
5x = 45
x = 9
4x = 36
Share is 36 and Marcos is 9
Answer:
4x+x =45
Step-by-step explanation:
x would be marcos, since we do not know his age, and share is 4x that amount, so you would have 4x(shares age) plus x(marcos age) to get your answer.
Please help!!!!!
Solve the equation 5(2y - 1) - 2(3y)= 1
Answer:
y = 3/2
Step-by-step explanation:
5(2y - 1) - 2(3y) = 1
First we use distributive property:
10y - 5 - 6y = 1
because 5 × 2y = 10y
and -2 × 3y = -6y
Now we combine the like terms:
4y -5 = 1
because 10y - 6y = 4y
Now we have to send the -5 to the other side. (when we send it to the other side it becomes positive because right now it is negative)
4y = 1 + 5
Again we combine the like terms:
4y = 6
(because 5 + 1 = 6)
Now we have to send the 4 to the other side because we need to get the y value. (when we send it to the other sidr it will be divided)
y = 6/4
and we simplify:
y = 3/2
And we cannot simplify or do anything else. So that is the answer.
Hope that helped!
y = -4x + 10 y = -6x + 16 Substitution
Answer:
The answer to this problem is x = 3 and y = -2.
Step-by-step explanation:
To solve this problem, we first have to remember how to solve problems using substitution. We first solve one equation completely in terms of another variable. In this case, this has already been done for us - the first equation is in the form y = f(x). Next, we should substitute this "value" or function for y into the other equation. This process is modeled below:
y = -4x + 10
y = -6x + 16
If we substitute, we get:
-4x + 10 = -6x + 16
Now this is a simple one variable equation that we can solve easily. First, we should add 6x to both sides, giving us:
2x + 10 = 16
Then, we should subtract 10 from both sides, yielding:
2x = 6
Finally, we can divide both sides by 2 to get:
x = 3
Now, we must plug in this value for x into one of our original equations (it doesn't matter which one we choose) to solve for the other variable, y.
y = -4x + 10
y = -4(3) + 10
y = -12 + 10
y = -2
Therefore, the answer to this problem is x = 3 and y = -2.
Hope this helps!
Answer:
x = 3
y = -2
Step-by-step explanation:
y = -4x + 10 first equation
y = -6x + 16 second equation
from the second equation:
6x = -y + 16
x = (-y + 16) / 6 third equation
substituying the value of the third equation into the first equation:
y = -4(-y+16)/6 + 10
y - 10 = -4(-y+16(/6
6(y-10) = -4(-y+16)
6*y + 6*-10 = -4*-y -4*16
6y - 60 = 4y - 64
6y - 4y = 60 - 64
2y = -4
y = -4/2
y = -2
from the third equation:
x = (-y + 16) / 6
x = (-(-2) + 16) / 6
x = (2+16)/6
x = 18/6
x = 3
Check:
from the first equation:
y = -4x + 10
-2 = -4*3 + 10
-2 = -12 + 10
Please Help me With this 30 points and brainliest to first person
Answer:
(4 * (1 + 2 * 3))^5
Step-by-step explanation:
Try many possibilites and see which one is greater.
The '5' should be an exponent, as it will make the result very large.
Multiplication is usually an operation that makes numbers very big.
From a full 50-liter container of a 40% concentration of acid, x liters are removed and replaced with 100% acid. (A) Write the amount of acid in the final mixture as a function of x (B) Determine the domain and range of the function (C) Determine if the final mixture is 50% acid PLEASE EXPLAIN...I DON'T UNDERSTAND THIS AT ALL
Answer:
A) 20+0.6[tex]x[/tex]
B) range is [0, 50] (i.e. both inclusive)
C) 8.33 litres
Step-by-step explanation:
Given that concentration of acid in 50 litre container is 40%.
Amount of acid in the container = 40% of 50 litres
Amount of acid in the container = [tex]\frac{40}{100} \times 50 = 20\ litre[/tex]
[tex]x[/tex] litres are removed.
Amount of acid removed = 40% of [tex]x[/tex] litre.
Now, remaining acid in the container = (20 - 40% of [tex]x[/tex]) litre
Now, replaced with 100% acid.
So, final acid in the container = (20 - 40% of [tex]x[/tex] + 100% of [tex]x[/tex] ) litre
Amount of acid in the final mixture:
[tex]20 - \dfrac{40}{100} \times x + \dfrac{100}{100} \times x\\\Rightarrow 20 +\dfrac{100-40}{100}x\\\Rightarrow 20 +\dfrac{60}{100}x[/tex]
Answer A) Amount of acid in the final mixture = 20+0.6[tex]x[/tex]
Answer B) [tex]x[/tex] can not be greater than 50 litres (initial volume of container) and can not be lesser than 0 litres.
so, range is [0, 50] (i.e. both inclusive)
Answer C)
Given that final mixture is 50% acid.
amount of acid = 50% of 50 litres = 25 litres
Using the equation:
[tex]20+0.6x =25\\\Rightarrow 0.6x =5\\\Rightarrow \bold{x =8.33\ litres}[/tex]
In the picture below
Answer : The value of x is 100.
Step-by-step explanation :
According to the question, the FH makes a line in which point G is present in between the line FH.
The diagram is shown below.
Given:
FG = (2x) meters
GH = 1000 meters
FH = 1200 meters
Now we have to calculate the value of x.
As we know that:
FH = FG + GH
Now putting all the given values in this expression, we get:
1200 = 2x + 1000
1200 - 1000 = 2x
200 = 2x
x = 100
Therefore, the value of x is 100.
Find the missing value.
Hint: Use the number line to find the missing value
-3 = -7
Answer:
is that all the context that is given?
What is a squared 9 in algebraic form?
f(x) = -3x2 – 20
Find f(-7)
Answer:
Step-by-step explanation:
f(-7)= -3(-7)^2 - 20
f(-7) = -3(49) - 20
= -147 - 20 = -167
hello, please help!! Thank you
I gave steps in the picture how to solve it was much easier to write it out then type it. hope this helps!
is 7.0001 a repeating decimal or a terminating decimal or a integer?
Answer:
7.000l is a terminatin decimal.
Step-by-step explanation:
It is an terminating decimal because it stops right at 1, and the one is not repating too. If it was repeating it would be a repating decimal. We know it's not also an integer because we dont see a ngegative sign next to the seven.
Therefore, 7.0001 is a terminating decimal.
Evaluate the following expression. 5^-1/5^0
Answer:
1/5
Step-by-step explanation:
5^-1/5^0
=5^-1/1
=1/5
What is the value of f(2) for f(x)=2x5−8x4+3x3−4x2+9x−1?(1 point)
Answer:
-39
Step-by-step explanation:
just took the quick check
Is 6p-8 monomial, binomial, or trinomial
Answer:
Binomial
Step-by-step explanation:
how many terms are in the equation?
2 = Binomial
Answer: Binomial
Step-by-step explanation:
It contains two terms in 6p-8 (6p, and 8)
Thus it is binomial
Monomial: contains one term
binomial: contains two terms
trinomial: contains three terms
Hope this helps!! :)
Please let me know if you have any question
How many lines pass through two points ?
Answer:
one
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Postulate 3: Through any two points, there is exactly one line.
Calculate the area of the shaded region. Use 3.14 for pi; round to the nearest tenth, if needed. HELP PLSSS I HAVE TO GET THIS DONE SOON!
Answer:
87.48
Step-by-step explanation:
First find the area of the square
12^2=144
find area of the 2 circles
9*3.14
but theres 2
18*3.14=56.52
144-56.52=87.48
what is the probability of choosing a card from a deck of cards that is a heart or a nine?
ZWXY is a right angle. If Z
is in the interior of ZWXY,
mZWXZ = 7x+8, and
mZZXY = 5x – 2, find the
value of x.
Answer:
x = 7
Step-by-step explanation:
The sum of the interior angles is 90°, so you have ...
(7x +8) +(5x -2) = 90
12x = 84 . . . . subtract 6; next, divide by 12
x = 7
Need to find the angles of <1 and <2.
Answer:
1< and 2< are equal to 125
Step-by-step explanation:
The angle of a straight line is 180, so it would be 180° minus 55°, and that equals to 125°
91.2727272727 simplify??
Answer:
91 +3409/12500
Step-by-step explanation:
Did you mean simplify as a fraction?
Question 9 of 10
Given the lease terms below, find the total lease cost, assuming that the
deposit is nonrefundable.
Terms:
• Length of lease: 24 months
• MSRP of the car: $21,400
• Purchase value of the car after lease: $17,100
• Down payment: $1500
• Monthly payment: $479
• Security deposit: $350
• Acquisition fee: $700
O A. $10,794
OB. $11,100
O c. $14,046
O D. $14,678
The total lease cost assuming that the deposit is nonrefundable is $14046.
What is Meant by Lease Cost?The term "Leasing Costs" refers to all fees paid or benefits granted to a tenant under an existing lease or a new lease, including I commissions for leasing or brokerage services, (ii) direct payments, tenant improvement allowances, work letters, or free rent, and (iii) rent allowances or rent credits.
Given:
Length of lease: 24 months
MSRP of the car: $21,400
Purchase value of the car after lease: $17,100
So, Monthly payment= $479
So, Monthly payment after 24 month
= 11496
Thus, total lease cost = Down payment + Security deposit + Acquisition
fee
+ payment for 24 months
Total lease cost = 1500+ 350+ 700+ 11496
= $14046
Hence, the lease cost is $14046.
Learn more about lease cost here:
https://brainly.com/question/14839133
#SPJ2
Is 6/5 an irrational number
Answer:
yes
Step-by-step explanation:
Answer: Yes it is, because this is written as a simple fraction. A non-simple fraction would be something like 2 1/2. Having that extra whole number in front makes it complex!
Step-by-step explanation:
The width of a rectangle measures (3.1s – 1.6) centimeters, and its length
measures (7.2s – 4.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
Answer:
Expression for perimeter of rectangle is:
[tex]\bold{Perimeter = (20.6s-12.4)\ centimeters}[/tex]
Step-by-step explanation:
Width of rectangle is given as [tex]( 3.1 s - 1.6 )[/tex] centimeters and
length of the rectangle is given as [tex](7.2s - 4.6)[/tex] centimeters.
To find:
The expression to represent the perimeter of rectangle in centimeters.
Solution:
First of all, let us have a look at the formula to calculate the perimeter of a rectangle.
Perimeter of a polygon is equal to sum of all the sides.
In rectangle, we have a total of 4 sides, 2 sides equal to the width and 2 sides are equal to the length of rectangle.
Therefore, perimeter of a rectangle is equal to twice the sum of width and length of the rectangle.
So, formula:
[tex]Perimeter = 2(l+w)[/tex]
Where [tex]l[/tex] is the length of rectangle and
[tex]w[/tex] is the width of rectangle.
Putting the values of length and width as given in the question statement to find its perimeter:
[tex]Perimeter = 2((3.1s-1.6) +(7.2s-4.6))\\\Rightarrow Perimeter = 2(10.3s-6.2)\\\Rightarrow \bold{Perimeter = (20.6s-12.4)\ centimeters}[/tex]
7. Ara and Vartan each have a pomegranate tree growing in their backyards. Ara’s tree is two times taller than Vartan’s. If the total height of the two trees is 25 feet, then how tall is each tree?
Answer:
The height of Ara's tree is 50/3 feet while Vartan's tree is 25/3 feet high
Step-by-step explanation:
Represent Ara's tree with A and Vartan's with V
Given
[tex]A = 2V[/tex]
[tex]A + V = 25[/tex]
Required
Determine A and V
[tex]A = 2V[/tex]
[tex]A + V = 25[/tex]
Substitute 2V for A in [tex]A + V = 25[/tex]
[tex]2V + V= 25[/tex]
[tex]3V = 25[/tex]
Divide both sides by 3
[tex]V =\frac{25}{3}\ feet[/tex]
Recall that [tex]A = 2V[/tex]
So:
[tex]A = 2 * \frac{25}{3}\ feet[/tex]
[tex]A = \frac{2 * 25}{3}\ feet[/tex]
[tex]A = \frac{50}{3}\ feet[/tex]
Hence, the height of Ara's tree is 50/3 feet while Vartan's tree is 25/3 feet high