Question:
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex]
Answer:
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex][tex]= sin(60^{\circ})[/tex]
Step-by-step explanation:
Given
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex]
Required
Simplify
In trigonometry:
[tex]tan(30^{\circ}) = \frac{1}{\sqrt{3}}[/tex]
So, the expression becomes:
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}[/tex]
Simplify the denominator
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}[/tex]
Express the fraction as:
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex][tex]= \frac{2}{\sqrt 3} / \frac{4}{3}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{2}{\sqrt 3} * \frac{3}{4}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{1}{\sqrt 3} * \frac{3}{2}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{3}{2\sqrt 3}[/tex]
Rationalize
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{3\sqrt{3}}{2* 3}[/tex]
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex] [tex]= \frac{\sqrt{3}}{2}[/tex]
In trigonometry:
[tex]sin(60^{\circ}) = \frac{\sqrt{3}}{2}[/tex]
Hence:
[tex]\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}[/tex][tex]= sin(60^{\circ})[/tex]
guys i NEED HELP!!!!!!!!! please i asked a bunch of times now and i want 2 go to bed PLS HELP MEEEEEEEEEEE if u give a fake answer i'll report it and you'll be missing out on brainiest and 16 points REAL FKN ANSWERS I MEAN IT I'M TIRED AND FED UP WITH PEOPLE JUST ANSWERING BY GOING "jkjaikkkjjhhhflajds" UR NOT FUNNY!
but for those of you who DO help bless your kind hearts and souls you are saving my life i haven't slept properly in days and i go back 2 school tomorrow plz & thx
in the answer just put the answers next to the numbers in the top left cuz they're not in order (i don't think they are)
Answer:
6) D
8) E
9) A
1) D
10) B
Answer:
6) D
8) E
9) A
1) D
10) B
Step-by-step explanation:hope this helps :)
brainliest if you answer correctly
Answer:
y is 1
Step-by-step explanation:
A set of floor speakers costs $466. If the extended warranty on the speakers costs 32% of the price of the speakers, how much does the extended warranty cost
Answer: 149.12
Step-by-step explanation:
to find out the extended warranty we do,
466*(32/100)=149.12
The extended warranty cost is $149.12.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, a set of floor speakers costs $466.
If the extended warranty on the speakers costs 32% of the price of the speakers.
Now, extended price =32% of 466
32/100 ×466
= 0.32×466
= $149.12
Therefore, the extended warranty cost is $149.12.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ5
Find the number of tiles required to be put in a floor with dimensions 25 m x 20 m. Each tile is a rhombus with side 25 cm altitude 10 cm
Answer:
8000
Step-by-step explanation:
Area of floor=25×20m
=500²
Area of each tile=area if each rhombus
=25×25=625cm²
No. of tiles required= area of floor/ area of each tile
=500×104⁴/ 625
=4/5 ×10×1000
=8000
hope it helps!
Can someone please help me? If it is correct I will give Brainliest
Thank you
Answer:
its C
Step-by-step explanation:
Answer: it would be B, here a picture for you to understand it
Step-by-step explanation: Hope you see the picture and hope this help
True or False? A triangle can have side lengths of 3, 3 , and 6
Answer:
No
Step-by-step explanation:
We can check with the Pythagorean Theorem.
a^2 + b^2 = c^2
a and b are always the smaller sides, the legs
c is the longer side, the hypotenuse
3^2 + 3^2 > 6^2
9 + 9 > 36
18 < 36
18 is not greater than 36, therefore this triangle can not have the side lengths 3, 3, and 6.
Find the missing factor B that makes the equality true.
-35x^6=(5x^2)(B)
Answer:
please mark me brainliest and follow me my friend.
a car travels 1/6 of the distance between 2 cities in 3/5 of an hour. At this rate, what fraction of the distance between the 2 cities can the car the car travel in 1 hour?
Answer:
5/18
Step-by-step explanation:
1/6 * 1 / 3/5 = 5/18
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 340 feet of antique picket fencing are to be used to enclose
the garden, find the dimensions of the garden
Answer:
The dimensions of the garden is 102 feet by 68 feet
Step-by-step explanation:
Here, we want to get the width and length of the garden
The perimeter is represented by the length of the fencing
From the question;
w = 2l/3
The formula for the perimeter is;
P = 2(l + w)
Thus;
340 = 2(l + 2l/3)
170 = (l + 2l/3)
Multiply through by 3
510 = 3l + 2l
5l = 510
l = 102 feet
w = 2/3 * l
w = 2/3 * 102
w = 68 feet
HELP PLEASE!!!
I don't understand how to work this out...
If possible, please explain how you got your answer. It would be very helpful!
Thanks!!
Answer:
Option A
Step-by-step explanation:
[tex]R = (\frac{V_f-Vi}{V_i} )100[/tex]
where,
[tex]V_f[/tex] is the final value
[tex]V_i[/tex] if the initial value
R is the investors rate of return
so,
[tex]R = (\frac{V_f-Vi}{V_i} )100\\\\R=(\frac{1500-1700}{1700})100 \\\\R=(\frac{-200}{1700})100 \\\\R=-11.8\\[/tex]
so the investors rate of return is -11.8%
I will give u Brainlest. Cake decorators use buttercream icing on 84% of all their cupcakes. How many cupcakes had buttercream icing if the bakery sold 2100 cupcakes during the holiday season?
Eric sells model cars from a booth at a local flea market. He purchases each model car from a distributor for $14 and the flea market charges him a booth fee of $30. Eric sells each model car for $20. How many cars will Eric have to sell to break even?
Answer: 5 cars
Step-by-step explanation:
Breakeven point = Fixed Cost/ Contribution margin
Fixed cost is $30 which is the flea market booth charge
Contribution margin is sales price less variable cost.
The Variable Cost is the amount he is charged by the distributor of $14.
Contribution Margin = 20 - 14
= $6
Breakeven point = 30/6
= 5 cars
Does the equation y=3/4x +7 describe a proportional relationship
What is the solution to the rational equation x/x^2-9 + 1/x+3 + 1/4x-12
x/x^2-9 + 1/x-3 = 1/4x-12
x/(x+3)(x-3)+1/(x-3)=1/4(x-3)
LCD: 4(x+3)(x-3)
4x+4(x+3)=(x+3)
4x+4x+12=x+3
7x=-9
x=-9/7
What is the 100th term of the sequence with a1 = 222 and d = -5?
PLEASE HELP VERY URGENTTTTTT!!!!!
Answer: -273
Step-by-step explanation:
This is an arithmetic progression and the formula to find the nth term is given as:
= a + (n-1)d
Therefore, the 100th term will be:
= a + (n-1)d
= a + (100 - 1)d
= a + 99d
where a = 222
d = -5
Therefore, a + 99d = 222 + 99(-5)
= 222 + (-495)
= 222 - 495
= -273
2/3 ÷ 2/4 =
1/4
4 2/4
1 2/6
2/3
5.) Robert can do 52 jumping jacks in 10 minutes. At this rate, how many jumping jacks
can Robert do in 35 minutes?
. Critique Reasoning Monica deposits $100 into
a savings account that pays a simple interest
rate of 3.4%. Paul deposits $200 into a savings
account that pays a simple interest rate of 2.2%.
Monica says that she will earn more interest in
one year because her interest rate is higher. Do
you agree? Justify your response.
Answer:
The answer would be no, Monica is wrong.
Step-by-step explanation:
By using the formula for simple interest; Time ( $ x Rate) = Interest
After a year, Monica would have gotten $40.80 in interest,
Paul would have gotten $81.60 in interest.
Because Paul deposited a higher amount of money than Monica, Paul earns more interest.
It costs $3 for children and $7 for adults to attend a school basketball game. If 5000 people attended the game and the total takings at the door was $25000, determine the number of children and the number of adults that attended the game, using simultaneous elimination.
Answer:
2500 children and 2500 adults
The number of children is 2500 and the number of adults that attended the game is also 2500.
System of equations:Let us consider that, number of children be x and number of adults be y that attend game.
Since, total 5000 people attend the game.
[tex]x+y=5000\\\\x=5000-y..........(1)[/tex]
It costs $3 for children and $7 for adults and the total takings at the door was $25000
[tex]3x+7y=25000 .............(2)[/tex]
Substitute value of x from equation 1 into equation 2.
[tex]3(5000-y)+7y=25000\\\\15000-3y+7y=25000\\\\4y=10000\\\\y=10000/4=2500[/tex]
So that, [tex]x=5000-2500=2500[/tex]
Thus, the number of children is 2500 and the number of adults that attended the game is also 2500.
Learn more about the system of equation here:
https://brainly.com/question/13729904
Soni has 196 pencils. If she puts equal amounts of pencils into eight boxes, she has four pencils left. How many pencils does she put in each box?
Which strategy could help solve this word problem?
Answer:
Division i think not 100% sure but i think tht
Step-by-step explanation:
Answer:
24 pencils in each box
Step-by-step explanation:
First, you would subtract 4 from 196 which would equal 192. Then, you would divide 192 by 8 since there are eight boxes which equals 24 pencils in each box.
Translate the sentence into an equation. The product of 6 and a number is 108. What is the solution to the equation?
Answer:
18
6 x ? = 108
108/6=18
6 x 18 = 108
Answer:
Your answer is 18
6x18=108
Hope This helps!!!
Got this right on Edge 2021!!!
Please mark brainliest!!!
Write the equation of the line fully simplified slope intercept form
Answer:
y = - 1/2x + 5
Step-by-step explanation:
the slope is -1/2 because the line is declining two units to the right for every one unit down. and the "b" is 5 because the line hits the y-axis at +5
The ratio of the length to the width of a rectangular patio is 5:2, and its
width is 5 feet. Find its length.
*
Answer:
12.5 ft
Step-by-step explanation:
5/2 = 2.5
5*2.5 = 12.5 ft
A builder wants to build a sump to store water in an apartment. The volume of the
rectangular sump will be modelled by V(x) = x3 + x2 - 4x - 4.
He planned in such a way that its length and breadth are (x + 1) and (x - 2) respectively.
How much he has to dig?
(a) (x + 1]
(b) (x - 2)
(c) (x-3)
(d) (x + 2)
(ii) If x = 4 meter, what is the storage capacity (in litres) of this sump?
(iii) A ladder is kept a point halfway from the base as shown in the figure. It just touches
the top of the sump. Find the length of the ladder, assuming x-42 (correct to 1 dp)
Answer:
1) b, 2) d, 3) dStep-by-step explanation:
The volume is the product of three dimensions
V = lwhGiven:
w = x + 1, l = x + 2 and V(x) = x³ + x² - 4x - 4
1) Let's find the height:
x³ + x² - 4x - 4 =x²(x + 1) - 4(x + 1) = (x² -4)(x + 1) = (x + 2)(x - 2)(x + 1)We got h = x - 22) x = 4 m
Volume is:
V = 4³ + 4² - 4*4 - 4 = 60 m³3) x = 4 m
Dimensions are:
w = x + 1 = 5 m, l = x + 2 = 6 m, h = x - 2 = 2 mFull surface area is:
2(lw + lh + wh) =2(5*6 + 6*2 + 5*2) = 104 m²Slope of line that passes through the points (19,-16) (-7,-15)
Answer:
m= -1/26
Step-by-step explanation:
plug into the formula and solve
PLS HELP (LAST QUESTION)
If you have 360 Nickels, how many dollars do you have?
- 18
- 7,200
- 340
- 380
Answer:
You would have $18
Step-by-step explanation:
Have a good day!
Which statement is true about angles 1 and 2?
AThey are congruent
BThey are right angles.
CThey are complementary
D They are supplementary
please answer, I haven’t no clue how to work it out
Answer:
C. x-2
Step-by-step explanation:
x² + 7x - 18 = 0
the factor must be p and q from the form.of
(x+p)(x+q) = 0
then find the value of p and q by this rules
p + q = 7
p x q = -18
p = 9
q = -2
(x + 9)(x + (-2)) = 0
(x+9)(x-2) = 0
Answer:
c.) [tex](x-2)[/tex]
Step-by-step explanation:
The given expression is written in the form [tex]ac^2+bx+c[/tex]. To factor, find two numbers whose sum is b and whose product is c:
_×_=-18
_+_=7
Use -2 and 7:
-2×9=-18
-2+9=7
Substitute the two numbers for b:
[tex]x^2-2x+9x-18[/tex]
[tex](x^2-2x)+(9x-18)[/tex]
Factor out common terms. The common term in the first parentheses is x and the common term in the second is 9:
[tex]x(\frac{x^2-2x}{x} )+9(\frac{9x-18}{9})\\\\x(x-2)+9(x-2)[/tex]
Cancel out one of the parentheses since they have the same terms and plug the factored numbers in:
[tex](x-2)(x+9)[/tex]
:Done
Check Your Work:
To see if the given factored form is true, simplify it using FOIL:
First, Outside, Inside, Last
[tex](x-2)(x+9)[/tex]
Multiply the first terms:
[tex]x*x=x^2[/tex]
Multiply the terms on the outside:
[tex]x*9=9x\\\\x^2+9x[/tex]
Multiply the inside terms:
[tex]-2*x=-2x\\\\x^2+9x-2x[/tex]
Multiply the last terms:
[tex]-2*9=-18\\\\x^2+9x-2x-18[/tex]
Combine like terms:
[tex]x^2+(9x-2x)-18\\\\x^2+7x-18[/tex]
Therefore, the factored form is true.
During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature?
Answer:-3 degrees
Step-by-step explanation:
just did 4.5-7.5
12(x - 2 - 3x) + 14
Helpppp
Answer:
-24x - 10
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Expression
12(x - 2 - 3x) + 14
Step 2: Simplify
Combine like terms (x): 12(-2x - 2) + 14Distribute 12: -24x - 24 + 14Combine like terms (Z): -24x - 10Answer:
-10/24
Step-by-step explanation:
12(x-2-3x)+14=0
12(-2-2x)+14=0
-24-24x+14
-10-24x=0
24x=-10
x=-10/24