Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
What was the price for one notebook?
Answer:
A notebook at the dollar store costs between 1-2 dollars
34 out of the 68 students at a school assembly were first-grade students. What percentage of the students at the assembly were first-graders?
Answer:
50%
Step-by-step explanation:
34/68=0.5=50%
Answer:
50%
Step-by-step explanation:
because yes
Jonathan is building an outdoor staircase for his deck. He uses 8 screws for every 2 steps. If there are 14 steps, how many screws does Jonathan need?
Answer:
56 screws
Step-by-step explanation:
So, first we can find how many screws he needs.
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws
The screws does Jonathan need is 56 screws.
It is required to find how many screws does Jonathan need.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Jonathan uses 8 screws for every 2 steps. If there are 14 steps.
So, first we can find how many screws he needs.
According to given question we have
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws.
Therefore, the screws does Jonathan need is 56 screws.
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A rectangular room is 15 feet long and 10 feet wide. A scale drawing of the room has a width of 5 inches. What is the length of the room in the drawing?
Answer:
7.5
Step-by-step explanation:
Plz help me I will give you brainliest and 10 points
Answer:
0.08522
Step-by-step explanation:
The diagram shows a square with a perimeter of 20 cm.
Not drawn
accurately
Eight of these squares fit together to make a rectangle.
Not drawnaccurately
What is the perimeter of the rectangle?
The perimeter of the rectangle is 70cm.
What is perimeter?Perimeter is the total length of the sides of a two-dimensional shape.
What is the formula for the perimeter of square?Perimeter of the square is given by
P = 4a
where,
a is the side length of the square.
P is the perimeter of the square.
What is the formula for the perimeter for the rectangle?Perimeter of the rectangle is given by
P = 2( l + b)
Where,
l is the of the rectangle
b is the breadth of the the rectangle
According to the given question.
We have the perimeter of the square is 20cm.
⇒ 4a = 20
⇒ a = 5cm
⇒ Each side length of the square is 5cm
And a rectangle made of 10 squares.
⇒ length of the rectangle = 5×5 = 25cm
and the breadth of the rectangle = 2 × 5 = 10cm
Therefore, the perimeter of the rectangle = 2(25 + 10) = 2 × 35 = 70cm
Hence, the perimeter of the rectangle is 70cm.
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Help please!!!!! Giving extra points!!!!
Answer:
16
Step-by-step explanation:
Answer:
I think 16...
Step-by-step explanation:
Adrian is drawing a map to show the directions from his house to his grandmother's house. He uses a scale of 1 1/2
inches represents 12 miles. If the distance from his house to his grandmother's house is 36 miles, how long is the drawing
on the map?
The length of the drawing on the map for 36 miles is given by the equation A = 4 1/2 inches
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
Let the number of miles be = 12 miles
So , 12 miles on the drawing represents = 1 1/2 inches
Now , the number of miles = 36 miles
12 x 3 = 36 miles
And , 36 miles on the drawing represents = 3 x 12 miles on the drawing
Substituting the values in the equation , we get
36 miles on the drawing represents A = 3 x ( 1 1/2 )
On simplifying the equation , we get
36 miles on the drawing represents A = 4 1/2 inches
Hence , the value on the drawing is 4 1/2 inches
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A. A cylinder just fits into a cube of side length 36 m Calculate the percentage
of empty space in the box.
Answer:
21.5%
Step-by-step explanation:
volume of cube: 36x36x36
volume of cylinder: πx18²x36
Cylinder percentage: (πx18²x36) / 36x36x36 = π / 4 = 0.785
percentage of empty space: 1 - 0.785 = 0.215 (21.5%)
The line of best fit for a scatterplot is shown what is the equation of this line of best fit in slope intercept form?
(pic provided)
1. y=-6x+3/4
2.y=6x+3/4
3. y=-3/4x+6
4. y=3/4x+6
Answer:
3. y=-3/4+6
Step-by-step explanation:
The y-int is 6, so you can already cross out the first two answers. Then, you know the slope is negative because the line is going downward, so -3/4 has to be the slope bc it is negative.
Answer:
y=-3/4x+6
Step-by-step explanation:
the y/intercept is (0,6) because that is the point where the line crosses the y-axis
knowing that use the point (0,6) and (4,3) to find the slope use rise over run so it goes up 3 and right 4
using the slope intercept equation y=mx+b it is y= -3/4+6
it is negative because its going downward
hope this makes sense and helps you guys!
You brought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
Answer:
8
Step-by-step explanation:
Answer:
Candy bars: $13
Step-by-step explanation:
$3 magazine + $13 total of candy bars = $19
Paul won 37 super bouncy balls playing hoops at county fair. At school he gave two to every student in his math class. He only had 3 remaining. How many students are in his class?
Answer:
17 students
Step-by-step explanation:
If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.
How you Can find the area of a composite figure?
Answer:
Here are the steps to find the area of a composite figure.
1. Split the composite figure into simpler shapes.
2. Find the area of each of the simpler shapes.
3. Add the area of all the simpler shapes together.
4. You'll have the area of the composite figure.
Let me know if this helps!
PLZ ANSWE ASAP ASAP ASAP LIKE RN ASAP PLZ PLZ
Answer: Kris's bike
Step-by-step explanation:
KRIS 297/4.5 = 66 gallons per mile
JAKE 366/6 = 61 gallons per mile
BEN = 265.2/5.2 = 52 gallons per mile
Enter the value of n for the equation 26 * 2n = 213
Answer:
4.09
Step-by-step explanation:
please answer the questions.
Answer:
1. 9 numbers (27, 36, 45, 54, 63, 72, 81, 90, 99)
2. 122 square cm
Step-by-step explanation:
break the shape into 2, find area of each, add those areas together
yoo someone help asaapp!
Answer:
A 76
Step-by-step explanation:
7x+8+7x-2+5x+16+110=360
19x+132=360
19x=228
x=12
∠E=5(12)+16
=76
Answer:
76. hope it helps.................
2.) Add unlike fractions using the butterfly method.
1 point
c) of the teacups in Lily's Tea Shop, 1/5 are teal and another 1/10 are yellow. What fraction
of the teacups are either teal or yellow?
3/10
5/10
7/10
O 1/10
Answer:
3/10
Step-by-step explanation:
1/5=2/10
2/10+1/10=3/10
Answer:
ITS 3/10 AND CAN SOMEONE PLS ANSWER MY MOST RECENT QUESTION.
What are the values of x and y?
A.
x equals 136 over 15 and y equals 17 over 15
B.
x equals 64 over 15 and y equals 17 over 15
C.
x equals 8 over 15 and y equals 136 over 15
D.
x equals 64 over 15 and y equals 136 over 15
Answer:
d. 8 over 15 = 136 over 15 this is the right answer okay
1. 10 x ____ = 180
2. 37 x 10 = ____
3. ____ tens = 650
Answer:
1. 18
2. 370
3. 65
Step-by-step explanation:
1. 180/10=18
2. 370 add a zero
3. tens means ·10 so 650/10=65
Answer:
1.)18
2.)370
3.)65 tens yw(:
Please help!!
Will mark brainliest
in the equation x+12=30 does x=16 explain your answer
If someone gave you 100,000$ dollars, what would you spend it on, and why?
1. ROBUX
2.FORTNITE VC
3. 2K 21 VC
Or 100,00$ for a house and car + own a Resturant
Answer:
I would use it for a house, car, and own rhe restaraunt
Answer:
House+Car+restaurant
Step-by-step explanation:
Imagine being such an addict that you spend it on a video game tho
ez points :)
BRAINLIEST PLSSSSS
3. If you buy a new car for $6,000 which depreciates at 4%/year,
what will the value be after 3 years?
Answer:
$5,308.42
Step-by-step explanation:
(see attached for reference)
recall that the formula for Depreciation
is given by
A = P ( 1 - r)^t,
where
A = final amount
P = principal amount = given as $6,000
r = depreciation rate = given as 4% = 0.04
t = time in years = given as 3,
Simply substitute these into the equation to get:
A = P ( 1 - r)^t
= 6000( 1 - 0.04) ^ 3
= 6000 (0.96)^3
= $5,308.42
What is the solution to the equation? 13 3/4+X= 7 1/ 4
Answer: x=-6 1/4
Step-by-step explanation:
What is the value of
2021
−
2223
+
2425
?
?
Answer:
2223
Step-by-step explanation:
We need to find the value of 2021-2223+2425.
Firstly subtract 2223 from 2021.
2021-2223 = -202
Now add -202 and 2425. So,
2425 +(-202) = 2223
So, the value of 2021-2223+2425 is 2223. Hence, this is the required solution.
When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer.
GIVING BRAINLIST PLEASE ANSWER CORRECT!!!
False
True
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.
We will find that working together, they need to work for 8 hours.
----------------------------------
Let's start by defining the variables that we will use:
A = rate at which Aran worksB = rate at which Beatrice works.C = rate at which Charlie works.Now let's see the given information:
"Aran and Beatrice can build an ant hill in 10 hours"
This can be written as:
(A + B)*10 h = 1 ant hill
"Aran and Charlie can build the ant hill in 12 hours"
This can be written as:
(A + C)*12 h = 1 ant hill
"Beatrice and Charlie can build the ant hill in 15 hours"
This can be written as:
(B + C)*15 h = 1 ant hill.
Then we have 3 equations:
[tex](A + B)*10 h = 1[/tex]
[tex](A + C)*12 h = 1[/tex]
[tex](B + C)*15 h = 1[/tex]
Where for commodity, I removed the "ant hill" unit.
Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.
I will isolate A in the first equation:
[tex]A = \frac{1}{10h} - B[/tex]
Now we can replace it in the second equation to get:
[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]
Now we can isolate C in the last equation to get:
[tex]C = \frac{1}{15h} - B[/tex]
Replacing that in the above equation we get:
[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]
This means that Beatrice alone would construct the hill in 24 hours.
Now that we know the value of B, we can use:
[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]
This means that Charlie needs 40 hours to finish the hill alone.
Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:
[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]
Now if the 3 ants work together, the total rate at which they work is:
[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]
This means that they need to work for the inverse of that rate
[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]
Working together, they need to work for 8 hours to complete an ant hill
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Which postulate proves that the triangles below are similar?
SSS
AA
SAS
These triangles are not similar
Answer:
AA~
Step-by-step explanation:
These triangles are similar but not congruent. One triangle is bigger than the other, meaning none of the side lengths are the same. On the triangles, two angles are given, a 53 degree and a 90 meaning that you would us the AA rule to determine if they are similar. Which they are.
The two triangles are similar triangles using AA postulate.
What are Similar Figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
Given one of the angles in both the triangles is equal to 53°, the other angle is 90°, which are also the vertical angles to each other. As shown below.
Hence, the two triangles are similar triangles using AA postulate.
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HELP ASAP YALL- PLS
Answer: x = 4
Step-by-step explanation:
since it is showing us that the angles are congruent, we know that the smaller triangle is just a scaled-down version of the larger one. in other words, it is the EXACT SAME triangle, just slightly smaller.
so, i redrew them next to each other, so i could compare them easily.
i looked at the corresponding sides that were given, and realized that the side that is 10 on the larger triangle is equal to 5 on the smaller triangle. the side that is equal to 6 on the larger triangle is equal to 3 on the smaller triangle. this concludes that the smaller triangle is exactly half the size of the larger triangle!
so, i figured (using logic) that x must equal 4, simply dividing its corresponding side (with a measure of 8) in half.
hope this helps! xoxo
