Step-by-step explanation:
Given sinA – cosA = 1/2 squaring on both the sides, we get (sinA – cosA)2 = (1/2)2 ⇒ sin2A + cos2A – 2sinA cosA = 1/4 ⇒ 1 – 2sinA cosA = 1/4 ⇒ 1 – (1/4) = 2sinA cosA ⇒ 2sinA cosA = 3/4 ∴ sinA cosA = 3/8 → (1) (sinA + cosA)2 = (sinA – cosA)2 + 4sinA cosA = (1/2)2 + 4(3/8) = (1/4) + (3/2) = 7/4 (sinA + cosA) = √(7/4) = (√7)/2 .
Given that,
[tex]\sin A = \dfrac 12\\\\ \implies \sin^2 A = \dfrac 14\\\\\ \implies 1-\cos^2 A = \dfrac 14\\\\\ \implies \cos^2 A = 1 - \dfrac 14 = \dfrac 34\\\\\ \implies \cos A = \pm \dfrac{\sqrt 3}2\\\\\text{Case 1:}\\\\\sin A + \cos A = \dfrac 12 + \dfrac{\sqrt 3}2 = \dfrac{1 + \sqrt 3}2\\\\\text{Case 2:}\\\\\sin A + \cos A = \dfrac 12 +\left(- \dfrac{\sqrt 3}2\right) = \dfrac 12 - \dfrac{\sqrt 3}2=\dfrac{1 - \sqrt 3}2[/tex]
Emilino needs to arrange chairs for a drama club
meeting at his school. There are 30 students coming.
What
are the different ways he can arrange the chairs so that each
row has the same number of chairs?
This is the same as saying "find the factors of 30". There
are 5 different ways.
Answer:
(1 row & 30 columns) (2 rows & 15 columns) (3 rows & 10 columns) (5 rows & 6 columns) (6 rows & 5 columns)
Step-by-step explanation:
1 * 30 = 30
2 * 15 = 30
3 * 10 = 30
5 * 6 = 30
6 * 5 = 30
please help me answer this question
1) The mathematical statements in Set A are linear equations (there's the equal to [=] symbol). The mathematical statements in Set B are linear inequalities (there are inequality signs like <, > etc).
2) Set A (=)
3) Set B (<, > etc.)
_______
Hope it helps ⚜ :))
how do you convert 56 feet into a decimal please help me pleaseeee
Answer:
[tex] \: [/tex]
One Square Feet is equivalent to 0.0022956820843815 Decimal.
Hence, to convert Square Feet to Decimal, we just need to multiply the number by 0.0022956820843815.
We are going to use very simple Square Feet to Decimal conversion formula for that.
see the calculation example given below.
Convert 56 Square Feet to Decimal ⇒ 56 Square Feet
= 56 × 0.0022956820843815 = 0.12855819672536 Decimal
What is (2x-7y)^2 simplified
Answer:
4x² - 28xy + 49y²
Step-by-step explanation:
(2x - 7y)²
= (2x - 7yy)(2x - 7y)
Each term in the second factor is multiplied by each term in the first factor, that is
2x(2x - 7y) - 7y(2x - 7y) ← distribute parenthesis
= 4x² - 14xy - 14xy + 49y² ← collect like terms
= 4x² - 28xy + 49y²
Is ABC" ADEF? If so, identify the similarity postulate or theorem that
applies
15
A. Similar - AA
B. Similar - SAS
C. Similar - SSS
D. Cannot be determined
here is answer
- BRAINLIEST answerer
The ∆ABC ~ ∆DEF by AA similarity Criteria.
What is Similarity?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Two angles in ∆ABC and their equivalent angles in DEF are congruent.
Hence, it follows that the triangles' third pair of angles would likewise be similar.
So, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
Then here the AA Similarity Criterion will be used.
Thus, ∆ABC ~ ∆DEF by AA Similarity rule.
Learn more about similarity here:
https://brainly.com/question/25502802
#SPJ7
Bruno and Willie need a total of $50,000 to start an accounting business. Bruno has spent a lot of time getting the business set up, so Willie agrees to contribute $12,000 more than Bruno. How much money will Willie contribute?
The amount contributed by Willie and Bruno is $31000 and $19,000 respectively.
Let amount contributed by Willie be x
Let amount contributed by Bruno be y
Since Willie agreed to contribute $12,000 more than Bruno;
Therefore;
x - y = 12000....…....... equation (1)x + y = 50,000...…....... equation (2)By solving the system of equations simultaneously;
2x = 62000x = 31000and y = 50,000 - 31000y = 19,000In essence; The amount contributed by Willie and Bruno is $31000 and $19,000 respectively.
Read more:
https://brainly.com/question/23612222
Solve pls brainliest
Answer:
a)0.085 b)19.6 percent
Step-by-step explanation:
Answer:
a) 0.085
b) 19.6%
Step-by-step explanation:
What is the output of y= 2/3x −4 when the input is 18?
Answer:
output = 8
Step-by-step explanation:
1. To solve for the output of the equation, we plug in the value of the input, 18, and simplify.
Keep in mind that the input is x, and the output is y.2. (Solving)
[tex]y=\frac{2}{3}(18)-4[/tex] [tex]y = \frac{36}{3}-4[/tex] [tex]y = 12 - 4[/tex] [tex]y = 8[/tex]Therefore, the output is 8.
An equation is formed when two equal expressions. The output of y= 2/3x −4 when the input is 18 is 8.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The output of y= (2/3)x −4 when the input is 18 are,
y = (2/3)x - 4
y = (2/3)18 - 4
y = 12 - 4
y = 8
Hence, the output of y= 2/3x −4 when the input is 18 is 8.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ2
The new iPhone 13 Pro Max cost p dollars. T-Mobile is running a promotion that gives you a 45% discount. Write an expression to represent the cost after discount.
The expression that represents the cost after discount is ?
Answer:
0.55p
Step-by-step explanation:
Iphone before discount = 100%p
Iphone after discount = 55%p
Expression = (1 - 0.45)p
Expression = 0.55p
-Chetan K
16. A scuba diver started at sea level and dove 100 feet. The
diver then rose 25 feet. Write and evaluate an expression that
shows the diver's current elevation relative to sea level.
Math
Answer:
His realation to sea level would be -75 since he would be below the ground/ sea level
Step-by-step explanation:
Pls brainliest
Pls help me solve thisss
Answer:
J (-5,2)
Hope this helps!
6973x63 pls explain how u did it!
Answer:
4,39299
Step-by-step explanation:
I multiplied 3 x all the numbers in 6,973, then 6 x all the numbers (I added a 0 before I multiplied, then added both the products and got my answer.
A smart watch was marked 150 and is sold at 120. Find discount percentage
Step-by-step explanation:
100 % = 150
1% = 100%/100 = 150/100 = 1.5
the discount was 150 - 120 = 30.
how many percent are in 30 ? that is our discount preventative.
30/1.5 = 20
so, the watch was sold with 20% discount.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5
Help would be appreciated right now
Answer:
AC = 20.5, CB = 14.5
Step-by-step explanation:
Let X be the distance of AC, and Y be the distance of CB. We can write 2 equations with the given information:
[tex]x=y+6\\x+y=35[/tex]
Now we have a system of equations that we can solve for both variables.
Solve by substitution:
[tex](y+6)+y=35\\2y+6=35\\2y=29\\y=14.5[/tex]
Then the next equation:
[tex]x=14.5+6\\x=20.5[/tex]
x = 20.5, y = 14.5
or
AC = 20.5, CB = 14.5
20.5 is 6 longer than 14.5, and they add up to 35cm, so this is our solution.
Bryan can run 2 miles in 20 minutes. How many miles can he run in 100 minutes?
Answer:
If Bryan can run 2 miles in 20 minutes, he can run 10 miles in 100 minutes.
Step-by-step explanation:
To determine the answer to this problem, we can first find how many minutes it takes Bryan to run one mile. Because it takes him twenty minutes to run two miles, it must take Bryan ten minutes to run one mile.
1 mile = 10 minutes
Multiply this by ten to find how many miles Bryan runs in 100 minutes.
10 miles = 100 minutes
Bryan can run 10 miles in 100 minutes.
Answer: 10 miles
Step-by-step explanation: They’re equivalent to the minutes. 20 minutes 2 miles, 40 minutes 4 miles and so on.
what is the pattern you notice when dividing 10,100,1000
Answer:
Step-by-step explanation:
Image result for what is the pattern you notice when dividing 10,100,1000
When dividing by ten, move the decimal point one place to the left. Place value is the value of a digit based on its location in the number. When dividing by 100, move the decimal place two places to the left. And, remember, if there's no decimal point, assume that the decimal falls at the end of the number.
Answer:
when you divide those numbers the place value shifts by 1.
Step-by-step explanation:
1000.0 to 100.00 to 10.000 to 1.0000 to .10000
Write the Equation
Equation
X Y
-2 5
-1 3
0 1
1 -1
y=-X+2
y=x+2
y=2x+1
y-2x+1
Answer:
y=-5×+13
Step1 inter change ×gy
Trigonometry:
Find the value of θ
Answer:
θ ≈ 50.1°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{61}{95}[/tex] , then
θ = [tex]cos^{-1}[/tex] ( [tex]\frac{61}{95}[/tex] ) ≈ 50.1° ( to the nearest tenth )
Consider the following proportion:
2
7
=
12
x
Use cross products to write the equation: 2x = 84.
What is the value of x?
Answer:
x=42
Step-by-step explanation:
divided by 2 equals 42 first you have to dive x by 2 and do the same for 80
identify the like terms of 3x, chose all the apply
3y
5x
3xy
-2x
3
7y
x
Answer:
5x, -2x, and x
Step-by-step explanation:
Like terms share the same variable and powers. This means that the options with 'x' as an variable would be the like terms of 3x.
5x , -2x , and x are like terms because they share the same variable, 'x'.
Hope this helps.
Consider the equation 12x - 15y = 70
Solve for x (in terms of y)
Solve for y (in terms of x)
PLEASE HELP MEEEE IM IN A TEST!
radius equal to 15 cm what is the circumference of the circle
Given:
Radius = 15 cm
To Find:
Circumference of the circle
Let's start.
We know that the formula of Circumference is
[tex] \sf \longmapsto2\pi r[/tex]
Put the values We know that the formula of [tex]\sf\pi[/tex] is 3.14Radius given is 15 centimetre[tex] \sf \longmapsto \: 2 \times 3.14 \times r[/tex]
[tex] \sf \longmapsto2 \times 3.14 \times( 15 \: cm)[/tex]
[tex] \sf \longmapsto6.28 \times (15 \: cm)[/tex]
[tex] \sf \longmapsto94.2 \: cm[/tex]
[tex] \boxed{\red{\boxed{\sf 94.2 \: cm}}}[/tex]
Drake is an online sales representitve who makes $37,500 per year plus 6.75 for each fee sales he makes. if drake makes an avarage of 200 sales per month what are his annaual earnings?
Answer:
no hes not hes a rapper..........Jk the answer is 53700
Step-by-step explanation:
Step-by-step explanation:
1,350 a month
16,200 a year
Community planners are planning to build a new community garden. They agree that the garden will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the length would remain at 15.8 yards but that the width would increase by 5.2 yards. So, the garden would now cover an area of 327.65 square yards.
Which equation can be used to determine the original width of the garden, w?
1: 327.65 = 5.2 (w + 15.8)
2: 327.65 = 15.8(w +5.2)
3: 327.65 = 2 (w +21)
Answer:
2)
Step-by-step explanation:
To find the original width, multiply 15.8 by w, and by 5.2.
You'll get 327.65 = 15.8w + 82.16.
Next, do the opposite of the symbol from both sides, 327.65 - 82.16 = 15.8w + 82.16.
The constant is 82.16, and the symbol is +, the opposite of plus is -, and thus subtract the constant from both sides.
You'll get 245.49 = 15.8w.
Now do the opposite of the symbol (a number next to a variable is multiplication, so do division, and divide 15.8 on both sides.
245.49/15.8 = 15.8w/15.8, which equals 15.5373417722.
A simple random sample of 30 students was selected from a normally distributed population of high school students. The following confidence intervals were calculated at 90, 95, and 99% confidence levels to estimate the average number of hours of sleep the students got each night. Determine which confidence level goes with each confidence interval. Between 7. 3 and 8. 7 hours of sleep: Between 7. 0 and 9. 0 hours of sleep: Between 7. 2 and 8. 8 hours of sleep:.
Answer:
between 7.0 and 9.0 hours of sleep
Step-by-step explanation:
got it right
Select two numbers that make the inequality true.
1/2x<10
Answer:
Any numbers below 20
Step-by-step explanation:
1/2x<10
Hope this helps :)
Based on the information marked in the diagram, AMNP and AQRS must be
congruent.
N
R
ма
P
A. True
B. False
Answer:
Yes, it is true by AAS theorem.
The triangles ΔMNP and ΔQRS are congruent triangles
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔMNP
Now , let the second triangle be ΔQRS
where the measure of angle ∠MNP = measure of angle ∠QRS = 90°
And , the measure of side NP = measure of side RS
And , the measure of ∠NPM = measure of angle ∠RSQ
So , two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA theorem
To learn more about congruent triangles click :
https://brainly.com/question/26131452
#SPJ7
Help me plz
I’m stuck
Also happy thanksgiving
Answer:
x = 13
angle A = 97degrees
Step-by-step explanation:
TO GET "x=13"
since the angle is an alternate angle , it adds up to 180deg so :-
A+B =180
6x + 5 + 4x + 45 = 180
then u add the like terms :-
10x + 50 = 180
then u substitute:-
10x = 180-50
10x = 130
10x÷10 = 130 ÷10 ( this is to cancel the 10 )
x = 13
___________________________________________________________________
TO GET "A=97"
since we need the magnitude of A, we need to .... um I dunno how to explain this soo.....
the equation for A = 6x + 5
180 is the sum of the 2 angles so :-
180 - 5 - (13 × 6) 13×6 is because x=13
180 - 5 - 78= 97
I subtracted these since we need to cancel to get to an answer
I hope u get it.... sorry if u can't understand
and sorry once again if this answer.... I did it in a rush
This one as well, does anyone know the answer?