Answer:
[tex]sin(x)\,cos(x)-cos^2(x)=\frac{\sqrt{3} -3}{4}[/tex]
Step-by-step explanation:
Recall the Pythagorean identity for cotangent:
[tex]1+cot^2(x)=csc^2(x)[/tex]
where the cosecant is the reciprocal of the sine function. So, since we know the value of the cotangent of the angle, we can derive the value of the square of the sine:
[tex]1+cot^2(x)=csc^2(x)\\1+(\sqrt{3})^2=\frac{1}{sin^2(x)} \\1+3=\frac{1}{sin^2(x)} \\4=\frac{1}{sin^2(x)}\\sin^2(x)=\frac{1}{4}\\ sin(x)=+/-\frac{1}{2}[/tex]
We can also use the Pythagorean identity for sin and cos, to find the value of [tex]cos^2(x)[/tex] and of cos(x):
[tex]cos^2(x)=1-sin^2(x)\\cos^2(x)=1-\frac{1}{4} \\cos^2(x)=\frac{3}{4}\\cos(x)=+/-\frac{\sqrt{3}}{2}[/tex]
We also notice that since the cotangent is positive, the angle "x" must be located in either the firs or the third quadrant, where both sine and cosine have the same sign (both positive in the first quadrant, and both negative in the third quadrant.
Then the requested quantity can be written as:
[tex]sin(x)\,cos(x)-cos^2(x)=(\frac{1}{2}) \,\frac{\sqrt{3} }{2} -\frac{3}{4} =\frac{\sqrt{3} }{4} -\frac{3}{4}=\frac{\sqrt{3}-3 }{4}[/tex]
If BE is a diameter of the circle, find
MAB
A. 400
B 50°
C. 75
D 80
Answer:
B 50˚
Step-by-step explanation:
What you want to do is to find all other measures and subtract them from 360, or find all measures to the left of BE, and subtract from 180.
You can find mCE easily: since the measure of an arc is twice the measure of its corresponding angle (as long as that angle is not a central angle), mCE = 2(25), or 50˚.
mDE equals 100˚. This is because it and arc BD are the only arcs right of BE, the diameter, meaning they, together, must equal half the circle. Since half a circle = 180˚,
180˚=80˚+x
x=180-80
x=100
Now, you can solve:
Method 1:
360˚=80˚+80˚+50˚+100˚+x
360-80-80-50-100=x
x=50˚
Method 2:
180˚=80˚+50˚+x
x=180-80-50
x=50˚
This corresponds to answer choice B.
Answer:
B.
Step-by-step explanation:
Are the following figures similar? (1 point)
Yes; the corresponding angles are congruent
No; the corresponding angles are not congruent
yes; the corresponding sides are proportional
no; the corresponding sides are not proportional
Answer:
yes the corresponding angles are congruent...
it can be wrong
Gabrielle went on a 72 mile trip to a soccer game. On the way back, due to road construction she had to drive 18 miles per hour slower. This made the trip take 9 hours longer. How fast did she drive to the soccer game?
Answer:
Gabrielle drove to the soccer game at the speed of 18 miles/hour
Step-by-step explanation:
Given: Distance covered = 72 miles
On the way back, she had to drive 18 miles per hour slower due to road construction which made the trip take 9 hours longer.
To find: speed
Solution:
Let speed be x miles/hour
Time taken = distance covered/time taken = [tex]\frac{72}{x}[/tex] hours
On the way back, she had to drive 18 miles per hour slower due to road construction
So, new speed = ( x - 18 ) miles/hour
Time taken as per new speed = [tex]\frac{72}{x-18}[/tex] hours
According to question,
[tex]\frac{72}{x-18}-\frac{72}{x}=9\\\frac{1}{x-18}-\frac{1}{x}=\frac{9}{72}\\\frac{x-x+18}{x(x-18)}=\frac{1}{8}\\x^2-18x-144=0\\x^2-24x+6x-144=0\\x(x-18)+6(x-18)=0\\(x-18)(x+6)=0\\x=18\,,\,-6[/tex]
Being a speed, x can not be negative. So, [tex]x=-6[/tex] is rejected
So,
Gabrielle drove to the soccer game at the speed of 18 miles/hour
anyone know this please ;)
Answer:
The planet to have the biggest mass is Jupiter
the radius of mercury is 2.44 × 10^5
the difference in mass between Jupiter and Saturn is 2.2 × 10⁴
What is the product?
(-35 +21)(45-1)
Answer:
-616
Step-by-step explanation:
First subtract 35 with 21 since 35 is a negative. then subtract 45 with 1
for the first parenthesis would be -14. the second parenthesis would be 44.
then multiply both of the answers together to get -616
Answer:-220
Step-by-step explanation:
Use the table of reciprocals to find the reciprocal of these numbers:
0.000 080 25
0.9596
Answer:
1000000/8025 = 40000/321 (simplified)
1000/9596
Step-by-step explanation:
Hi there,
There is an alternative way to do this....
First it is important to understand what a reciprocal is. The reciprocal of any number x is the number 1/x. The reciprocal of a number is also its multiplicative inverse, which means that the number times its reciprocal must equal 1. For a number such as 2, the reciprocal would be 1/2. For a fraction such as 2/5, the reciprocal would be 5/2.
Finding the reciprocal of a decimal can be done in a number of ways.
Change the decimal to a fraction first.
Ex. 0.25 is 25/100 and is equivalent to the fraction 1/4. Therefore Its reciprocal would be 4/1 or 4.
Keep the decimal and form the fraction 1/?? which can then be or converted to a decimal.
Ex. 0.75 The reciprocal is 1/0.75. Using a calculator, the decimal form can be found by performing the operation: 1 divided by 0.75. The decimal reciprocal in this case is a repeating decimal, 1.33333....
After finding a reciprocal of a number, perform a quick check by multiplying your original number and the reciprocal to determine that the product is 1:
(0.25)(4) = 1.00
(0.75)(1.33....) = 1 but it is easier to see for sure with repeating decimals if you use the fractions instead of the decimals.
(3/4)(4/3) = 12/12 = 1
Hope this helps, Mark as brainliest if liked it! thanks!
Please help! Correct answer only!
There is a raffle for a $380 prize. Out of 100 tickets, one ticket will win the prize, and the other tickets will win nothing. If you have a ticket, what is the expected payoff?
Answer:
$3.80
Step-by-step explanation:
380/100= an expected payoff of 3.8 dollars. Hope this helps!
if g(x)= -3 +1, Find x if g(x)= 16
Answer:
X= -5
Step-by-step explanation:
Replace the g(x) with 16.
16= -3x +1
Move -3x on other side.
3x+16=1
Subtract one from both sides.
3x= -15
Divide both sides by 3 to get x by itself.
x= -5
how many squares would have to be shaded so that 1/6 of the shape is shaded?
Answer:
3 squares
Step-by-step explanation:
The question given is not complete, the diagram of the shape is supposed to be attached. But I would provide you with a diagram and show you how to solve this type of problem.
The diagram of the shape is attached below. Firstly, you have to count the number of squares in the shape. As it can been seen from the diagram, there are a total 18 squares (i.e 6 squares on each row × 3 squares on each column).
Secondly you have to find 1/6 of the total number of the squares in the shape. 1/6 of the total number of the square in the shape = 1/6 × 18 = 3 squares
Therefore 3 squares would have to be shaded so that 1/6 of the shape is shaded
A teacher has a 2-gallon (32-cup) container of juice. She gives each student a 1/2 cup of juice. Which equation represents the amount of juice that remains, y, after x students are served? a. y = 32x - 1/2 b. y = 1/2x - 32 c. y = -1/2 x + 32 d. y = -32 x + 1/2 WILL GIVE BRAINLIEST FOR GOOD EXPLANATION
Answer:
total cup = 32
1 student = 1/2 cup
find remaining cup = y
*we don't know how many students are there, so we just let it be x .
remaining cup = total cup - cup drank by students
y = 32 - 1/2x
y = -1/2x + 32 ( option c )
why 1/2x ? because we don't know how many students drank the juice, so we just let it be x .
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-2 is the slope
Step-by-step explanation:
Slope (gradient) = rise/run or (y1 - y2/x1 - x2)
We will take the points so that we have a whole number:
Therefore the two points are:
(10,0) and (30, -40)
Now the gradient;
(y1 - y2/x1 - x2)
0 - -(40) / 10 - 30
40/-20
-2/1
-2
Mark my answers as brainliest if helped thanks!
PICTURE ATTACHMENT IS BELOW
Answer:
10% = 1/10
20% = 1/5
100% = 3/3
75% = 3/4
Step-by-step explanation:
Answer:
Awnser is down below
Step-by-step explanation:
75= 3/4
20= 1/5
10 = 1/10
100= 3/3
Hope this helps :)
Please answer no rush first CORRECT answer gets Brainiest.
The answer is 2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment...
L+S = 17 3L + 2S=46
Please show your work
Answer:
S= 5, L= 12
Step-by-step explanation:
To find the value of L and S, we need to first label the 2 equations.
L +S= 17 -----(1)
3L +2S= 46 -----(2)
From (1):
L= 17 -S -----(3) (-S on both sides)
Subst. (3) into (2):
3(17-S) +2S= 46
3(17) -3S +2S= 46 (expand)
51 -S= 46
-S= 46 -51 (-51 on both sides)
-S= -5
S= 5 (divide by -1 throughout)
Subst. S=5 into (3):
L= 17 -5
L= 12
Direct variation: if y = 4, when x = -2, find x when y = 6
Answer:
-3
Step-by-step explanation:
Because when y is 4, x is 4/-2 = -2
So when y is 6,
x= 6/-2
= -3
15x - 5y = 30 in slope intercept form
Answer:
y = 3x - 6
Step-by-step explanation:
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
15x - 5y = 30
Subtract 15x from each side
15x-15x - 5y =-15x+ 30
-5y = -15x+30
Divide each side by -5
-5y/-5 = -15x/-5 +30/-5
y = 3x - 6
Answer:
[tex]y = 3x - 6[/tex]
Step-by-step explanation:
[tex]15x - 5y = 30 \\ - 5y = 30 - 15x \\ \frac{ - 5y}{ - 5} = \frac{30 - 15x}{ - 5} \\ y = - 6 + 3x \\ y = 3x - 6[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Can somebody help meeee witthhhh thisss plssss
Answer:
7.) (m+4)(m-16)
8.) Area= 3x^3-5x^2+7x+3
Step-by-step explanation:
7.) m^2-12m-64
=(m^2+4m)+(-16m-64)
=m(m+4)-16(m+4)
=(m+4)(m-16)
8.) Area = L(W)
x^2-2x+3(3x+1)
=x^2(3x)+x^2(1)+(-2x)(3x)+(-2x)(1)+3(3x)+3(1)
=3x^3+x^2-6x^2-2x+9x+3
=3x^3-5x^2-2x+9x+3
=3x^3-5x^2+7x+3
The equation x2 - 7x=0 when solved is:
Answer:
x =0 x=7
Step-by-step explanation:
x^2 - 7x=0
Factor out an x
x(x-7) =0
Using the zero product property
x =0 x-7 =0
x =0 x=7
I'm just so lost...
Help!
Answer:
Step-by-step explanation:
HELP
PLEASE.
Simplify the expression.
x^2+2x-24/x^2-x-42
Answer:
[tex] \frac{x - 4}{x - 7} [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 2x - 24 }{ {x}^{2} - x - 42 } \\ \frac{(x + 6) (x - 4)}{(x - 7)(x + 6)} \:the \: term \: will \: be \: simplified (x + 6) \\ and \: we \: will \: be \: left \: with \: \frac{x - 4}{x - 7} [/tex]
Answer:
Step-by-step explanation:
x² + 2x - 24 = x² + 6x - 4x - 4 * 6
= x(x + 6) - 4(x + 6)
= (x + 6) (x - 4)
x² - x - 42 = x² -7x + 6x - 6 * 7
= x(x - 7) + 6(x - 7)
= (x - 7) (x + 6)
[tex]\frac{x^{2}+2x-24}{x^{2}-x-42}=\frac{(x + 6)*(x-4)}{(x+6)(x-7)}\\\\\\=\frac{x-4}{x-7}[/tex]
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
y = 2x - 2
y = 2x + 2
y = x + 2
y = x-2
Answer:
A line in form of y = ax + b passes (0, 2)
=> 2 = 0x + b => b = 2
This line also passes (4, 6)
=> 6 = 4x + 2 => x = 1
=> Equation of this line: y = x + 2
=> Option C is correct
Hope this helps!
:)
Answer:
A line in form of y = ax + b passes (0, 2)
=> 2 = 0x + b => b = 2
This line also passes (4, 6)
=> 6 = 4x + 2 => x = 1
=> Equation of this line: y = x + 2
=> Option C is correct
Hope this helps!
:)
Step-by-step explanation:
Tomas works as an underwater photographer. He starts at a depth of 20 feet, ascends 9 feet, descends 12 feet, and then descends 15 feet more. What is the diver's final depth?
Answer:
38 feet
Step-by-step explanation:
what is the meaning of the word 'coplanar'
Answer:
It means in the same plane
Please help ! I don’t understand :(
Answer:
A. The number quadrupled each week
Step-by-step explanation:
f(x)= 3(4)^x
As per the function, each week number increases 4 times
So the answer choice is A
Which of these triangles appears not to be congruent to any others shown
here? Check all that apply.
A
B
C
D
E
F A. Triangle A
B. Triangle B
C. Triangle C
D. Triangle D
E Triangle E
F. Triangle F
Answer:
Options (B) and (D)
Step-by-step explanation:
If two triangles have the same size and shape they are said to be congruent triangles.
Triangles given in the attachment,
Triangles A and E appear to be congruent.
And triangles C and F appear to be congruent.
[Since corresponding sides of these triangles don't appear to be the same in measure]
Remaining triangles B and D do not appear to be congruent.
Therefore, Options (B) and (D) will be the answer.
Evaluate [(40 + 5) − 3^2] ÷ 9 ⋅ 2. (1 point)
Answer:
[(40 + 5) − 32] ÷ 9 ⋅ 2
[(45) − 32] ÷ 9 ⋅ 2
[(13)] ÷ 9 ⋅ 2
[(13)] ÷ 9 ⋅ 2
_
1.4... ⋅ 2
_
2.8... ←Answer
Step-by-step explanation:
What is the probability that you’re on mars right now?
The probability of you being on Mars right now is very slim, because no one that we know of currently lives on Mars.
Which of the following is the correct factored form of the given equation?
4x2 - 11x + 6 = 0
(2x + 3)(2x + 2) = 0
(2x - 3)(2x - 2) = 0
(4x - 3)(x - 2) = 0
Answer:
[tex](4x - 3)(x - 2) = 0[/tex]
Last answer is correct
Step-by-step explanation:
[tex]4 {x}^{2} - 11x + 6 = 0 \\ 4 {x}^{2} - 8x - 3x + 6 = 0 \\ 4x(x - 2) - 3(x - 2) = 0 \\ (4x - 3)(x - 2) = 0[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
(x+9)(x+3)
x*x = x^2
x*3 = 3x
9*x = 9x
9*3 = 27
Answer = x^2 + 12x + 27
Hope this helps
Answer:
x^2+12x+27
Step-by-step explanation:
have a nice day:)
Raj’s farmhouse is 1245km away from hiswarehouse. Daily he drivesa certain distance and then his friend Rohantakes aturn to drive his carfor 412km distance to reach thewarehouse.(a)What distance does Raj drivedaily?
Answer:
Step-by-step explanation:
Subtract the distance driven by Rohan from the total distance
Distance driven by Raj = 1245 - 412
= 833 km