Answer:
From sin²θ + cos²θ = 1, we have;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ
Step-by-step explanation:
The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ
We have;
(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;
(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1
Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ = 1
From which we can get;
(sin²θ + cos²θ)·(sin²θ + cos²θ) = 1
Given that sin²θ + cos²θ = 1
Therefore;
1 × 1 = 1
To get to the initial equation in the question, we have;
sin²θ + cos²θ = 1
(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1
(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1
∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ = 1 - 2·sin²θ·cos²θ
Therefore;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.
Let $S = 2010 + 2011 + \cdots + 4018$. Compute the residue of $S$, modulo 2009.
Notice that
2010 ≡ 1 mod 2009
2011 ≡ 2 mod 2009
2012 ≡ 3 mod 2009
...
4017 ≡ 2008 mod 2009
4018 ≡ 0 mod 2009
So really, S is just the sum of the first 2008 positive integers:
[tex]S=\displaystyle\sum_{n=1}^{2008}n=\frac{2008\cdot2009}2[/tex]
where we invoke the formula
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
and so S ≡ 0 mod 2009.
area of parallelogramis 30 cm^2. if the length of two adjacent sides are 6 cm and 10 cm respectively. find its diagonal
Answer:
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos 30)=5.663 ( rounded to the nearest hundredth)
Step-by-step explanation:
Area=height * base
30=h*6
h=30/6=5 cm
height=asinФ
sinФ=5/10=1/2 (Ф=30)
alternate angle=180
180-30=150 degrees
diagonal²=a^2+b^2-2abcos150
d²=10²+6²-2(10)(6)(-√3/2)
d=√136+60(√3)
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos30)=5.663
Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7. m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °
Answer:
m∠5 = 77
Step-by-step explanation:
∠3 & ∠ 5 are the co interior angles in the same side of the transversal
∠3 + ∠5 = 180 {sum of co interior angles is 180}
3x + 4 + 2x +11 = 180 {Add like terms}
5x + 15 = 180
Subtract 15 from both sides
5x + 15 - 15 = 180 -15
5x = 165
Divide both side by 5
5x/5 = 165/5
x = 33°
m∠5 = 2x + 11 = 2*33 + 11
= 66 + 11
= 77
Answer:
m∠3 is (3x + 4)° and m∠5 is (2x + 11)°.
Angles 3 and 5 are "same side interior angles"
The equation "(3x + 4) + (2x + 11) = 180" can be used to solve for x.
m∠5 = "77°"
Step-by-step explanation:
what happens to 3y / 2y as y increases?
Answer: Nothing
Step-by-step explanation:
If you multiply the numerator and denominator of a fraction by any number(apart from 0), it doesn't change.
Hope it helps <3
Answer:
it is the same
Step-by-step explanation:
it is decreasing not increasing
Sophia‘s favorite homemade cookie recipe requires one cup of chocolate chips for 10 servings if the number of cups required for multiple batches is proportional to the number of servings being made how many cups of chocolate chips will she need to make enough cookies for 30 servings
Answer:
3 cups
Step-by-step explanation:
We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches
[tex]\frac{c}{b}[/tex]
[tex]\frac{1}{10} = \frac{c}{30}[/tex]
We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)
[tex]30 \cdot 1 = 30\\30 \div 10 = 3[/tex]
Therefore, she needs 3 cups of chocolate chips to make 30 servings.
Answer:
3 cups
Step-by-step explanation:
We can use ratios to solve
1 cup x cups
---------------- = ----------------
10 servings 30 servings
Using cross products
1*30 = 10x
Divide by 10
30/10 = x
3 =x
3 cups
!!!!!!WILL GIVE BRAINLEIST !!!!!!
Answer:
[tex]\boxed{Median = 152}[/tex]
Step-by-step explanation:
Observation = 568 , 254 , 152 , 101 , 100
In ascending order:
=> 100 , 101 , 152 , 254 , 568
Median is the middlemost no. So here:
Median = 152
Answer:
152
Step-by-step explanation:
If you set the data in an ascending order, you will find 152 to be the middle value, thus being the median
The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? Consider as significant any result that differs from the mean by at least 2 standard deviations. That is, significant values are either less than or equal to muminus2sigma or greater than or equal to muplus2sigma.
Answer:
Yes, it would be statistically significant
Step-by-step explanation:
The information given are;
The percentage of jawbreakers it produces that weigh more than 0.4 ounces = 60%
Number of jawbreakers in the sample, n = 800
The mean proportion of jawbreakers that weigh more than 0.4 = 60% = 0.6 = [tex]\mu _ {\hat p}[/tex] =p
The formula for the standard deviation of a proportion is [tex]\sigma _{\hat p} =\sqrt{\dfrac{p(1-p)}{n} }[/tex]
Solving for the standard deviation gives;
[tex]\sigma _{\hat p} =\sqrt{\dfrac{0.6 \cdot (1-0.6)}{800} } = 0.0173[/tex]
Given that the mean proportion is 0.6, the expected value of jawbreakers that weigh more than 0.4 in the sample of 800 = 800*0.6 = 480
For statistical significance the difference from the mean = 2×[tex]\sigma _{\hat p}[/tex] = 2*0.0173 = 0.0346 the equivalent number of Jaw breakers = 800*0.0346 = 27.7
The z-score of 494 jawbreakers is given as follows;
[tex]Z=\dfrac{x-\mu _{\hat p} }{\sigma _{\hat p} }[/tex]
[tex]Z=\dfrac{494-480 }{0.0173 } = 230.94[/tex]
Therefore, the z-score more than 2 ×[tex]\sigma _{\hat p}[/tex] which is significant.
Answer:
Step-by-step explanation:
min 452, max 507, so 494 is not unusual.
Help asap please and please explain so I could try the rest on my own
Answer:
7
Step-by-step explanation:
It has a 45 45 90 ratio, so if the hypotenuse is 7 root 2, then the two sides have to be 7.
What is the solution to the following equation?
5(2x - 6) + 20 = 10
09
05
03
O2
Answer:
x = 2
Step-by-step explanation:
5(2x- 6) + 20 = 10
10x - 30 = -10
10x = 20
x = 2
Answer:
O2
Step-by-step explanation:
5(2x-6)+20=10
Use distirbutive property:
10x-30 because, 5×2 = 10, and 5×6=30
Now we have
10x-30+20=10
Now combine the like terms
10x-10=10
Send the 10 to the other side(it turns into positive 10 because it was negative 10 on the other side)
10x = 10+10
10x=20
Divide 10 by both sides
x/10 = 20/10
x=2
Hope that helped
j is 7 times as large as 6. Solve for j. j=
Answer:
42
Step-by-step explanation:
7 times as large as 6 = 7 * 6
7 * 6 = 42
Hope this helps
Answer:
42
Step-by-step explanation:
A car travels 32 km due north and
then 46 km in a direction 40° west of
north. Find the magnitude of the
car's resultant vector.
Answer:
73.2km
Step-by-step explanation:
first you have to decompose 46 km into y and x components.
x=sin40°*46km
x=0.64*46km
x=29.44km
y=cos40°*46km
y=0.76*46km
y=34.96
now you add the y components together
32+34.96=66.98
finally use Pythagorean thereom to find the resultant vector.
a*a+ b*b=c*c
66.98*66.98+29.44*29.44=c*c
c*c= 4486.3+866.7
c=√5353
c=73.2 km this is the approximate value
Solve this system of linear equations. Separate
the x- and y-values with a comma.
15x + 4y = -80
5x + 5y = 10
Answer:
(-8,10)
Step-by-step explanation:
hope i helped!
u can substitute if u want to recheck
can i get brainliest pls?
-Zylynn
Please answer it now
Answer:
s= 15 (nearest integer), 14.8 (to nearest 10ths)
Step-by-step explanation:
here you need to apply the cosine rule,
[tex] {s}^{2} = {u}^{2} + {t}^{2} - 2ut \cos(s) [/tex]
substituting the values,
u= 13, t=5 and angle S as 60 and solving will give you the answer 14.76 (2 dp)
Darnell is making improvements to his 3: 13 feet by 12 feet bedroom. Which deal would he best for him?
Paying $7.25 per sq feet
Paying $6.75 per sq feet plus a $100 installation fee
Answer:
paying $7.25 per sq feet
Step-by-step explanation:
So we can start off by solving the area:
12*13=156
so the total area is 156 feet sq
the first deal:
156/7.25= about $21.52
the second deal:
156/6.75= about $23.11, however with the installation fee, it will cost even more.
NEED HELP ON THIS A S A P
Answer:
150
Step-by-step explanation:
The radius of a cylinder is doubled and its height is halved. Find the ratios of their surface areas.
Answer: 1:1
Step-by-step explanation:
Let r be the radius and h be the height of a cylinder.
Formula: Curved surface area of cylinder = [tex]2\pi rh[/tex]
Now, if radius of a cylinder is doubled and its height is halved, then new radius will be R= 2r and new height will be [tex]H=\dfrac{1}{2}[/tex]
Now, new surface area = [tex]2\pi RH= 2\pi(2r)\dfrac{h}{2}= 2\pi rh[/tex]
Ratio of curved surface areas : [tex]\dfrac{\text{Surface area}}{\text{New surface area}}=\dfrac{2\pi rh}{2\pi rh}=\dfrac{1}{1}[/tex]
Hence, the ratios of their surface areas = 1:1 .
Please answer it now in two minutes
Answer:
m∠C = 90°
Step-by-step explanation:
Triangle BDC is a right triangle with the measure of angle D = 90°
By applying Cosine rule in the given triangle,
Since, Cosine of any angle in a right triangle is a ratio of Its adjacent side and Hypotenuse (Opposite side of the right angle)
CosC = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
CosC = [tex]\frac{\text{DC}}{\text{BC}}[/tex]
CosC = [tex]\frac{7}{8}[/tex]
[tex]C=\text{Cos}^{-1}(\frac{7}{8})[/tex]
C = 28.955
C = 29°
Therefore, m∠C = 29° will be the answer.
Please answer this question now
Answer:
x=33
Step-by-step explanation:
x-9=24 the tangent of the circle are equal in length
x=33
i rlly need help :( this is hard
Answer:
A
Step-by-step explanation:
The domain does not exist when the denominater of an equation is zero. So in this case if x was -2 and we added 2 the denominator would be zero, and that value does not exist in the domain. Hope this helps!
continuation of previous question :)
Answer:
Below
Step-by-step explanation:
First let's determine the slope if thus function
Let m be the slope of this function
m = [0-(-4)]/ 2-0 = 4/2 =2
So our equation is:
y = 3x +b
b is the y-intercept wich is given by the image of 0
Here it's -4
So the equation is:
y = 2x-4 wich is also y = x-2 after simplifying
●●●●●●●●●●●●●●●●●●●●●●●●
A line that is parallel to this one will have the same slope.
Examples:
● y= 2x+3
● y = 2x-7
■■■■■■■■■■■■■■■■■■■■■■■■■■
A line that is perpendicular to this one and has a slope m' satisfy this condition:
m*m'= -1
m'= -1/m
m' = -1/2
So this line should have a slope that is equal to -1/2
Answers from the choices:
y = -1/2 x +1/2
y+1= -1/2 (x-3)
which of the following has the least steep graph?
A.) y = 1/2x + 3
B.) y = x + 24
C.) y = 3x - 16
D.) y = 2x + 7/15
Answer:
A) y=1/2x+3
Step-by-step explanation:
Please help I don't understand this at all
Answer:
Since ΔABC is equilateral, ∠ACB = 60°. Since ΔCED is isosceles (we know this because CE = ED from the graph), ∠ECD = ∠EDC from Base Angles Theorem, and since the sum of angles in a triangle is 180°, they measure (180 - 32) / 2 = 74° each. Since BCD is a straight line, it measures 180° so we can write:
60 + x + 74 = 180
134 + x = 180
x = 46°
Answer:
46 degrees
Step-by-step explanation:
Since triangle ABC is equilateral that means each angle in that triangle is 60 degrees.
We also know that for triangle ECD angle C and angle D have to be 74 degrees, because a triangle has 180 degrees in total and the only unique angle is at the top which is 32. So it is 180-32=148, than 148/2=74.
We than know that a half circle is 180 degrees aswell, so we do 180-60=120
120-74=46
Find x ÷ y, if x = 3 5/6 and y = 3 3/4 .Express your answer in simplest form.
Answer:
23/30
Step-by-step explanation:
x/y
(3 5/6)/(3 3/4)
((3*6)+5/6)/((3*4)+ 3/4)
(18+5/6)/(12+3/4)
(23/6)/(15/4)
(23/6)*(4/15)
(23*3)/(6*15)
(69/90)
23/30
Answer:
1 1/45
Step-by-step explanation:
The length of a rectangular field is twice its breadth. If the area of the rectangular field is 98 sq. M., then what is the perimeter of the field? Also find the approximate length of the diagonal of the field.
Answer:
Perimeter = 42mlength of the diagonal ≈ 16mStep-by-step explanation:
The Area of the rectangular field is expressed as A = LB and its perimeter
P = 2(L+B)
L is the length of the rectangular field
B is the Breadth of the rectangular field
If the length of a rectangular field is twice its breadth i.e L = 2B and the area is 98m² then;
98 = LB
98 = 2B*B
98 = 2B²
B² = 98/2
B² = 49
B = √49
B = 7m
if B = 7m
L = 98/B
L = 98/7 = 14m
The perimeter of the field P = 2(L+B)
P = 2(14+7)
P = 2*21
P = 42m
The perimeter of the field is 42m.
The length of the diagonal of the field can be expressed using Pythagoras theorem.
d = √L²+B²
d = √14²+7²
d = √196+49
d = √245
d = 15.7m ≈ 16m
Hence, the approximate length of the diagonal of the field is 16m
Given that a quadrilateral PQRS is a parallelogram, PQ and RS are opposite sides, PQ = 6x + 10, RS = + 12, and QR = 31 which of the following statements are correct?. More than one answer may be correct.
- Opposite sides are congruent
- The diagonals are perpendicular
- The parallelogram PQRS is a square
- Perimeter = 106
- PS = 31
- x = 4
- None of these answers are correct
Answer:
option 1 & option 5
Step-by-step explanation:
In a parallelogram,
1) opposite sides are congruent
2) So, PS = QR = 31
Answer:
Opposite sides are congruent
PS = 31
Step-by-step explanation:
based on what I learned when I was grade 9 and this topic is one fof my favorite so Yeh
hope its correct (～￣▽￣)～
Which description best describes the solution to the following system of equations? y = −2x + 3 y = −x + 6
Answer:
Step-by-step explanation:
-2x + 3 = -x + 6
-x + 3 = 6
-x = 3
x = -3
y = 3 + 6
y = 9
(-3, 9)
Identify the discrete data.
A. The number of friends you invited to your last party
B. Your height
C. The time it takes you to complete a crossword puzzle
D. Your weight
Answer:
The answer is option A.
The number of friends you invited to your last party
Hope this helps you
Marx and Engels believed that a. people in a good environment would behave unselfishly. b. people should create utopian communities. c. the capitalist system should be destroyed. d. workers should improve conditions by taking political office. Please select the best answer from the choices provided A B C D
Q;- Marx and Engels believed that a. people in a good environment would behave unselfishly. b. people should create utopian communities. c. the capitalist system should be destroyed. d. workers should improve conditions by taking political office. Please select the best answer from the choices provided A B C D
A;- Marx and Engels believed that the capitalist system should be destroyed.
Please help I will give out brainliest
Answer:
All the points change, there are no invariant points
Step-by-step explanation:
The given parameters are
To translate the square OABC by the vector [tex]\dbinom{1}{3}[/tex], we have;
The coordinates of the point O is (0, 0)
The coordinates of the point A is (3, 0)
The coordinates of the point B is (3, 3)
The coordinates of the point C is (0. 3)
The translation is by moving 1 step right and three steps up to give;
O' is (0+1, 0+3) which is (1, 3)
A' is (3+1, 0+3) which is (4, 3)
B' is (3+1, 3+3) which gives (4, 6)
C' is (0+1, 3+3) which gives (1, 6)
As all the points change, there are no invariant points and the number of invariant points is zero.
To get to the park from her house, Rachel walked 4 kilometers due north and then 3 kilometers due west. On the way back, she cut across a field, taking the shortest
possible route home,
How far did Rachel walk on the round-trip?
Answer:
12 km
Step-by-step explanation:
Using the Pythagorean Theorem, you know that 3^2 + 4^2 = x^2, so 9 + 16 = x^2, which means that x = the square root of 25, which is 5. Then you add all three lengths of the triangle together to get the round trip. 3 + 4 + 5= 12.