Expanding each square on the left side, you have
(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)
(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)
so that adding them together eliminates the identical middle terms and reduces to the sum to
x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)
Collecting terms to factorize gives us
(y² + x²) sin²(A) + (x² + y²) cos²(A)
(x² + y²) (sin²(A) + cos²(A))
and sin²(A) + cos²(A) = 1 for any A, so we end up with
x² + y²
as required.
A system of two linear equations has infinitely many solutions. The first equation is y=5x+3. What is the value of p in the second equation if the second equation is represented by 10x–2y=p?
p=
Answer:
Step-by-step explanation:
According to a Gallup poll, 60% of American adults prefer saving over spending. You randomly select 4 adults and ask if they prefer spending over saving. Construct a probability distribution for the random variable x. Then graph the distribution. (Histogram)
Expected Value ______________________________
Standard Deviation _____________________________
B –
I-
N-
S-
Interpretation
Using the binomial distribution, it is found that:
The expected value is of 2.4.The standard deviation is of 0.76.The distribution is given by the histogram.For each person, there are only two possible outcomes, either they prefer saving, or they prefer spending. The preferences of each person are independent of any other person, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
In this problem:
60% prefer saving over spending, hence [tex]p = 0.6[/tex]4 adults are selected, hence [tex]n = 4[/tex].Then:
[tex]E(X) = np = 4(0.6) = 2.4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{2.4(0.6)(0.4)} = 0.76[/tex]
The histogram is sketched at the end of the answer.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
8. Lara invested a total of $1000 in two simple interest accounts. Account A pays
5% annual interest while Account B, pays 6% annual interest. The total interest
she earned after one year was $58. How much did she invest in each account?
Answer:
$200 at 5%$800 at 6%Step-by-step explanation:
Let x represent the amount invested at the higher rate. Then 1000-x is the amount invested at the lower rate. The total earnings are ...
0.05(1000-x) +0.06x = 58
50 +0.01x = 58 . . . . . . . . . . . simplify
0.01x = 8 . . . . . . . . . . . . . . . subtract 50
x = 800 . . . . . . . . . . . . . . . multiply by 100; amount at 6%
(1000-x) = 200 . . . . . . . find the amount invested at 5%
Lara invested $200 at 5% and $800 at 6%.
Which numbers are all divisible by 5?
-)))
A)
224, 777, 215, 466, 991
B)
335, 105, 430, 375, 265
©
235, 111, 730, 374, 232
D
332, 350, 265, 425, 510
Answer: B) 335, 105, 430, 375, 265
Step-by-step explanation:
Since each number ends in either a 5 or a 0, they are all divisible by 5.
Therefore, B is the correct answer.
Answer:
335, 105, 430, 375, 265
335, 105, 430, 375, 265
Determine whether each sequence is geometric. Explain.
256, 128, 64, 32, ...
Answer:
Its geometric because each number is being divided by 2.
What is this word phrase as a math expression? 4 times the sum of a number and 11
1 point
4(x + 11)
4x + 11
4 + (x + 11)
4x + 11 x
Answer:
i think that the correct answer is 4x+11
What is correct A, B or C
Answer:
A is the correct solution
Step-by-step explanation:
3x³ + 4x² + 0x - 1 / x - 2
3 10 20
-2 | 3 4 0 -1
- (3 -6)
10 0
- (10 -20)
20 -1
- (20 -40)
39
3x² + 10x + 20 + 39/(x - 2)
(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)
Answer:
(x - 10)(x + 2)
Step-by-step explanation:
We are looking for two things that multiply together to give us
x^2 - 10x - 20
These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)
We know the first term in the binomial has to be x, because x times x is x^2.
And then we are looking for two numbers that multiply to -20 but also add up to -8.
-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)
Answer:
Option C
Step-by-step explanation:
x² - 8x - 20
x² - (10x - 2x) - 20
x² - 10x + 2x - 20
x(x - 10) + 2(x - 10)
(x - 10)(x + 2)
Hence
Option C is correct
Write the expression:
the sum of a number and it's opposite
Answer:
0
Step-by-step explanation:
-5 5
<-+-+-+-+-+-+l-+-+-+-+-+->
l 0 l
<-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+->
-8 -7 -6 -5 -4 3 -2 -1 0 1 2 3 4 5 6 7 8
graph l. (l points down). Thanks!
Answer:
the sum of a number and it's opposite= x - (x)
Step-by-step explanation:
The opposite number of 2 would be -2. The opposite number of 4 would be -4 and vice versa.
Because the oppposite number is just a number that is the opposite operation of something, finding the sum of a number and it's opposite will always make the sum 0.
Sammy and her family are on a trip. So far, they have traveled 225 miles and are 25% of the way to their destination. How many total miles will they travel?
what is (3×100)+(1×110)+(4×11,000) in decimal form
The first term of an AP is p & it's common difference is q. What it's 10th term?
The first term of an AP = p
The common difference = q
We know that
nth term of an AP = a+(n-1)d
10th term = a+(10-1)d = a+9d
t10 = p+9q
Tenth term of the AP is p+9q
also read similar questions: a) The sixth term of an AP is twice the 3rd term and the first term is 3. Find the common difference and the 10th term....
https://brainly.com/question/19517085?referrer
If the 17th term of an AP exceeds the 10th term by 7, then the common difference is_____
https://brainly.com/question/16821782?referrer
How much power does it take to lift a 40N object. 8 meters high in 3 seconds. Show work 8)
Answer:
Step-by-step explanation:
power = work / time
work = force x distance
force = newtons
w = fd
w = 40N(8m)
w = 320J
p = w/t
p = 320J/3s
__
p = 106.66
(sixes repeat)
What is the value of t in the equation 3(t − 4) = 2t + 1?
Answer: 13
Step-by-step explanation:
Distribute t.
Multiply 3 by each value in parentheses to get
3t - 12 = 2t + 1
Add 12 to both sides
3t = 2t + 13
Subtract 2t from both sides
t = 13
Answer:
t = 13
Step-by-step explanation:
[tex]3(t-4)=2t+1\\\\3t-12=2t+1\\\\t-12=1\\\\t=13[/tex]
99 points
solve the system of equations by graphing
k12 test interim checkpoint 4
Answer:
Step-by-step explanation:
f ( x 2 − 3 x + 2 ) = − x 2 + 3 x + 3
So; 1. Find the sum of 64.2 + 3.4 =_____ Find the difference 514 - 1.72=_____
FOR MY BROTHER TWIN'S
" Please answer this today☺️ "
The total length of 3 pipes is 24 inches. The middle-sized pipe is 6 inches longer than the smallest. The largest is twice as long as the smallest. How long is the middle-sized pipe?
Find the area of the circle whose diameter is 68 cm
Answer:
1156πcm²
Step-by-step explanation:
Diameter = 68cm
Therefore radius = 68 ÷ 2 = 34cm
Area of a circle = πr²
= π × 34cm × 34cm
= π × 1156cm
= 1156πcm²
NOTE: In case you're given the value of pi, substitute it into the formula to get your answer
Please someone help me i dont want fail
Answer:
D
Step-by-step explanation:
(point D)
Answer:
Point D
Step-by-step explanation:
5 units right on the x axis, 3 units down on the y-axis.
What is f ( x ) = 2x + 2
A .4
B . 2
C . -2
Pick only 1 answer !!! Thank you
Answer:
X = -1 (unsure as to how this is not an answer but I have checked my work)
Step-by-step explanation:
( f(x) = y )
1. y = 2x + 2
-2 -2
2. -2 = 2x
/2 /2
3. -1 = x
Question is in picture
IS MNL=QNL? Why or why not?
Answer:
B) Yes, they are both right angles.
Step-by-step explanation:
Can somebody help me as soon as possible I’ll give brainliest
Two numbers multiply to be 0 and add to be -81?
Answer:
0 and -81
Step-by-step explanation:
So, we know anything times zero is zero, and anything added or subtracted to zero would give you that number, meaning one of these numbers is zero.
Zero plus -81 will give you the same number, -81, and zero times -81 will give you zero since anything added to or subtracted to zero is that number.
What is the constant of proportionality in the following equation?
y = 5x + 0
Answer:
5
Step-by-step explanation:
y is always 5 times greater than x
PLS HELP i will GIVE BRAINLESS)!!!! Some friends play history trivia. Players gain 1 point for a correct answer. Players lose 1 point for an incorrect answer. The player with the greatest score wins. The players’ scores are shown in the table. a. List the players from worst score to best score. Show your work.SOLUTION b. Check your answer to problem 3a. Show your work. 3 Player Score Brett27 Ellema 21 Felipe 13 Jennifer 0 Kamal 12 Riley25
Answer:
0,12,13,21,25
Step-by-step explanation:
jennifer-0, kamal-12, felipe -13, ellma-21, riley 25
basically least to greatest order
Please HELP Write the graph's domain and range in interval notation.
Step-by-step explanation:
Domain: x€ [ -7;7]
Range : y€ [-6;4]
For the domain, the graph's x-values are from -7 to 7
For the range, the graph's y-values are from -6 to 4
Pre college need help with this question
Answer:
the domain is {7,-4,1,4,}
the range is {1,-5,2,-7}
Step-by-step explanation:
In one month Karissa earned $600 at her part-time job, and $50 was withheld for federal income tax. Suppose she earns $900 next month. How much will be withheld for federal income tax?
Don't get me wrong, I am not exactly sure but I believe it is supposed to be 75$.
Pls help I’ll brainlest help I’m failing do it on a paper and put it in the answer box
Find the equation of the line passing through point (-1, -2) and having
slope 1/5. Show work.
Answer:
Y=1/5x+ -2
Step-by-step explanation:
Hope this helps
