Expand the binomials, then simplify, then invoke the Pythagorean identity:
(p sin(B) - r cos(B))² + (r sin(B) + p cos(B))²
= (p² sin²(B) - 2pr sin(B) cos(B) + r ² cos²(B)) + (r ² sin²(B) + 2pr sin(B) cos(B) + p² cos²(B))
= p² (sin²(B) + cos²(B)) + r ² (cos²(B) + sin²(B))
= p² + r ²
Solve the system of equations using elimination 2x+y=3 and 3x-y=12
You found a great deal on CDs for gifts! You were
able to buy 12 CDs for $15! What was the cost per
CD?
Answer:
80 cents per cd
Step-by-step explanation:
when finding that answer you divide 12/15 which equals .8
What is the inverse of the function fx) = 2x + 1?
Answer:
X=2y+1
X-1/2=y
Anyone please help me to do 4 ) f
One side of a triangle is 2 times the second side. The third side is 15 feet longer than the second side. The perimeter of a
triangle is 47 feet. Find the length of each side.
Dresdobou
Answer:
16, 8, 23
Step-by-step explanation:
2x+x+x+15=47
4x+15=47
4x=32
x=8
2x=16
x+15=23
PLEASE HELPPO I BEFGG
Answer:
-1.75, -1 1/2, -3/4, 1/4, 0.75
Step-by-step explanation:
I hope this helped and if it did I would appreciate it if you marked me Brainliest. thank you and have a nice day!
choose a number between 67 and 113 as a multiple of 3, 5 and 10
Answer: 90
Step-by-step explanation:
90 / 3 = 30
90 / 5 = 14
90 / 10 = 9
Therefore, 90 is between 67 and 113. It is also a multiple of 3, 5, and 10.
I have a coupon to save 30% off of my bill. If my bill is originally $45.00
how much will I pay?*
Answer:
$31.50
Step-by-step explanation:
the decrease will be $13.50
A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?
Step-by-step explanation:
f(2)=18-2=16
f(3)=16-2=14
f(4)=14-2=12
Then,
f(5)=12-2=10
the answer is 10
F(x)=4x 2 +2x+6f, left parenthesis, x, right parenthesis, equals, 4, x, squared, plus, 2, x, plus, 6 What is the value of the discriminant of fff? How many distinct real number zeros does fff have?
Answer:
Discriminant = -92
the equation has no distinct real numbers
Step-by-step explanation:
Given the function f(x) = 4x^2 + 2x + 6 where;
a = 4, b = 2 and c= 6
The discriminant is expessed as D = b^2 - 4ac
Substitute;
D = 2^2 - 4(4)(6)
D = 4 - 96
D = -92
Hence the discriminant is -92.
Since the discriminant is less than zero i.e D< 0, this shows that the zeros of the equation are not real but complex numbers. Hence, the equation has no distinct real numbers
Answer:
-92 is the discriminant
0 real value 0's
Step-by-step explanation:
A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.
Given :
A rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
To Find :
The dimensions of the page such that the least amount of paper is used.
Solution :
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy ....1)
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, area of paper is :
A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( 36/y + 2 )( y + 2 )
Now, differentiating above equation and equating with 0 :
[tex]3 - \dfrac{108}{y^2}=0\\\\y = \pm 6[/tex]
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
The length are breadth is x = 6 and y = 6 inch respectively.
Given;
Each rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
We have to find ;
The dimensions of the page such that the least amount of paper is used.
Therefore,
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, Area of paper is : A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( [tex]\frac{36}{y}[/tex] + 2 )( y + 2 )
Now, Differentiating above equation and equating with 0 :
[tex]3 -\frac{108}{y^{2} } = 0[/tex]
[tex]\frac{3y^{2} - 108 }{y^{2} } = 0[/tex]
[tex]3y^{2} - 108 = 0 \\3y^{2} = 108\\y^{2} = \frac{108}{3} \\y^{2} = 36\\y = 6[/tex]
then; xy = 36
6x = 36
x =[tex]\frac{36}{6}[/tex]
x = 6inches
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
For more information about the Area of dimension click the link given below.
https://brainly.in/question/12894735
Lydia gets kicked out of class twice in 20 minutes. How many times will she get kicked out in 6 hours?
Pop Smoke drops 3 new mixtapes per month. How many years has it been if he drops 45 new tapes?
Answer:
for the first answer : 36
for the second answer : 1 year and 3 months
Step-by-step explanation:
first answer :
ahe gets kicked out 2 times in 20 mins
6 hours = 6 × 60 mins = 360 mins
let the number of times she gets kicked out in 6 hours / 360 mins be "n"
therefore ;
n= (360×2) ÷ 20 = 36
therefore answer is 36 times.
-----------------------------------------------------------------
second answer :
3 new tapes in 1 month
let the number of years be "n"
therefore:
3×12 = tapes per year = 36 tapes per year
so, n = 45÷36 = 1 (as quotient) year and 3 (as remainder) months.
answer : 1 year and 3 months
shasta claimed that the equation x^2+25=0 can be solved by using its factored form of (x+5i)^2=0, and that -5i is the only zero for this function. which statement is true?
Answer:
The given equation will have two roots as +5i and -5i
Step-by-step explanation:
Shasta claimed that the equation x^2+25=0 can be solved by using its factored form of (x+5i)^2=0, and that -5i is the only zero for this function
The given equation is [tex]x^2+25 =0[/tex]
This clearly shows it will have complex roots, and since it is a quadratic equation it will have 2 complex roots
[tex]x^2 = -25 \\x = \sqrt{-25} \\x= \sqrt{-1}* \sqrt{25}\\[/tex]
[tex]x = i\sqrt{25}[/tex]
x = ± 5i
It will be false to say that -5i will be the only complex root to this equation.
The given equation will have +5i and -5i as its roots.
Lets verify
x = +5i
[tex](5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25\\-25 + 25 = 0[/tex]
x = -5i
[tex](-5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25 \\-25 + 25 \\ = 0[/tex]
сатре о
Find the condition that the roots of the quadratic equation
ax2 + cx + C =0
may be in the ratio m:n
Answer:
[tex]mnb^2 = ac(m+n)^2[/tex]
Step-by-step explanation:
Given
[tex]ax^2 +bx + c = 0[/tex]
Required
Condition that the roots is in m : n
Let the roots of the equation be represented as: mA and nA
A quadratic equation has the form:
[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]
or
[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]
We have the roots to be mA and nA.
So, the sum is represented as:
[tex]Sum = mA + nA[/tex]
[tex]Sum = A(m + n)[/tex]
And the product is represented as:
[tex]Product = mA * nA[/tex]
[tex]Product = mnA^2[/tex]
By comparing:
[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]
with
[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]
[tex]Sum = -\frac{b}{a}[/tex]
[tex]Product = \frac{c}{a}[/tex]
So, we have:
[tex]Sum = -\frac{b}{a}[/tex]
[tex]A(m + n) = -\frac{b}{a}[/tex]
Make A the subject:
[tex]A = \frac{-b}{a(m+n)}[/tex]
[tex]Product = \frac{c}{a}[/tex]
[tex]mnA^2 = \frac{c}{a}[/tex]
Substitute [tex]A = \frac{-b}{a(m+n)}[/tex]
[tex]mn(\frac{-b}{a(m+n)})^2 = \frac{c}{a}[/tex]
[tex]mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a}[/tex]
Multiply both sides by a
[tex]a * mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a} * a[/tex]
[tex]\frac{mnb^2}{a(m+n)^2} = c[/tex]
Cross Multiply:
[tex]mnb^2 = ac(m+n)^2[/tex]
Hence, the condition that the ratio is in m:n is
[tex]mnb^2 = ac(m+n)^2[/tex]
2. There is 3/4 ft of ribbon to go on each of the 3 packages. You decide to divide the ribbon evenly
for each package. How much ribbon does each package get?
1/4 ft
3/12 ft
2 1/4 ft
9/4
WILL GIVE BRAINLIEST
Solve the quadratic function using square root X+10x+25 =18
Answer:
= − 7 /1 1 in fraction form
Step-by-step explanation:
STEP 1: Multiply by 1
1 + 1 0 + 2 5 = 1 8
+ 1 0 + 2 5 = 1 8 STEP 2: Combine like terms
+ 1 0 + 2 5 = 1 8
1 1 + 2 5 = 1 8 STEP 3: Subtract 2 5 from both sides of the equation
11x+25=18
1 1 + 2 5 − 2 5 = 1 8 − 2 5
STEP 4: Simplify by subtracting the numbers
1 1 + 2 5 − 2 5 = 1 8 − 2 5
11x+25−25=18−25 1 1 = 1 8 − 2 5 1 1 = -7
STEP 5: Divide both sides of the equation by the same term 1 1 = − 7 11x/ 11x = −7/ 1 1 (set up as a fraction) STEP 6: Cancel terms that are in both the numerator and denominator
= − 7 /1 1 SOLUTION
= − 7 /1 1
A scientist is working with 15 meters of gold wire. How long is the wire in millimeters
The length of the gold wire that is 15 metres in millimetres is 15000 mm
How to convert the length of the wire?The scientist is working with 15 metres of gold wire.
The wire is in metres.
Therefore, let's convert it millimetres.
1 m = 1000 mm
15 m = ?
cross multiply
length(mm) = 15 × 1000
length(mm) = 15000 mm
learn more on length here: https://brainly.com/question/308075
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Best answer gets brainliest hurry ASAP
Answer:
42 minutes
Step-by-step explanation:
Algebra 1 help, please!! ............................................................................
Answer:
D
Step-by-step explanation:
(f-g)(x) = 3ˣ + 10x - (5x - 3)
= 3ˣ + 10x - 5x + 3 {Combine like terms}
= 3ˣ + 5x + 3
Answer:
d
Step-by-step explanation:
BRANLIEST TO THE RIGHT ANSWER!! NEED HELP ASAP!
Answer:
1
Step-by-step explanation:
1
30 POINTS!!!!!!!
A family is taking a trip to the beach 145 miles away. They have 10 gallons of gas in their car’s gas tank and the car is averaging 14 miles per gallon. Explain why estimating to determine if they have enough gas to make the trip is NOT going to be okay in this instance.
Answer:
No they don't.
Step-by-step explanation:
I did 14 x 10. Since it's 14 per gallon and they have 10. I got 140. 140 is not enough for the trip. They need 145.
Answer:
6.0
Step-by-step explanation:
common sense
Which choice is equivalent to the expression below? (V= square root)
V -125
A. 5iV-5
B. -5i
C. 5i V5
D. 5i
E. V125
Answer:
C
Step-by-step explanation:
i = [tex]\sqrt{-1}[/tex]
[tex]\sqrt{125}[/tex] is equal to 5[tex]\sqrt{5}[/tex]
Since it is [tex]\sqrt{-125}[/tex], then you must have i as well
5i[tex]\sqrt{5}[/tex]
please give a heart to give thanks :)
a crown would be nice too :)
graph the inequality y is less than x-3
Answer:
i do believe that its y<x-3
Step-by-step explanation:
Marion is twice as old as judy. Six years agot Marion was three times as old as judy was then. Find the age of each girl now.
Pls show work, I will give brainliest
9514 1404 393
Answer:
Marion is 24, Judy is 12
Step-by-step explanation:
Let j represent Judy's age now. 6 year ago, the relation was ...
3(j -6) = (2j) -6
3j -18 = 2j -6 . . . . . eliminate parentheses
j = 12 . . . . . . . . . . . add 18-2j
2j = 24 . . . . . . . . . Marion's age now
Judy is 12; Marion is 24.
What is the slope given: y= -x + 5
Options:
1
5
-1
0
Answer:
5
Step-by-step explanation:
If 65% of a number is 169 and 15% of the same number is 39, find 80% of that number.
Answer:
208
Step-by-step explanation:
169/65%=260= the original number
260 x 80% = 208
Answer:
208 is 80% of that number
Step-by-step explanation:
to find the number, take 65/100 (or 65%), and set it equal to 169/x (because x is the number that 169 is 65% of, so we need to find x)=> 65/100=169/x
Next, cross multiply to get 16900=65x
Divide both sides of the equation by 65 to get 260=x, which means that 260 is the mystery number that the question speaks of. Then, to get 80% of 260, set 80/100 equal to x/260=> 80/100=x/260
cross multiply to get 20800=100x
divide both sides by 100 to get 208
Therefore, the answer is 208
Write an equation for the nth term of the arithmetic sequence.
2, 5, 8, 11, ...
Answer:
An equation for the nth term of the arithmetic sequence.
[tex]a_n=3n-1[/tex]
Step-by-step explanation:
Given the sequence
2,5,8,11,...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
here
a₁ = 2computing the differences of all the adjacent terms
d = 5-2 = 3, d = 8-5=3, d=11-8=3Using the nth term formula
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting a₁ = 2, d = 3
[tex]a_n=2+\left(n-1\right)3[/tex]
[tex]=2+3n-3[/tex]
[tex]=3n-1[/tex]
Thus, an equation for the nth term of the arithmetic sequence.
[tex]a_n=3n-1[/tex]
Please help thank you so much
Answer:
This is the correct solution for your question
Find 1000% of 99 pls help
Step-by-step explanation:
1000% of 99 = 10 * 99 = 990.
PLEASE PLEASE HELP MEEEE!!!!
Answer:
The answer is D) f(x) = 1/3 x^2 -1
Step-by-step explanation:
the key is at the end, the minus 1
Answer:
The answer is D!
Step-by-step explanation: