Hope you could get an idea from here.
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The equation [tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex] has been proved to be true
The equation is given as:
[tex]\frac pq = \frac qr[/tex]
Cross multiply
[tex]pr = q^2[/tex]
Rewrite as:
[tex]q^2 = pr[/tex]
Also, we have:
[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex]
Substitute [tex]q^2 = pr[/tex]
[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3[/tex]
Expand
[tex]p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3[/tex]
Simplify
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3[/tex]
Rewrite as:
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3[/tex]
Substitute [tex]pr = q^2[/tex]
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3[/tex]
[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3[/tex]
Divide q^6 by q^3
[tex]p3+q3+r3=r^3 +q^3 + p^3[/tex]
Rewrite the equation as:
[tex]p3+q3+r3=p^3 +q^3 + r^3[/tex]
Hence, the equation has been proved
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Help me!!! due in 2 mins!!!
Simplify??!?!?????!!!! ;). Pleeeeaaaassseee
Please help me with this question :)
I will mark you as brainliest
[tex]\text{Given that,}\\\\s_1 = 5.95,\\\\s_2 = 5.42\\\\\\F= \dfrac{(s_1)^2}{(s_2)^2} = \dfrac{(5.95)^2}{(5.42)^2} = 1.21[/tex]
A square is cut diagonally into two equal parts. If each part has an area of 50cm^2, then what is the perimeter of each part?
50 points the answer isnt 30 so dont say it is because it isnt
Answer:
its 25.
Step-by-step explanation:because 50 divided by 2 is 25.
Answer:
40 units
Step-by-step explanation:
1) Find the side length of the square
Let the side be "s".
[tex]\rightarrow \frac{1}{2} \times s \times s = 50 \ \text{cm}^{2}[/tex]
[tex]\rightarrow s \times s = 50 \times 2[/tex]
[tex]\rightarrow s \times s = 100[/tex]
[tex]\rightarrow \sqrt{s \times s} = \sqrt{100}[/tex]
[tex]\rightarrow s = \±10[/tex]
[tex]\rightarrow s = 10 \ \text{units}[/tex] (Side lengths can never be negative)
2) Find the perimeter of the square
[tex]\text{Perimeter of square = 4(s) = 4(10) = 40 units}[/tex]
There are 5 possible toppings for a burger - mustard, ketchup, mayonnaise, lettuce, and tomato. How many possible combinations?
Answer:
25
Step-by-step explanation:
Evaluate the function for x =2 and x = 6
f(x) = 4x −3
will mark brainliest (NO LINKS OR ANSWERS WITHOUT EXPLANATION)
Answer:
6x² -xy -35y²
Step-by-step explanation:
Use the distributive property, and combine terms.
(2x +5y)(3x -7y) -2xy
= 2x(3x -7y) +5y(3x -7y) -2xy
= 6x² -14xy +15xy -35y² -2xy
= 6x² +(-14 +15 -2)xy -35y²
= 6x² -xy -35y²
Someone please help me on both the questions!!!
Step-by-step explanation:
al nth term:
numerator:
[tex] = {n}^{2} [/tex]
denominator:
[tex] = n + 1[/tex]
so nth term :
[tex] = \frac{ {n}^{2} }{n + 1} [/tex]
b). 1; 11; 27; 49
first difference: 10; 16; 22
second difference :6
formula for 1st difference:3a+b
formula for 2nd difference:2a
Therefore:
2a=6
a=3
3a+b=10
sub in a
3(3)+b=10
9+b=10
b=1
sub into quadratic formula
[tex] {an}^{2} + bn + c[/tex]
[tex](3) {(1)}^{2} + (1)(1) + c = 1[/tex]
[tex]3(1) + 1 + c = 1[/tex]
[tex]3 + 1 + c = 1[/tex]
[tex]4 + c = 1[/tex]
[tex]c = - 3[/tex]
So Tn:
[tex]3 {n }^{2} + 1n - 3[/tex]
Step-by-step explanation:
a)
it is clearly a sequence of the square numbers over the numbers+1.
1/2 = 1²/(1+1)
4/3 = 2²/(2+1)
9/4 = 3²/(3+1)
16/5 = 4²/(4+1)
so, the nth term would be
n²/(n+1)
b)
an² + bn + c creates the sequence with increasing n (n = 1, 2, 3, 4, ...)
since for sequence the first starting value is often not generated by the general expression, we have to focus on n = 2, n = 3 and n = 4, and with that we get 3 equations with 3 variables (a, b, c) that we can solve :
n = 2
a×2² + b×2 + c = 11 = 4a + 2b + c
n = 3
a×3² + b×3 + c = 27 = 9a + 3b + c
n = 4
a×4² + b×4 + c = 49 = 16a + 4b + c
the first equation gives us
c = 11 - 4a - 2b
when we use this in the second equation, we get
27 = 9a + 3b + 11 - 4a - 2b = 5a + b + 11
b = 16 - 5a
now we use both of that in the third equation :
49 = 16a +4(16 - 5a) + 11 - 4a - 2(16 - 5a) =
= 16a + 64 - 20a + 11 - 4a - 32 + 10a =
= 2a + 43
2a = 6
a = 3
b = 16 - 5a = 16 - 5×3 = 16 - 15 = 1
c = 11 - 4a - 2b = 11 - 4×3 - 2×1 = 11 - 12 - 2 = -3
The formula to find the area of a triangle is A = { bh where b=base and h=height. Rearrange the
equation to highlight b, the base of the triangle, in terms of the area and height.
Answer:
A=B+H
Step-by-step explanation:
I rearange the letters and also I put a plus singe
[tex]\huge \dag \sf{Answer \: it}[/tex]
Refer to attachment.
Note: Spams not allowed.
Don't Copy
If you don't know the answer don't answer
Need Answer with explanation.
Thank You!
Answer:
[tex]option \: (b) \: is \: ur \: answer \: to \: the \: question \: [/tex]
[tex]to \: know \: the \: answer \: with \: proof[/tex]
[tex]refer \: to \: the \: above \: attatchment[/tex]
[tex]f = \frac{rn}{1 - r} [/tex]
[tex]\huge \tt༆ Answer ༄[/tex]
The required expression is ~ B
[tex] \boxed{ \sf \: F = \dfrac{ RN }{ 1 - R} }[/tex]
Refer to the attachment for Solution ~
Pleaseeeee helpppp asapp
Please help me, you can see the parabola down below. Please.
Determine the equation of the parabola in Vertex Form. Work must be shown.
Answer:
let me check....
Step-by-step explanation:
1/3 + 1/2 + 4/5 jdnjfnawbfaibgfiabfwhbruwbrfywhfywg8eyfhwa8uofhawufhaw
Answer: 49/30 or, 1 19/30
What is the measure of the angle in the polygon shown below?A.B.C.D.
C.130°
Answer:
Solution given:
no of sides(n)=6
now
total interior angle of polygon having 6 sides is
(n-2)*180=(6-2)*180=4*180=720°
we have
Sum of interior angle of polygon: 720°
130°+100°+130°+130°+100°+?=720°
590°+?=720°
?=720°-590°
?=130°
please help asap for brainlist
Answer:
it's (2,-4)
hope it helps
The statement below is a different way to say that the sides of these similar parallelograms are proportional.
Complete the equations that go with the statement.
b/c = s/r
_________
o0o0o0o0o0
c/d = r/q
________
o0o0o0o0
Two triangles are shown on the coordinate plane. Which statement regarding the triangles is correct? A. The area of the small triangle is half the area of the large triangle. B. The area of the small triangle is twice the area of the large triangle. C. The slope of one hypotenuse is equal to the opposite reciprocal of the other. D. The slopes of the two hypotenuses are equal.
Answer:
B
Step-by-step explanation:
B
Solve the following system of equations.
8x+3y=18
-7x-4y=-13
x= y=
Answer:
x=3
y=-2
Step-by-step explanation:
Just ask!
Hope this helps.
(✿◡‿◡)
Carol wants to make a sculpture using brass and aluminum, with the dimensions shown below, Aluno Bree The area of the aluminum section can be found using the equation 1 1 А zah - 1 3 bh 2 Which of the following shows the aluminum section's area formula solved for me A h=2A(a - b) B. 2A h= ab С. A h= 2(a - b) D. h Ala-b) 2
The aluminum section's area formula solved for h is [tex]h =\frac{A}{a - b}[/tex]
From the complete question, the expression of the area (A) in terms of variables a, b and h is:
[tex]A = ah - bh[/tex]
Factor out h from the expression on the right-hand side
[tex]A = h(a - b)[/tex]
Divide both sides of the equation by (a - b)
[tex]\frac{A}{(a - b)} = h[/tex]
Remove the bracket
[tex]\frac{A}{a - b} = h[/tex]
Rewrite the above equation as follows:
[tex]h =\frac{A}{a - b}[/tex]
Hence, the aluminum section's area formula solved for h is [tex]h =\frac{A}{a - b}[/tex]
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Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs $1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost $17.
Graph
A combination of veggies that costs $17 but does not weigh 10 pounds.
Select all that apply.
Group of answer choices
D. 10 pounds of zucchini and 1 pound of broccoli
B. 4 pounds of zucchini and 6 pounds of broccoli
A. 6 pounds of zucchini, and 4 pounds of broccoli
C. 2 pounds of zucchini and 7 pounds of broccoli
Answer:
okay for the buying vegetables problem. It wants us to write an equation in ST that gives us enough. The amount of pounds of cauliflower Capital C is our first very bold and broccoli bee is our second variable. So Capital C that says Karl Power costs $2 per pound so we can write to see and then broccoli is a dollar 25 per pound. So plus a dollar 25 times being is equal to the total cost that we spent. And the total we spent was $10. Okay, so there's our equation and standard corn. Thank you.
Which system of equations is equivalent to the following system? 3x 5y = 29 x 4y = 16 3x 5y = 29 â’x â’ 4y = 16 3x 5y = 29 â’3x â’ 12y = â’48 â’3x â’ 5y = 29 x 4y = 16 â’9x â’ 15y = 87 x 4y = 16.
The correct option is (B). [tex]3x+5y=29[/tex] And [tex]-3x-12y=-48[/tex].
Given Equations,
[tex]3x + 5y = 29......(1)[/tex]
[tex]x + 4y = 16.......(2)[/tex]
We have to find out Which system of equations is equivalent to the Given system of Equations.
1). System of equation are,
[tex]3x+5y=29\\-x-4y=16[/tex]
taking - common and transposing to R.H.S we get,
[tex]x+4y=-16[/tex]
This equation is not equal to equal (2), so the option (1) is not the system of equation equivalent to given Equations.
Similarly, on checking other options,
2. system of equation,
[tex]3x+5y=29\\-3x-12y=-48[/tex]
Taking -3 common from L.H.S. we get,
[tex]-3(x+4y)=-48\\\\x+4y=\dfrac{-48}{-3}[/tex]
[tex]x+4y=16[/tex].
Hence the Above system of equation is equivalent to the given system of equation.
So, there is no need to check option (3) and option (4).
Hence the correct option is (B).
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1943 divided by 67.Show steps please.
Answer: Long Division Calculator with Decimals
look this up see if it helps
Step-by-step explanation:
Boris has 10 pairs of jeans, 15 T-shirts, and 7 sweaters in his closet. Write the ratio of sweaters to pairs of jeans using a colon.
Brainliest to a person who gets it right.
Answer: 7:10
Step-by-step explanation: You are asked to find the ratio of sweaters to pairs of jeans. All you do is write the 7 sweaters and the 10 pairs of jeans. And you get a ratio of 7:10. Since this cannot be reduced any further, you just leave it as it is.
Hope this helps.
a 16 ounce package of hamburger meat has 3% fat how much of the total package is fat
Multiply the total weight by the percentage
16 ounces x 0.03 = 0.48
0.48 ounces is fat
write the equation of the line that is parallel to y=4x+12 through the point (2,3).
Answer:
y = 4x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x + 12 ← is in slope- intercept form
with slope m = 4
Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
To find c substitute (2, 3 ) into the partial equation
3 = 8 + c ⇒ c = 3 - 8 = - 5
y = 4x - 5 ← equation of parallel line
Which is the graph of 2x-4y>6?
Solving for x :-
2x - 4y > 6
=》x - 2y > 3
=》x > 3 + 2y
Solving for y :-
2x - 4y > 6
=》x - 2y > 3
=》y < x - 3/2
■ See the attachment for the graph. Since you have not shared the graphs..any graph which looks like this in your question is the correct one.
____
Hope it helps ⚜
Consider the following sequence and type the next number in the sequence.
55, 48, 41,34
Answer:
27 20 13
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
It follows a pattern of -7 every time.
55,(-7) 48,(-7) 41, (-7)34
55-7=48
48-7=41
41-7=34
34-7=27
Hope this helps! Have a great day!
Taylor Swift estimates the cost of a new Tesla model S to be $85,000. The actual cost is $100,690.
What is the percent error in Taylor's estimate? Round your answer to the nearest whole percent.
Answer:
should be 15%
Step-by-step explanation:
formula is |85,000 - 100,690| ÷ 100,690 × 100
May I please receive help?
No files or links please!
graph y= -4/3 x+2 using the slope and y-intercept
slope: 3
y-intercept: (0,-2)
Answer: there you go
Step-by-step explanation:
how do you find the ratio of something
Answer:
To calculate the ratio of an amount we divide the amount by the total number of parts in the ratio and then multiply this answer by the original ratio. We want to work out $20 shared in the ratio of 1:3. Step 1 is to work out the total number of parts in the ratio. 1 + 3 = 4, so the ratio 1:3 contains 4 parts in total.
Step-by-step explanation:
Step-by-step explanation:
hope it will help you a lot.......