Answers
[tex]\dfrac{6+ \sqrt{27}}{4-\sqrt3} \\\\\\=\dfrac{\left(6+\sqrt{27}\right)\left(4+\sqrt 3 \right)}{\left(4-\sqrt 3\right) \left(4+\sqrt 3\right)}\\\\\\=\dfrac{24+6\sqrt 3+4\sqrt{27}+\sqrt{27\cdot 3}}{4^2 - \left(\sqrt 3 \right)^2}\\\\\\=\dfrac{24+6\sqrt3+4\sqrt{9\cdot 3} +\sqrt{81}}{16-3}\\\\\\=\dfrac{24+6\sqrt 3 +12\sqrt 3 + 9 }{13}\\\\\\=\dfrac{33+18\sqrt 3}{13}\\\\\\\text{Hence, r = 33 and s = 18}[/tex]
Related Questions
The function f is given by f(x) = (x + 3)^2 - 1.
1) Write the coordinates of the vertex of the graph of f.
2) Does the graph open up or down? How do you know?
Answers
Answer:
the coordinate of the vertex is going to be (-3,-1) and it's concave up
Step-by-step explanation:
1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)
2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up
In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive
Suppose y varies directly with x where y=21 when x=7 find y when x = 15
Answers
Evaluate the expression for x = 5 and y = -1
xy - y =
Answers
Answer:
-4
Step-by-step explanation:
xy-y = ?
(5)(-1)-(-1) = ?
-5 + 1 = -4
Hope that helps
Identify the slope in the following equation: y= -x + 7
PLEASE HELP!!!!
Answers
Answer: The slope is -1 because this equation is already in y=mx+b so we dont have to apply the y2-y1 over x2-x1 formula you can easily identify the slope when its in y=mx+b because the slope always has a x after the number for example: 4x
Answer:
It is the coefficient of the x, when the y is isolated. In this case it is -1.
The figure below shows the number of dots in each of the first four terms of a pattern.
image 3946d177031641899e8a9055b29f185e
Which of these can be used to determine
N
, the number of dots, given
t
, the number of the term in the pattern?
N
=
4
(
t
−
1
)
N = 4 ( t − 1 )
N
=
3
t
+
1
N = 3 t + 1
N
=
3
(
t
−
1
)
+
1
N = 3 ( t − 1 ) + 1
N
=
3
t
+
2
Answers
Answer:
there is nothing just a a codding log
Step-by-step explanation:
is (1, 3) a solution to the system of equations
8x + y = 11
12x + 2y = 18
Answers
Answer:
(1, 3) a solution to the system of equations
8x + y = 11
12x + 2y = 18
Step-by-step explanation:
ay están todos los deberes de la semana pasada gunnorni
Answer:
x=1 and y=3
Step-by-step explanation:
yes x=1 and y=3 is the solution for the equation.just by making y in the first equation subject of the formula and replacing in the second equation.
Answer this correct and I will give you extra points.
Answers
Answer:
he didnt subtract each equations on both sides
5y-6=4y+1
-4 -4
y -6=1
+6=+6
y=7
Step-by-step explanation:
hope that wrk
1. 6(12+4)
2. 10+4(2+20)
3. 7(4+19)
Answers
Answer:
1. 6 x 16 = 96
2. 10 + 4 x 22 = 10 + 88 = 98
3. 7 x 23 = 161
Step-by-step explanation:
Just a little help please ☺️
Simplify
(3^8/3^5)3
3^9
3^39
3^10
3^6
Answers
[tex]\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9[/tex]
What is the solution to the system of equations?
y = -2x – 6
4x - y = -36
A (15, 24)
B (-7, 8)
C (-5, 4)
Answers
The blueprint for Moreno's living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new blueprint? (The width is 8)
Answers
Answer:
Part a) The scale of the new blueprint is
Part b) The width of the living room in the new blueprint is
Step-by-step explanation:
we know that
The scale of the original blueprint is
and
the width of the living room on the original blueprint is 6 inches
so
Find the actual width of the living room, using proportion
Find the actual length of the living room, using proportion
Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room
simplify
Find the width of the living room in the new blueprint, using proportion
Which statement about f ( x ) = x 2 + 5 x − 84 is true?
Answers
Answer:
It is False
Step-by-step explanation:
Write a two- column proof.
Given: 3x = x + 12
Prove: x =5
Answers
2x=12
x=12/2
x=6
Which of the following points would be on the graph of
the equation y=-40 + 6?
-4, -10)
(-4, 22)
(1, -10)
(1, - 2)
О
-
о
Answers
Step-by-step explanation:
To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
HELPPPPPPPPPPPPPppPPPPPPPPPPpppp
Answers
A negative [-] times a positive [+] is a negative [-]
A negative [-] times a negative [-] is a positive [+]
A positive [+] and a positive [+] is a positive [+]
Since the quotient is a positive [+] 35, that means there had to have been two negatives [-] to make a positive. The answer is -5
WORK:
35/ 7 = 5
~ Remember to add negative (-)
So the answer is -5
Figure A is a scale image of figure B.
Pls help!!!
Answers
x = 5.25
since there is a scale factor of 1.75, you multiply 3 * 1.75 and get 5.25
hope this is helpful!
PLEASE ANSWER ASAP WORTH 10 PTS
Describe the graph of the line y = -5.
line with slope of -5
horizontal line
crosses the x-axis
vertical line
Answers
Can someone please help me with 54? It’s the last one and it’s due in 1 hour Tysm if you do!!
Answers
Answer:
The awnser should be 4. (3x4 = 12, 12 x 4 = 48, 48 x 12 = 192, 192 x 4 = 768. )
Step-by-step explanation:
(Hope this helps, Happy holidays!!)
round 0.006772 to 1 significant figure
Answers
Answer:
0.007
Step-by-step explanation:
0's before other numbers are non-significant. Then you just round your number.
Hope that helps
-
5. Tanya wants to subtract 62 - 48. What are some
ways she can find the difference? Choose a way
and show the work needed to find the difference
Answers
Solve each system by elimination
10x-8y=4
-5x+3y=-9
Answers
[tex]10x-8y =4~~~....(i)\\\\-5x+3y=-9~~~...(ii)\\\\\text{Multiply equation (ii) by} -2\\\\10x-6y = 18~~~...(iii)\\\\(iii)-(i):\\\\10x-6y - 10x +8y = 18 -4\\\\\implies 2y = 14\\\\\implies y= \dfrac{14}2 = 7\\\\\text{Substitute y = 7 in equation (i):}\\\\10x-8(7) =4\\\\\implies 10x - 56 =4\\\\\implies 10x = 4+56\\\\\implies 10x = 60\\\\\implies x = \dfrac{60}{10} = 6\\\\\\\text{Hence (x,y) = (6, 7)}[/tex]
Convert the equation g(x) = −(x − 7)2 +5 into standard form.
Answers
Answer:
7
Step-by-step explanation:
You have to add 2 and 5, the rest is stuff to distract you
Prove the triangles are similar.
Answers
Answer:
SAS similarity
Step-by-step explanation:
The two triangles MON and MQP are such that
Angle M = Angle M
MO/MQ = MN/MP
Therefore, Triangle MON ~ Triangle MQP (SAS similarity)
Solve for x in the equation x2 + 4x-4=8.
O x = -6 or x = 2
X=-2+2/2
O x = -2 or x = 6
O x=2+2V5
Answers
[tex] {x}^{2} + 4x - 4 = 8 \\ = > {x}^{2} + 4x - 4 - 8 = 0 \\ = > {x}^{2} + 4x - 12 = 0 \\ = > {x}^{2} + 6x - 2x - 12 = 0 \\ = > x(x + 6) - 2(x + 6) = 0 \\ = > (x - 2)(x + 6) = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 6 [/tex]
Answer:
x = -6 or x = 2
Hope you could get an idea from here.
Doubt clarification - use comment section.
Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14
Answers
2(3n - 7) + 2(n + 5)
6n - 14 + 2n + 10
Simplify
8n - 4
So the answer would be C
Matthew wants to buy a new pair of jeans. If the jeans were originally $65.00, but are on sale with a 10% discount, how much will Matthew have to pay for the jeans?
Answers
10% off means the jeans will sell for 90% of the original price ( 100% - 10% = 90%)
Multiply the original price by 90%
65.00 x 0.90 = 58.50
He will pay $58.50
Basket A had 7 times as many plums as Basket B at first. Zoe put 58 more plums in each basket. Now Basket A has thrice as many plums as Basket B. How many more plums are there in Basket A than Basket B now?
Answers
Answer:
174 plums
Step-by-step explanation:
a=7b
a+58=3b
7b+58=3b
4b=58
b=14.5
29,203 earlier
87,261 now
261-87=174
A box contains 8 red balls and 8 black balls. A
woman takes balls out at random without looking at
them. Once a ball is taken out it is not replaced back in
the box. How many balls must she select to be sure of
having at least three balls of the same color?
Answers
Answer:
At least 5 times
Step-by-step explanation:
Number of balls to be selected for having assurance of at least three balls of the same colour is equals to 5 balls.
What is without replacement ?" Without replacement means if an item is drawn from the set of items it is not kept back which represents sample space is decrease by as per the number of selection is done in first draw."
According to the question,
Number of red balls in a box = 8
Number of black balls in a box =8
As per the condition of without replacement we get,
In this case worst selection case could be
Alternate balls are of different colour
Black →Red → Black → Red → fifth ball is either Red or Black
Hence, 5balls must be selected for assuring at least three balls of the same colour .
Learn more about without replacement here
https://brainly.com/question/22221548
#SPJ2
through (-4 0) perp y=2x-4 point slope form
Answers
Look at paper for work
Can someone plz help :(((((
What is the area, in square inches, of the rectangle?
Answers
Answer:
What are the side lengths?