Answer:
P + Q = 1
Step-by-step explanation:
Given: [tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex] = P - [tex]\sqrt{Q}[/tex]
This is a question on surd, so we need to rationalize the denominator to have;
[tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex] * [tex]\frac{1+\sqrt{3} }{1+\sqrt{3} }[/tex] = [tex]\frac{1+\sqrt{3}+\sqrt{3} + 3}{1+\sqrt{3}-\sqrt{3} -3 }[/tex]
= [tex]\frac{4+ 2\sqrt{3} }{1-3}[/tex]
= [tex]\frac{4+2\sqrt{3} }{-2}[/tex]
= -2 - [tex]\sqrt{3}[/tex]
Thus,
-2 - [tex]\sqrt{3}[/tex] = P - [tex]\sqrt{Q}[/tex]
⇒ P = -2 and Q = 3
Therefore, the value of P + Q = -2 + 3
= 1
Thus,
P + Q = 1
A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
f(1) = 6; f(n) = 6 + d(n − 1), n > 0
f(1) = 6; f(n) = 6 ⋅ d(n − 1), n > 0
f(1) = 6; f(n) = 6 ⋅ d(n + 1), n > 0
f(1) = 6; f(n) = 6 + d(n + 1), n > 0
Answer:
a.
f(1)=6; f(n)=6+d(n-1), n>0
Step-by-step explanation:
We are given that
First layer has squares, a=6
Second layer has squares, a2=12
We have to find an arithmetic explicit formula to determine the number of squares in each layer.
[tex]d=a_2-a_1=12-6[/tex]
nth term of an A.P
[tex]a_n=a+(n-1)d[/tex]
Substitute the value of a
Now, we get
[tex]a_n=6+(n-1)d[/tex]
f(1)=a=6
[tex]a_n=f(n)=6+d(n-1)[/tex]
Hence, option a is correct.
a.
f(1)=6; f(n)=6+d(n-1), n>0
Answer:
f(1) = 6; f(n) = 6 + d(n − 1), n > 0
Step-by-step explanation:
I took the test on flvs and got it right.
100% Guaranteed Correct :)
, Hope this helps
Have a great day!!
In a GEOMETRIC sequence, the first term is 21 and
the common ratio is 2. Find the 15th term.
Answer:
344064
Step-by-step explanation:
hope it is well understood
Find four fractions between 1/10 and 1/8
9514 1404 393
Answer:
5/48, 5/46, 5/44, 5/42
Step-by-step explanation:
We can choose unit fractions with denominators between 8 and 10, separated by (10-8)/5 = 0.4 units:
1/8.4 = 5/42
1/8.8 = 5/44
1/9.2 = 5/46
1/9.6 = 5/48
__
Check
1/8 = 0.1255/42 ≈ 0.1195/44 ≈ 0.1145/46 ≈ 0.1095/48 ≈ 0.1041/10 = 0.100_____
Additional comment
There are an infinite number of such fractions. We are given unit fractions with different denominators, so it works reasonably well to choose denominators between those given. Then the trick is to convert the fraction to a ratio of integers. In this case, multiplying by (5/5) does the trick.
__
Another approach is to write the fractions with a common denominator, then choose numerators between the ones given. For example, 1/10 = 4/40, and 1/8 = 5/40, so you could write some fractions with numerators between 4 and 5. Possibilities are 4.1/40 = 41/400, 4.3/40 = 43/400, 4.7/40 = 47/400, 4.9/40 = 49/400.
What is the length of bc
The shaded area in the distribution below represents approximately 95% of the data. Use the diagram to find the mean and the standard deviation.
Answer:
mean = 85, standard deviation = 3.5
Step-by-step explanation:
The empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviation of the mean and 99.7% falls within three standard deviation of the mean.
From the diagram since the shaded are is approximately 95% of the data. Hence 95% falls within two standard deviations of the mean.
σ = standard deviation, μ = mean
Hence; μ ± 2σ = (78, 92)
μ - 2σ = 78 (1);
μ + 2σ = 92 (2)
Adding equation 1 and 2, gives 2μ = 170
μ = 85
μ - 2σ = 78
85- 2σ = 78
2σ = 7
σ = 3.5
i need help in this plz!!!!
Step-by-step explanation:
1) = {5(x+y)} - 2x
= 5x + 5y - 2x
= 3x + 5y
2)= {2(p×q)} + (p×q)
= (2p×2q)+ p×q
= 4pq + pq
= 5pq
3)= 6a + (8b + 2a)
= 8a + 8b
= 8(a+b)
4)= 3x² + ( x²+7x)
= 4x² + 7x
= x(4x+7)
Answer:
Step-by-step explanation:
72) 5*(x +y) - 2x
= 5x + 5y - 2x {Distributive property}
= (5x - 2x) + 5y {Combine like terms}
= 3x + 5y
73) 2*(pq) + pq
= 2pq + pq {Combine like terms}
= 3pq
74) 6a + (8b + 2a)
= 6a + 2a + 8b {Combine like terms}
= 8a + 8b
75) 3*x² + (x² + 7x)
= 3x² + x² + 7x {Combine like terms}
= 4x² + 7x
Look at the figure. Which surface of the figure is represented by plane EFHG?
the right side
the back
the top
the bottom
247 divided by 7
[tex]247 \div 7[/tex]
Answer:
247/7 = 35 2/7
247/7 = 35 reminder 2
247/7 = 35.2857142857...
Step-by-step explanation:
35
----------------------------------
7 | 247
21
-----------
37
35
---------
2
247/7 = 35 2/7
247/7 = 35 reminder 2
247/7 = 35.2857142857...
A local store sells oranges at a price for 6 fo $9.00. If Alley wants to buy 10 oranges what would the total price be?
Answer:
15$
Step-by-step explanation:
you need to check how much of e costs and you do that by dividing the price by the amount and than comes up to 1.5 that's for 1 and for 10 it's 15 hope that helps
Distribute and simplify the radicals below
Answer:
i think A is answer you should to do
Line K has a slope of -3/4. If the slope of of lines that are perpendicular to each other are opposite reciprocals, what is the slope of a line perpendicular to line k?
Answer:
+4/3
Step-by-step explanation:
-3/4 * -1 = 3/4 then flip it to 4/3
Answer:
4/3
Step-by-step explanation:
the slope of a perpedicular line is the inverse times negative one.
1)the inverse of -3/4 is -4/3
2)-4/3*-1 is 4/3
Please help me with this I really need help (ಥ_ಥ)
Answer:
i can help you i know this question
Which set of fractions is ordered from least to greatest?
Answer:
The answer is 7/12 , 6/8 , 4/5 from least to greatest.
Answer
7/12, 6/8, 4/5
Which equation represents the graphed function?
.
10.30
O y=-3+3
O y=3x-3
O y = 3x - 2 / 2
O ya **+3
19T
HELP PLSSSSS ON KHAN ACADEMY
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
See this attachment
tìm x,y nguyên tố thỏa mãn:y^2-2x^2=1
Answer:
dx/dy = y/2x
Step-by-step explanation:
-4x × dx/dy = -2y..... that's all
what type of polynomial is p(x)=4x−2x2+3
a. quadratic
b. quartic
c. quintic
d. cubic
Answer:
a. quadratic.
The given polynomial p(x)=4x−2x²+3 is a quadratic polynomial. The correct option is A.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
In the given polynomial p(x)=4x−2x²+3 it can be observed that the degree of the polynomial is 2 or the highest power of the variable is 2.
Therefore, the given polynomial p(x)=4x−2x²+3 is a quadratic polynomial. The correct option is A.
To know more about quadratic polynomials follow
https://brainly.com/question/1214333
#SPJ5
The slope of MN is -3 which segment is parallel to MN
Answer:
B and D
Step-by-step explanation:
What’s the answer? Help
Answer:
$14
Step-by-step explanation:
x = price of scarf 1
y = price of scarf 2
together they cost $25
x + y = 25
one scarf costs $3 more than the other
x = y + 3
now we use that in the first equation again
y+3 + y = 25
2y +3 = 25
2y = 22
y = $11
=> x = y +3 = 11 + 3 = $14
What is the product?
43 .4-3
0)
1)
4)
6)
Answer:
1
Step-by-step explanation:
So we can actually simplify the exponents here. The power rule for exponents is that when multiplying, you add the exponents. So,
3 + (-3) = 0
so the number is now 4^0.
Everything by the power of 0 is equal to 1, so the answer is 1.
Hope this helps !!
-Ketifa
**HELP**
find the angle measures given the figure is a rhombus.
Answer:
m<1=74
m<2=37
Step-by-step explanation:
m<2 is the same as the other angle, 37 degrees. So now we need to find the other angle in the triangle.
37+37+x=180.
The total degree of a triangle is 180.
x=106
Subtract that from 180 to get m<1.
180-106=74
I hope this helps!
Good luck!
Si Martha retira de su cuenta el 10% para los transportes del mes. ¿Cuál es el nuevo saldo de la cuenta?
Respuesta:
0,9 veces
Explicación paso a paso:
Deje que la cantidad en la cuenta de Martha se denote como x, que es la cantidad en la cuenta = x
Porcentaje retirado para transporte = 10%
El porcentaje total siempre será del 100%
Por lo tanto, si se retira el 10%, entonces; el porcentaje restante es:
Porcentaje total: porcentaje gastado en transporte
(100% - 10%) * monto en cuenta
90% * x = 0,9 * x = 0,9x
Saldo de cuenta nueva = 0.9x
By converting to an exponential expression, solve log3 (x + 9) = 5.
Answer:
[tex]{ \tt{ log_{3}(x + 9) = 5 }} \\ { \tt{x + 9 = {3}^{5} }} \\ { \tt{x + {3}^{2} = {3}^{5} }} \\ { \tt{x = {3}^{5} - {3}^{2} }} \\ { \tt{x = 234}}[/tex]
which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2
Which expressions are equivalent to 2^5•2^4? Check all that apply.
Answer:
2⁵×2⁴=2⁹
2⁵×2⁴=2×2×2×2×2×2×2×2×2
2⁵×2⁴=4⁵
2⁵×2⁴=8³×2
Answer:
[see below]
Step-by-step explanation:
Recall the product rule: [tex]a^x+a^y=a^{x+y}[/tex]
[tex]2^5 + 2^4 = 2^{5 + 4} = \boxed{2^9}[/tex]
Other expressions could be:
[tex]2^{-2} *2^{11}=2^{-2+11} = \boxed{2^9}[/tex]
[tex](2*2*2*2*2)(2*2*2*2) = 2^5 + 2^4 = \boxed{2^9}[/tex]
Hope this helps.
The diagonals of a quadrilateral must be bisect each other and be perpendicular to gurarantee that the quadrilateral is a parrelogram
Answer:
False
Step-by-step explanation:
A quadrilateral is a closed geometrical figure that have four sides and four vertices. Thus the following includes in a quadrilateral : parallelogram, square, rhombus, rectangle and trapezium.
If the diagonals of the quadrilateral bisects each other and are perpendicular to each other, then the quadrilateral forms a rhombus.
Hence the answer is FALSE.
If AABC is reflected across the y-axis, what are the coordinates of A'?
Answer:
-2,-4
Step-by-step explanation:
Need help on this please!!! 10 points!!!
Answer:
I think the answer is the first one ... am i right...
Find the slope of the line passing through the points (-2, -8) and (9,-8).
slope:
To get that answer, apply the slope formula
m = (y2 - y1)/(x2 - x1)
m = (-8 - (-8))/(9 - (-2))
m = (-8 + 8)/(9 + 2)
m = 0/11
m = 0
Any line with slope 0 is completely horizontal.
As a quick rule of thumb: if the y coordinates of the two points are the same, then the slope is 0 on this horizontal line.
Can someone help me out
answer is
4ft* 5ft
= 20ft^2
