Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=9a²b
there's the greatest common factor of the 2 monomials
Hope this helps!
Help Pleasss I will give brainlyest!!!! :D
Answer: The answer is 2,4. May I have the brainiest? pls I only need one more.
If f(x) = 4x ^ 2 - 4x - 8 and g(x) = 2x ^ 2 + 3x - 6 then f(x) - g(x) * i * s
Answer:
[tex]4 {x}^{2} - 4x - 8 - (2 {x}^{2} + 3x - 6) = 4 {x}^{2} - 4x - 8 - 2 {x}^{2} - 3x + 6 = 2 {x}^{2} - 7x - 2[/tex]
Pls solve the above question
Kindly don't spam+_+
Answer:
Step-by-step explanation:
Given expressions are,
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex] and [tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
Remove the radicals from the denominator from both the expressions.
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}} \times \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{p}=\sqrt{\frac{(\sqrt{10}-\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{5}}[/tex]
[tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\times \frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{q}=\sqrt{\frac{(\sqrt{10}+\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}[/tex]
[tex]\sqrt{q}-\sqrt{p}-2\sqrt{pq}=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}-\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}}-2(\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}})(\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}})[/tex]
[tex]=\frac{1}{\sqrt{5}}(\sqrt{10}+\sqrt{5}-\sqrt{10}+\sqrt{5})-\frac{2}{5}[(\sqrt{10})^2-(\sqrt{5})^2)][/tex]
[tex]=\frac{1}{\sqrt{5}}(2\sqrt{5})-\frac{2}{5}(10-5)[/tex]
[tex]=2-2[/tex]
[tex]=0[/tex]
please simplify this one. I need answers fast as possible .(chapter name : surds )
[tex] \sqrt[5]{32} \times 2 \sqrt[3]{81} \\ = {32}^{ \frac{1}{5} } \times 2 {(81)}^{ \frac{1}{3} } \\ = ({{2}^{5}})^{ \frac{1}{5} } \times {2({3}^{3})}^{ \frac{1}{3} } \\ = {2}^{1} \times 2({3}^{1}) \\ = 2 \times 2 \times 3 \\ = 4 \times 3 \\ = 12[/tex]
This is the answer.
Hope it helps!!
how do we get 24 using 3,3,7 and7
Answer:
2 Answers. #1. +11. [3+(3/7)] times 7 is 24. DarkBlaze347 May 1, 2015. +5. Good job, DB! civonamzuk May 1, 2015.
35 Online Users.
Step-by-step explanation:
brainliest please and follow:D
RESUELVE USANDO LAS PROPIEDADES DE LA POTENCIA
PLISSSSSSSSS CON PROCEDIMIENTOOOOOOO
Answer:
Tenemos dos propiedades de la potencia en este caso:
Para un numero real A:
[tex]A^0 = 1[/tex]
[tex](A^n)^m = A^{n*m}[/tex]
En este caso nuestra ecuación es:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0[/tex]
usando la segunda propiedad, podemos reescribir como:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0 = (\frac{0.1234}{-3.2098})^{4*3*0} = (\frac{0.1234}{-3.2098})^0[/tex]
Y acá tenemos un numero real a la potencia 0, sabemos que esto es igual a 1, entonces:
[tex](\frac{0.1234}{-3.2098})^0 = 1[/tex]
Rajah / Diagram 5 (b) Dalam Rajah 6, PQ ialah tangen sepunya dua bulatan. AQ dan BQ ialah tangen bagi bulatan yang masing-masing berpusat E dan F. Cari nilai x dan y. In Diagram 6, PQ is the common tangent of two circles. AQ and BQ is the tangent to the circles with centre E and F respectively. Find the value of x and y. [3 markah.
Answer:
36281629273781646181993836619946527189119292937467482919198$7473828191927364732818919283838292927383883829118661552621718919191019284746617171819001187373765252728
Step-by-step explanation:
173899918377+28910873638282
How many cubes with side lengths of 1/2 cm does it take to fill the prism?
Answer:
24
Step-by-step explanation:
You first find out how many cubes can fit into each measurement, then multiply them. (2*4*3=24)
Answer:
It will take 24 cubes to fill the rectangular prism.
Step-by-step explanation:
Find the volume of a cube with side lengths of 1/2 cm:
1/2^3 = 1/8
1/8 cm^3
Find the volume of the whole rectangular prism (lwh):
1 x 3/2 x 2
= 3/2 x 2
= 3
3 cm^3
Divide the volume of the prism by the bolume of one cube:
3 ÷ 1/8 = 24
Therefore it will take 24 cubes to fill the prism. Hope this helps!
A family has inherited $300,000. If they choose to invest the $300,000 at 12\% per year compounded quarterly, how many quarterly withdrawals of $25000 can be made? (Assume that the first withdrawal is three months after the investment is made).
Step-by-step explanation:
ejejejejrjruruehehhr
Drag the tiles to the correct boxes to complete the pairs.
Match each division of rational expressions with its quotient.
Answer:
Step-by-step explanation:
Um where is the diagrahm
A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: (5x+1)(7x−7) where x is measured in meters. Multiply the binomials to find the area of the plot in standard form
Answer:
35x^2 - 28x - 7
Step-by-step explanation:
Suppose U1 and U2 are i.i.d. Unif(0,1) withU1=0.1 and U2=0.8. Use the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees.
a. 0.326
b. 0.326
c. 0.663
d. 1.96
Answer:
0.663 ( c )
Step-by-step explanation:
U1 = 0.1 , U2 = 0.8
using the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variable
first step : generate single obsⁿ from N ( -1,4 )
attached below is the detailed solution
Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6 Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9 Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6
Answer:
[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex] --- number of flips
Required
[tex]P(x = 3)[/tex]
The probability of getting a head is:
[tex]p = \frac{1}{2}[/tex]
[tex]p = 0.5[/tex]
The distribution follows binomial probability, and it is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}[/tex]
[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]
Answer:
Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?
Answer: A
Step-by-step explanation:
a/b=2/5 and b/c=3/8 find a/c
Answer:
3/20
Step-by-step explanation:
By question it's given that ,
[tex]\implies \dfrac{a}{b}=\dfrac{2}{5}[/tex]
[tex]\implies \dfrac{b}{c}=\dfrac{3}{8}[/tex]
And we need to find out the value of a/c .For that Multiply both of them , we have ;
[tex]\implies \dfrac{a}{b} \times\dfrac{b}{c}=\dfrac{2}{5}\times \dfrac{3}{8} \\\\\implies \dfrac{a}{c}= \dfrac{3}{20}[/tex]
Hence the required answer is 3/20 .
a boat leaves port at 13:52 and arrives at its destination 3 and a half hours later. at what time does the boat arrive
16:52
Hope this helps! :)
Find all the roots of the equation
[tex] {x}^{6} - 64 = 0[/tex]
Answer:
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Step-by-step explanation:
[tex]x^{6} -64 = 0\\(x^{3} -8)(x^{3} + 8) = 0\\ \\( x - 2) (x^{2} + 2x + 4)( x + 2) (x^{2} -2x + 4) = 0\\[/tex]
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i