Answer:
It just makes doing things (like adding and subtracting other numbers) easier if the denominator is a real number. Other than that we just do it out of tradition
This step is done to make the denominator go from a complex number in the form a+bi into a purely real number in the form a^2+b^2 (where 'a' and b are any real numbers).
This is because multiplying a+bi with its conjugate a-bi leads to the following steps
(a+bi)(a-bi)
(a)^2 - (bi)^2 ... difference of squares
a^2 - b^2*i^2
a^2 - b^2*(-1) .... recall that i^2 = -1
a^2 + b^2
----------------
So for example, if your denominator was 2+3i, then you'd multiply that by the conjugate 2-3i and you'd end up with the final denominator of 2^2+3^2 = 4+9 = 13. In this case, a = 2 and b = 3.
Note: make sure to multiply both top and bottom by a-bi (not just the denominator).
Simplify
(2m^4)^4*-n^5
this is the last questions but I'm confused
Answer:
-16m^16 n^5
Step-by-step explanation:
(2m^4)^4*-n^5
= 2^4*m^16*(-n^5)
= 16 m^16 * (-n^5)
= -16m^16 n^5
hopefully this will help
Remember the rule
(a^m)^n=a^mnPLEASE HELP! I’ll DO BRAINLIEST!!!!! Plss
For f(x) = 3x + 1 and g(x) = x ^ 2 - 6 , find (fg)(x)
A) 4x^2-6x-8
B) 3x^3+x^2-6x-6
C) 3x^2-17
D) 3x^3+x^2-18x-6
9514 1404 393
Answer:
D) 3x^3 +x^2 -18x -6
Step-by-step explanation:
The distributive property applies.
(f·g)(x) = f(x)·g(x) = (3x +1)(x^2 -6) = 3x(x^2 -6) +1(x^2 -6)
(f·g)(x) = 3x^3 -18x +x^2 -6 . . . . . eliminate parentheses
(f·g)(x) = 3x^3 +x^2 -18x -6 . . . . put in standard form
solve the equation:
[tex]4 \sqrt{3 - \frac{1}{x} } - \sqrt{ \frac{x}{3x - 1} } = 3[/tex]
Are the solutions of the equation solutions of
[tex] \frac{(1 - 2x)^{2} \times (x^{2} - 9) }{ -{x}^{2} - x + 6} \geqslant 0[/tex]
?
Answer:
Step-by-step explanation:
[tex]4\sqrt{3-\frac{1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\4\sqrt{\frac{3x-1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\\\put ~\sqrt{\frac{3x-1}{x}} =a\\4a-\frac{1}{a} =3\\4a^2-1-3a=0\\4a^2-4a+1a-1=0\\4a(a-1)+1(a-1)=0\\(a-1)(4a+1)=0\\a=1,-\frac{1}{4}\\[/tex]
[tex]\sqrt{\frac{3x-1}{x} } =1\\3x-1=x\\3x-x=1\\2x=1\\x=\frac{1}{2}[/tex]
when a=-1/4
[tex]\sqrt{\frac{3x-1}{x} } =-\frac{1}{4} \\[/tex]
[tex]\frac{3x-1}{x} =\frac{1}{16} \\48x-16=x\\47x=16\\x=\frac{16}{47}[/tex]
[tex]\frac{(1-2x)^2 \times (x^2-9)}{-x^2-x+6} \geq 0,\\both ~numerator ~and~denominator ~are~of~same~sign.\\\frac{(1-2x)^2(x^2-9)}{-x^2-3x+2x+6} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{-x(x+3)+2(x+3)} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{(x+3)(-x+2)} \geq 0\\(1-2x)^2\geq 0~(always)\\x\neq -3\\case.~1.\\both~numerator~and~denominator >0\\\frac{x-3}{-x+2} \geq 0\\x-3\geq 0\\x\geq 3\\-x+2> 0\\-x>-2\\x<2\\so~ solution~ is~ (-\infty,-3)U(-3,2)U[3,\infty)[/tex]
case 2.
both numerator and denominator are negative.
[tex]x-3\leq 0\\x\leq 3\\-x+2\leq 0\\-x\leq -2\\x\geq 2\\solution~is~(-\infty,-3)U(-3,3]U[2,\infty)[/tex]
Pleaseee someone help meeee
Answer: Quadrant 1 because both numbers are Positive
Hope this helps...
Have a great day
hted by f(x) = 4
4.0
3
The type of function
represented
does the great pyramid of giza fit the golden ratio? why or why not?
Step-by-step explanation:
hope it helps thanks
pls mark me brainliest
Please answer the question no photos and no words just plain working out
Correct answer will get brainliest
Answer:
Step-by-step explanation:
volume of a prism =base area * length
35 = base area * 7
35/7 = base area
5 cm^2 =base area
base area= [tex]\frac{1}{2}*b*h[/tex]
5=[tex]\frac{1}{2}*4*h[/tex]
5=2*h
5/2=h
2.5=h
Can someone help me? It's urgent and thank you!
Answer:
15.2%
Step-by-step explanation:
There are 12 marbles in total and there are 5 red marbles, so the probability of getting a red marble is 5/12. There are now 11 marbles and there are 4 blue marbles. So the probability of getting a blue marble is 4/11.
You multiply these 2 values together.
5/12 * 4/11 = 20/132 = 0.1515
This is about 15.2%
Answer:
option b : 15.2 %
Step-by-step explanation:
5 Red , 4 Blue, 3 Yellow
Total balls = 12
[tex]Probability \ of \ choosing \ red = \frac{5C_1}{12C_1} = \frac{5}{12}\\\\Probability \ of \ choosing \ blue \ without \ replacement = \frac{4C_1}{11C_1} = \frac{4}{11}\\\\Probability \ of \ red \ and \ then \ blue = \frac{5}{12} \times \frac{4}{11} = 0.1515\\\\Probability \ in \ percentage = 0.1515 \times 100 = 15.15 = 15.2 \%[/tex]
Suppose that QRS is isosceles with base q r. Suppose also that m q equals (5x - 14(degrees and Mr equals (4x - 2)degree
PLEASE HELP ME
Answer:
<S= 88degrees
<Q = <R = 46degrees
Step-by-step explanation:
Since the base angles of the isosceles triangle are equal hence;
<Q = <R
5x - 14 = 4x -2
5x - 4x = -2 +1 4
x = -2 + 14
x = 12
Since <Q = 5x - 14
<Q = 5(12) - 14
<Q = 60 - 14
<Q = 46degrees
Also <Q = <R = 46degrees
Similarly; <S + <Q + <R =180
<S +46 + 46 = 180
<+92 = 180
<S = 180 - 92
<S= 88degrees
In a study conducted at a large long-term care facility, two data collectors examined 56 pressure ulcers on 40 different subjects. The examinations were independently performed on the same day. A comparison of the results indicated that the data collectors scored 54 of the 56 (correlation coefficient 0.96) pressure ulcers identically using the Braden Scale for pressure ulcer assessment. What can be determined from this finding?
Answer:
Interrater reliability between the two data collectors was high
Step-by-step explanation:
Explanation-
Interrater reliability is the consistency of observations between two or more observers. An Agreement of 54 out of 56 scores would indicate a high level of interrater reliability. The data collection method was appropriate for pressure ulcer risk assessment. The risk assessments did not have to be done by both evaluators at the same time.ima give branliest if you answer this correctly
Answer:
Step-by-step explanation:
It 1 2
how do -12.5and -10.5 compare ? choose the correct symbol
Answer:
<
Step-by-step explanation:
-10.5 is close to zero than -12.5 therefore it is greater. (Negatives are different than positives because the close they are to zero, the bigger they actually are.)
Hope this helps!
:)
Three times one number added to five times another number is 54. The second number is two less than the first. Use a system of equations to find the numbers
Answer:
8 and 6
Step-by-step explanation:
If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.
You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.
The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.
Next, we add 10 to both sides. This gives 8x=64.
From there, we isolate the x by dividing both sides by 8, giving x=8.
To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).
This comes to y=8-2, therefore y=6.
**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!
A sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. Each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. Which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?
A. t = s - 18
10t = 12s + 32
B. s = t - 18
12s = 10t + 32
C. s = t - 18
10s = 12t + 32
D. t = s - 18
12t = 10s + 32
Answer:
[tex]\text{B .}\\\begin{cases}s=t-18, \\12s=10t+32\end{cases}[/tex]
Step-by-step explanation:
The each issue of the sports magazine, [tex]s[/tex], has 18 fewer pages than each issue of the technology magazine, [tex]t[/tex], we have equation [tex]s=t-18[/tex]. This eliminates answer choices A and D.
The second equation can be written from the fact that the total number of pages in all the sports magazines, [tex]12s[/tex], is 32 more than the total number of pages in all the technology magazines, [tex]10t[/tex]. Thus, we have equation [tex]12s=10t+32[/tex], eliminating answer choice C and leaving answer choice [tex]\boxed{\text{B .}\\\begin{cases}s=t-18, \\12s=10t+32\end{cases}}[/tex]
can u help me plzx part 2
Surface area hw help pls
Answer:
Find the perimeter first then the are
Step-by-step explanation:
Use the Venn diagram to calculate probabilities.
Circles A, B, and C overlap. Circle A contains 12, circle B contains 11, and circle C contains 4. The overlap of A and B contains 5, the overlap of B and C contains 3, and the overlap of C and A contains 6. The overlap of the 3 circles contains 8.
Which probabilities are correct? Select two options.
P(A|C) = Two-thirds
P(C|B) = StartFraction 8 Over 27 EndFraction
P(A) = StartFraction 31 Over 59 EndFraction
P(C) = Three-sevenths
P(B|A) = StartFraction 13 Over 27 EndFraction
Answer:
The first one
The fourth one
Step-by-step explanation:
Draw a venn diagram (see picture)
A|C= (A∩C)/C
(6+8)/(6+8+3+4)= 2/3
C|B= (C∩B)/B
(8+3)/(11+5+8+3)= 11/27
A=(12+5+8+6)/(11+5+8+3+4+6+12) = 31/49
C= (4+6+8+3)/(12+5+11+6+8+3+4)= 3/7
P(B|A)= (B∩A)/A
(5+8)/(12+5+6+8) = 13/31
Answer:
A and D
Step-by-step explanation:
edge 2021
If x is a positive integer, for how many different values of x is StartRoot StartFraction 48 Over x EndFraction EndRoot a whole number? 2 3 6 10
Answer:
3
Step-by-step explanation:
According To the Question,
Given that, 'x' is a positive integer . And We have to find the number of different values of 'x', So that the value of [tex]\sqrt{\frac{48}{x} }[/tex] is a Whole number.Then First, we have to find those values of 'x' for which the given fraction is a square.
We Know, All the factors of 48 are {1,2,3,4,6,8,12,16,24,48} .
Now, From the above factors, only (3,12 & 48) can give us a square number.
Therefore,
If x=3, Then [tex]\sqrt{\frac{48}{3} } = \sqrt{16}[/tex] ⇒ 4If, x=12, Then [tex]\sqrt{\frac{48}{12} } = \sqrt{4}[/tex] ⇒ 2If, x=48, Then [tex]\sqrt{\frac{48}{48} } = \sqrt{1}[/tex] ⇒ 1Thus, There are 3 whole numbers (3,12,48).
Answer:
bbbbbbbbbbbbbbbbb
Step-by-step explanation:
A factory produces 10,000 boxes of granola bars a day. Each box contains 12 bars. If each bar contains 135 calories, how many calories are contained in a box? a. 1,350,000 calories c. 1,620 calories b. 11.25 calories d. 833 calories
Answer:
1620
Step-by-step explanation:
You don’t use the 10,000.
12 bars/box x 135 calories/box=1,620 per box
Megan is shopping at a store that sells jewelry, scarves, and purses. The cost of all of the items at the store includes tax. Megan buys 3 bracelets and 3 necklaces. Each bracelet costs $5. Megan pays the clerk $40 and gets $4 change. What is the cost, in dollars, of one necklace?
Answer: 7$
Step-by-step explanation: 40-4= 36 | 3x5=15 | 36-15=21 | 21/3=7
Need answers ASAP I don’t wanna go to summer school
Answer:
? = A) 4
Step-by-step explanation:
If we notice line FG and QR are similar.
FG = 24 and QR = 8. The relationship between the the two sides is that FG is 3 times more than QR ---> 8 x 3 = 24.
This relationship is true for the rest of the triangles since they are stated to be similar:
FG = 3(QR)
24 = 3(8)
EG = 3(6)
18 = 3(6)
Finding PQ:
EF = 3(PQ)
12 = 3(?)
? = 4
Therefore, the unknown side is 4.
PLEASE HELP ITS TIMED LITTERALY IM BEGGING :(( 32 points WITH BRAINLIEST!!
Answer:
I think it might be C but I'm not 100% sure!
Step-by-step explanation:
You have to find a line of best fit (a line through the dots) but it's kind of tricky to do that so I think it's probably C but it could also be A. Just use your best judgement on this one!
Answer:
C
Step-by-step explanation:
If you graph all 4 and plot all 4 of the point, line c is the most accurate and lines up the best out of all 4.
Please can someone help me with this question?
Answer:
a = 16 π cm² Exact answer
a = 50.24 cm² Decimal approximation
Step-by-step explanation:
Radius of the circle
16/2 = 8
Area of the circle
a = πr²
a = π4²
a = 16 π cm² Exact answer
a = 16 * 3.14
a = 50.24 cm² Decimal approximation
i need help on this i don't understand this. plz help with steps plz. thanks!!
Please give me the answer and show me how you solved it
Answer:
Step-by-step explanation:
Whenever you're simplifying radicals and there are numbers involved, ALWAYS find the prime factorization of the number. It will always help...Promise! 8 = 2 * 2 * 2 or 2³. So we can rewrite that radical as
[tex]\sqrt[3]{2^3}[/tex] Cubing "undoes" a cubed root, so the answer is 2
Answer: the answer is 2
help please, kind of confused
Answer:
Step-by-step explanation:
Yikes. This is quite a doozy, so pay attention. We will begin by factoring by grouping. Group the first 2 terms together into a set of parenthesis, and likewise with the last 2 terms:
[tex](2d^4+6d^3)-(18d^2-54d)[/tex] and factor out what's common in each set of parenthesis:
[tex]2d^3(d+3)-18d(d+3)[/tex]. Now you can what's common is the (d + 3), so factor that out now:
[tex](d+3)(2d^3-18d)[/tex] BUT in that second set of parenthesis, we can still find things common in both terms, so we continue to factor that set of parenthesis, carrying with us the (d + 3):
[tex](d+3)2d(d^2-9)[/tex] BUT that second set of parenthesis is the difference of perfect squares, so we continue factoring, carrying with us all the other stuff we have already factored:
[tex](d+3)2d(d+3)(d-3)[/tex]. That's completely factored, but it's not completely simplified. Notice we have 2 terms that are identical: (d + 3):
[tex]2d(d+3)^2(d-3)[/tex] is the completely factored and simplified answer, choice 3)
V is the midpoint of UW
and X is the midpoint of TW
If TU=p+14 and VX=p–6, what is the value of p?
Answer:
p = 2
Step-by-step explanation:
2VX = TU
2(p - 6) = p + 14
2p - 12 = p + 14
p = 2
Evaluate the expression when a=3 and b=-6.
- 3a + b
Answer:
-15
Step-by-step explanation:
a = 3 and b = -6.
- 3a + b
Substitute for a and b
adding negatives is subtracting
-3(3) - 6
Multiply
-9 - 6
add
-15
X + 24 + 4 + 63 = 180
Answer:
x=89
Step-by-step explanation:
180-91=89
Answer:
x = 89
Step-by-step explanation:
x + 24 + 4 + 63 = 180
x + 91 = 180
x = 89
The ratio of seventh graders to eighth graders at junior high school is 9:10. If there is 90 eighth graders, how many seventh graders would be there?
Answer:
81
Step-by-step explanation:
To find the base unit of the ration, divide 90 by 10, which is 9. Then multiply 9 (the base unit) by 9 (the ratio of the seventh graders) and that equals 81
