Answers
[tex] \frac{3}{ \sqrt{5} - 2 } [/tex]
Rationalize the denominator by multiplying the numerator and denominator by the denominator. (Important: if the denominator has a minus sign, change to plus and vice versa)
[tex]⟹\frac{3 \times \sqrt{5 + 2} }{ (\sqrt{5} - 2 ) \times ( \sqrt{5} + 2) } [/tex]
[tex] ⟹ \frac{3 \sqrt{5} + 6 }{ \sqrt{25} + 2 \sqrt{5} - 2 \sqrt{5} - 4 } ⟹\frac{3 \sqrt{5} + 6 }{5 - 4} [/tex]
[tex] ⟹\frac{3 \sqrt{5} + 6}{1} ⟹3 \sqrt{5} + 6[/tex]
Problem 2.[tex] \frac{6 - \sqrt{12} }{ \sqrt{3} + \sqrt{10} } [/tex]
Rationalize the denominator.
[tex] ⟹\frac{(6 - \sqrt{12} ) \times ( \sqrt{3} - \sqrt{10} )}{ (\sqrt{3} + \sqrt{10} ) \times ( \sqrt{3} - \sqrt{10} } [/tex]
[tex]⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ \sqrt{9} - \sqrt{30} + \sqrt{30} - \sqrt{100} } [/tex]
[tex]⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{3 - 10} ⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ - 7} [/tex]
[tex] ⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + \sqrt{12 \times 10} }{ - 7}⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 4 \sqrt{3 \times 10} }{ - 7} [/tex]
[tex] ⟹ - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
Therefore:
1. [tex]3 \sqrt{5} + 6[/tex]
2. [tex] - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
I hope these helpRelated Questions
24. The relative frequency of getting a HEAD when tossing a coin is ⅜. How many HEADS would you expect if the coin is tossed 400 times?
Answers
The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.
Answers
The length and width is 32 inches and 10 inches.
Let us assume the width of rectangle be w. So, length of rectangle = 3w + 2. As per the known fact, the length and width of rectangle for perimeter is related as - Perimeter = 2 (length + width)
Keep the values in formula to find the value of width
84 = 2 (3w + 2 + w)
Performing addition in bracket
84 = 2 (4w + 2)
Performing multiplication
84 = 8w + 4
8w = 84 - 4
Performing subtraction
8w = 80
w = 80 ÷ 8
Performing division
w = 10 inches
Finding length now -
Length = 3×10 + 2
Length = 30 + 2
Length = 32 inches
Hence, the length and width is 32 inches and 10 inches.
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Which number sentence is not true?
A.|-20|<20
B.|9|=9
C.|-20|>|9|
D.|9|<|20|
Answers
Answer:
A
Step-by-step explanation:
that should be an equal sign
what is the sum of the number k and the number before it and the number after it?
Answers
Answer:
3k
Step-by-step explanation:
k+(k-1)+(k+1)=3k
Helppppppppp pleaseeeeee
Answers
Answer:
The answer is yes. Since there is no x^2
Solve 2(x - 3) ≥ -3 (-3 + x)
Answers
Answer:
x ≥ 3
Step-by-step explanation:
2(x - 3) ≥ -3(-3 + x)
2x - 6 ≥ 9 - 3x
5x - 6 ≥ 9
5x ≥ 15
x ≥ 3
Answer:
x ≥ 3
Step-by-step explanation:
write, calculate, divide both sides
Which expression is equivalent to the quotient of x and 8 times the difference of 19 and x?
Answers
Answer:
(x/8)(19 - x)
Step-by-step explanation:
The quotient is the answer to a division problem.
The difference is the answer to a subtraction problem.
"Times" indicates multiplication, which you could look at it as a link between the two functions, or quantities (them being the constants and variables sectioned off into parenthesis).
Evaluate |r| when r=−29.
Answers
Reason: The absolute value erases the negative sign.
Saying |-29| = 29 means that the number -29 is 29 units from 0 on the number line.
Answer: 29
Step-by-step explanation: The absolute value of -29 is 29. An absolute value is a number's distance from 0. -29 + 29 = 0, therefore the absolute value is 29.
Write the function whose graph is the graph of y=x³ +3, but is reflected about the y-axis.
Answers
Answer:
Reflected function is y = - x³ + 3
Step-by-step explanation:
When a function f(x) is reflected about the y-axis, the reflected function becomes g(x) = f(-x)
f(x) = x³ + 3
f(-x) = (-x)³ + 3 =-x³ + 3
i really need you guys help.
Answers
Answer:
y = - 8x + 3
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 = - 8x - 2 ← is in slope- intercept form
with slope m = - 8
• Parallel lines have equal slopes , then
y = - 8x + c ← is the partial equation of the parallel line
to find c substitute (- 0.5, 7 ) into the partial equation
7 = 4 + c ⇒ c = 7 - 4 = 3
y = - 8x + 3 ← equation of parallel line
Suppose the line tangent to the graph of fat x=3 is y= 4x+2 and suppose y=6x-1 is the line tangent to the graph of g at x = 3. Find the line tangent to the following curves at x = 3.
a. y = f(x)g(x)
b.y = f(x)/g(x)
Answers
The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
a)y=24x²+8x-2 at x=3.
b) y=(4x+2)/(6x-1) at x=3.
What is tangent?The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
Given
f at x=3 is y= 4x+2
g at x=3 is y=6x-1
f(3)= 4x+2 and g(3)=6x-1
y=f(x)g(x)
at x=3,
Solution for a:
y=f(3)g(3)
=(4x+2)(6x-1)
=24x²-4x+12x-2
=24x²+8x-2
So y=24x²+8x-2 at x=3.
Solution for b:
y=f(3)/g(3)
=(4x+2)/(6x-1)
So y=(4x+2)/(6x-1) at x=3.
Therefore y=24x²+8x-2 at x=3 for y = f(x)g(x) and y=(4x+2)/(6x-1) at x=3 for y = f(x)/g(x).
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Please help! Thank you
Answers
Determine which of the numbers below is a possible order of magnitude estimate of the
quantity described.
The weight of a grain of rice.
Select one:
O a. 0.000001 ounces
O b. 0.0006 ounces
OC.0.006 ounces
O d. 0.01 ounces
Answers
4m - t=m, for m
Solving for M
Answers
The solution of the given equation 4m - m - t = 0 for m is t/3.
According to the given question.
We have a linear equation in two variables i.e. 4m - t = m.
As we know that, an equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Since, we have to solve the given equation 4m - t = m for m. So, the solution of the equation 4m - t = m for m is given by
4m - t = m
⇒ 4m - m - t = 0 (subtracting m both the sides)
⇒ 3m - t = 0
⇒ 3m = t (adding t both the sides)
⇒ m = t/3.
Hence, the solution of the given equation 4m - m - t = 0 for m is t/3.
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[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
Answers
(A) (m,n) = g(n,m) for all positive integers m,n,
(B) (m,n + 1) = g(m + 1,n) for all positive integers m,n,
(D) (2m,2n) = (g(m,n))2 for all positive integers m,n
Explanation[tex] \rm f(m,n,p) = \sum \limits_{i = 0}^{p} {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \dfrac{(n + i)!}{p!(n - p + i)!} \times \dfrac{(n + p)!}{(p - i)!(n + i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!n!} \times \dfrac{n!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex] \rm f(m,n,p) = {}^{n + p} C_{p}{}^{m + n} C_{p}[/tex]
[tex] \rm \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} = {}^{m + n} C_{p}[/tex]
Now,
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} [/tex]
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} {}^{m + n} C_{p}[/tex]
[tex] \rm g (m,n) = {2}^{m + n} [/tex]
[tex] \rm(A) \: g(m,n) = q(n,m)[/tex]
[tex] \rm(B) \: g(m,n + 1) = {2}^{m + n + 1} [/tex]
[tex] \rm g(m + n,n ) = {2}^{m + 1 + n} [/tex]
[tex] \rm(D) \: g(2m,2n) = {2}^{2m + 2n} [/tex]
[tex] = \rm( {2}^{m + n} {)}^{2} [/tex]
[tex] = \rm(g(m,n)) {}^{2} [/tex]
Suppose Albers Elementary School has 76 teachers and Bothel Elementary School has 24 teachers. If 3 teachers teach at both Albers and Bothel, compute the total number of teachers employed at Albers and Bothel combined.
Answers
The number of teachers that work in both schools is 97.
What is an addition?The addition is a way of combining things and counting them together as one large group.
We have,
Number of teachers in Alberts Elementary school = 76
Number of teachers in Bothel Elementary school = 24
Number of teachers that work in both schools = 3
The number of teachers that work in both schools:
= 76 + 24 - 3
We are subtracting 3 from the total because 3 teachers that work in both schools have been added twice.
= 100 - 3
= 97
Thus the number of teachers that work in both schools is 97.
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Determine whether the relation is a function. Explain. { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) } Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the elements –2, 3, 4, and 5 are in both the domain and the range. cross out D) No; the element 5 occurs twice in the range.
Answers
Yes; for each element of the domain, there is only one element of the range.
Function and relationsFor a relation in coordinate form to be a function, there is must nor be repetition in the value of its coordinate.
Given the following relation as shown { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) }, since there is no repetition in its domain values, hence the relation is a function.
We can conclude therefore that Yes; for each element of the domain, there is only one element of the range.
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The area of a rectangular barn is 119 square feet. its length is 10 feet longer than the width. find the length and width of the wall of the barn.
Answers
The length of the field with area 119 square feet is 17 feet and the width of the feet is 7 feet.
The area is the total region or space in two dimension that is covered by a figure , surface or object. Area of a rectangle is calculated by the product of its length and width.
A rectangle has 4 sides where each pair of opposite side is equal .The length of a rectangle is normally the longer side and the width defines the shorter side.
Given the area of the barn is 119 square feet.
Let us consider the width of the barn to be x feet. As the length is 10 feet longer than the width then we will find the length to be ( x +10 ) feet.
Area = length × width
or, 119 = x × (x+10)
or, 119 = x² +10x
or, x² +10x - 119=0
Now we will solve the quadratic equation thus formed by middle term-factorization method:
or, x² +17x - 7x - 119 = 0
or, x ( x + 17 ) - 7 ( x + 17) = 0
or, ( x + 17 ) ( x - 7 ) = 0
Now either x + 17 = 0 or x - 7 =0
Therefore either x = 7
or, x = -17 (The width cannot be a negative value)
∴Width = 7 feet and length = 7 + 10 = 17 feet.
Therefore the length of the field is 17 feet and the width of the feet is 7 feet.
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A shredding machine can shred 20 sheets of paper in 14 seconds. The bin has room
for 1000 sheets of shredded paper.
How long will it take to fill the bin if the machine has to stop for 3 minutes after every
200 sheets to prevent overheating?
Answers
Answer:
See below
Step-by-step explanation:
Rate = 20 sheets / 14 seconds = 10/7 sheet / sec
every 200 sheets is 4 rest periods = 12 minutes
1000 sheets / (10/7 sheet/ sec) + 12 min
700 seconds + 12 minutes
= 700 seconds + 720 seconds = 1420 seconds = 23 min 40 sec
Kelly wants to find out if the townspeople would be in favor of creating a local dog park. she pulls an equal number of people from several age groups and from different areas of town. Is this study likely to yield valid results? Explain.
Answers
Answer: Yes
Step-by-step explanation: Kelly's results are likely to be correct mainly because she pulled votes from several different age groups. The fact that she asked several age groups whether or not they would be in favor of creating a local dog park shows that her results are likely to yield valid results.
Which of the following values are solutions to the given
equation?
|x + 2| = 5
Be sure to select ALL numbers which are solutions.
(Select all that apply.)
x = -5
x = -2
x = 3
x = -7
x = -3
x = 7
Answers
Answer:
X= -7
X = 3
Step-by-step explanation:
| x + 2| = 5
|-7 + 2| = 5
|-5| = 5
5 = 5
|x + 2| = 5
|3 + 2| = 5
|5| = 5
5 = 5
X= -7
X = 3
Let f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4. Find the rule for the function.
Answers
The rule f ( x ) - g ( x ) is given as x^3 - x^2 + 18
Given data
f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4
How to find f(x) - g(x)f(x) - g(x) = ( x3 + 10 ) - ( x2 - 8 )
= ( x3 + 10 ) - ( x2 - 8 )
opening the parenthesis gives
= x3 + 10 - x2 + 8
collecting like terms gives
= x3 - x2 + 18
Hence we can say that f(x) - g(x) = x3 - x2 + 18
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complete question
The complete question is attached
1. If you deposit P3,000 in BPI bank account that pays 0.125% interest annually, how much will be in your account after 3 years?
2. If you deposit money today in an account that pays 10.5% annual interest, how long will it take to double your money?
3. What is the future value of a 3% 7-year ordinary annuity that pays20,000 each year?
4. (refer to #3) if this were an annuity due, what would its future value be?
5. I want to retire in 20 years. I currently have P 1,250,000 and I will need P20 million at retirement. What annual interest rate must I earn to reach my goal, assuming this is my only investment fund?
Round off your answer up to four decimal places.
Answers
The amount that would be in the account kept with BPI bank in 3 years is P3,011.2640
It would 6.9422 years for the deposit to double if interest rate is 10,5%
What is future value of immediate amount?
The future value of deposit today in 3 years means its future equivalent when the amount has earned interest over the 3 years period
FV=PV*(1+r)^N
FV=future value after 3 years=unknown
PV=immediate deposit=3,000
r=annual interest rate=0.125%
N=number of years that the deposit lasted=3
FV=3000*(1+0.125%)^3
FV=P3,011.2640
Time taken to double:
FV=future value=3000*2=6000
PV=3000
r=annual interest rate=10.5%
N=number of years that it takes initial deposit to double=unknown
6000=3000*(1+10.5%)^N
6000/3000=(1.105)^N
2=(1.105)^N
take log of both sides
ln(2)=N*ln(1.105)
N=ln(2)/ln(1.105)
N=6.9422 years
Annuity:
FV=PMT*(1+r)^N-1/r
FV=future value of annuity=unknown
PMT=annual payment=20000
r=interest rate=3%
N=number of annual payments=7
FV=20000*(1+3%)^7-1/7%
FV= 153,249.2436
FV=PMT*(1+r)^N-1/r*(1+r)
FV=20000*(1+3%)^7-1/7%*(1+7%)
FV= 157,846.7209
20,000,000=1,250,000*(1+r)^20
20,000,000/1,250,000=(1+r)^20
16=(1+r)^20
(16)^1=(1+r)^20
divide indexes on both sides by 20
(16)^(1/20)=1+r
r=(16)^(1/20)-1
r=14.8698%
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Does the equation 2(3X + 8) equal 2X +16+ 4X have a solution
Answers
infinitely many solutions
Example
Simplify left side using distributive property to 6x+16. Combine like terms (2x and 4x) on the right side to 6x+16. Both sides simplify to the same expression (left side = right side) so there are infinitely many solutions. You can plug in any real number for x and the left side will always equal the right side.
An object is moving at a speed of 360 kilometers per hour. Express this speed in miles per day. Round your answer to the nearest whole number.
Answers
Amount of Amy's pocket money each day is 3 times as much as the pocket money of Flora's. And the amount of Paul's pocket money is $7 more than Amy's. If they have $980 of pocket money each week, how much pocket money does Paul have each day?
Answers
Answer:-
Paul has $64 pocket money each day.
Explanantion:-
Let amy ,flora and Paul 's pocket money be x,y and z respectively.
So,
By the question :
x = 3y
So, y = x/3 - eqn i
z = 7 + x - eqn ii
7(x + y + z) = 980
x + y + z = 140
Now,
x + y+ z = 140
x + x/3 + 7 + x = 140
or, 2x + x/3 = 133
or, 6x + x = 399
so, x = 399/7
so, x = $57
Now,
z = 7 + x
= 7 + $57
= $64
Give the slope of a line that is perpendicular to the line 2x+2y=1 .
-1
Answers
Answer:
- 1
Step-by-step explanation:
2x + 2y = 1
=> 2y = - 2x + 1
=> y = - x + 1
=> Slope = - 1
solve the following: The quotient of c and −19 is 38.
Answers
Answer:
your quotient should be 57
so you would start with 38 and you gotta think hmm
C+(-19)=38
okay so you would change -19 to positive 19
and then add that to 38
and then you would get 57
so therefore C=57
so
57+(-19)=38
Answer:
57
Step-by-step explanation:
Explain how to graph the line with the equation y = 3/4x - 5
Answers
Answer:
A graphing calculator can help you.
Here is the graph, it is in the photo.
Saul wants to bike 48 kilometers to taste some really good mangoes.
1. Write an equation that represents how many hours (t) the48km start text, k, m, end text trip will take if Saul bikes at a constant rate of r kilometers per hour.
2. How many hours will the48km48, end text trip take if Saul bikes at a constant rate of 20 kilometers per hour?
hours
Answers
Answer:
[tex]\textsf{1)} \quad t=\dfrac{48}{r}[/tex]
[tex]\textsf{2)} \quad \sf 2.4\:hours=2\:hours\:24\:minutes[/tex]
Step-by-step explanation:
Part 1[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]
Given:
Time = t hoursDistance = 48 kmSpeed = r km/hSubstitute the given values into the formula:
[tex]\implies t=\dfrac{48}{r}[/tex]
Part 2Substitute r = 20 km/h into the derived equation from part 1 and solve for t:
[tex]\implies t=\dfrac{48}{20}=2.4\: \sf hours[/tex]
Note: 2.4 hours = 2 hours 24 minutes
Answer: 2.4 hours
Step-by-step explanation: t=time
r=rate so question one is equal to t=48/r
then question 2 is 48/20=2.4