Answer:
√45 =6.71
Step-by-step explanation:
[tex]\sqrt{45} = 6.708203932\\\\= 6.71[/tex]
Evaluate the geometric series or state that it diverges. sigma^infinity_k=0(8/9)^k Select the correct choice below and, if necessary, fill in the answer box to complete your choice. sigma^infinity_k=0(8/9)^k The series diverges.
The series converges, since |8/9| = 8/9 < 1.
Let [tex]S_n[/tex] denote the n-th partial sum of the series,
[tex]S_n=\displaystyle\sum_{k=0}^n\left(\frac89\right)^k[/tex]
[tex]S_n=1+\dfrac89+\left(\dfrac89\right)^2+\cdots+\left(\dfrac89\right)^n[/tex]
Multiply both sides by 8/9:
[tex]\dfrac89S_n=\dfrac89+\left(\dfrac89\right)^2+\left(\dfrac89\right)^3+\cdots+\left(\dfrac89\right)^{n+1}[/tex]
Subtract this from [tex]S_n[/tex] to eliminate all but the first term in
[tex]S_n-\dfrac89S_n=1-\left(\dfrac89\right)^{n+1}[/tex]
Solve for [tex]S_n[/tex]:
[tex]\dfrac19S_n=1-\left(\dfrac89\right)^{n+1}[/tex]
[tex]S_n=9-9\left(\dfrac89\right)^{n+1}[/tex]
As [tex]n\to\infty[/tex], the exponential term vanishes, so that
[tex]\displaystyle\lim_{n\to\infty}S_n=\sum_{k=0}^\infty\left(\frac89\right)^k=\boxed{9}[/tex]
3/4 and 1/6 whats the least common denomiator
Answer:
The lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of fractions. It is the smallest positive integer that is a multiple of each denominator in the set. Fractions write with fraction bar / like 3/4 .
Step-by-step explanation:
A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is a Jack or a Club.
Answer:
3/13 or 23.1%
Step-by-step explanation:
Consider the following geometry problems in 3-space Enter T or F depending on whether the statement is true or false.1. Two planes parallel to a third plane are parallel 2. Two lines parallel to a plane are parallel 3. Two lines orthogonal to a third line are parallel 4. Two lines parallel to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines orthogonal to a plane are parallel 7. Two lines either intersect or are parallel 8. Two planes either intersect or are parallel 9. Two planes orthogonal to a line are parallel 10. A plane and a line either intersect or are parallel 11.Two planes orthogonal to a third plane are parallel
Answer:
Step-by-step explanation:
1) Two planes parallel to a third plane are parallel - True
2) Two lines parallel to a plane are parallel - False
3) Two lines orthogonal to a third line are parallel - False
4) Two lines parallel to a third line are parallel - True
5) Two planes parallel to a line are parallel - False
6) Two lines orthogonal to a plane are parallel - True
7) Two lines either intersect or are parallel - False
8) Two planes either intersect or are parallel - True
9) Two planes orthogonal to a line are parallel - True
10) A plane and a line either intersect or are parallel - True
11) Two planes orthogonal to a third plane are parallel - False
Jamie makes plates and bowls. She needs to ship 48 plates and 54 bowls to a store. She wants to ship the same number of items in each box. Plates and bowls are shipped separately. A.What is the greatest number of items she can ship in each box?
Answer: 6
Step-by-step explanation:
Given, Jamie needs to ship 48 plates and 54 bowls to a store.
If she wants to ship the same number of items in each box such that plates and bowls are shipped separately. .
then the greatest number of items she can ship in each box = GCD (48,54)
[GCD = Greatest common divisor]
Prime factorization of both numbers:
48 = 2 x 2 x 2 x 2 x 3
54 = 2 x 3 x 3 x 3
GCD (48,54)= 2 x 3 = 6
Hence, the greatest number of items she can ship in each box =6
Answer:6
Step-by-step explanation:
So here's the problem writen down.
48 = 2 x 2 x 2 x 2 x 3
54 = 2 x 3 x 3 x 3
GCD (48,54)= 2 x 3 = 6
What is the value of X
Answer:
x = 7
Step-by-step explanation:
The 2 angles add up to 180°, as the definition of a line.
8x - 46 + 10x - 8 = 180
18x - 54 = 180
18x = 126
x = 7
How do we know if the line y=x has a postive slope?
Lenght of the room is 20ft and the width is 12ft what is the perimeter
Answer:
P=2(a+b)
=2(20+12)
=2×32
=64 feet
Step-by-step explanation:
The perimeter would equal 2l + 2w, which would lend to the equation 2(20) + 2(12), or 20 + 20 + 12 + 12 = perimeter.
Answer:
64ft.
Step-by-step explanation:
(20ft+20ft)+(12ft+12)= 64ft
Is the square root of 42 rational or irrational? Explain
☽------------❀-------------☾
Hi there!
~
[tex]\sqrt{42}[/tex] ≈ [tex]6.4807406984087...[/tex]
So [tex]\sqrt{42}[/tex] is irrational (since the decimal portion doesn't terminate or repeat)
❀Hope this helped you!❀
☽------------❀-------------☾
(The other person copied there answer from google!)
Which two operations are needed to write the expression that represents “eight more than the product of a number and two”?
Answer:
c
Step-by-step explanation:
What is the defining quality of an organic compound? It must be comprised entirely of carbon and hydrogen atoms. It must be part of a living being. It must contain carbon. It must be in solid form.
Answer:
It must contain carbon.
Step-by-step explanation:
get it right on test.
Answer: it must contain Carbon.
Step-by-step explanation: If a compound doesn’t contain carbon, it isn’t an organic compound
The formula rho equals m over V, where ρ = density, m = mass, and V = volume, is used to calculate density. Solve this formula for m.
Answer: A
Step-by-step explanation:
The formula for mass , m= ρ* V
What is Density?Density, mass of a unit volume of a material substance.
The formula for density is d = M/V, where d is density, M is mass, and V is volume.
Given:
ρ = m/V
where
ρ = density, m = mass, and V = volume.
So, for solving for m we have
m= ρ* V
Hence, formula for mass , m= ρ* V.
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Silas wrote a number as a fraction with an integer in both
the numerator and the denominator. Which of the following
statements correctly describes the number?
Select one:
It could be either rational or irrational
o
It must be rational and not irrational
o
It must be irrational and not rational,
It could be neither rational nor irrational
Answer:it must be irrational and not rational
Step-by-step explanation:
What percent of 52 is 12 ? Round your answer to the nearest tenth .
Approximately 23. It is simple, but if you are asking because you don't know how to find it, divide the smaller number by the bigger number. Then, multiply this number by 100.
Hope I helped!
Greg is saving to buy a tablet that costs $235. He already has $25 saved up. Each week, Greg earns $15 babysitting and $25 as a cashier, but he spends $10 on lunches. Write and solve an equation to find how many weeks it will take Greg to have enough money saved to buy the tablet.
Answer:
235=30x-25
Step-by-step explanation:
235+25=30x-25+25
260=30x
260/30=30x/30
x=8.66 or 9 weeks
The equation is 30x + 25 = 235. And the number of weeks will be 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Greg is saving to purchase a tablet that costs $235. He as of now has $25 set aside. Every week, Greg procures $15 looking after children and $25 as a clerk, however, he burns through $10 on snacks.
Let x be the number of weeks. Then the equation is given as,
25x + 15x - 10x + 25 = 235
Simplify the equation, then the number of weeks is given as,
25x + 15x - 10x + 25 = 235
30x = 235 - 25
30x = 210
x = 210 / 30
x = 7 weeks
The equation is 30x + 25 = 235. And the number of weeks will be 7.
More about the Algebra link is given below.
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§
A scuba diver is 4 2/3 feet below the
surface of the water. She then dives another 2 1/2 feet. How far below the surface of the water is the scuba diver.
Answer:
-7 1/6
Step-by-step explanation:
it wants to know how far BELOW the sea level she is so you take both of the factions and add them -4 2/3 + -2 1/2 = -7 1/6
Answer this fast and I’ll make you Brainly!!!
Answer:
this is for the num 3 questions and above cuz im only in 4th grade and idk what this is: okay, 3: 6 times C. 4: x minus 1. 5. tdivided by 2. 6: 3 times t subtract 4
Step-by-step explanation:
Evaluate 2 – 10+ 8- (-2).
Steps to solve:
2 - 10 + 8 - (-2)
~Simplify
2 - 10 + 8 + 2
~Subtract
-8 + 8 + 2
~Add
0 + 2
~Add
2
Best of Luck!
Answer:
2
Step-by-step explanation:
first you do this first (-2) then the 2 - is gone then 10 + 8- is 2
what type of numbers can be written as a fraction p/q, where p and q are integers and q is not equal to zero
Answer:
rational number
Step-by-step explanation:
The description is of the set of numbers called the "rational numbers."
A rational number is a fraction of integers that when divided, you either get an integer, a terminating decimal, or a non-terminating, repeating decimal.
Classify 2√by the subsets of the real numbers to which it belongs.
Select all that apply.
Natural
Rational
Real
Whole
Integer
Irrational
Glados
spent the day at the mall, First, she bought
three bikes for $10 each. Later, she found 22
dollar bills. Write the total change
an integer.
to Glado's
funds as an integer ?
Answer:
3(10)+30
(-30) (the amount she lost) +22 (the amount she gained)= -8
Glados lost 8 dollars while at the mall.
Six machines can polish 42 tables in one hour. What is the ratio of the number of machines to the number of tables polished in one hour?
64.8 divided by 3.6
Answer:
The answer is 18.
Step-by-step explanation:
Putting it straight into the calculator as you see it gives you 18.
Answer:
18
Step-by-step explanation:
Hope this helps : )
Please help quickly!!:)) Appreciate it x+y=6 y+4=x Choices: (11/2, 1/2) (5, 1) (21/2, 11/2) (1, 5)
Answer:
B: (5,1)
Step-by-step explanation:
So we have the system of equations:
[tex]x+y=6\text{ and}\\y+4=x[/tex]
We can solve this system using substitution.
Substitute the second equation into the first. Use x. So:
[tex](y+4)+y=6[/tex]
Combine like terms:
[tex]2y+4=6[/tex]
Subtract 4 from both sides:
[tex]2y=2[/tex]
Divide both sides by 2:
[tex]y=1[/tex]
So, the value of y is 1.
To find x, substitute this back into the second equation:
[tex]y+4=x[/tex]
Substitute 1 for y:
[tex]1+4=x[/tex]
Add:
[tex]x=5[/tex]
Therefore, our answer is (5,1).
The answer is B.
And we're done!
the function y=-x^2+2x-3 has a value of
Find the value of x by factoring.
What multiplies to -3 and adds to 2?
[tex]y=(x+3)(x-1)[/tex]
Meaning that the x-intercepts are at (-3,0) and (1,0).
Hope this helps.
頑張って!
(f - 5)(-2) + 111
Need help
The Answer is : -2f+121
Graph y = – 3x + 6 using the interactive graphing calculator. Which of the following statements are true?
The line increases from left to right.
The line crosses the x-axis at –3.
The line crosses the y-axis at 6.
As the input increases, the output decreases.
The line does not enter quadrant II at all.
The point (3.5, –4.5) lies on
The correct statement is line crosses the y-axis at 6 and the input increases, the output decreases.
It is required to choose the following statements are true.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers
Given:
The given line equation are
y=-3x+6
We have to find the which statement is true.
The line crosses the y-axis at 6.
As the input increases, the output decreases.
Therefore, the correct statement is line crosses the y-axis at 6 and the input increases, the output decreases.
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The graph of the equation is y = -3x + 6 and is plotted
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -3x + 6
where the slope of the line is m = -3
Now , The line crosses the y-axis at 6:
True. To find the y-intercept, we set x = 0 and solve for y: y = -3(0) + 6. This gives y = 6. Therefore, the line crosses the y-axis at y = 6.
As the input increases, the output decreases:
True. Since the coefficient of x is negative, as x increases, the output y decreases.
Hence , the equation of line is solved
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Which multiplication equation can be used to explain the solution to 15 divided by 1/3
Answer:Multiply by the reciprocal, also sometimes referred to as "Keep, Change, Flip." Here is how it works. You rewrite the division question as a multiplication question by flipping the second fraction over. Next, keep the first number, change the division to multiplication and then flip the second fraction over.
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
33x33x33333333
3. Complete the following table with the mathematical statements that
4(x-3)
= 20.
3
correspond to the proofs used to solve
Proof
Statements
4(x - 3)
= 20
3
Given
Multiplication Property of Equality
Distributive Property
Addition Property of Equality
Answer:
Step-by-step explanation:
Question (3)
The given expression is,
[tex]\frac{4(x-3)}{3}=20[/tex]
Statements Proof
1). [tex]\frac{4(x-3)}{3}=20[/tex] 1). Given
2). [tex]4(x-3)=60[/tex] 2). Multiplication property of equality
3). 4x - 12 = 60 3). Distributive property
4). 4x = 72 4). Addition property of equality
5). x = 18 5). Division property of equality
Question (4)
Equations are,
5x + 10 = 30 ------(1)
5(x + 10) = 30 ------(2)
From equation (1),
5x + 10 = 30
5x = 30 - 10
x = 4
From equation (2),
5(x + 10) = 30
(x + 10) = 6
x = 6 - 10
x = -4
Therefore, solutions of both the equations are different.
Solve the following equation. 6x−15=4x+55 6 x − 15 = 4 x + 55
Answer:
x = 35
Step-by-step explanation:
Solve for x:
6 x - 15 = 4 x + 55
Hint: | Move terms with x to the left hand side.
Subtract 4 x from both sides:
(6 x - 4 x) - 15 = (4 x - 4 x) + 55
Hint: | Combine like terms in 6 x - 4 x.
6 x - 4 x = 2 x:
2 x - 15 = (4 x - 4 x) + 55
Hint: | Look for the difference of two identical terms.
4 x - 4 x = 0:
2 x - 15 = 55
Hint: | Isolate terms with x to the left hand side.
Add 15 to both sides:
2 x + (15 - 15) = 15 + 55
Hint: | Look for the difference of two identical terms.
15 - 15 = 0:
2 x = 55 + 15
Hint: | Evaluate 55 + 15.
55 + 15 = 70:
2 x = 70
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 x = 70 by 2:
(2 x)/2 = 70/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
x = 70/2
Hint: | Reduce 70/2 to lowest terms. Start by finding the GCD of 70 and 2.
The gcd of 70 and 2 is 2, so 70/2 = (2×35)/(2×1) = 2/2×35 = 35:
Answer: x = 35