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The sum of 2ab2 and (-5ab2) is the same as the sum of (-6ab2) and

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The sum of 2ab2 and (-5ab2) is the same as the sum of (-6ab2) and

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If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number? 42

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The digits are x and y

multiply sum of digits by 7
7(x+y) you get the original number which would be 10x+y
so
7x+7y=10x+y

if reverse digits, new number is18 more than sum
10y+x=18+x+y

so we got

7x+7y=10x+y
10y+x=18+x+y
we can minus x+y from both sides in all the equations to obtain

6x+6y=9x
9y=18

last one, divide both sides by 9
y=2

sub back
6x+6y=9x
6x+6(2)=9x
6x+12=9x
minus 6x both sides
12=3x
divide both sides by 3
4=x

the number is 42

why did you write it down there, oh well

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The sum of two numbers is 42 . The smaller number is 10 less than the larger number. What are the numbers?

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The sum of two numbers is 42 . The smaller number is 10 less than the larger number. What are the numbers?

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19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.

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there are 6 numbers per cube,

 the chance of rolling one and getting the number 1 is a 1/6 probability

for the sum to be odd, you need to roll either a 2, 4 or 6 on the second cube so that gives you a 3/6 probability

 so 1/6 x 3/6 = 3/36 which can be reduced to 1/12

 so you have a 1/12 probability

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The sum of three consecutive natural numbers is 528, find the numbers.

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The sum of three consecutive natural numbers is 528, find the numbers.

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Rewrite 35 +63 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor

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Answered by answersmine AT 22/10/2019 – 03:45 AM

To find this answer you would need to first find the GCF, which would be 7. Next, you would take both numbers (35 and 63) and divide them by 7, getting 5 and 9, and adding them together you would get 14. So your answer would be 7 and 14, since when you multiply those numbers, you get 98, which is the sum of 35 and 63.

Post your answer

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Find the sum of the arithmetic sequence. 3,5,7,9,….,21

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The sum of any arithmetic sequence is the average of the first and last terms times the number of terms.

Any term in an arithmetic sequence is:

a(n)=a+d(n-1), where a=initial term, d=common difference, n=term number

So the first term is a, and the last term is a+d(n-1) so the sum can be expressed as:

s(n)(a+a+d(n-1))(n/2)

s(n)=(2a+dn-d)(n/2)

s(n)=(2an+dn^2-dn)/2

However we need to know how many terms are in the sequence.

a(n)=a+d(n-1), and we know a=3 and d=2 and a(n)=21 so

21=3+2(n-1)

18=2(n-1)

9=n-1

10=n so there are 10 terms in the sequence.

s(n)=(2an+dn^2-dn)/2, becomes, a=3, d=2, n=10

s(10)=(2*3*10+2*10^2-2*10)/2

s(10)=(60+200-20)/2

s(10)=240/2

s(10)=120

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The sum of two consecutive even integers is 234. what is the larger integer?

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The sum of two consecutive even integers is 234. what is the larger integer?

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Each of the following correctly match an English phrase with a mathematical expression except _____. a) a number times seven, 7x b) a number subtracted from seven, 7 – x c) the sum of a number and seven, 7 + x d) a number divided by 7, 7/x

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Each of the following correctly match an English phrase with a mathematical expression except _____. a) a number times seven, 7x b) a number subtracted from seven, 7 – x c) the sum of a number and seven, 7 + x d) a number divided by 7, 7/x

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Find the sum of the following infinite geometric series, if it exists. 2/5+12/25+ 72/125…

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Find the sum of the following infinite geometric series, if it exists. 2/5+12/25+ 72/125…

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Find the sum of the following infinite geometric series, if it exists. 1/2+(-1/4)+1/8+(-1/16)…

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Find the sum of the following infinite geometric series, if it exists. 1/2+(-1/4)+1/8+(-1/16)…

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The sum of two numbers is 52. The difference is 38. What are the two numbers?

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The sum of two numbers is 52. The difference is 38. What are the two numbers?

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Simplify the sum. (2u3 + 6u2 + 3) + (2u3 – 7u + 6) A. 9 – 7u + 6u2 + 4u3 B. 0u3 + 6u2 – 7u + 9 C. 0u3 – 7u2 + 6u – 9 D. 4u3 + 6u2 – 7u + 9

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Simplify the sum. (2u3 + 6u2 + 3) + (2u3 – 7u + 6) A. 9 – 7u + 6u2 + 4u3 B. 0u3 + 6u2 – 7u + 9 C. 0u3 – 7u2 + 6u – 9 D. 4u3 + 6u2 – 7u + 9

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Which equation represents the sentence? The sum of 14 and a number is 8 times the number.

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Which equation represents the sentence? The sum of 14 and a number is 8 times the number.

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Approximate the area under the function between a and b using a left hand sum with the given number of intervals. f(x)=x^2 a=0 b=4 4 intervals

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The length of each interval is (b-a)/i where i=number of intervals, a=starting value and b=ending value
so (4-0)/4=4/4=1
each interval is 1 unit in width

ok
the values of the heights are
f(0)
f(1)
f(2)
f(3)

f(0)=0
f(1)=1
f(2)=4
f(3)=9

1(0+1+4+9)
1(14)
14 is the aproximate area under the curve from a=0 to a=4

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Given int variables k and total that have already been declared, use a for loop to compute the sum of the squares of the first 50 counting numbers, and store this value in total. thus your code should put 1*1 + 2*2 + 3*3 +… + 49*49 + 50*50 into total. use no variables other than k and total.

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Given int variables k and total that have already been declared, use a for loop to compute the sum of the squares of the first 50 counting numbers, and store this value in total. thus your code should put 1*1 + 2*2 + 3*3 +… + 49*49 + 50*50 into total. use no variables other than k and total.

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Find the sum of the convergent series 7 0.7 0.007

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Find the sum of the convergent series 7 0.7 0.007

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In parallelogram ABCD, if angle C=110 and angle D=70, what is the sum of the measures of angle A and angle B?

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The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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The sum of two numbers is 44 . Their difference is 22 .

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The sum of two numbers is 44 . Their difference is 22 .

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One-third of the sum of 7 and a number

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=  x+y=84.8 …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

H^2=P^2+B^2

(44.8)^2=x^2+z^2  ………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

H^2=P^2+B^2

(72)^2=y^2+z^2 …………[3]

Subtract [2] and [3]

(72)^2-(44.8)^2=y^2+z^2-x^2-z^2

5184-2007.04=(x+y)(x-y)

3176.96=(84.8)(x-y)

37.464=x-y ……….[4]

Add equation [1] and [4], to get values of x and y

x+y+x-y=84.8+37.464

2x=122.264

x=61.132

Substitute x in [1]

x+y=84.8

61.132+y=84.8

y=23.668

Substitute value of x in equation [2], to get z

(44.8)^2=x^2+z^2

(44.8)^2=(23.668)^2+z^2

2007.04-560.174224=z^2

z=sqrt{1446.865776}

z=38.06

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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Sara is 33 years younger than Rolando. The Sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R. A. s+r=33 s=r-105 B. s+r=105 r=s-33 C. s+r=105 s=r-105 D. s+r=105 s=r-33 E. None of these

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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Find the sum. Correct answer gets brainliest.

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Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       $6,800   $10,500  $8,400    $66,000   $4,700

Pay subject to FICA S.S.         $421.60  $651.00  $520.80 $4092.00 $291.40
6.2%, (First $118,000)

Pay subject to FICA Medicare $98.60 $152.25    $121.80    $957.00    $68.15
1.45% of gross

Pay subject to FUTA Taxes      $40.80  $63.00     $50.40    $396.00  $28.20
0.6%

Pay subject to SUTA Taxes   $367.20  $567.00  $453.60  $3564.00 $253.80
5.4% (First $7000)

Totals                                     $928.20 $1,433.25 $1,146.60 $9,009.00 $641.55

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The sum of 4 consecutive integers is 130. what is the third number in the sequence?

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Answer:

The third number in the sequence 31, 32, 33, 34 is 33

Step-by-step explanation:

let first number be the smallest number be x.

Consecutive numbers are those numbers that follow each other in order and they should have a difference of 1 between every two numbers.

Then, the four consecutive integers are x , (x+1), (x+2) , (x+3)

Given: the sum of 4 consecutive integers is 130.

From the given condition we have,

x+(x+1)+(x+2)+(x+3)=130

Like terms states that contain the same variables raised to the same power.

Combine like terms we get,

4x+6=130

Subtract 6 from both the sides, we get

4x+6-6=130-6

Simplify we get,

4x=124

Divide both sides by 4;  frac{4x}{4}= frac{124}{4}

On simplify we get, the value of x i.e, x=31

the sequence we have, 31, 32, 33, 34,

therefore, the third number in the sequence is, 33.

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Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron?

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Ahemmm having x-intercepts of -3 and -5.. ..well, that simply means, -3 and -5 are roots or solutions or zeros of the equation

it namely means x = -3 and x = -5, an x-intercept is when the graph touches the x-axis, at that point, the y-intercept is 0, so the point is (-3, 0) and (-5, 0)

if the roots are -3, and -5, then

bf begin{cases}
x=-3implies x+3=0implies &(x+3)=0\
x=-5implies x+5=0implies &(x+5)=0
end{cases}\\
-------------------------------\\
(x+3)(x+5)=0implies (x+3)(x+5)=yimplies x^2+8x+15=y

if you have the zeros/x-intercepts/solutions of the polynomial, all you have to do is, get the factors, as above, and get their product, to get the parent original polynomial.

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The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?

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The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?

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