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

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# Tag: sum

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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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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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### 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.

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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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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. 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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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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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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Find the sum of the convergent series 7 0.7 0.007

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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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**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.**

**S**o, AC ⊥ BD

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

AC= AO+OC

AC= …….[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

………[2]

**Applying Pythagorean theorem in ΔCOD**

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

…………[3]

**Subtract [2] and [3]**

……….[4]

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

**Substitute x in [1]**

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

**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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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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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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**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,

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

Combine like terms we get,

Subtract 6 from both the sides, we get

Simplify we get,

Divide both sides by 4;

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

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

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

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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

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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