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

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

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?

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.

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.

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

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

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?

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

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…

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)…

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?

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

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.

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

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.

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

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?

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 .

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

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.

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= …….

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  ………

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z  …………

Subtract  and    ……….

Add equation  and , to get values of x and y   Substitute x in   Substitute value of x in equation , 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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## 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

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.

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?

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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## 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?

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 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.