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
multiply sum of digits by 7
7(x+y) you get the original number which would be 10x+y
if reverse digits, new number is18 more than sum
so we got
we can minus x+y from both sides in all the equations to obtain
last one, divide both sides by 9
minus 6x both sides
divide both sides by 3
the number is 42
why did you write it down there, oh well
The sum of two numbers is 42 . The smaller number is 10 less than the larger number. What are the numbers?
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
The sum of three consecutive natural numbers is 528, find the numbers.
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.
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:
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
10=n so there are 10 terms in the sequence.
s(n)=(2an+dn^2-dn)/2, becomes, a=3, d=2, n=10
The sum of two consecutive even integers is 234. what is the larger integer?
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
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. 1/2+(-1/4)+1/8+(-1/16)…
The sum of two numbers is 52. The difference is 38. What are the two numbers?
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
Which equation represents the sentence? The sum of 14 and a number is 8 times the number.
the values of the heights are
14 is the aproximate area under the curve from a=0 to a=4
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.
Find the sum of the convergent series 7 0.7 0.007
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.
The sum of two numbers is 44 . Their difference is 22 .
Option C – BD=76 cm
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?
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
The diagonals are perpendicular.
So, AC ⊥ BD
Let O be the point where diagonal intersect let let the partition be x and y.
Perpendicular bisect the diagonal BD into equal parts let it be 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
Nearest to whole number BD=76 cm
Therefore, Option c – BD=76 cm is correct.
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.
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
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
The third number in the sequence 31, 32, 33, 34 is 33
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.
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.
The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?