Given:
The expanded form of [tex](x+s)(x-t)[/tex] is [tex]x^2+Kx-40[/tex].
Where, s, t, K are positive integers.
To find:
The smallest possible value of K.
Solution:
The expanded form of [tex](x+s)(x-t)[/tex] is [tex]x^2+Kx-40[/tex]. It means,
[tex](x+s)(x-t)=x^2+Kx-40[/tex]
[tex]x^2-tx+sx-st=x^2+Kx-40[/tex]
[tex]x^2+(s-t)x-st=x^2+Kx-40[/tex]
On comping both sides, we get
[tex]K=s-t[/tex] ...(i)
K is a positive integer if s>t.
And
[tex]st=40[/tex]
The factor pairs of 40 are (1,40), (2,20), (4,10), (5,8), (8,5), (10,4), (20,2) and (40,1).
Since s>t, therefore the possible values for (s,t) are (8,5), (10,4), (20,2) and (40,1).
Using (i), find the value of K for each factor pair.
[tex]K=8-5=3[/tex]
[tex]K=10-4=6[/tex]
[tex]K=20-2=18[/tex]
[tex]K=40-1=39[/tex]
Therefore, the smallest possible value of K is 3.
(-2x+5y-3z)2
try to do it
Answer:
the answer is −4x+10y−6z
Step-by-step explanation:
(−2x+5y−3z)2
Use the distributive property to multiply −2x+5y−3z by 2.
−4x+10y−6z
Answer:
(-2x+5y-3z)2
-2x*2+5y*2-3z*2
-4x+10y-6x
Step-by-step explanation:
Hope this helps u!!
write an equation in slope-intercept form for a line that passes through the given point and that is perpendicular to the given line.
x= -7; (0.2)
would y= -1/2x -7 work? or no, because -7 is the slope for the one given above?
Answer:
Step-by-step explanation:
x= -7; (0.2)
x = 1.4
----------------
y =− 2 x −7
I really hope this helps
what is the result when the number 38 is decreased by 4%
Answer:
1.52
Step-by-step explanation:
38 decreased by 4% = 36.48
Absolute change (actual difference):
36.48 - 38 = - 1.52
Someone please help thank you
Answer:
Step-by-step explanation:
[tex]9+3x\leq 24\\3x\leq 15\\x\leq 5[/tex]
So use closed (dark) circle and draw line to left from 5.
Solve the system by elimination.
{y= 16x+44
{y= -x^2 +8x+28
Answer:
x= -4, y= -20
Step-by-step explanation:
y= 16x+44
(y= -x²+8x+28) * (-1)
multiply both sides by -1
y= 16x+44
-y= x²-8x-28
add the equations to eliminate y
y-y= x²+16x-8x+44-28
0= x² +8x +16 this is the same with (x+4)²=0 so x= -4
go back to the first equation and substitute x with -4 and solve for y
y= 16*(-4) +44 = -64+44 = -20
An employee puts $3,000 into a retirement fund that offers 7% interest compounded annually. The employee makes no other deposits or withdrawals. Which amount is closest to the interest that the employee will have earned after 4 years?
Answer:
$840
Step-by-step explanation:
Given data
Principal = $3000
Rate= 7%
Time= 4 years
The expression for the simple interest is
SI= PRT/100
substitute
SI= 3000*7*4/100
SI= 30*7*4
SI= $840
Hence the interest is $840
640 divided by 16= 16 divided by 16 =1
Factorise fully [tex]3y^{3} -12y[/tex]
Answer:
[tex] {3y}^{3} - 12y \\ = 3y( {y}^{2} - 4) \\ = 3y( {y}^{2} - {2}^{2} ) \\ = 3y(y - 2)(y + 2) \\ = 3y(y + 2)(y - 2)[/tex]
a^2-b^2=(a+b)(a-b)
a=y b=2
3y(y+2)(y-2)
A survey showed that 90% of students would select roller coasters as their favorite ride at an
amusement park. Out of 5,000 students predict how many wouldselect roller coasters as
their favorite ride?
Answer:
4500 students
Step-by-step explanation:
5000 / 100 = 50
50 x90 = 4500 :D
A student has a total of 233 points on three tests. The scores on the first and second tests are the same. The third score exceeds the second (or the first) by 14. Find the three scores.
Answer:
Let the scores on the first two test be x
Let score for third test be 14 exceeds second( or first) = x + 14
Total = 233
x + x + (x + 14) = 233
3x + 14 = 233
3x = 219
x = 73
Score of the third test = x + 14 = 73 + 14 = 87
Therefore, the scores are 73, 73, 87
A school received a $7,563 grant for new supplies to be evenly distributed among 18 classroom teachers. How much money will each classroom teacher receive, to the nearest dollar?
$42
$43
$420
$430
$420
Step-by-step explanation:
$7,563/18
=$420.1667
=$420.17 (to the nearest dollar means to the nearest full dollar and since 17 cents is not up to 50, you remove it )
= $420
HELPpppp MeeeeE PLZ!!!!!!!!
Answer:
answer is a
Step-by-step explanation:
Determine the approximate value of ø
a)41.89
b) 48.20
c)33.70
d)56.30
Answer:
B,48.2
Step-by-step explanation:
To solve this we need to use SOH, CAH, TOA
we have the adjacent and hypotonouse so it's easiest to use CAH
let theta (angle) = x
cos(x)=4/6
to cancel the cos mulitply both sides by cos^-1 (2nd --> cos)
x=48.1896851
which rounds to 48.2
Zoe and hannah share tips in the ratio 3:7 last week zoe recieved £24 how much did hannah recive last week
Answer:
56
Step-by-step explanation:
Zoe and Hannah shared tips in the ratio
3:7
Last week Zoe received $24
Hence the amount received by Hannah can be calculated as follows
3/7= 24/x
168= 3x
x= 168/3
= 56
Hence Hannah received €56
If m∠2=4x and m∠4=3x- 8. I have to fine m∠1
Answer:
c
Step-by-step explanation:
THIS IS AREA OF CIRCLES PLS ANSWER
Answer:
75ft^2
Step-by-step explanation:
A = pi*r^2
The circle already gives the diameter and the diameter is two times the radius, so if you were to divide the diameter by two, you would get 5.
Knowing the radius is 5 and seeing how they replaced pi with 3 we can set up the equation.
3*(5)^2 = A
Simplify
3*25
Multiply
Area=75ft^2
Can someone plzzz help
Answer:
sorry i dont know
Step-by-step explanation:
AB= please answer :)
Answer:
8.77 or 8.80
Step-by-step explanation:
sin (20) = 3/x
x (sin)20)) = 3
divide by sin(20)
x= 8.77 or 8.8
Plz sove and u will earn 30pts
Answer:
Pg. 1:
Triangle A: Obtuse
Triangle B: Obtuse
Triangle C: Acute
Triangle D: Right
Pg. 2:
Question 1: Figure A
Question 2: None
Question 3: Figure C
Pg. 3:
Triangle A: Scalene
Triangle B: Equilateral
Triangle C: Isosceles
Triangle D: Isosceles
Pg. 4:
A: Triangle
B: Circle
C: Rectangle
Hope that helped!
Step-by-step explanation:
Find the missing height of a rectangular prism that has a volume of 137.5 inches with a width of 2.5 and length 10 in
Answer:
The answer would be 5.5
Step-by-step explanation:
To prove it, 10 x 2.5 x 5.5 would equal 137.5
When a graph is symmetric about the origin, it is an function.
When a graph is symmetric about the y-axis, it is an function.
A function is considered if f(-x) =
f(x), and it is considered
=
if f(-x) = -f(x).
Answer:
odd; even; even; odd
Step-by-step explanation:
The answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We know when the graph is symmetric about the origin it is an off function.
When the graph is symmetric about the y axis it is an even function.
When f(-x) = f(x) it is an even function
When f(-x) = -f(x) it is an odd function.
Thus, the answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
I need this before the 24th!
100 points!
Answer:
The interval is [4,7]
Step-by-step explanation:
The rate of change is given by
f(x2) - f(x1)
-------------------
x2 -x1
We want the rate of change to be 56
f(x2) - f(x1)
------------------- = 56
x2 -x1
We also know that the x2 is 7 so f(x2) = 192
192 - f(x1)
------------------- = 56
7 -x1
192 - f(x1) = 56( 7 -x1)
192 - f(x1) = 392 -56x1
Now we need to pick points from the table and see where it is true
(6,96)
192 - 96 = 392 -56*6
96=56 False
( 5,28)
192 - 28 = 392 -56*5
164=112 False
(4,24)
192 - 24 = 392 -56*4
168=168 True
The interval is [4,7]
heyy! i’ll give brainliest please help
Answer:
A
Step-by-step explanation:
Just A!
Answer:
Step-by-step explanation:
Never capitalize the seasons
$3 subtracted from the cost of the book
Answer:
x = 11 explanation : " $3 subtracted from the cost of the book just number 8! " As an equation this would be : x - 3 = 8 SOLVE x - 3 = 8 + 3 + 3 x = 11 KEY x = cost of book
hope it helps
When you use a paint can opener to a can of paint you use the paint can opener as a simple machine called a _____ class______
Answer:
FIrst blank: lever
And, did you mean to put class?
Step-by-step explanation:
Jasmine has of a pizza left. She is going to divide the leftovers into 6 equal
pieces. What fraction of the whole pizza will each piece be?
Answer:
1/6
Step-by-step explanation:
Juana tiene en su cuenta bancaria $98.857. Si expide un cheque por $39.948 y deposita otro por $10.845 ¿Cuánto dinero le queda a Juana en su cuenta bancaria?
Opción A: Quedan $58.064
Opción B: Quedan $48.154
Opción C: Quedan $69.754
RESPUESTA:
Answer:
um could you transkate to english so i can answer your question?
Step-by-step explanation:
WILL GIVE BRAINLIEST (NO LINKS ALLOWED)
Washington Irving wrote literature that reflected:
A. the growing influence of women on social equality movements.
B. the social effects of increased immigration from Europe.
C. the expansion of political rights for nonwhite Americans.
D. the rapid pace of social change in the United States.
Answer: D
Step-by-step explanation:
trust me
please help me for brainiest):):):):):):
Answer:
You can find 0.5% of a number by multiplying the number by
Step-by-step explanation:
I need help with this!!