Answers
Solution:
iv) Given equation: [tex]x^{2} - y^{2} - 4x - 2y + 3[/tex]
Since we are given two variables, we need to split the original expression into two quadratic expressions as
[tex]x^{2} - 4x + 4 - y^{2} - 2y - 1[/tex]
Factoring x first:
[tex]x^{2} - 4x + 4 =[/tex] [tex]x^{2} - 2x - 2x + 4[/tex]
= [tex]x (x - 2) - 2 (x-2)[/tex]
= [tex](x-2)(x-2)[/tex]
[tex]= (x-2)^{2}[/tex]
Factoring y now:
[tex]-y^{2} - 2y - 1 = -1(y^{2} + 2y + 1)[/tex]
= [tex]-1(y^{2} + y + y + 1)[/tex]
= [tex]-1[ y(y+1) + 1(y+1)][/tex]
= [tex]-1 [(y+1)(y+1)][/tex]
= [tex](y+1)(-y-1)[/tex]
Therefore, the original expression becomes
[tex](x-2)^{2}+(y+1)(-y-1)\\or \\(x-2)(x-2) + (y+1)(-y-1)[/tex]
Related Questions
What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9
Answers
Answer:
2519
Step-by-step explanation:
In each case, the remainder is 1 less than the divisor. This means the number of interest will be 1 less than the least common multiple of 5, 6, 7, 8, 9, 10.
The prime factors of these numbers are ...
5 = 5
6 = 2·3
7 = 7
8 = 2³
9 = 3²
10 = 2·5
The unique factors are 2, 3, 5, 7. When they are used to their highest powers, the resulting product is ...
2³·3²·5·7 = 2520
The number of interest is 1 less than this, so is 2519.
2519 is the least positive integer that will give the required remainders.
I WILL GIVE BRAINLIEST Hey can someone tell me simply HOW to come to this conclusion? im a bit confiused as to how, dont want to cheat i want to learn. (P.S ive missed multiple grades which has left me with alot of gaps to fill.)
Answers
Answer:
Option B, x + 2y = 8
Step-by-step explanation:
When two lines are parallel, their gradients are equal i.e M1 = M2
(Note: When two lines are perpendicular, the product of their gradients is equal to - 1 i.e M1M2 = -1)
Gradient of a line = (y2 - y1)/(x2 - x1)
Using coordinates (-4,0) and (4,-4)
Gradient of the line = (-4-0)/[4-(-4)]
= -4/4+4
= -4/8
= -1/2
Therefore gradient of the parallel line is -1/2
Equation of a line using slope intercept form
(y - y1) = m(x - x1)
The parallel line passes through point (2,3)
y - 3 = -1/2 ( x - 2)
2(y - 3) = -1(x - 2)
2y - 6 = -x + 2
2y + x = 8
I hope this helps you to learn....
If a dozen exercise books cost 144, what will 14 of the same books cost
Answers
So you take the 144 divide 12(the dozen) so we could find how much 1 cost, it was 12. You added 2 more books so we add(12x2)+(144). That equals to 168
Hope this helps!
someone please help me i swear i'll give brainliest
Answers
I’m getting really stuck on these questions, help?
Answers
Answer:
m<-1 and 13/15
Step-by-step explanation:
write the equation of the line with slope -3/2 passes through the point (-12,16)
Answers
Answer:
Step-by-step explanation:
You have two pieces if information: the slope of a line and a point on the line. So you can use the "point-slope" formula in order to write the equation of this line. It is a fill-in-the-blank type of formula.
y - y1 = m(x - x1)
In this fill-in-the-blank formula the y1, the m, and the x1 will be filled in with the numbers you were given.
The problem gave the slope as -3/2 , this is your m. On these linear equation problems and formulas, m always stands for the slope.
So fill that in:
y - y1 = -3/2 (x - x1)
They also gave you a point, that is the (x1, y1) that you need to fill in the formula. The point was (-12, 16), so -12 will be your x1 and 16 will be your y1. Fill it in!
y - 16 = -3/2 (x - -12)
Simplify that ugly 'minus a negative' in the parenthesis.
y - 16 = -3/2 (x + 12)
If you were never told what form of equation to write, or they said "any form of the equation", then you're done!
This is in "point-slope" form.
y - 16 = -3/2(x+12) Ta-da!
If you need to change it to "slope-intercept' form then there are a few more steps.
y - 16 = (-3/2)x + (-3/2)12
y - 16 = (-3/2)x - 18
+16 +16
y = -3x/2 - 2 This is y=mx+b (called slope-intercept form)
Simon walks a total of 45.55 miles in march sand 35.7 miles in April.
How many miles does Simon walk in all march and April?
Enter your answer in the box.
|__|
Answers
Answer:
[tex]81.25[/tex]
[tex]45.55 + 35.7[/tex]
4. Para el siguiente triángulo rectángulo, encuentra la medida del lado desconocido.
Answers
A print shop charges $20 to set up the graphic for printing t-shirts. The store then charges $12 per shirt for purchasing up to 10 shirts. The charge decreases to $10 if a customer purchases 10-20 shirts. If a customer purchases more than 20 shirts, each shirt will cost $7. What will it cost a soccer team to have 15 shirts printed?right and grab a piecewise function that models the situation answer the question
Answers
Answer:
see below for the piecewise function$170 for 15 shirtsStep-by-step explanation:
The cost function c(n) for n T-shirts can be written according to the problem statement:
[tex]c(n)=\begin{cases}20+12n&\text{for }n<10\\20+10n&\text{for }10\le n\le20\\20+7n&\text{for }n>20\end{cases}[/tex]
For an order of 15 shirts, the cost will be ...
c(15) = 20 +10(15) = 170
The soccer team's 15 shirts will cost $170.
Can someone plz help Me?
Answers
Answer:
A
Step-by-step explanation:
because if you use a graph you can get it right you count the boxes and you get 4 units but please double check.
Answer:
A
Step-by-step explanation:
Which numbers between 10 and 99 have digits that differ by 4 and add to 6
Answers
Answer:
A
Step-by-step explanation:
Correct option is A)
Let a 3-digit number ABC
Case (1)
If A=7, then B and C can be any digit but not 7
so, total 9 digits (0,1,2,3,4,5,6,8,9) can replace B and C
Then total such combinations =1(9)(9)=81
Case (2)
If B=7 then A can be any digit but not 0 and 7, because if A=0 it will be a 2-digit number.
And C can be any digit but not 7
Then total combinations =(8)(1)(9)=72
Case (3)
If C=7 then A can be any digit but not 0 and 7, because if A=0 it will be a 2-digit number.
And B can be any digit but not 7
Then total combinations =(8)(9)(1)=72
So, total numbers between 99 and 1000 which have exactly one of their digits as 7 are =81+72+72=225
Solve the quadratic for x. Select all that apply.
x? + 7x - 30 = 0
O A. X=3
O B. X=-6
C. X=-10
D. X=-3
O E.X=5
O F.x=6
Answers
Hope this helps
please help anybody hm
Answers
Answer:
its C
Step-by-step explanation:
im smart
The sum of three times a number and 5 is 32
Answers
Answer:
The number is 9.
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]
Let the no. be x.
[tex]:\implies\tt{3x + 5 = 32} \\ \\ \\ :\implies\tt{3x = 32 - 5} \\ \\ \\ :\implies\tt{3x = 27} \\ \\ \\ :\implies\tt{x = \frac{27}{3} } \\ \\ \\ :\implies\tt{x = 9}[/tex]
who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?
Answers
Answer:
I believe Descartes
Step-by-step explanation:
René Descartes was one of the key figures in the Scientific Revolution of the 17th Century.
is y = 2/3x - 7 proportional or not?
Answers
Answer: No, it is not a direct proportion equation
Explanation:
Direct proportions are always in the form [tex]y = kx[/tex] where k is any nonzero real number. So for example, we could have the equation [tex]y = 9x[/tex]. The y intercept of any direct proportion is always zero. Visually, such equations will go through the origin.
Something like [tex]y = \frac{2}{3}x-7[/tex] has a y intercept of -7 and it doesn't fit the form [tex]y = kx[/tex], so it's not a direct proportion equation.
Two plans for reaching a goal are given below. Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7. 20 per hour. Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6. 50 per hour. Which of the following is a true statement? a. Only plan A will work for achieving the goal. B. Only plan B will work for achieving the goal. C. Both plans will work for achieving the goal. D. Neither plan will work for achieving the goal.
Answers
Answer:
C, both plans will work for achieving the goal.
Step-by-step explanation:
For plan A, you must multiply 7.20 by 9, then multiply the product by 8. The answer is 526.4 This means that plan A will work, and more than the original goal will be saved up.
For plan B, you must multiply 6.50 by 15, then multiply the product by 6. The answer is 585. This is more than the original goal, so plan B would work as well.
This means that C is correct, because both plans will work for achieving the goal.
Answer:
C
Step-by-step explanation:
Edged 2022
Find the value of each variable in the given figures
Answers
Answer:
q = 22
Step-by-step explanation:
(7q - 46)° + (3q+6)° = 180 (linear pair property)
7q - 46 + 3q + 6 = 180
10q - 40 = 180
10q = 180 + 40
10q = 220
q = 220/10 = 22
m∠ABD = (7q - 46)° = 7(22) - 46 = 154 - 46 = 108°
m∠DBC = (3q + 6)° = 3(22) + 6 = 66 + 6 = 72°
Plzzz help me.please reply fast
Answers
Answer:
x=458
Step-by-step explanation:
1729-810=919
919-790=129
810-129=681
681-112=569
112-1=111
569-111= 458 (which is the answer)
Answer:
I get 458, but please check the calculations.
Step-by-step explanation:
See attachment. I worked down the pyramid until I has enough information to calculate x. For example, 919 had to be the difference of (1729 - 810) for a sum of 1729. 129 had to be the difference of (919-790). 681 is the difference of (810 - 129). And so on . . .
What is the sum of the addition equation 0.7 + 0.2 = ________?
Answers
Answer:
7+2=9 so the answer is 0.9
Step-by-step explanation:
What is the y-intercept of the line?
Answers
Answer:
1
Step-by-step explanation:
Jorge has 2% + 1 saved in his piggy bank. Lou Ellen has X-2 saved in the bank. What is
the minimum amount Jorge will have in savings for them to have $163 together. Letj
represent Jorge,
Answers
Answer:
yeyeyeeyeyeeyeey
Step-by-step explanation:
Pick the corrrect one form the dropdown
Answers
Answer:
easy
Step-by-step explanation:
Its very easy for any human to be able to see and compare data as when they are right next to eachother, so you can easily prove a good strong point
I don’t anderstands but i wanna help
Answers
please help asap please
Answers
Answer:
Step-by-step explanation:
slope is 4 y is 3
Answer:
slope is 4 y = 3
Step-by-step explanation:
Plz mark as brainliest
A furniture maker used 5/6 of a can of paint to paint some chairs. He used 1/6 of a of paint for each chair. How many chairs did he paint? Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
5 chairs
Step-by-step explanation:
then you'd get 5 so the answer is 5.
Just divide 5/6 / 1/6,
Answer:
5
Step-by-step explanation:
This is a question of division, the total quantity of paint used will be the amount of paint needed per chair × the number of chairs;
This is an equation, which can be rearranged to give:
Number of chairs painted = total paint used/paint needed per chair
Total paint used = ⅚
Paint needed per chair = ⅙
Therefore:
Number of chairs painted = (⅚)/(⅙)
Number of chairs painted = ⅚ × 6
Number of chairs painted = 5
how many possible number of facemask and face shield can an online seller could sell to get an amount of the least php2 000 based on the data above
Answers
Pls help peeps would be appreciated
Answers
Answer:
A.
Because it has it two sides equal
Help me, I'm really tired atm
Answers
Step-by-step explanation:
6/15 = 12/30 = 24/60 = 48/75
Answer:
Step-by-step explanation:
elena went to a sporting goods store that was having a sale she bought a tennis racket and 3 cans of tennis balls the tennis racket is normally 43 all tennis rackets are marked done 15 percent one can of tennis balls is 4 the tennis balls are not marked done the sale tax is 8.5 how much will she pay for everything including tax
Answers
The amount that she will have to pay for everything is $52.68.
First step is to calculate the cost of 3 can of tennis ball
Cost of cans=3 x $4
Cost of cans=$12
Second step is to calculate the discount
Discount=15% x $43
Discount=$6.45
Third step is to calculate the cost of total racket
Total racket=$43 -$6.45
Total racket=$36.55
Fourth step is to calculate the amount that Elena will pay including tax
Amount=($12 + $36.55) + [($12 + $36.55)x 0.085]
Amount=$48.55 + ($48.55 x 0.085)
Amount=$48.55+$4.13
Amount=$52.68
Inconclusion the amount that she will have to pay for everything is $52.68.
Learn more about tax here:https://brainly.com/question/25033929