Answers
Step-by-step explanation:
Note that the denominators in the expression are perfect squares:
[tex] {x}^{2} - 5xy + 6 {y}^{2} = (x - 2y)(x - 3y)[/tex]
[tex] {x}^{2} - 4xy + 3 {y}^{2} = (x - y)(x - 3y)[/tex]
[tex] {x}^{2} - 3xy + 2 {y}^{2} = (x - y)(x - 2y)[/tex]
We can then write the given expression as
[tex] \frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}[/tex]
[tex] \frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}[/tex]
[tex] = \frac{1}{(x - 2y)(x - 3y)} + \frac{a}{(x - y)(x - 3y)} + \frac{1}{(x - y)(x - 2y)}[/tex]
[tex] = \frac{(x - y)(x - 2y) {(x -3y)}^{2} + a {(x - y)}^{2} (x - 2y)(x - 3y) + (x - y){(x - 2y)}^{2}(x - 3y) }{ {(x - y)}^{2} {(x - 2y)}^{2} {(x - 3y)}^{2} } [/tex]
Related Questions
Which point would not be a solution to the system of linear inequalities shown below? y\ge x+5\hspace{50px}y\ge\frac{2}{3} x+6 y≥x+5y≥ 3 2 x+6 (12, 7) (-12, 1) (-12, 9) (-12, 6)
Answers
Answer:
(12,7) is not a solution
Step-by-step explanation:
Given
[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]
Required
Point that is not a solution
We have:
[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]
Substitute [tex]\frac{2}{3}x + 6[/tex] for y in the first inequality
[tex]\frac{2}{3}x + 6 \ge x + 5[/tex]
Collect like terms
[tex]\frac{2}{3}x - x \ge 5-6[/tex]
[tex]-\frac{1}{3}x \ge -1[/tex]
Solve for x (the inequality will change because we are to divide by a negative number_
[tex]x \le -1/-\frac{1}{3}[/tex]
[tex]x \le 3[/tex]
Without solving further, we can conclude that the first option is not a solution.
Because (12,7) implies that [tex]x =12[/tex]
Compare [tex]x =12[/tex] to [tex]x \le 3[/tex], then [tex]x \le 3[/tex] is false
Originally a rectangle has dimensions 12in by 8in. if the same amount increases on both sides, the area is doubled find the new dimensions
Answers
Step-by-step explanation:
Let the increase in the size of the length and breath be 'x'.
The area of the rectangle = 12in × 8in
=96 in²
From the question,
(12+x)(8+x)=96×2 in²
or, 96+12x+8x+x²= 192
or, x²+20x+96-192=0
or, x²+20x-96=0
or, x²+24x-4x-96=0
or, x(x+24)-4(x+24)=0
or, (x-4)(x+24)=0
Either, Or,
x-4=0 x+24=0
Therefore, or, x= –24 (Which is impossible)
x=4
So the new dimensions are 12+4=16 inch and 8+4=12 inch.
what is the solution to x^2 + 6x +7
Answers
Answer:
D) [tex]\frac{-6\pm\sqrt{8} }{2}[/tex]
Step-by-step explanation:
[tex]x^2+6x+7=0[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-6\pm\sqrt{6^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-6\pm\sqrt{36-28} }{2}[/tex]
[tex]x=\frac{-6\pm\sqrt{8} }{2}[/tex] <-- correct option but not simplified fully
[tex]x=\frac{-6\pm2\sqrt{2}}{2}[/tex]
[tex]x=-3\pm\sqrt{2}[/tex]
Evaluate the expression below when x = 7 and y = 8.
5x2−3y
Answers
Answer:
221
Step-by-step explanation:
Substitute x = 7 and y = 8 into the expression
5(7)² - 3(8)
= 5(49) - 24
= 245 - 24
= 221
Could someone please help me with this?
Answers
Answer:
Equal
Equal
Equal
Supplementary
Step-by-step explanation:
Just learn the angles tbh, you will need them in the future
the trapezium is drawn on a centimetre grid
Answers
Answer:
21 cm²
Step-by-step explanation:
Applying,
A = (a+b)h/2............. Equation 1
Where A = area of the trapezium, a = length of the first parallel side, b = length of the second parallel side, h = height.
From the diagram
Given: a = 5 cm (5 grids), b = 9 cm (9 grids), h = 3 cm (3 grids)
Substitute these values into equation 1
A = 3(5+9)/2
A = 3(14)/2
A = 3×7
A = 21 cm²
What is the obesity threshold weight for a young adult American male?
Answers
Answer:
If your BMI is 18.5 to 24.9, it falls within the normal or Healthy Weight range. If your BMI is 25.0 to 29.9, it falls within the overweight range. If your BMI is 30.0 or higher, it falls within the obese range.
Step-by-ste
Answer:
218.7 lbs is your answer
can someone pls help for brainlest
Answers
Answer:
The answer to the question is B,2:55
Answer:
2:55 B
Step-by-step explanation:
Each number 1 2 3 etc are counting by 5's. 11, five times is 55. It cannot be D because the shorter needle determines the hour and the longer one is on 11. It can't be A because counting by 5 starts with 1 not 12 it rotates clockwise not anti-clockwise. It can't be C because for it to be 50, it would need to be on the 10 not on 11.
Write an equation of the line that passes through (5,0) and is parallel to the line
y = -3x + 2
Answers
Answer:
y=-3x+15
is the equation that passes through the point (5,0) and is the parallel line to y=-3x+2
Step-by-step explanation:
find the slope of the original line and use the point-slope formula y-y₁=m(x-x₁) to find the parallel line of y=-3x+2, which if done correctly you should end up with y=-3x+15.
hope this helps
Find the equation with a line with slope 7
_
2 passing through the point (-2,9).
Answers
Answer:
y = 7/2 x+16
Step-by-step explanation:
The equation for a line is y = mx+b where m is the slope and b is the y intercept
y = 7/2 x+b
Substitute the point into the equation
9 = 7/2(-2)+b
9 = -7+b
9+7 = b
16 = b
y = 7/2 x+16
can someone help please!!
find the maximum value of function f(x) = -1.1x^2 - 3.6x + 1
Answers
Step-by-step explanation:
everything can be found in the picture
Select the correct answer.
What is in simplest form?
A. 8√4
B. 17√2
C. 4√ 17
D. 2√17
Answers
Please help asap!! I will mark you as brainliest :)
Answers
Answer:
3, 0, -5, -6
Step-by-step explanation:
7)
when x= -8, f(x) = 8-5 or 3
when x= -5 f(x) = 5-5 or 0
when x= 0, f(x) = 0-5 or -5
when x=1, f(x) = -1-5 or -6
What is the measure of <JHM
25
45
50
90
Answers
David participating in a 6-day cross-country biking challenge. He biked for 65, 56, 57, 58 , and 67 miles on the first five days. How many miles does he need to bike the last day so that his average (miles) per day ?
Answers
Answer:
Hi
Step-by-step explanation:
Please like I am noob I neeed brainliest
Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did she have?
Answers
Answer:
0.05n + 0.25q = 1.60
q = 3n
0.05n + 0.25(3n) = 160
0.05n + 0.75n = 1.60...multiply by 100 to get rid of the decimals
5n + 75n = 160...answer D
Step-by-step explanation:
(meow) <3
A new pair of Air Jordan's that sells for $150 decreases at a rate of 14% each year. Find the value of the shoes after 5 years (round to the nearest cent).
Answers
Answer:
$45
Step-by-step explanation:
If it looses it value of 14 % every year, by the end of 5 years, the value would go down by 70%. So, 150x0.7= 105, 150-105=45, so it would be. worth. 45% in 5 years.
The dolphin is 20 feet below the serface of the ocean.
Answers
Answer: we wont be able to answer if there is no fill out box
Step-by-step explanation:
Answer:
Can you complete the sentence?
A car was bought for D750,000 and was sold for D775,000 calculate the percentage profit
Answers
The school is having a bake sale. It costs $6 to make a cake. The school wants to make a 25% profit on each cake. How much should the school charge for each cake?
Answers
Answer:
$1.50
Step-by-step explanation:
25% of 6 is basically just 6/4, which is 1.5.
This is money we're talking about, so the answer is $1.50
A sample of a radioactive isotope had an initial mass of 120 mg in the year
2010 and decays exponentially over time. A measurement in the year 2015
found that the sample's mass had decayed to 50 mg, What would be the
expected mass of the sample in the year 2018, to the nearest whole number?
Answers
Answer:
2015-2010=5
50÷5=10
120-50=70
2017-2015=2
2*10=20
70-20=50mg
2018=50mg
Kiran's father is 65 years old. He is 8 years older than three
times Kiran's age. Find Kiran's age?
Answers
Answer:
let kiran's age be x
kiran's father's age is 65
acc.to ques
kiran's father is 8 years older than 3 times kiran's age ....which gives us the equation as follows
8+3x =65
therefore
3x =65-8
3x =57
x =57/3
x= 19 ans
so kiran's age is 19 years.
Answer:
kiran is 19 years old.
Step-by-step explanation:
kiran's father age = 65
let kiran's age be x
kiran's father is 8 years older than three times kiran's age means 8 + 3x
so according to the question equation is
65 = 8 + 3x
65 - 8 = 3x
57/3 = x
19 = x
therefore kiran's age is 19 years.
Solve the equation for x.
Answers
Answer:
x = 7
Step-by-step explanation:
2x + 34 = 4x + 20
2x = 14
x = 7
Please help quadratic equation!! 20 points
Answers
Answer:
x=4,−2
Step-by-step explanation:
Because Step 1. Move all terms to one side.
{x}^{2}-2x-8=0
x
2
−2x−8=0
2 Factor {x}^{2}-2x-8x
2
−2x−8.
1 Ask: Which two numbers add up to -2−2 and multiply to -8−8?
-4−4 and 22
Step 2. Rewrite the expression using the above.
(x-4)(x+2)
(x−4)(x+2)
and going to;
(x-4)(x+2)=0
(x−4)(x+2)=0
And Step 3. Solve for xx.
1 Ask: When will (x-4)(x+2)(x−4)(x+2) equal zero?
When x-4=0x−4=0 or x+2=0x+2=0
2 Solve each of the 2 equations above.
x=4,-2
x=4,−2
x=4,-2
Our Answer is:
x=4,−2
I Hope It's Helps
Answer:
2 and -4
tso numbers when added gives -2 and 8 incase it's not clear enough.
BRAINIEST AND 15 POINTS HELP FAST!!!
In the square below, the two semi-circles are congruent. Find the area of the
shaded region. If necessary, round your answer to two decimal places.
Answers
Answer:
3.44.
Step-by-step explanation:
We can see that in this square, the radii of the semicircles are 2. Using that, we can calculate that the area of each one is 6.58. Both combined is 12.56. Now, the original area of the circle was 16. 16 minus 12.56 is equal to 3.44, so the area of the shaded region is 3.44.
Answer:
3.44
Step-by-step explanation:
enter it just like that in ape x
Evaluate the following expression at x = -4
-5x-1
Answers
Substitute X in the expression :
-5(-4) - 1
-5 • -4 = 20
20 - 1 = 19
Kelly is going two work two part-time jobs during the school year. When she works for her dad, she will make $8.00 per hour. When she works at a day care center, she will make $14.00 per hour. To pay her car payment, Kelly needs to make at least $84.00 a week and can work no more than 10 hours total per week. Write an inequality to represent the difference combinations of hours working for her dad,X, and hours working for the daycare center,Y, Kelly can work if she wants to earn at least $84 per week
Answers
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of hours Kelly works for her dad per week and y represent the number of hours Kelly works in the daycare center per week.
Since she wants to make $84 per week, hence:
8x + 14y ≥ 84 (1)
Also, she can work a maximum of 10 hours per week, hence:
x + y ≤ 10 (2)
Using equation 1 and 2 and plotting the constraints on geogebra online graphing tool, the solution to the problem is at points:
A(0, 6), B(0, 10) and C(9.3, 0.7)
I am timed. Please answer this.
Answers
Answer:
9
Step-by-step explanation:
because volume of a prism is area × length
so area of triangle is 4*4/2=8 so 72÷8=9.
hope this helps:)
One floor is randomly taken from a
vase containing 5 red flowers,
2 white flowers, and 3 pink flowers.
Find the probability of taking a red
or a pink flower.
Answers
8/10 or 8 out of 10 chance.
Both numbers are divisible by 2.
8/2= 4 & 10/2= 5
4/5 chance in picking red or pinks flowers. You have an 80% chance which are pretty high odds.
please answer quickly easy 10 points but please answer quick
Answers
Answer:
He traveled 520 miles
Step-by-step explanation:
8 x 65 = 520
Answer: 520 miles
Step-by-step explanation:
Data: Juan drove 8 hours
Drove at an average Speed of 65 mph
Miles driven=x
Only step: Multiply 65 by 8 which is 520
Explanation: Since Juan drove at an average speed of 65 miles per hour, that means he drove 65 mile for every hour he drove. So since he drove for 8 hours, you multiply 8 hours by 65 miles so that you get get the total amount of hours driven by him.
Don't forget to add "Miles" to the end of your answer because most math teachers tend to want that in an answer like this.
I hope this helps(Mark brainiest if you want to, thanks)
