Answer:
[tex]radius = \sqrt{13}[/tex] or [tex]radius = 3.61[/tex]
Step-by-step explanation:
Given
Points:
A(-3,2) and B(-2,3)
Required
Determine the radius of the circle
First, we have to determine the center of the circle;
Since the circle has its center on the x axis; the coordinates of the center is;
[tex]Center = (x,0)[/tex]
Next is to determine the value of x through the formula of radius;
[tex]radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]
Considering the given points
[tex]A(x_1,y_1) = A(-3,2)[/tex]
[tex]B(x_2,y_2) = B(-2,3)[/tex]
[tex]Center(x,y) =Center (x,0)[/tex]
Substitute values for [tex]x,y,x_1,y_1,x_2,y_2[/tex] in the above formula
We have:
[tex]\sqrt{(-3 - x)^2 + (2 - 0)^2} = \sqrt{(-2 - x)^2 + (3 - 0)^2}[/tex]
Evaluate the brackets
[tex]\sqrt{(-(3 + x))^2 + 2^2} = \sqrt{(-(2 + x))^2 + 3 ^2}[/tex]
[tex]\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}[/tex]
Eva;uate all squares
[tex]\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}[/tex]
[tex]\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}[/tex]
Take square of both sides
[tex](3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9[/tex]
Evaluate the brackets
[tex]3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9[/tex]
[tex]9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9[/tex]
[tex]9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9[/tex]
Collect Like Terms
[tex]6x -4x + x^2 -x^2 = 4 -4 + 9 - 9[/tex]
[tex]2x = 0[/tex]
Divide both sides by 2
[tex]x = 0[/tex]
This implies the the center of the circle is
[tex]Center = (x,0)[/tex]
Substitute 0 for x
[tex]Center = (0,0)[/tex]
Substitute 0 for x and y in any of the radius formula
[tex]radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}[/tex]
[tex]radius = \sqrt{(x_1)^2 + (y_1)^2}[/tex]
Considering that we used x1 and y1;
In this case we have that; [tex]A(x_1,y_1) = A(-3,2)[/tex]
Substitute -3 for x1 and 2 for y1
[tex]radius = \sqrt{(-3)^2 + (2)^2}[/tex]
[tex]radius = \sqrt{13}[/tex]
[tex]radius = 3.61[/tex] ---Approximated
if the first step of the equation -8 - 7x = -5x - 10 is " add 10" then what should be done next?
Answer:
Add 7x to each side
Step-by-step explanation:
-8 - 7x = -5x - 10
Add 10 to each side
-8 - 7x+10 = -5x - 10+10
2 -7x = -5x
Add 7x to each side
2-7x+7x = -5x+7x
2 = 2x
Answer: See below
Step-by-step explanation:
[tex]-8 - 7x = -5x - 10[/tex]
I believe it is adding 8 on both sides
The next step after adding 8 on both sides is adding 5x on both sides
[tex]-7x=-5x-2[/tex]
[tex]-7x+5x=-5x-2+5x[/tex]
[tex]-2x=-2[/tex]
x=1
Which statement correctly compares
1–201 and
1512
ol-201 = 151
ol-201 < 51
l-201 > 151
Answer:
Option B.
Step-by-step explanation:
Consider the correct question is "Which statement correctly compares
1. -201 and 151
-201 = 151
-201 < 51
-201 > 151"
The given numbers are -201 and 151. We need to compare these numbers.
We know that all negative numbers are less than positive numbers.
So,
-201 < 151
If both numbers are negative, then the larger negative number is the smaller number.
Therefore, the correct option is B.
Solve for h. 3/7=h/14-2/7
Answer:
h = 10
Step-by-step explanation:
Given
[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]
Multiply through by 14 to clear the fractions
6 = h - 4 ( add 4 to both sides )
10 = h
Answer:
10
Step-by-step explanation:
We start out with 3/7 = h/14 - 2/7
add 2/7 to both sides:
(5/7) = h/14
Multiply both sides by 14 to get rid of the fraction:
h = 10
Solve for x 3x - 4 = 2x - 10
Answer:
-6
Step-by-step explanation:
To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:
3x-4=2x-10
+10 +10
3x+6=2x
-3x -3x
6=-x
/-1 /-1
x=-6
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer:
[tex]x = -6[/tex]
Step-by-step explanation:
Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.
To do this, we can subtract 2x from both sides which gets us
[tex]x - 4 = -10[/tex]
Add 4 to both sides:
[tex]x = -6[/tex]
Hope this helped!
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
I NEED HELP ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!
Answer:
D
Step-by-step explanation:
Both are exponential decay.
Answer:
D.Step-by-step explanation:
f(0) = 24, f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)
and f(0) > f(1) > f(2) means f is decreasing in (0,2)
g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)
and g(0) > g(2) means g is decreasing in (0,2)
You have been saving $12 each week for many weeks. One day, you decide to count your savings and find that you have $384. Write and solve a multiplication equation to find how many weeks w you have been saving.
Answer:
Hope I helped! Brainleist!
Step-by-step explanation:
you get $12/week
and you have $
your equation is
y=12x
now...
y = 384
so
384=12x
x= 32
Ella's pet snake is 42 inches long, and Roya's pet snake is 8 feet long. How many inches longer is Roya's snake?
Answer:
54 inches
Step-by-step explanation:
First, let's convert the measurements into a common measurement.
Since inch is the smallest measurement here, let's use that.
Ella's pet snake is 42 inches long.
Roya's pet snake is 8 feet long. There are 12 inches in one foot. Therefore, 8 feet would mean 12 times 8 or 96 inches.
Therefore, Roya's snake is 96 inches long.
To find out how many inches longer is Roya's snake, subtract:
96 - 42 = 54.
Therefore, Roya's snake is 54 inches longer than Ella's.
Evaluate the expression 5^-2
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{1}{25}}[/tex]
When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:
[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]
Solve for y.
y/-1 +-7=-11
Answer:
y = 4
Step-by-step explanation:
Move all terms not containing y to the right side of the equation.
-y = -4
Multiply each term in − y = − 4 by − 1
y = 4
Hope this can help you
Peter attempted to use the divide-center method to find the line of best fit on a scatterplot.
What was his mistake?
He had a different number of points to the left of the vertical line than to the right of the vertical line.
He had a different number of points above the line of best fit than below the line of best fit.
He didn’t approximate the center of the cluster located on the left side of the vertical line and of the cluster located on the right side of the vertical line.
He didn’t connect the centers of the clusters on the left side and right side of the vertical line to produce the line of best fit.
Answer:
He had a different number of points to the left of the vertical line than to the right of the vertical line.
Step-by-step explanation:
Divide-center method is the method which involves dividing the data on the graph into two equal parts and then fin the line of best fit. The center of each group is approximated and then a line is constructed between two centers which is estimated as line of best fit.
When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain. Yes. The formula for s is divided by n, while the formula for σ is divided by N − 1. Yes. The formula for s is divided by n − 1, while the formula for σ is divided by N. No. The formula for both s and σ is divided by n − 1. No. The formula for both s and σ is divided by N.
Answer:
Yes. When computing the sample standard deviation, divide by n −1. When computing the population standard deviation, divide by N
Step-by-step explanation:
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
HELP ASAP
[tex]Given that $33^{-1} \equiv 77 \pmod{508}$, find $11^{-1} \pmod{508}$ as a residue modulo 508. (Give an answer between 0 and 507, inclusive.)[/tex]
===================================================
Work Shown:
[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]
Notice how 33*77 = 2541 and 11*231 = 2541
[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.
So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]
when a 200 g solution A and 400g of saline solution B are mixed a 6% salt solution is created also when a 400g of saline solution A and 200g of solution B are mixed 7% salt is created find what percent concentration of saline and saline b solution are
Answer:
A = 8%, B = 5%
Step-by-step explanation:
Let
a=concentration of solution A (in percent)
b=concentration of solution B (in percent)
Given
2a+4b = 0.06*(2+4) ...........(1)
4a+2b = 0.07*(4+2) ...........(2)
2(1) - (2)
4a-4a +8b-2b = 6 (2*0.06-0.07)
6b = 6(0.05)
b = 0.05 .............(3)
Substitute (3) into (1) and solve for a
2a+4(0.05) = 0.36
2a = 0.16
a = 0.08
Evaluate 5 - t/3 when t =12
Answer:
1
Step-by-step explanation:
Plug in t = 12 in the expression
[tex]5-\frac{t}{3}=5-\frac{12}{3}[/tex]
= 5 - 4/1
= 5 - 4
= 1
Answer:
[tex]\Huge \boxed{1}[/tex]
Step-by-step explanation:
[tex]\displaystyle 5-\frac{t}{3}[/tex]
The value of [tex]t[/tex] in the expression is 12.
Replace the [tex]t[/tex] variable with 12.
[tex]\displaystyle 5-\frac{12}{3}[/tex]
Evaluate the expression.
[tex]5-4[/tex]
[tex]1[/tex]
Autumn runs a farm stand that sells peaches and grapes. Each pound of peaches sells
for $2 and each pound of grapes sells for $4. Autumn sold 35 more pounds of grapes
than pounds of peaches and made $200 altogether. Graphically solve a system of
equations in order to determine the number of pounds of peaches sold, 2, and the
number of pounds of grapes sold, y.
Answer:
She sold 10 pounds of peaches and 45pounds of grapes
Step-by-step explanation:
X= pounds of peaches
x+35=pounds of grapes
2x+4(x+35)=200
2x+4x+140=200
6x=200-140
6x=60
x=10
She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)
If 2x+5=8x, then 12x=?
Answer:
[tex]\boxed{10}[/tex]
Step-by-step explanation:
[tex]2x+5=8x[/tex]
[tex]\sf Subtract \ 8x \ from \ both \ sides.[/tex]
[tex]2x+5-8x=8x-8x[/tex]
[tex]-6x+5=0[/tex]
[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]
[tex]-6x+5-5=0-5[/tex]
[tex]-6x=-5[/tex]
[tex]\sf Divide \ both \ sides \ by \ -6.[/tex]
[tex]\displaystyle \frac{-6x}{-6} =\frac{-5}{-6}[/tex]
[tex]\displaystyle x =\frac{5}{6}[/tex]
[tex]\sf Evaluate \ 12x.[/tex]
[tex]\displaystyle 12 \cdot \frac{5}{6} =\frac{60}{6} =10[/tex]
Answer:
10
Step-by-step explanation:
2x+5=8x: First, you are going to subtract 2x from both sides of the equation.
5=6x: Now divide 6x from each side of the equation.
x=5/6: now plug in 5/6 by multiplying this number by 12.
Your final answer should be 10.
Diagram shows helicopter H flying towards an island P
When the helicopter is 100 m above sea level, the pilot sees a man fishing from boat Q. Given the angles of depression of the island P and boat Q from H are 22° and 61.5° respectively.
Calculate the distance, in M, of PQ
Please help me to explain :(
Answer:
193.21 m
Step-by-step explanation:
make a vertical line down from the helicopter that is 100m
tan 61.5 = 100/x x = 54.3 (distance from the point directly below helicopter to boat)
tan 22 = 100/x x = 247.51 (distance from the point directly below helicopter to the island
247.51 - 54.3 = 193.21 (distance from boat to island)
Jonah will cover a cube in wrapping paper. Each edge of the cube is 25 cm long. What is the least amount of
wrapping paper he needs to cover the cube?
15 625 square centimeters
25 square centimeters
37.5 square centimeters
42 25 square centimeters
Save and Exit
Next
Subm
MO
Answer:
3750 cm²
Step-by-step explanation:
To find the answer, we need to find the surface area of the cube. The surface area formula for a cube is 6a² where a = the length of an edge. We know that a = 25 so the surface area is 6 * 25² = 6 * 625 = 3750 cm².
Answer:
37.5 hopefully this is the answer you were looking for!
Step-by-step explanation:
solve the equation: csc(4x)-2=0
Step-by-step explanation:
csc(4x) − 2 = 0
csc(4x) = 2
sin(4x) = 1/2
In radians:
4x = π/6 + 2kπ, 5π/6 + 2kπ
x = π/24 + kπ/2, 5π/24 + kπ/2
In degrees:
4x = 30° + 360°k, 150° + 360°k
x = 7.5° + 90°k, 37.5° + 90°k
Which graph represents the solution set of this inequality?
10c + 5 < 45?
Answer:
see below
Step-by-step explanation:
10c + 5 < 45
Subtract 5 from each side
10c + 5-5 < 45-5
10c < 40
Divide by 10 on each side
10c/10 < 40/10
c < 4
Open circle at 4 and the line going to the left
What is the value of this expression? (the best answer receives a brainiest)
Answer:
answer is D
Step-by-step explanation:
2^4=16
16+(16-12)=20
over
(6+9)/(7-4)
15/3=5
so the new equation is 20/5=4
Answer:
D. 4
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Exponents
[tex]\frac{16 + (16 -3(4))}{(6+9)/(7-4)}[/tex]
Step 2: Parenthesis
[tex]\frac{16 + (16 -12)}{15/3}[/tex]
Step 3: Parenthesis
[tex]\frac{16 + 4}{15/3}[/tex]
Step 4: Divide
[tex]\frac{16 + 4}{5}[/tex]
Step 5: Add
[tex]\frac{20}{5}[/tex]
Step 6: Divide
4
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
land and sea corporation has just purchased some shoreline property, and according to their calculations it will cost 2.5 times as much to develop the land as much as it did to buy it. If land and sea believe it will end up spending a combined total of $13,457,500 on both the land and its developments, how much must be the land alone have cost?
Answer:
5,383,000 / *improvments cost 8,074,500
Step-by-step explanation:
if 2.5 is by 'times' then,
13,457,500 / 2.5 =
5,383,000
Which means the cost of the land is 5,383,000
To check just multiply:
5,383,000 x 2.5 = 13,457,500
*Extra
13,457,500 - 5,383,000
= the cost of improvements = 8,074,500
Hope this helps, and have a good day :)
Answer:
$3,845,000
Step-by-step explanation:
Land cost = lDevelopment cost = dTotal cost = $13,457,500As per given:
d= 2.5 lThen total is:
l+2.5l= 134575003.5l= 13457500l= 13457500/3.5l= $3845000Cost of the land alone is $3,845,000
I NEED HELP PLEASE I GIVE 5 STARS !
Answer:
C. 2[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Square root of 116 is 10.7703296
Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She sold $600 in clothing on Saturday and $1200 in clothing on Sunday. How much did she earn over the two days? A. $252 B. $291 C. $392 D. $532
Answer:
I hope this helps!
Answer D
Step-by-step explanation:
Step-by-step explanation:
salary per day =$140
bonus on sales =14%
sales on Saturday =$600
bonus on Saturday sales=14/100*$600
=$84
sales on Sunday =$1200
bonus on Sunday sales=14/100*$1200
=$168
total amount she earned over the two days=$140+$84+$168
=$532
PLEASE HELP ASAP THANKS!!!!!!!!
Answer:
x-√x -12
Step-by-step explanation:
(√x +3)(√x -4)=
x-√x -12
Answer:
the answer is C
Step-by-step explanation:
I used PEMDAS and school knowledge that I learned 2 years ago that I can't explain much, cause I i am bad at math, most of the time
Does someone know how to solve this?
Answer:
6 quarts
Step-by-step explanation:
8 bags
--------
2 quarts
Multiply top and bottom by 3
8*3 bags
--------
2*3 quarts
24 bags
--------------
6 quarts
Answer:
6
Step-by-step explanation:
2 quarts of iced tea = 8 tea bags.
x quarts of Iced tea = 24 tea bags
=> 2/8 = x/24
=> Multiply the extremes and means
=> 8x = 48
=> 8x / 8 = 48 / 8
=> x = 6
6 quarts of iced tea can be made with 24 tea bags.
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?
Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]
Thus, the expression is (x² - 6y² + 3xy).
