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
PLEASE HELP I NEED ANSWERS!!
Answers
Step-by-step explanation:
2. Commutative Property of Multiplication
3. Associative Property of Multiplication
4/5/6 Distrubtitive Property.
D. A car was sold for
$26,350. Its value decreases
by 17% each year.
a) Find an explicit formula
for cost of the car Cn after
the nth year.
b) What is the car's value
after 8 years?
c) After 3 years, how much
has the car's value
decreased?
Answers
a. The explicit formula for the cost of the car in the nth year is $26,350(0.83^n) .
b. The car's value after 8 years is $5,934.79.
c. The decrease in the value of the car is $11,283.41.
The formula that can be used to determine the value of the car with a decline in value is:
FV = P (1 - r)^n
FV = Future value of the car
P = cost of the car
R =rate of deprecation
N = number of years
Cost of the car after n years = $26,350 x (1 - 0.17)^n
$26,350(0.83^n)
Car's value after 8 years = $26,350 x (1 - 0.17)^8
$26,350(0.83^8) = $5,934.79
Decrease in the value of the car after 3 years= cost of the car - value of the car in 3 years
Value of the car in 3 years = $26,350 x (1 - 0.17)^3 = $15,066.59
$26,350 - $15,066.59 = $11,283.41
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can some pls help me ☹?
Answers
Answer:
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Step-by-step explanation:
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Solve for x
-1/5x -25 = -9
Answers
Answer:
-80
Step-by-step explanation:
you pass the 25 to the right side adding and the the 1/5 multiplying by -5 to the right side
What is the equation of the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction) and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form
Answers
Step-by-step explanation:
Slope-intercept form: y = mx + b
Step 1: Find the slope.Solve for [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]y2-y1 = \frac{11}{12} -\frac{19}{20}[/tex]
[tex]x2-x1 = \frac{1}{3} -\frac{2}{5}[/tex]
To solve for the fractions you need a common denominator.
[tex]y2-y1 = \frac{11*20}{12*20} -\frac{19*12}{20*12} = \frac{220}{240} -\frac{228}{240}=\frac{-8}{240} = \frac{-1}{30}[/tex]
[tex]x2-x1 = \frac{1*5}{3*5} -\frac{2*3}{5*3} = \frac{5}{15} -\frac{6}{15}=\frac{-1}{15}[/tex]
To divide fractions you keep (the first equation), change (the division sign to multiplication), and flip (the second fraction).
[tex]\frac{y2-y1}{x2-x1}=\frac{\frac{-1}{30} }{\frac{-1}{15} } = \frac{-1}{30}*\frac{15}{-1} =\frac{-15}{-30}=\frac{1}{2}[/tex]
Step 2: Plug slope and a point into y=mx+b to solve for b.[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{2}[/tex])*([tex]\frac{1}{3}[/tex])+b
[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{6}[/tex])+b
[tex]\frac{11}{12}-\frac{1}{6}[/tex] = b
[tex]\frac{11*6}{12*6}-\frac{1*12}{6*12}=\frac{66}{72} -\frac{12}{72} =\frac{54}{72}=.75[/tex]
b = .75
y = [tex]\frac{1}{2}+.75[/tex]
Find an ordered pair (x, y) that is a solution to the equation 3x-y=4
Answers
Answer:
(0,-4)
Step-by-step explanation:
3(0) - (-4) = 4
0 + 4 = 4
i don't understand how to do this someone help me math!!
Answers
Answer:
-8
Step-by-step explanation:
ky^2 = -5y + 7y^2 +9y - 15y^2 -4y
ky^2 = -8 y^2
k = -8
Answer:
8
Step-by-step explanation:
We believe the problem here requires that all of the coefficients in the expression on the left be zero. That is, the equation will be true for any value of y.
We can work this a couple of ways. One of them is to simplify the given expression. Let 'a' represent our unknown coefficient.
[tex]-ay^2-[-5y-y(-7y-9)]-[-y(15y+4)]=0\\\\-ay^2-[-5y+7y^2+9y]+[15y^2+4y]=0\\\\-ay^2-[7y^2+4y]+15y^2+4y=0\\\\(-a-7+15)y^2+(-4+4)y=0\\\\(-a+8)y^2=0[/tex]
In order for this to be zero for all values of y, we must have (-a+8) = 0.
a = 8
The missing coefficient is 8.
_____
Since this expression must be true for every value of y, another way to work this is to choose a value of y. This will tell us what the coefficient must be for the expression to be zero. Let y = 1.
-a·1² -[-5·1 -1(-7·1 -9)] -[-1(15·1 +4)] = 0
-a -[-5-(-16)] -[-19] = 0
-a -11 +19 = 0
-a +8 = 0
a = 8 . . . . . . same as above
_____
Additional comment
The many minus signs are intended to make sure you're comfortable with arithmetic with negative coefficients and negative numbers. The key, of course, is that -(-a) = +a. The opposite of the opposite is the original.
We have assumed that the dash at the beginning of the line (before the answer box) is intended to be a minus sign. If that is not the case, then your answer will be -8, instead of 8.
Mario started his homework at 3:30 he finished 25 minutes later what time did he finish his homework
Answers
Answer:3.55
Step-by-step explanation:
you add the time dude
On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}
Answers
Answer:
Step-by-step explanation:
Domain is all the x's and range is all the y's. There's no reason why you couldn't pop any x into the given equation and calculate it and get a number out. So literally ANY x can be used and found on this graph. So the domain is all real numbers, one of the first two answers is going to be the right one. Now, the range is all the y's on the graph. The problem says that the parabola opens down, which means it has a highest point. There is no graph above that point. That's the point (-1, 16). So 16 is the highest y-value you can find on the graph. All the rest of the y's are smaller. The range is all the y's such that the y's are 16 and smaller...in math that's written {y | y <= 16} So the second answer is the right one.
The domain is all real numbers. The range is {y | y ≤ 16}
How to determine the domain and the range?The attached graph completes the question
Calculating the domain
The function is given as:
f(x) = -x² - 2x - 15
The above function is a parabola or a quadratic function.
Quadratic functions have their domain to be the set of all real numbers.
Hence, the domain is all real numbers.
Calculating the range
On the graph, we have the maximum value of y to be:
Maximum = 16
Because the parabola opens down, the range would be:
y ≤ 16
Hence, the range is {y | y ≤ 16}
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pls answer don’t scam
Answers
Answer:
y=x
step by step:
graph equation is y=mx+c
y intercept (c) is 0
gradient (m) is 1
gradient is represented as (m), so the equation is just y=1x, simplified-> y=x
Answer:
money = 2×tickets
Step-by-step explanation:
For 1 ticket sold, $2 is collected. for 8 tickets sold, $16 is collected. The relationship appears to be proportional with a constant of proportionality of $2 per ticket.
The axes are labeled "money" and "tickets", so we can write the equation ...
money = 2×tickets . . . . . where money is in dollars
__
If you like, you can use y to represent dollars collected, and x to represent tickets sold. Then the equation is ...
y = 2x
What is the equation of the line that passes through the point (-1, -7) and has a
slope of 2?
Answers
Answer:
y = 2x - 5
Explanation:
Since the slope is given as 2, we can substitute this into the equation:
y = 2x+b
Now, we can manipulate the point (-1,-7) to be in the form of a y-intercept - (0, y).
Note that a slope of 2 = 2/1, which means the rise = 2(which is added to the y) and run = 1(which is added to the x).
Adding this to our point of (-1,-7), we get:
((-1+1),(-7+2)) = (0, -5)
Therefore -5 is our y-intercept.
Now, substituting -5 into our equation, we get:
y = 2x + -5
Answer:
y=2x-5
Step-by-step explanation:
The slope-intercept form of an equation looks like y=mx+b. Where m is the slope and b is the y-intercept. The slope is already given to us, so m is 2.
To find b use the equation [tex]b=y_1-m*x_1[/tex]. So, to find the y-intercept use b=-7-(2*-1). This equals b=-5.
So, plug in the values to get the final equation y=2x-5.
plss help me with this:(((
Answers
Answer:
11) 7 ( Answer A)
12) (-2) ( Answer D)
Step-by-step explanation:
You can use y = m x + c to answer these questions.
In the equation y = m x + c,
m = slope
c = y - intercept
According to the question,
they have given the equation,
y = 7 x - 2
So, you can replace it with y = m x + c like this.
y = 7 x - 2
↑ ↑
m c
There fore,
slope = 7
y - intercept = ( - 2)
And now let's write the answers for the question.
11) 7 ( Answer A)
12) (-2) ( Answer D)
Hope this helps you :-)
Find the slope of the line going through the pair of points: (11, 7), (-9, 8)
20
O-20
0 - 20
O 20
Answers
Answer:
1/-20 or -0.05
Step-by-step explanation:
y2-y1/x2-x1 (11,7) and (-9,8)
8-7/-9-11= 1/-20 we flipped we got -20
Hope this help ;)
4% percent of a number is what fraction of that number?
Answers
Answer:
1/25
Step-by-step explanation:
Convert to a fraction by placing the expression over 100 .
Answer : 4/100 and / or 1/25
Step-by-step explanation:
when converting percentages to fractions its always out of 100
for example, if the percentage is 4% then its 4/100
6. You have inherited a piece of land in the shape of a quadrilateral. It has the given measurements as shown. Find the length needed for a fence to be constructed from point A to point D. Find the angle mearurements of ÐA and ÐL. Also, find the area of the quadrilateral.
Answers
Answer:
Add up all the sides of the quadrilateral and the answer is the perimeter
Step-by-step explanation:
Which of the following
Answers
Answer:
which of the following what??
Step-by-step explanation:
..
Iqbal and Sachin have bookshelves of the same size and holding books of the same sizes. Iqbal's shelf is 7/8 full and Sachin's shelf is 12/15 full. If 351 more books of the same size are distributed among them, then they can fill their shelves completely. How many books does Sachin have now?
a)
864
b)
865
c)
800
d)
850
Answers
Answer:
540 books
Step-by-step explanation:
It is given that Iqbal's shelf is 7/8 full ..
→ That Means we can say that, iqbal's shelf is (1 - 7/8) = 1/8 is Empty .....
Similarly,
Sachin's shelf is 12/15 full.
→ That Means we can say that, sachin's shelf is (1 - 12/15) = 3/15 is Empty.....
→ Both total Empty = (1/8 + 3/15)
Taking LCM of denominator ,
→ (15+24 /120)
→ 39/120
→ 13/40 part is Empty in both .
Now, it has been said that, when 351 more books are distributed among them , both shelves filled completely .
So, we can say that :----
→ 13/40 part ---------------- 351
→ 1 part ---------------------- 351*40/13 = 1080 = Total Books in Both Selves .
__________________
Now, since bookshelves of the same size and holding books of the same sizes ,,
→ Both have Books in Each = 1080/2 = 540 books .
Which expression is equivalent to 7x + 5x?
a. 12x
b.12x^2
c. 35x
d. 35x^2
Answers
Answer:
12x
Step-by-step explanation:
P l e a s e NO LINKS!
Which word has reflectional symmetry across a horizontal line?
A. BOOK
B. LOOK
C. NOOK
D. ROOK
Answers
Answer:
A BOOK
Step-by-step explanation:
pretty sure its that
The word BOOK shows a reflection symmetry across a horizontal line.
Hence, option (A) is correct.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Solve with the help of options,
(A)
BOOK
To find the reflection across a horizontal line,
When word B reflected over horizontal line, it is symmetrical
Word O is symmetrical.
And K is also symmetrical across a horizontal line.
Therefore, BOOK is a reflection symmetry across a horizontal line.
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How to you get 28 from the numbers 3, 6, 2, and 8, while only using each number once?
Answers
Answer:
3x6+2+8=28
Step-by-step explanation:
3x6=18
18 + 2 = 20
20 + 8 = 28
Answer:
9 1/3 or 9.33, 28/6 or 4 4/6, 14 and 28/8 or 3 4/8
Step-by-step explanation:
( 1 ) The number 28 divided by 3 gives 9 1/3 or 9.33.
( 2 ) Using a calculator, if you typed in 28 divided by 6, you'd get 4.6667. You could also express 28/6 as a mixed fraction: 4 4/6.
( 3 ) 28 divided by 2 is 14.
( 4 ) Using a calculator, if you typed in 28 divided by 8, you'd get 3.5. You could also express 28/8 as a mixed fraction: 3 4/8.
What is the area of the following circle? Use 3.14 for pi and enter your
answer as a decimal.
p=7
units2
Answers
if Sophia took a bath at 9:36 and finish at 10:30 how much time did she use in taking a bath
Answers
Answer:
54 minutes
Step-by-step explanation:
1) There are 60 minutes in an hour. So, you can do 60-36 to find the first value. (24)
2) Add 24 minutes to 30 and get 54 minutes.
x over 2 +2= 15 two step equations
Answers
Answer:
[tex]\boxed{\boxed{\sf x=84}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x}{6} +2=16[/tex]
Multiply both sides of the equation by 6:
[tex]\sf x+12=96[/tex]
Subtract 12 from both sides:
[tex]\sf x=96-12[/tex]
Subtract 12 from 96:
[tex]\sf x=84[/tex]
_________________________________
Answer:
[tex] \sf \: \longmapsto\frac{x}{6} + 2 = 16[/tex]
[tex]\sf \: \longmapsto\frac{x}{6} = 16 - 2[/tex]
[tex]\sf \: \longmapsto \frac{x}{6} = 14[/tex]
[tex]\sf \: \longmapsto \: x = 14 \times 6[/tex]
[tex]\sf \: \longmapsto \: x = 84[/tex]
Step-by-step explanation:
[tex]\fbox {\fbox {\fbox {\fbox{ \pink{HeavenMistress}}}}}[/tex]
1. Nimish bought a motorcycle for ₹37,690 and sold it for ₹39,100. Find his
profit or loss.
Answers
Answer:
1410
Step-by-step explanation:
Selling Price= 39100
Buying Price= 37690
Profit= Selling Price - Buying price
=39100-37690
=1410
His profit: ₹39,100 - ₹37,690 = ₹1,410
=> [tex]\frac{1,410}{37.690}[/tex] × 100% ≈ 3.75% (than the original price)
His profit is 3.75% than the original price
ok done. Thank to me :>
f(x) = -3x +4 when x = -5 show every step
Answers
Answer:
f(-5) = 19
Step-by-step explanation:
f(x) = -3x + 4
f(-5) = -3(-5) + 4
f(-5) = 15 + 4
f(-5) = 19
Answer: The answer is 19
Step-by-step explanation: We know that the X value is -5 so we substitute that in for -3x to get (-3 x -5) We end up geting 15, next we add 4 and get 19. Basically the answer is 19. Have a great day.
Forgot to add the F(-5) sorry.
A football is kicked into the air. Its height above the ground is approximated by the equation h=20t-5[tex]t^{2}[/tex], where h is the height in meters and t is the time in seconds since the football was kicked.
a)what are the zeros of the relation? when does the football hit the ground?
Answers
Answer:
Zeroes - x=0 and x=4
Football hits the ground at x=4 (4 seconds)
Step-by-step explanation:
1) Plug equation in graphing calculator and graph function.
2) Find zeroes
3) The second zero is when the football hits the ground
pls help me
do maths
Answers
50 POINTS PLEASE HELP FILL IN BLANKS!!!!
An ______ is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. ______ are groups of points that are all graphed close together. A ____ occurs when there are points clustered at two different spots on a scatter plot.
Answers
Answer:
Outlier, clusters, and gap in your value.
Step-by-step explanation:
An OUTLIER is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. DATA CLUSTERS are groups of points that are all graphed close together. A GAP IN VALUE occurs when there are points clustered at two different spots on a scatter plot.
The national debt of a country is
$27,895,168,401,112. What is this number as a
product of a single digit and a power of 10?
Answers
Answer: [tex]3 \times 10^{13}[/tex]
Explanation:
Highlight the first digit on the very left (2). The 7 right next to it means we'll round that 2 up to a 3. Every other digit becomes a zero.
The number 27,895,168,401,112 rounds to 30,000,000,000,000 which is the number 30 trillion.
It converts to the scientific notation [tex]3 \times 10^{13}[/tex] because we basically start with 3.0 and move the decimal point 13 spots to the right to arrive at 30 trillion as shown above.
how many days would it take to eat an water buffalo
Answers
Answer:
Size:
The water buffalo is the largest bovine. It is 8 to 9 feet (2.4 to 2.7 meters) from head to rump with its tail adding an extra 2 to 3.3 feet (60 to 100 centimeters). They weigh a massive 1,500 to 2,650 lbs. (700 to 1,200 kilograms). The African buffalo is smaller, but they are still quite impressive in size. They are 4.26 to 4.92 feet long (130 to 150 cm) from head to hoof and weigh 935 to 1,910 lbs. (425 to 870 kg).
Habitat:
Water buffalo live in the tropical and subtropical forests of Asia. They are aptly named, for they spend most of their time in water. Their hooves are extra wide and prevent them from sinking into mud at the bottom of ponds, swamps and rivers.
Habits
Buffalo are social animals and live in groups called herds. Water buffalo herds are segregated by gender. Young males stay with the maternal herd for about three years, and then they join a male herd. Maternal herds have up to 30 females and their offspring. Male herds have up to 10 members. African buffalo herds are mostly of mixed gender. They do have a few all-male herds, but these usually consist of old males. An African herd often has more than 1,000 members.
Diet
Buffalo are herbivores, and so eat only vegetation. Their favorite foods are grass and herbs, but water buffalo will also eat aquatic plants. Both African and Asian buffalo will eat shrubs and trees when they can't find grass or herbs to eat.