Answer:
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
Step-by-step explanation:
1 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)
2
=a
2
+2ab+b
2
.
({x}^{2}+2xy+{y}^{2})({x}^{2}+2xy+{y}^{2})(x
2
+2xy+y
2
)(x
2
+2xy+y
2
)
2 Expand by distributing sum groups.
{x}^{2}({x}^{2}+2xy+{y}^{2})+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
2
(x
2
+2xy+y
2
)+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
3 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2xy(x
2
+2xy+y
2
)+y
2
(x
2
+2xy+y
2
)
4 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}({x}^{2}+2xy+{y}^{2})x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
(x
2
+2xy+y
2
)
5 Expand by distributing terms.
{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}{x}^{2}+2{y}^{3}x+{y}^{4}x
4
+2x
3
y+x
2
y
2
+2x
3
y+4x
2
y
2
+2xy
3
+y
2
x
2
+2y
3
x+y
4
6 Collect like terms.
{x}^{4}+(2{x}^{3}y+2{x}^{3}y)+({x}^{2}{y}^{2}+4{x}^{2}{y}^{2}+{x}^{2}{y}^{2})+(2x{y}^{3}+2x{y}^{3})+{y}^{4}x
4
+(2x
3
y+2x
3
y)+(x
2
y
2
+4x
2
y
2
+x
2
y
2
)+(2xy
3
+2xy
3
)+y
4
7 Simplify.
{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x
4
+4x
3
y+6x
2
y
2
+4xy
3
+y
4
answer: x^4+4x^3 y+6x^2 y^2+4xy^3+y^4
Which ordered pair is a solution of the equation y=2x+5
A. (3,11)
B. (2,7)
C. (1,6)
Answer:
A(3,11)
Step-by-step explanation:
[tex]y = 2x + 5[/tex]
[tex]2×3 = 6[/tex]
[tex]6 + 5 = 11[/tex]
Which of the following expressions can be factored by grouping? (Select all that apply.)
a^2 - 9 a + 7 ab + 63 b
3 a + 4 ab - b - 12
ab + 6 b - 2 a - 12
x^3 + 9 x^2 + 7 x + 63
ay^2 + a - y^2 - 1
Answer:
Options (3), (4) and (5)
Step-by-step explanation:
1). a² - 9a + 7ab + 63b
= a(a - 9) + 7b(a + 9)
Now we can not solve this problem further.
Therefore, can't be factored by grouping.
2). 3a + 4ab - b - 12
= a(3 + 4b) - 1(b - 12)
We can't solve it further.
Therefore, can't be factored by grouping.
3). ab + 6b - 2a - 12
= b(a + 6) - 2(a + 6)
= (b - 2)(a + 6)
We can be factored this expression by grouping.
4). x³ + 9x²+ 7x + 63
= x²(x + 9) + 7(x + 9)
= (x² + 7)(x + 9)
Therefore, the given expression can be factored by grouping.
5). ay² + a - y² - 1
= a(y² + 1) - 1(y² + 1)
= (a - 1)(y² + 1)
This expression can be factored by the grouping method.
Options (3), (4) and (5) are the correct answers.
Use the given figure to find the length of x.
Answer:
x = 18
Step-by-step explanation:
This problem can be solved using concept of Pythagoras theorem.
Pythagoras theorem states that in a right angled triangle, if "a" and "b" are sides containing the right angle and h is hypotenuse then the relation between them is [tex]a^2 + b^2 = h^2[/tex]
_________________________________________
Given in the problem
a = 24
b = x
h = x+12
applying Pythagoras theorem
[tex]24^2 + x^2 = (x+12)^2\\=> 576 + x^2 = x^2 + 24x + 144\\=>576 = x^2 + 24x + 144 - x^2\\=> 576 = 24x + 144 \\=> 576 - 144= 24x\\=> 432 = 24x\\=> x = 432/24 = 18[/tex]
for (x+12)^2 we have used formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
Thus, value of x is 18.
1.) Predict how many times you will roll a number less than 3 if you roll a standard number cube 100 times. Round to the nearest integer, if necessary.
You will roll a number less than 3 about____
times.
2.) you flip a fair coin 28 times. About how many times would you expect heads to appear?
If a fair coin is flipped 28 times then heads should appear about______
times.
Step-by-step explanation:
i dont know one. but number to is 14. hope it helps
"Two complementary angles are not congruent."
Answer:
40 and 50,20 and 70
Step-by-step explanation:
complementary angles are angles that added equal to an angle of 90 degrees and it says they are not congruent so the two angles are diferent
the given statement "Two complementary angles are not congruent" is not true. The counter-example is 45°+45°=90°.
The given statement is "Two complementary angles are not congruent."
What are complementary angles?Two angles are Complementary when they add up to 90°.
Now, if we add 45°+45°=90°
Therefore, the given statement "Two complementary angles are not congruent" is not true. The counter-example is 45°+45°=90°.
To learn more about complementary angles visit:
brainly.com/question/5708372.
#SPJ2
Here is a list of numbers.
17
18
19
20
21
22
23
24
a) From the numbers in the list, write down a number that is a factor of 20
b) From the numbers in the list, write down a number that is a multiple of
both 3 and 7
c) Write down all the prime numbers from the list
Answer:
A=20 B=23 C=17,19,23
Step-by-step explanation:
A=20
B=23
C=17,19,23
A man measured his height and found 5.7 feet. However, after he carefully measured his height a second time, he found his real height to be 5 feet.What is the percent error the man made the first time he measured his height?
Answer:
percentage error = 12.28%
Step-by-step explanation:
5 x 0.14 = 0.7
5 x 1.14 = 5.7
as increase is not the same as error decrease.
We use the same numbers 12.28% = 0.1228.
5.7 x 0.1228 = 0.69996 = 12.28%
5.7 - 0.69996 = 5.00004 foot. As decrease.
And find it is correct.
His error therefore was 12.28% out.
As we work the first numbers 5.7 and can only x by a number to see 5ft
We take 5.7 x 0.1228 and find 0.69996 when taken from 5.7 ft. is unmistakably 5 foot. (5.00004) ft.
Answer:
14%
Step-by-step explanation:
percent error = (experimental measure - real measure)/(real measure) * 100%
percent error = (5.7 ft - 5 ft)/(5 ft) * 100%
percent error = (0.7 ft)/(5 ft) * 100%
percent error = 0.14 * 100%
percent error = 14%
CAN PLEASE PLEASE GET HELP PLEASE I NEED IT PLEASE AND THANK YOU
Answer:
Step-by-step explanation:
the domain for (2x-1)/(x^2-7) is x not equal to +/- sqrt(7)
the numerator of a fraction is 1 more than twice its denominator if 4 is added to both the numerator and the denominator the fraction reduces to 5/3 find the denominator
Answer:
11
Step-by-step explanation:
Given Fraction
Let the denominator = x
The numerator is 2x + 1
2x + 1
=====
x
The new fraction
2x + 1 + 4
=========
x + 4
Equation
2x + 5 5
====== = ====
x + 4 3
Solution
Cross Multiply
3(2x + 5) = 5(x + 4)
Remove the brackets
6x + 15 = 5x + 20
Subtract 5x from both sides
6x - 5x + 15 = 20
Subtract 15 from both sides
x = 20 - 15
x = 5
============
Answer
2(5) + 1 = 11
The original numerator is 11
Select all true statements
Answer:
f(x) has a larger growth rate
f(x) is always greater than g(x)
Step-by-step explanation:
f(x) = 2/5 x
g(x) = -2x
the slope of f(x) when graphed is 2/5 x, which is a positive value making it a larger growth rate than g(x) and it also will always be greater since the value of f(x) is positive
therefore the correct true statements are:
f(x) has a larger growth rate, and f(x) is always greater than g(x)
options 1 and 3
Step-by-step explanation:
option 1 is correct because f (x) is positive hence making it greater than g(x) which is negative.
Find the domain and range of the relation. {(−7,−18),(−23,21),(4,13),(−17,22),(2,−10)}
Answer: Domain = all x values and Range = all y values
Step-by-step explanation:
The domain of a function is all the allowed x values that make the function true. Luckily you were already given the domain. Its all the x values.
The range of a function is pretty much all the allowed y values of a function. Or, what y values the function can be equal to. So that's just all the y values
When listing the domain and range, you generally want to do it from least to greatest and you do not want to repeat any values
Answer:
D:{ -23,-17,-7,2,4}
R:{-18,-10,13,21,22}
Step-by-step explanation:
The domain is the input
D:{ -7,-23,4,-17,2}
We normally put them in numerical order
D:{ -23,-17,-7,2,4}
The range is the output
R:{-18,21,13,22,-10}
We normally put them in numerical order
R:{-18,-10,13,21,22}
What is the domain of f(x)=√(x)?
Answer:
f(x)=√x f ( x ) = x is x≥0 x ≥ 0
Step-by-step explanation:
The domain of the function f(x)=√x f ( x ) = x is x≥0 x ≥ 0 . The range of a function is the set of results, solutions, or ' output ' values (y) to the equation for a given input.
Can someone help me on this math question?
Answer:
23°.
Step-by-step explanation:
Look closely at the spots where A and C connect. They end in the same exact place, suggesting that they are the same number of degrees.
It's a no-brainer.
The solution of the equation 10 - (x +2) = 7x is -
5
-2
0
1
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
We have the equation
[tex]10-(x+2)=7x[/tex]
The first thing we need to do is distribute the negative throughout the parenthesis
[tex]10-x-2=7x[/tex]
Now, we can combine like terms
[tex]8-x=7x[/tex]
Now we can add x to each side
[tex]8x=8[/tex]
And lastly, we can divide each side by 8
[tex]x=1[/tex]
Our last step is to check our answer
[tex]10-(1+2)=7(1)\\\\10-(3)=7\\\\7=7[/tex]
Answer:
1
Step-by-step explanation:
1) 10-x-2=7x
2) -x + 8 = 7x
3) 8x=8
4) x=1
If BCDE is congruent to OPQR then BE is congruent to _____
Answer:
If BCDE is congruent to OPQR then BE is congruent to RO
A sloth is climbing down a tree at a constant speed. The sloths height changes by -55 feet in 11 minutes. Which expression represents change in the sloths height each minute?
-55•(-11)
-55•11
-55 divided by 11
-55 divided by (-11)
There are 48 students studying a foreign language at the
community college. If the only two foreign languages offered are
French and Spanish, and 28 students are studying French, which of
the following represents the ratio of students studying Spanish to
the total number of foreign language students?
Answer:
5/12
Step-by-step explanation:
If 28 students are studying French, then the remaining 20 are studying Spanish. The ratio of those studying spanish to the total number of students is 20/48. This can be simplified to 5/12.
Answer:
5 to 12
Step-by-step explanation:
Since 28 students are already taking French, then you have to subtract that from the total students, giving you 20 students who take Spanish. So the ratio for Spanish students to total students would be 20 to 48. But that can be simplified (since all ratios need to be simplified) to 10 to 24. And that can again be simplified to 5 to 12.
Hope this helped!
100 points, will give brainliest!
Suppose that in circle with center P, and a central angle, ∠OPQ, intersects minor arc OQ, where the measure of arc OQ = 82◦, and the measure of ∠OPQ is (5x – 3) ◦.
What is the value of x?
Thank you so much for helping!
Hope you are doing well
Answer:
x=17
if a book is 33 hour and 45 min long ,how many days would it take you to read it if you read 5 hours a day.
Answer:
7 days
Step-by-step explanation:
Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan (θ +x) and sin (θ +x))
Answer:
tan (θ+x)= -33/56
sin (θ+x)=33/65
Step-by-step explanation:
cosθ= -4/5 , sin x = -12/13
cosθ= -4/5; θ is in the third quadrant=> sinθ=-√(1-cos² θ)
sinθ=- √(1-16/25)=- √(9/25)=-3/5
sinx= -12/13; x is in the fourth quadrant=> cosx=+√(1-sin²x)
cosx=√(1-144/169)= √(25/169)=5/13
tgθ= sinθ/cosθ=(-3/5)/(-4/5)=3/4
tgx= sinx/cosx=(-12/13)/(5/13)= -12/5
tan (θ+x)=(tgθ+tgx)/(1-tgθ*tgx)
tan (θ+x)=(3/4-12/5)/(1+3/4*12/5)=(-33/20)/56/20)= -33/56
sin (θ+x)=sinθcosx+coxθsinx=-3/5 *5/13 +-4/5 * (-12/13)=-15/65+48/65=33/65
Terrell wrote that 5-4.2=8. Which statement about this answer is true?
Answer:
No.
Step-by-step explanation:
No. 5 - 4.2 = 0.8
Answer: 8 is wrong because a number gets smaller, not larger, when you take 4.2 from it.
Step-by-step explanation: I had this on my Imagine Math. The reason why this is wrong is because 5 – 4.2 doesn't not equal 8!Estimation might help. 5 doesn't need to be rounded. 4.2 is rounded to 4...5-4 = 1The Actual answer is actually 0.8.I hope this helps :)
Which of the following represents 1 < x <_ 6
a. [1/6]
b. (1,6]
c. (1,6)
d.[1,6)
Answer:
The correct answer is
b.(1,6]
What is the area of a circle that has a radius of 16.25? USE 3.14 FOR PI!!!!
DO NOT ROUND.
Answer:
730.61664
Step-by-step explanation:
area equals πr2=π·15.252≈730.61664
Answer:
829.15625 units squared
Step-by-step explanation:
The formula for area is A= 3.14 * (r^2). 16.25^2 is 264.0625. 3.14 * 264.0625 is 829.15625.
Attention!
I have tons of math questions waited to be answer on my page check them out and get points!
Answer:
ok
Step-by-step explanation:
ok
Answer:
I will try but how many are there?
Step-by-step explanation:
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that apply. p ∧ q, p ∨ q, p → q, q → p, p ↔ q, q ↔ p
Answer: the answer is p v q and q -> p
Step-by-step explanation:
edg 2022
Jill invested $20,000 in an account that earned 5.5% annual interest, compounded annually. What is the value of this account after 10 years? Express your answer rounded to the nearest cent.
Answer:
A = $ 34,162.89
Step-by-step explanation:
A = $ 34,162.89
A = P + I where
P (principal) = $ 20,000.00
I (interest) = $ 14,162.89
Compound Interest Equation
A = P(1 + r/n)nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Answer:
34,162.89
Step-by-step explanation:
What is the range of the data
represented in the dot plot below?
2
3
0
Answer:
Range = 3
Step-by-step explanation:
First, start off by ordering the list from least to greatest. Then, subtract the least number (0) from the greatest number (3), which will get you the range of 3.
Hope this helps! :D
45x^7 divided by 9x^2
Answer:
5x^5
Step-by-step explanation:
45x^7 ÷ 9x^2=45÷9 × x^7÷x^2= 5x^5
The right answer is 5x^5
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
About how much medicine is in a medicine bottle
Answer:
For measuring such small amounts of medicine, your doctor may give you a 1 cc syringe (there is that cubic centimeter thing again - remember, it is the same as a milliliter - ml).
...
measurement of medicines.
1/4 teaspoon 1.25 ml
1 teaspoon 5 ml
1-1/2 teaspoon 7.5 ml
1 tablespoon 15 ml
Step-by-step explanation:
Answer:
Depends on the medicine, some have more some have less there is no set amount
Step-by-step explanation:
Pls give brainliest i had 40 down to 1 for no reason, i will thank you for it via ur profile and comments also a thanks would be appreciated too
I hope this helps u! ;)
CO
Table A shows the Fahrenheit temperatures for select Celsius temperatures. Table B shows the Celsius
temperatures for select Fahrenheit temperatures.
Table A
Table B
с
-10
0
10
20
30
F
14
32
50
68
86
F
14
32
50
68
86
C
-10
0
10
20
30
The tables show that the two functions are
ordered pair
✓ for the other function
because the ordered pair (x, y) for one function is the
A Intro
Answer:
it's is a
because the law states
Answer:
First 1 is Inverse and the second one is y=x