Answer:
B. X-6 and E. X + 4
Step-by-step explanation:
B. X-6
(-6)^2 + 2(-6) - 24
36 - 12 - 24
36 - 36 = 0
E. X + 4
(4)^2 + 2(4) - 24
16 + 8 - 24
24 - 24 = 0
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answer:
Step-by-step explanation:
y4−
(y2−9)(y2+9)
9
Distribute:
=y4+
−1
9
y4+9
Combine Like Terms:
=y4+
−1
9
y4+9
=(y4+
−1
9
y4)+(9)
=
8
9
y4+9
Answer:
=
8
9
y4+9
The polynomial expression is divisible by 9
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial be represented as A
Now , A = y⁴ - (y² - 9)(y² + 9)
To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.
First, we can simplify the expression inside the parentheses:
y² - 9 = (y - 3)(y + 3)
y² + 9 = (y + 3i)(y - 3i)
where i is the imaginary unit, i.e., i² = -1.
Substituting these expressions back into the original equation, we get:
y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)
Now, we can factor out (y − 3)(y + 3) from the second term:
y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)
= y⁴ - (y² - 3^2)(y² + 3²)
= (y²)² - (3²)²
= (y² + 3²)(y² - 3²)
= (y² + 9)(y² - 9)
= (y + 3i)(y - 3i)(y + 3)(y - 3)
Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.
Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.
Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9
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Can someone help me and show how to write the perimeter equation for x to this polygon.50 points Find x for full 70 points
Answer:
10x + 8 = 21
x = 1.3
Step-by-step explanation:
a)
In pentagon ABCDE,
AB = DE = 2x + 3 and BC = CD = x + 1
Perimeter of pentagon ABCDE = 21
4x + 2(2x + 3) + 2(x + 1) = 21
4x + 4x + 6 + 2x + 2 = 21
[tex] \purple {\boxed {\bold{10x + 8 = 21}}} [/tex]
b)
10x = 21 - 8
10x = 13
[tex]x = \frac{13}{10} \\ x = 1.3 \: cm [/tex]
If you 20 points invested $1,000 this year and the investment return is 7% annually, how much would you have in 20 years? Use this formula: A=P(1+r)^t (P represents initially investment, r represents the rate, and t represents the
time in years)
Answer:
2400 I'm sorry if im wrong I tried
Step-by-step explanation:
2x - 3 > 15 or 3 + 7x < 17
Answer:
2x-3>15 and 3-7x>17 =
3-7x>17
-7x>14
x<-2
Step-by-step explanation:
Sorry this is not a proper equation. I think you meant this equation.
2x-3>15 and 3-7x>17
for this equation the answer is
3-7x>17
-7x>14
x<-2
Are the graphs of the lines in the pair parallel ? Explain.
Y=2/3x-17
3-x - y = -6
A.)Yes, since the slopes are the same and the y-intercepts are different.
B.)No, since the slopes are different.
C.)No, since the y-intercepts are different.
D.)Yes, since the slopes are the same and the y-intercepts are the same.
So the right answer is of option D
Look at the attached picture
Hope it will help you...
Good luck on your assignment
2) There are four nickels and five dimes in
your pocket. You randomly pick a coin
out of your pocket and place it on a
counter. Then you randomly pick another
coin. Both coins are nickels.
Are the events independent or dependent?
What is the probability?
Answer:
dependent and 1/6
Step-by-step explanation:
dependent because the person didn't replace it.
4/9 times 3/8 which is 12/72 which equals to 1/6
A circle with circumference 6 has an arc with a
340º central angle.
Answer:
17.80236
Step-by-step explanation:
I will give you brainliest if you answer correctly!!
Answer:
The answer is B.
Step-by-step explanation:
asap-worth 25% of overall
Answer:
ummm
Step-by-step explanation:
what is the question
for the write a story just make your own problem and answer it idk wut the the other one is
Answer:
1.) Alex and Jemma decided that they will separate the dozen doughnuts that they bought. Since Jemma loved doughnuts she got 7, and Alex got 5.
2.) 35:49
Divide 35 and 5.
35/5=7
Multiply 7 by 7.
7 x 7=49.
The missing side will be 35:49
Gilbert wants to build a triangular flower garden by the front porch of his house. The garden will be 6 feet long near the front of the house and 4 feet long next to the walkway.
What will be closest to the length, in feet, of the longest edge of his garden?
A. 2
B. 4.5
C. 7.2
D. 10
Answer:
7.2
Step-by-step explanation:
use the Pythagorean theorem to find the length of the hypotenuse
a squared+ b squared= c squared
4 squared+ 6 squared = c squared
16+ 36= c squared
52= c squared
52 = 7.2 squared
Which values are solutions to the inequality below
Check all that apply
2. Which linear function is shown on the graph?
A. y = 3x - 2
B. y= -3x - 2
c. y=x-2
D. y=-x-2
ahmed sells beaded necklaces each large necklace sells for $5.60 and each small necklace sells for $4.50 how much will he earn from selling 3 large necklaces and 6 small necklaces ?
Answer:
$43.8
Step-by-step explanation:
Large necklace = LN
Small necklace = SM
LN sells for 5.60
SN sells for 4.50
LN = 5.60
SN = 4.50
you have 3 LN and 6 SN.
LN total = 3 x $5.60 = 16.8
SN total = 6 x 4.50 = 27
Add both the totals.
27 + 16.8 = 43.8
Hope this helps!
Answer:
HE/SHE earns $43.80.
Step-by-step explanation:
5.60 x 3 = $16.80
4.50 x 6 = $27.00
In totle:
16.80+27.00= 43.8The grades on a geometry midterm at Springer are roughly symmetric with u = 73 and 0 = 3.0.
Umaima scored 72 on the exam.
Find the z-score for Umaima's exam grade. Round to two decimal places.
Answer:
z = - 0.33
Step-by-step explanation:
Given that:
Mean (μ) = 73, standard deviation (σ) = 3.0
Z score is a measure in statistics to determine the number of standard deviation a value is above or below the mean of what is measured. If the value is above the mean it is positive but if it is below the mean it is negative. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate z-score for Umaima's exam grade, we need to calculate the z score of 72
For x = 72, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{72-73}{3} =-0.33[/tex]
z = - 0.33
Answer:
−0.33
Step-by-step explanation:
just did it oh khan
What is the measure of
Answer: Q = 124 and P = 29
Step-by-step explanation:
Triangles always = 180 degrees so do straight lines.
Answer:
P=29
Step-by-step explanation:
I took the diagnostic
If this helps please rate and give a thanks:)
Add me as a friend!
Good Luck!!
Is this SAS or Not SAS
Answer:
yes it is sas
Step-by-step explanation:
because one side is shared, they both have right angles and the other side is a given.
Answer:
SAS
Step-by-step explanation:
The sides are all equivalent so it is indeed a SAS triangle.
After the dimensions of an equilateral triangle are increased by a scale factor of 2.5, the perimeter is 45 units. What were the side lengths of the original triangle?
Answer:
Original side of triangle = 6 units
Step-by-step explanation:
Given:
Perimeter = 45 units
Scale factor = 2.5 (Increase)
Find:
Original side of triangle = ?
Computation:
Original Perimeter = Perimeter / Scale factor
Original Perimeter = 45 units / 2.5
Original Perimeter = 18 units
Perimeter of an equilateral triangle = 3 (Side)
18 units = 3 (Side)
Side = 6 units
Original side of triangle = 6 units
Write these numbers as fractions. Simplify the answers. 0.5, 12.3, 0.07, 0.625
0.5 => 5/10 => 1/2
12.3 => 123/10
0.07 => 7/100
0.625 => 625/1000 => 25/40 => 5/8
Answer:
see below
Step-by-step explanation:
0.5, 5/10 = 1/2
12.3 = 12 3/10
0.07 = 07/100
0.625=625/1000 =5/8
What is the constant in -4×_9
Answer:
Do u have like a worksheet for the problem because that kinda confusing , but I would love to help if you could screens shot or post the pic.
Step-by-step explanation:
Enter the value of the 8 in the following number. 438.13
Answer:
8
Step-by-step explanation:
It is in the one's place, so it is just 8x1, which is 8
I need help with this please!
Answer:
The equation of a circle using the center [tex](2,0)[/tex] and the radius [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
Step-by-step explanation:
-Directions:
To determine the following circle on a graph, you need the to look for a point that lands exactly on the center of the circle and to find the radius, you need look for a point that lands exactly on the outline of the circle and start counting from the center, to the point. Then, use both the center and the radius for the equation of a circle. After putting the center and radius on the equation of a circle, simplify the radius by the exponent [tex]2[/tex], because according to the equation of a circle, the radius is [tex]r^2[/tex].
-The equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
-Finding the center and the radius for the equation of a circle:
Center: [tex](2,0)[/tex] Radius: [tex]7[/tex]
[tex](x-2)^2+(y-0)^2= 49[/tex]
My phone rang midway between 10:53 A.M. one day and 1:05 P.M. the next day. It rang at
a) 11:58 P.M.
b) 11:59 P.M.
c) 12:59 A.M.
d) 1:59 A.M.
Step-by-step explanation:
So lets count the time between 10:53 and 1:05
7 Mins to 11
2 Hours to one
5mins to 1:05
Total 2 hours 12 mins divided by 2 to find the middle
1 hour 6 mins. We add 1 hr 6 mins to 10:53.
10:53 + 6mins equals 11:59
11:59 + 1hour = 12:59
Answer c
The marked price of a water cooler is $ 4500. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.
Answer:
$3690
Step-by-step explanation:
Let's first find what percent of the original price it is being sold for.
100%-18%=82%
The water cooler is being sold for 82% of its original price.
Let's now find 82% of 4500.
0.82*4500=3690
The selling price is $3690
Answer:
3690
Step-by-step explanation:
the original price is 4500
for decreasing or discount we use this formula x discount upo 100 multiply by the original price. so for this question if we apply the formula it will be
18upon 100 x4500. the answer comes as 810. noww we subtract the original price from the discounted price. so 4500-810=3690. comes as ur selling price
In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A and B map to C, A and B'after the dilation. What
is the length of CB? Use the distance formula to help you decide: d = (x2-x)+(y2 - y.)?
18+
164
A = (8.15)
B = (12, 13)
12
101
C = (8.10)
The length of line segment CB is 5 units.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Given that, A=(8, 15), B = (12, 13) and C = (8, 10)
Here, substitute (x₁, y₁)= (8, 10) and (x₂, y₂)=(12, 13) in distance formula, we get
CB = √[(12-8)²+(13-10)²]
= √(4²+3²)
= √(16+9)
= √25
CB= 5 units
Therefore, the length of CB is 5 units.
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Angela is using a number cube for a game with faces labeled 1, 2, 3, 4, 5, and 6. Is the number cube fair? Explain why or why not.
Answer: Yes
Step-by-step explanation: It is equal because each side has a chance of it rolling on either 1,2,3,4,5, and 6.
Percentages equal to 100% and how?
Answer:
2 or more percents add up to 100% or one percent is 100%
Step-by-step explanation:
I NEED HELP PLZZZZZZ!!! I NEED TO WRITE SOMETHING...……..
Bob withdrew money from an ATM, put the receipt in an envelope, and filled in the information in his check register.
Explain why it is important for Bob to keep the receipt and record the information in his check register.
Answer:
It is important for bob to keep the receipt and record in the register so he can monitor how much money he has in the account. It prevents being overdrawn. Recording debits and deposits helps with budgeting.
What is the numerator of the next term in the arithmetic sequence?
1/2 2/2 3/2 4/2
Answer:
5
Step-by-step explanation:
The numerator is the value on top, above the denominator. In an arithmetic sequence you are increasing by the same amount each time. In this case, you are increasing by 1/2 each time. 4/2 plus 1/2 is 5/2, so your numerator is 5.
A bill at a restaurant is $48.50. There is a 5% tax
added and then a 20% tip added. What is the total
cost?
Answer:
$61.11
Step-by-step explanation:
When the price of something has a certain percent added to it, you can first convert that percentage to a decimal and then add 1, since 1 is the original price. Therefore, we can set up the following equation:
48.50*1.05*1.20=$61.11
Hope this helps!
