Answer:
Step-by-step explanation:
So in this example we'll be using the difference of squares which essentially states that: [tex](a-b)(a+b)=a^2-b^2[/tex] or another way to think of it would be: [tex]a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})[/tex]. So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:
[tex]x^8-16 = (x^4-4)(x^4+4)[/tex]
Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:
[tex]x^4-4 = (x^2-2)(x^2+2)[/tex]
So completely factored form is: [tex](x^2-2)(x^2+4)(x^4+4)[/tex]
I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because [tex]x^2+4 = x^2-(-4)[/tex]. and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: [tex]x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)[/tex] just something that might be useful in some cases.
We can factor this into [tex](x^{4}+4)(x^{4} -4)[/tex].
This is because we use difference of two squares where [tex]x^{2} -y^{2} = (x+y)(x-y)[/tex]
So we rewrite x^8-16 to x^8-4^2.
This can then be written to the equation I put at the start.
p.s. The reason its [tex]x^{4}[/tex] is because [tex]x^{4} * x^{4} = x^{8}[/tex]
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)
Which description best compares the graphs given by the equations:
x - 5y = -5 and -5x - 25y = 25
a. parallel
b. perpendicular
c. intersecting but not perpendicular
d. None of the above.
x - 5y = -5, -5x - 25y = 25
First, you'll need to get the x variable by itself.
x - 5y = -5
+5 +5
x = 0
So x is plotted on the 0.
For the second part of the first equation, you'll be looking for what the y variable represents.
x - 5y = -5
-x -x
-5y = -5
5 5
y = 1
So y is plotted on the 1 on the vertical line above the 0.
For the first part of the second equation, you'll do the same thing as in the first equation.
-5x - 25y = 25
+25 +25
-5x = 50
5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.
For the second part of the second equation, you will do the same thing as in the first equation.
-5x - 25y = 25
+5 +5
-25y = 30
25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.
Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.
Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.
Intersecting means the lines may or may not be of equal length but will touch each other.
By visual inspection, determine the best-fitting regression model for the
scatterplot,
Answer:
Linear
Step-by-step explanation:
The line is relatively straight.
The data in the tables below were collected from first year students at a community college. The variable is “number of credit cards.” Two of the probabilities are missing.
Number of credit cards 0 1 2 3 4 5
Number of students 122 40 28 2 2 6
Based on this data, we can estimate the probability that a randomly selected student has X number of credit cards using relative frequencies to create a probability distribution. Note: There are 200 students.
Number of credit cards 0 1 2 3 4 5
Probability 0.14 0.01 0.01 0.03
Use this information to answer the first two questions below.
What is P(0)? (Hint: Find the relative frequency for this outcome. There are 200 students in the data set.)
The probability that number of credit cards is 0 is 0.61
What is Probability ?Probability is the likeliness of an event to happen ,
It has a range from 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty
The data for the college students is given and it has been asked to determine P(0)
The total students are 200
and the students that have no credit card from the data is 122
Therefore
P(0) = 122/200 = 0.61
Therefore the probability that number of credit cards is 0 is 0.61
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Which graph represents the equation x2 = 8y?
Answer:
The second graph.
Step-by-step explanation:
If you plug the equation into the desmos graphing calculator, you'll get the second graph.
Hope this helped! :)
How do you compute -3+9-7
Answer:
-1
Step-by-step explanation:
-3 + 9 = 6, 6 - 7 = -1
Question 22 of 25 Which inequality matches the verbal description? Marc is saving up for a computer. He has $250 saved already. To earn more, he works part-time at a job that pays $16 per hour. Let y represent the price of the computer he chooses, and let x represent the number of hours he works. To purchase the computer, he will need to save at least y dollars.
A. y≤ 250+ 16x
B. y≤ 16x-250
C. yz 250-16x
D. yz 250x + 16
Faruq has a identical markers, b identical pencils, and no other writing utensils in his locker. How many different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed?
Your answer should be an expression, which might involve the variables a and/or b.
The number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b
How to calculate the different collection of writing utensils?Since Faruq has a identical markers, b identical pencils, and no other writing utensils in his locker and we require the number of collections or ways he could bring them to school without coming to school empty-handed, we use combination mathematics since order does not matter.
Now, Faruq can either come to school with one marker and one pencil or one pencil or one marker.
So, the combination for one marker and one pencil is n = a × b = ab
The combination for one marker is n' = a
The combination for one pencil is n" = b
So, the total combination is N = n + n' + n"
= ab + a + b
So, the number of different collections of writing utensils could Faruq bring to class if he doesn't want to show up empty-handed is ab + a + b
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Pls Help! Geometry
Find the area of the shaded region
Answer: 112.5 square cm
Step-by-step explanation:
The area of the rectangle is [tex](20)(9)=180[/tex] square cm.
The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.
So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.
Consider functions f and g. What is the value of x when (g x f)(x) = 4
By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)
How to find the result of composition between two functionsLet be f and g functions, there is a composition of f in terms of g when the input of the former is output of the latter. Hence, we have the following relationships:
g(x):
- 2 → 4
f(x):
6 → - 2
By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)
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Suppose that $7000 is placed in an account that pays 9% interest compounded each year. Assume that no withdrawals are made from the account.
Answer:
half question
Step-by-step explanation:
I'm sorry sir but I would like you to make sure if you have posted the whole question
thank you
25. A wheelchair access ramp has an angle of elevation of 16°. If the ramp
reaches to the top of a 22 inch high porch, how long is the ramp?
79.82 in.
76.81 in.
73.82 in.
81.5 in.
Answer:
C. 76.81
Step-by-step explanation:
We must use one of the trigonometric ratios to find the length, L, of the ramp. If we use 16 as the reference angle, the 22 in would be our opposite side and the ramp length is the adjacent.
Therefore, we must use tan, which is [tex]\frac{opposite}{adjacent}[/tex]:
[tex]tan (16)=\frac{22}{L} \\\\L*(tan(16)=22)\\\\L*tan(16)=22\\[/tex]
[tex]\frac{L*tan(16)}{tan(16)}=\frac{22}{tan(16} \\\\L=79.815=79.82 in.[/tex]
Perform the operation. 3/a^2b + 2/ab^2
The simplified form of the expression is 3b+2a/(ab)²
Sum of fractionsFractions are written as a ratio of two integers. Given the expression below;
3/a^2b + 2/ab^2
Find the LCM
3/a^2b + 2/ab^2 = 3b+2a/a²b²
3/a^2b + 2/ab^2 = 3b+2a/(ab)²
Hence the simplified form of the expression is 3b+2a/(ab)²
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help!! find the volume of the cone
Answer:
hi. 3.14multipled by 12 multipled by 21Translate the following from words to an algebraic expression or equation, denoting the unknown by n.
15% of the amount by which a number exceeds 10,000
The translation from words to an algebraic expression, denoting the unknown by n is 0.15(n + 10,000)
Algebraic expressionlet
unknown number = n
a number exceeds 10,000= n + 1000
15% of the amount by which a number exceeds 10,000= 15%(n + 10000)
= 15/100(n + 10,000)
= 0.15(n + 10,000)
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{(4z-7,z-4,z) |z is any real number} z=-5
The set when z = -5 is {-27, -9, -5}
How to determine the set elements?The set is given as:
{(4z-7,z-4,z) |z is any real number}
When z=-5, we have:
4z - 7 = 4(-5) - 7 = -27
z - 4 = -5 - 4 = -9
z = -5
So, we have:
{(4z-7,z-4,z) |z is any real number} ⇒ {-27, -9, -5}
Hence, the set when z = -5 is {-27, -9, -5}
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Y=24-4x fill in the table using this function rule
X Y
1 ?
4 ?
5 ?
6 ?
X = 1 4 5 6
Y = 20 8 4 0
Mathematical FunctionsFrom the function: Y = 24 - 4X
If X = 1, then Y = 24 - 4(1) = 20
If X = 4, then Y = 24 - 4(4) = 8
If X = 5, then Y = 24 - 4(5) = 4
If X = 6, then Y = 24 - 4(6) = 0
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your heart beats 86 times per minute proportional or non proportional
........................
Answer:
???????
Step-by-step explanation:
?????
A square has a perimeter of 24cm. What is the length of each side?
Quick process:
⇒ Square has 4 sides
⇒ We have been given that the perimeter is 24 centimeters
⇒ Each side is equal in value and each side added up together must equal 24.
⇒ So to finish this out we need to divide the given perimeter which is 2 4 by the amount of side a square has which is 4.
⇒ So 24/4 = 6
Check the answer:
6 + 6 = 12
12 + 12 = 24 √
Perimeter of a square =24cm
Formula=4s
So 4s=24
s=24/4
s=6
Therefore side of the square is 6cm.
Mark me brainliest
The town of pratt has a population of about 8,260,000. express this number in scientific notation
Answer:
8.26 x 10^6
Step-by-step explanation:
Scientific notation mean multiply by 10 power
Please help
Which quadrilaterals are not rhombuses?
Choose each correct answer.
Answer:1 and 3
Explanation:by definition a rhombus is parallelogram a with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.
Which graph shows the solution to this system of linear inequalities? y>2x+3 y<-2x-4
The graph that shows the solution to the given system of linear inequalities is shown below
Graph of InequalitiesFrom the question, we are to draw the graph that shows the solution to the given system of linear inequalities
The given system of linear inequalities is
y>2x+3
y<-2x-4
The graph that shows the solution to the given system of linear inequalities is shown below
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The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Picture posted below
Option B) is correct 0.4068 portion of crocodiles live between 17.5 and 20.5
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years.
Z-table is tabulated data that gives the information of value of percentage of data.
standard deviation = 2.6 ; mean (μ)= 18
lives between 17.5 and 20.5
x= (20.5+17.5)/2=19
Z = (X - μ) / σ
z=-(19-18)/2.6
z= 0.38
While compare it with the z table is gives 0.4068.
Thus the required value of Z = 0.4068
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
The required distance AB is given by .[tex]\sqrt{17}[/tex]
What is transformation?Transformation, is process which is used to change the position of the bor shapes.
Since, coordinate of A(0,0) B(1,4)
After transformation T: (x, y) (x + 2, y + 1) of A, B it become A'(2, 1), B '(3,5)
Now,
Distance = √(x2-x1)^2+(y2-y1)^2
AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ; A'B' = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ;
A(0,0) B(1,4) A'(2, 1), B '(3,5)
AB= [tex]\sqrt{(1-0)^2+(4-0)^2}[/tex] A'B'= [tex]\sqrt{(3-2)^2+(5-1)^2}[/tex]
AB= √17 A'B' = √17
Thus, the required distance AB and A'B' = √17.
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Work out the area of this triangle.
6 cm
11 cm
12 cm
Step-by-step explanation:
there is a right angle formed in this question
this leads us to Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=11²+6²
Hyp²=121+36
Hyp²=157
Hyp=√157
Hyp=12.529964086
Hyp=12.5
if I am right mark as brainliest but if you consider I am wrong then you can correct me, Everyone learns everyday I am glad I help
The scale in the drawing is 2 cm : 5 m. Select from the drop down the correct numbers into the boxes to give the length, width, and area of the actual room.
The length, width, and area will be 25m, 15m, and 375m².
How to calculate the area?From the information given, the scale in the drawing is 2cm : 5m and the length and width are given as 10cm and 6cm respectively.
Length = 10cm = 10 × 2.5 = 25m
Width = 6cm = 6 × 2.5m = 15m
Area = Length × Width
Area = 25 × 15
Area = 375m²
Therefore, the area is 375m².
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Jason has exactly four wooden toy blocks with digits on them. Two of the blocks have the digit 0, one of the blocks has the digit 1, and one of the blocks has the digit 2. How many distinct positive integers can he form using one or more of the blocks, without using each block more than once?
The number of positive integers is 24
How to determine the number of positive integers?The digits of the wooden toys are:
0, 0, 1, 2
Since each block cannot be used more than once, and there are four blocks in total;
The number of positive integers is;
Integers = 4!
Expand
Integers = 4 * 3 * 2 * 1
Evaluate
Integers = 24
Hence, the number of positive integers is 24
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Ethan ran 3/4 miles. Megan ran 7/8 miles. How much further did Megan run? Answer in simplest form.
Answer:
2/16 or 0.625
Step-by-step explanation:
Find a common denominator for the two fractions. It will be 16. 3/4=12/16
7/8=14/16 or you can do it in decimal form. 3/4=.25 and 7/8= .875
.875-.25=.0.625
[tex]\large\boxed{\frac{1}{8}\ \text{miles}}[/tex]
We need to subtract Ethan's distance from Megan's. First, we need to have a common denominator in the fractions.
Multiply both the numerator and the denominator in [tex]\frac{3}{4}[/tex] by [tex]2[/tex] to get [tex]\frac{6}{8}[/tex], which is equivalent. Now, both numbers have a denominator of [tex]8[/tex] and can be subtracted.
Now, simply subtract the numerators, leaving the denominator alone.
[tex]\frac{7}{8}-\frac{6}{8}=\frac{7-6}{8}=\boxed{\frac{1}{8}}[/tex]
Use finite differences to determine whether each relationship is linear, quadratic, or
neither.
x y
-5 17
-4 7
-3 1
-2 -1
-1 1
The function relationship is a quadratic function
How to determine the function type?The function is given as:
x y
-5 17
-4 7
-3 1
-2 -1
-1 1
Remove the x values:
y: 17 7 1 -1 1
Calculate the difference between the consecutive y values
Difference: 10 6 2 -2
Because the first difference are not equal, it means that the function is not a linear function.
Calculate the difference between the above differences
Difference: 4 4 4
Because the second differences are equal, it means that the function is a quadratic function.
Hence, the function relationship is a quadratic function
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Given the quadratic equation: x^(2)+6=0, find all solutions for x
Answer:
[tex]x=i\sqrt6[/tex]
[tex]x=-i\sqrt6[/tex]
Step-by-step explanation:
x^2=-6
x=[tex]\sqrt-6[/tex]