please tell me how to solve this step
fast correct answer will be marked brainliest and other copies from website will be reported........
Answers
Answer:
See Explanation
Step-by-step explanation:
From your question, what you need is the explanation;
Given that [tex](x - 1 - \sqrt{2})(x - 1 + \sqrt{2})[/tex] is a factor of p(x)
Required: Simplify
[tex](x - 1 - \sqrt{2})(x - 1 + \sqrt{2})[/tex]
Group the expression above
[tex]((x - 1) - \sqrt{2})((x - 1) + \sqrt{2})[/tex] -------- Expression 1
The expression can be expanded using difference of two squares;
[tex](a - b)(a + b) = a^2 - b^2[/tex]
By comparison, Expression 1 can be rewritten as
[tex](x - 1)^2 - (\sqrt{2})^2[/tex]
Open both brackets
[tex](x - 1)(x - 1) - (\sqrt{2})(\sqrt{2})[/tex]
Expand the above expression
[tex](x(x - 1) -1(x - 1)) - 2[/tex]
[tex](x^2 - x -x + 1)- 2[/tex]
[tex](x^2 - 2x + 1)- 2[/tex]
Remove bracket
[tex]x^2 - 2x + 1- 2[/tex]
[tex]x^2 - 2x - 1[/tex]
Hence,
If
[tex](x - 1 - \sqrt{2})(x - 1 + \sqrt{2})[/tex] is a factor of p(x)
Then
[tex]x^2 - 2x - 1[/tex] is a factor of p(x)
Related Questions
Instructions
Search your home for a rectangular prism. Some examples are a cereal
box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following. Show all work for calculations.
Part 1).List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 3 1/2in
Width: 1 1/2in
Height: 7in
Part 2) Describe the shape of the cross section when the box is cut parallel to the base.
• The cross section had a rectangular shape and goes through the box minimizing the width of the shape.
Part 3) What is the surface area of the box?
• 80.5 square inches
Part 4) What is the surface area of the box if it is scaled up by a factor of 10?
• 805 square inches
Part 5) What is the volume of the box?
• 36.75 square inches
Part 6) What is the volume of the box if it is scaled down by a factor of 1/10?
Answers
Find the slope of a line parallel to the line
12x + 3y = 15.
A parallel line would have slope m =
The solution is
Answers
Answer:
The answer is - 4Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
12x + 3y = 15
Express it in the form y = mx + c
3y = -12x + 15
Divide all terms by 3
y = - 4x + 5
From the equation m = - 4
Since the lines are parallel their slope are also the same
So the slope of the parallel line is also - 4
Hope this helps you
How many students all together?
Answers
Answer:
from the top of my head if I read the bars right I think its 98 but I could really see the bars
Answer:
102
Step-by-step explanation:
24+12+5+17+6+19+4+15= 102
HURRY I NEED HELP for 20 points
Beginning at the origin, how far do you travel along the y-axis when plotting the point below? (6, 12)
Answers
Answer:
the answer is 12
Step-by-step explanation:
because (6, 12) x axis is 6, and the 12 is the y axis. Meaning that you would go 12 along the y axis.
Answer:
I believe the answer is 12
This graph shows how the length of time a canoe is rented is related to the rental cost. What is the rate of change shown in the graph? A. $3/hour B. 3 hours/dollar C. $6/hour D. 6 hours/dollar
Answers
Answer:
what is the answer?
Step-by-step explanation:
Answer:
C. $6/hour
Step-by-step explanation:
AP3X
PLEASE HELP ASAP Eva is at a sushi restaurant. She ordered 2 pieces of squid for a total of $3.50, 1 piece of eel for $3.25, 3 pieces of tuna for a total of $6.75, and 4 pieces of crab for $8.00. Which list shows the unit cost of each pieces of sushi from least to greatest? A. squid, crab, tuna, eel B. eel, squid, tuna, crab C. squid, eel, crab, tuna D. eel, tuna, crab, squid
Answers
Answer:
I do not have enough time to put them in order if you don't mind but i can list the prices.
Step-by-step explanation:
each piece of squid is 1.25
each piece of tuna is 3.25
each piece of crab is 2.00
hope this helps <3
Answer:
A
Step-by-step explanation:
HELP ASAP Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answers
Answer:
$252
Step-by-step explanation:
This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.
Jan's " give away " = Ami + 36, Jan - 108, Toy + 72
Toy's " give away " = Ami + 72, Jan + 36, Toy - 108
Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.
144 + 72 + 36 = 252 dollars ( in total )
Answer:
The answer is 252
Step-by-step explanation:
5 mL =____gtt
A. 75
B. 100
C. 50
D. 25
Answers
Answer:
Answer:
b. 100
Step-by-step explanation:
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
y-2x = -2
y- x = 1
A. More than 1 solution
B. x = 4, y = 3
C. No solution
O D. x = 3, y = 4
Answers
Answer:a x=3 y=-4
Step-by-step explanation:
Let f be defined as shown. Which statement is
true?
Answers
The inverse of f exists
The inverse of f does not exists
Answers
Answer:
[tex]\boxed{\sf \ \ \ the \ inverse \ of \ f \ does \ not\ exist \ \ \ }[/tex]
Step-by-step explanation:
hello,
for one x you cannot get several values of f(x), otherwise this is not a function
as 6 and 7 gives 0 it means that
f(6)=f(7)=0 which is fine for f
but then for [tex]f^{-1}[/tex] it would mean that 0 has two different images
and this is not possible
so the inverse of f does not exist
hope this helps
Please help me match these formulas . :)
Answers
Answer:
1. equilateral triangle
2. rectangle
3. circle area
4. trapezoid
5. circle circumference
6. parallelogram
7. regular polygon
8. triangle
Hope that helps.
SOMEONE PLS HELP ME!!! The mean of a set of five different positive integers is 15. The median is 18. Find the maximum possible value of the largest of these five integers.
Answers
Answer:
35
Step-by-step explanation:
We know that the mean is 15 and the median is 18. In order to solve this problem, we can work backwards. First, image the scenario:
15, 15, 15, 15, 15.
We want the median to be 18, we we can add 3 to the middle number and then subtract three from the first number (in order to keep the mean constant). Thus, we have:
12, 15, 18, 15, 15.
Now, we can subtract and add in order to find the largest number. For instance, we can subtract 11 from 12 and add that 11 to the last number:
1, 15, 18, 15, 26
Next, we can subtract 13 (not 14 because each of the numbers should be different) from the second number and add that to 26:
1, 2, 18, 15, 39.
Finally, the most we an do is to add 4 to the fourth number and subtract 4 from 39 because we want to keep the median 18. Thus:
1, 2, 18, 19, 35.
Each value is distinct.
The largest possible value is 35.
Answer:
35.
Step-by-step explanation:
Since the mean of the five different positive integers is 15, you can assume that they all add up to be 5 * 15 = 75. The median is 18, which means that the rest of the four numbers add to be 75 - 18 = 57, with two numbers higher than 18 and two numbers lower.
You want to find the highest possible values for the maximum, you want to have very low minimums (so you can keep the maximum high). Since the question asks for different positive integers, the lowest numbers you can have are 1 and 2. So far, you have 1, 2, and 18 in your data set, so you have 57 - 3 = 54 to work with for your maximum.
You still want the highest value for the largest of the integers, so the fourth number will be 19. That is because that is the lowest you can go that is still higher than the median. Then, in your data set, you will have 1, 2, 18, and 19, which add up to be 40.
Since all five numbers add to be 75, the maximum will be 75 - 40 = 35.
To make sure this is correct, check your work. 1 + 2 + 18 + 19 + 35 = 75. 75 / 5 = 15. The mean is 15. The middle number is 18, so the median is 18. All five are different positive integers.
And there you have it! The maximum possible value of the largest of these five integers is 35.
Hope this helps!
Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 13 inches, side 14 inches, and blank hypotenuse.
a.
91 in.
b.
46.1 in.
c.
19.1 in.
d.
182 in
Answers
Answer:19.1
Step-by-step explanation:
Answer:
B. 46.1 in
Step-by-step explanation:
First, we must find the hypotenuse of the triangle.
Since this is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
13 and 14 are the legs, because they form the right angle. x is the hypotenuse because it is opposite the right angle.
13^2+14^2=x^2
Evaluate each exponent.
13^2=13*13=169
14^2=14*14=196
169+196=x^2
Add 169 and 96
365=x^2
Take the square root of both sides.
√365=√x^2
√365=x
19.1049732=x
Round to the nearest tenth.
19.1=x
The hypotenuse is 19.1 inches
Now, find the perimeter. Add up all the sides of the triangle: the legs (13 in and 14 in) and the hypotenuse (19.1 in)
13 in +14 in +19.1 in
46.1 in
The perimeter is 46.1 inches and B is correct.
I NEED HELP !!! If the probability of an event is StartFraction 2 over 7 EndFraction, what must be the probability of its complement?
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
StartFraction 4 over 7 EndFraction
StartFraction 5 over 7 EndFraction
Answers
Answer:
The answer is StartFraction 5 over 7 EndFraction
Answer:
The probability of the complement of the original event is 5/7.
Step-by-step explanation:
The probability of the complement of an event is 1 less the probability of the event, so
We get: 1 - 2/7, or 5/7
The probability of the complement of the original event is 5/7.
Note that 5/7 and 2/7 add up to 7/7, or 1.
Hey guys please help find the area
Answers
Answer:
70.15 ft²
Step-by-step explanation:
The figure consists of two adjacent equilateral triangles (all angles are 60 degrees and all outer edges are 9 ft).
If we focus on one of these equilateral triangles, we can get the final area by multiplying the area of that one triangle by 2.
The formula for the area of a triangle is (1/2)(base)(height). Remembering to multiply this by 2, we get
area of figure = (base)(height)
√3
= (9 ft)(9 ft)(--------) = (81 ft²)(1.732) = 70.15 ft²
2
Name the similar triangles. ΔABC ~ ΔDEF ΔABC ~ ΔEDF ΔABC ~ ΔDFE ΔABC ~ ΔFED
Answers
Answer:
Since ∠E ≅ ∠A and ∠D ≅ ∠B, the answer is ΔABC ~ ΔEDF.
Answer:
option 2
Step-by-step explanation:
Which of the following is the correct scientific notation for 0.00566 meters?
A. 566 x 10-5 m
B. .566 x 10-3 m
C. 5.66 x 10-3 m
D. 5.66 x 103 m
Answers
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
Answers
Answer:
B. Quadratic Function
Quadratic Term: 15x^2
Linear Term: 9x
Constant Term: -6
Step-by-step explanation:
1. F.O.I.L (firsts, outers, inners, lasts) the function
BREAK APART: 3x(5x - 2) and 3(5x - 2)
(fx) = 15x^2 - 6x + 15x - 6
f(x) = 15x^2 + 9x - 6
There is a square in the function, therefore it is quadratic. The quadratic term is the term being squared, and you go from there.
Help help please.....Thanks
Answers
Hey there! :)
Answer:
56.7 kg.
Step-by-step explanation:
Use the density formula to solve for the mass:
D = m/V.
Rearrange in terms of mass, or 'm':
DV = m.
Solve for the volume:
0.06 × 0.9 × 1.5 = 0.081 m³.
Plug this into the equation along with the density:
700 × 0.081 = 56.7 kg.
Find the volume of a cylinder that has the following dimensions. Do not round your answer.
(Use 3.14 for pi.)
Radius = 5 cm
Height = 0.25 m
Volume = __ cm3
Answers
Answer:
19.625 cm^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 * 5^2 * .25
V =19.625 cm^2
Please help answer this question Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pencil costs $0.59. Can Minni buy 2 stickers and 2 erasers? [Use the inequality 0.35x + 0.99y + 0.59 ≤ 4] (1 point) Select one: a. Yes, because the total will be $3.27 b. Yes, because the total will be $1.93 c. No, because the total will be $4.27 d. No, because the total will be $5.93
Answers
Answer: A
Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.
Then you multiply: .35(2)=.70. .99(2)=1.98.
Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A
Answer:
A. yes, because the total will be $3.27
Step-by-step explanation:
0.35x + 0.99y + 0.59 ≤ 4
0.35(2) + 0.99(2) + 0.59 ≤ 4
0.70 + 1.98 + 0.59 ≤ 4
3.27 ≤ 4
You are miguel Cervantes de Navas y colon, captain in the royal spanish army in Sevilla in the year 1842. Outside your barracks window is a stack of cannonballs, as shown in the illusion. On an idle afternoon you dicide to calculate the number of cannonballs in the stack. What is the number of cannonballs? A. 650 B. 506 C. 623 D. 571
Answers
Answer:
650
Step-by-step explanation:
1st row has 1 ball
2nd row has 4 balls
3rd row has 9 balls
4th row has 16 balls
We can see that the number of balls is the square of the row number. There are a total of 12 rows. So, rest of the rows has:
5th row has 25 balls
6th row has 36 balls
7th row has 49 balls
8th row has 64 balls
9th row has 81 balls
10th row has 100 balls
11th row has 121 balls
12th row has 144 balls
If we add up all those, we get total number of balls
please mark me brainliest!
Does it matter which dimensions you select for the length and the width when you find the area of a rectangle? Explain. I need this by 1 : 36
Answers
Answer:
The area of a rectangle is the product of the length and the width of the rectangle.
The dimensions chosen for length and width of a rectangle must be the lengths of two adjacent sides. The area is the product of the two dimensions. It does not make a difference which one you call length and which one you call width since length * width = width * length because of the commutative property of multiplication.,
Answer:
To find the area you need both the length and width
A= lw
Practically it doesn't matter which one you call length or width as long as both of them used in the calculation. The product of them doesn't change.
23 more than the product of 7 and a number
Answers
Answer:
7x + 23
Step-by-step explanation:
Remember BPEMDAS.
Product of 7 and a number means 7 times a variable: 7x
23 more than part means 23 + whatever we just did, so:
7x + 23
Answer:
23+7x
Step-by-step explanation:
23 + (7 * x)
23+7x
HELP QUICK ILL GIVE A Brainliest to the first person Which of the answer choices is a coordinate point from the table below?
Answers
Answer:
2/$5.00
Step-by-step explanation:
It's the only one that makes sense
Answer:
4,10
It is the only option on the table
Step-by-step explanation:
Simplify (*x* +2x? - 5x)+(-3x + x +1)+(3+* + 2x).
A. 3x + 2x* - 3x2 – 3x² +1
B 4x*- 3x + x2 + 4x +2
C. 4x4 - 3x + 3x² + 4x +2
D. 4x*- 3x + 3x? - 3x + 1
Answers
Answer:
D
Step-by-step explanation:
4x^4+3x^2-3x^3-3x+1
Help please....Thanks
Answers
Answer:
16 x 66 = 1056mm^2
Step-by-step explanation:
What is the form of the Sum of Cubes identity?
Answers
Answer:
D. a³+b³=(a+b)(a²-ab+b²)
Explanation:
That is the form of the Sum of Cubes identity
Point Q(-1,5) is reflected across the line x=-1. What are the coordinates of its image?
(15)
(1-5)
-1.5)
Answers
Answer:
(- 1, 5 )
Step-by-step explanation:
Since the x- coordinate of Q, x = - 1 lies on the line of reflection.
The point Q will remain unchanged, that is
coordinates of image are (- 1, 5 )
What is the slope of the line shown below? A. -1/3 B. 1/3 C. -3 D. 3
Answers
Answer:
C. -3
Step-by-step explanation:
Plugging both of those points into the slope formula gets you a slope of -3.