We need to use a technique called dot multiplication. In this technique, we multiply the magnitude of two given vectors by the value of the angle between them.
In the question, the value of the angle between two vectors [tex]cos(45^0)[/tex] and the coordinates of the two vectors are given. Let's multiply them by the dot product to get the result.
Formula: [tex]u.v=|u||v|cos(a)[/tex]
[tex]u=3i+2j[/tex]
[tex]v=i+5j[/tex]
[tex]cos(a)=\frac{1}{\sqrt{2}}[/tex]
To find the magnitude of a vector, we square the coordinates, add them up and take the square root of the result.
[tex]Magnitude=\sqrt{x^2+y^2+z^2+...}[/tex]Result: [tex]u.v=|\sqrt{(3^2)+(2^2)}||\sqrt{(1^2)+(5^2)}|.\frac{1}{\sqrt{2}}=(13\sqrt{2})\frac{\sqrt{2}}{2} =13[/tex]
An equation is shown below:
6(2x – 11) + 15 = 3x + 12
Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)
Part B: What value of x makes the equation true? (4 points)
Source
StylesFormatFontSize
Answer:
x = 7
Step-by-step explanation:
Distribute -
12x − 66 + 15 = 3x + 12
Combine Numbers and Variables -
12x - 51 = 3x +12
Get x on one side (isolate x) -
9x - 51 = 12
9x = 63
Divide 9 -
x =7
In a diagram showing two parallel lines cut by a trasversal, the measures of two same side interior angles are both given as 3x. Without writing and solving an equation, can you determine the measures of both angles? Explain. Then write and solve an equation to find the measures
Answer:
90 degrees
Step-by-step explanation:
Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.
Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.
3x + 3x = 180
6x = 180
x = 30
3x = 3*30 = 90
Which of the following is a function?
A. {(2,9), (2,8), (-3,7), (-3,6))
B. ((-4,3), (1,0), (1,2), (2,3)}
C. {(2,1), (4,2), (6,3), (8,4))
D. {(1,2), (-2,3), (1,3), (-2,2))
Answer: C
Step-by-step explanation:
A function only exists if each x-value has only one possible y-value.
C is the only function because each x-value has only one y-value.
The other answer choices have x-values that have multiple y-values. In answer choice A, it has (2,9) and (2,8). In answer choice B, the set has (1, 0) and (1,2). And in answer D, it has (1,3) and (1,2)
Answer + Step-by-step explanation:
let f be the relation that we are studying.
f is a function if it associates a unique output (number) to each input (number) .
A. {(2,9), (2,8), (-3,7), (-3,6))
Since f(-3) = 7 and f(-3) = 6
Then
f associates -3 to two different outputs 7 and 6.
Then
f cannot be a function.
B. ((-4,3), (1,0), (1,2), (2,3)}
Since f(1) = 0 and f(1) = 2
Then
f cannot be a function.
C. {(2,1), (4,2), (6,3), (8,4))
f is a function.
D. {(1,2), (-2,3), (1,3), (-2,2)
Since f(-2) = 3 and f(-2) = 2
Then
f cannot be a function.
Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Answer:
[tex]644cm^2[/tex]
Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to [tex]2\times(30+100+120)-72=428 cm^2[/tex].
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's [tex]2\times(24+48)+72=216cm^2[/tex].
So the total surface area is [tex]428+216=644cm^2[/tex].
does someone mind helping me with this? Thank you!
Compute the surface area obtained by rotating the curve y = 3 x , for x is in [1, 125] about the y-axis
Answer:
Given,
y=x³ ,0≤x≤2
We have to find the surface area of the surface by rotating the curve about the x axis.
For rotation about the x axis, the surface area formula is given by-
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
let u=1+9x⁴
du=36x³dx
dx/36x³
Substituting u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
therefore, the exact surface area is 203.06 square units.
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Answer:
In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.
Given: y=3x, for x is in [1,125] about the y axis.
y=x³ ,0≤x≤2
Lets find the surface area of the rotating curve,
Finding surface area for rotation along x-axis,
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
Assuming u =1+9x⁴
du=36x³dx
=dx/36x³
Substituting respective values of u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
hence, the surface area is 203.06 square units.
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help math pls lots of points!!!!!
Answer:
(f ￮ g)(11) = - 1
Step-by-step explanation:
evaluate g(11) then substitute the result obtained into f(x)
g(11) = 11 - 7 = 4 , then
f(4) = [tex]\sqrt{4}[/tex] - 3 = 2 - 3 = - 1
Erin has developed a new lotion that will help children with sensitive skin. she invests $15,225 in equipment to manufacture and package her lotion. each bottle costs $3.25 to manufacture and sells for $12. how many bottles of lotion must she make and sell before her business breaks even? a. 998 bottles b. 1740 bottles c. 174 bottles d. 1269 bottles
Her business will break even when she contains sold 1740 bottles of her lotion.
How many bottles of lotion must she make and sell before her business breaks even?Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.
"Break even" occurs when Revenue = Costs.
($12/bottle)x = $15225 + ($3.25)x
Simplifying the above equation, we get
$8.75x = $15225
Diving both sides of the equation by 8.75, we get
$8.75x/8.75 = $15225/8.75
x = 1740 bottles
Therefore, the value of x = 1740 bottles.
Her business will break even when she contains sold 1740 bottles of her lotion.
Therefore, the correct answer is option b. 1740 bottles.
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Hey I'm sunny, and i request someone's help (please)
1. Value of b (b - 4.21 = 87.654)
2. Divide: 1.86 and 8.4
3: Compare: 1.92
that's it
Bye! - SunnyBunny <3
The computation shows that the value of b will be 91.864.
How to illustrate the information?From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:
b - 4.21 = 87.654
b = 87.654 + 4.21
b = 91.864
Also. dividing 1.86 and 8.4 will be:
= 1.86/8.4
= 0.2213
Therefore, the values are 91.864 and 0.2213.
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Find the volume of the following cubes: (b) 15 m 18.4 ft Find the volume of each of cubes whose a side length is given as: (b) (c) 5.6 ft (f) 12 m 80 cm (a) 5 cm (d) 4.5m Solve (e) (c) 4.2 inch 4 m 20 cm
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
The district attorney said the misdemeanor charges against Paul Pelosi were filed "based on the extent of the injuries sustained by the victims."
Us media said that either Paul Pelosi or his lawyer would enter a plea at his arraignment on Wednesday. According to the Napa County District Attorney's Office, misdemeanor penalties for driving while intoxicated and causing injury include up to five years of probation, a minimum of five days in jail, a fine, completion of a court-ordered DUI course, and more.
After her husband s car accident, the US media reported that her brother was killed in a car collision when she was still a teenager. In 1957, Paul reportedly crashed his car near SAN Mateo County at 16. Paul suffered a broken collarbone in the crash, while his elder brother was pronounced dead on arrival at the hospital. Paul, then 16, was acquitted by a jury.
His past skeletons in closet don't stop there. Public data shows that Nancy Pelosi has more than $114 million net worth. Reports indicate that much of that comes from Mr. Paul's holdings of stocks, options, and investments.
Which number belongs to the set of rational numbers and the set of integers?
F. –5.5 H. –0.5
G. – 115 J. –15
The number which belongs to the set of rational numbers and the set of integers is -115 which is third option,-15 which is fourth option.
Given four options:
–5.5 –0.5– 115 –15We are required to find the number which is included in the set of rational numbers and the set of integers.
Rational numbers are those numbers which can be written in the form of p/q in which q cannot be equal to zero because if q becomes zero then the fraction becomes infinity.
-5.5 is not a rational number,
-0.5 is also not a rational number.
-115 is a rational number and also an integer.
-15 is a rationalnumber and also an integer.
Hence the number which belongs to the set of rational numbers and the set of integers is -115 which is third option,-15 which is fourth option.
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The height and weight of adults can be related by the equation y=48.3x−127 where x is height in feet and y is weight in pounds.
What does the slope of the line represent?
A. the average number of pounds per foot tall
B. the number of pounds heavier an adult one foot taller would weigh
C. the height of an adult weighing zero pounds
D. the number of adults in the sample
we conclude that the correct option is A, the slope is:
"the average number of pounds per foot tall"
What does the slope of the line represent?The linear equation:
y = 48.3*x - 127
Relates the height, x, and the weight, y of an adult.
Then the slope, which is 48.3, should have units of mass over height.
Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.
Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:
"the average number of pounds per foot tall"
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When taking a 17 question multiple choice test, where each question has 3 possible answers, it would be unusual to get or more questions correct by guessing alone?
Answer: If you’re talking on a percentage basis, it would be extremely unlikely to get a majority of the questions correct.
Step-by-step explanation:
Consider formula a to be v = startfraction 2 pi r over t endfraction and formula b to be v2 = gv = g startfraction m subscript central over r endfraction.. write the letter of the appropriate formula to use in each scenario. determine the tangential speed of the moon given the mass of earth and the distance from earth to the moon. determine the tangential speed of a satellite that takes 90 minutes to complete an orbit 150 km above earth’s surface.
The tangential speed of the satellite above the Earth's surface is [tex]7.588 * 10^{3} m/s[/tex].
What is Tangential speed?Tangential speed is the linear component of speed along any point on a circle that is involved in a circular motion. The object or circle moves with a constant linear speed at any point along the circle. This is known as the tangential speed.[tex]v=wr\\v=\frac{2\pi r}{T}[/tex]The tangential speed of a satellite at the given radius and time is calculated as follows:
[tex]v=\frac{2\pi *(150*10^{3}+6371*10^{3} }{90*60} \\v=7.588*10^{3} m/s[/tex]
Therefore, the tangential speed of the satellite above the Earth's surface is [tex]7.588 * 10^{3} m/s[/tex].
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The correct question is shown below:
Consider formula A to be v = and formula B to be v2 = G. Write the letter of the appropriate formula to use in each scenario. Determine the tangential speed of the moon given the mass of Earth and the distance from Earth to the moon. Determine the tangential speed of a satellite that takes 90 minutes to complete an orbit 150 km above Earth’s surface.
Answer: first box is B
second box is A
Explanation:
right on edge as of 2022
he system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
How to solve the given system of equations:Here we have the system of equations:
(2/3)*x + (5/2)*y = 15
4x + 15y = 12
To solve the system of equations, we first need to isolate one of the variables in one of the equations, I will isolate x on the second equation.
4x = 12 - 15y
x = (12 - 15y)/4
Now we can replace that in the other equation:
(2/3)*x + (5/2)*y = 15
(2/3)* (12 - 15y)/4 + (5/2)*y = 15
Now we can solve that for y.
2 - (10/4)*y + (5/2)*y = 15
2 = 15
That is a false equation, then we conclude that the system of linear equations has no solutions.
This means that the two lines are parallel lines, then a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Where a and b are two real numbers.
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Answer:Your answer is
There are no solutions.
Step-by-step explanation:Brainliest Please?
If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
0 A. 3x2 + 6
OB. 5x²-6
OC. 5x²-4
OD. 3x² - 4
Answer:
Option A is correct.
3x^2+6
Step-by-step explanation:
We have to find (f-g)(x):
We can write it f(x)-g(x), so substitute the values:
f(x)-g(x)=(4x^2+1)-(x^2-5)
=4x^2+1-x^2+5
=3x^2+6
What is the Y-Intercept of the line that has a slope of -4 and passes through the point (4,-6)
Answer:
Y-intercept = 22
Step-by-step explanation:
The equation of a line in slope-intercept format is given by the equation y=mx+c
where m is the slope and c the y-intercept.
(The y-intercept is the value of y when x = 0)
Slope given as -4
And we know it passes through the point(4,6) ie at x=4, y =6
Substitute in above equation to get value of c, the y-intercept
6 = -4(4) + c
6 = -16 + c
c = 22
And this is the y-intercept
The equation of the line is y = -4x + 22
See attached figure for graph
Use the scatter plot and line of best fit to predict the value of y when x equals 1910.
I'll go for 40.
To find the value of y,
draw a line up from the x - axis at 1910,
all the way up to cross the blue line;
then, draw a horizontal line from the point where the recent line meets the blue one.
Now read of the value you get for y.
Hope this helps!
Estimate √50 to the hundredths place.
Answer:
7.07
Step-by-step explanation:
Answer:
7.07
Step-by-step explanation:
Hello!
Let's find two perfect square numbers that are directly before and after 50.
[tex]\sqrt{49} < \sqrt{50} < \sqrt{64}[/tex][tex]7 < \sqrt{50} < 8[/tex]Since the square of 7 is the closest, we can use that as our whole number.
To find the decimal...49 is 1 away from 50, and 64 is 14 away. Rewriting it as a fraction and we get [tex]\frac{1}{14}[/tex]. The decimal is 0.07142857142.
Now, put 7 and 0.07142857142 together and we get 7.07142857142. Rounding that, we get 7.07.
The real value of Root 50 is 7.071067811865475, so the decimals were really close.
please help me, i will give brainliest!! help me please
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
Ratio = Number of event 1 : Number of event 2 (in same unit, if necessary)
10
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
11
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
1 minute = 60 seconds1 week = 7 days1 hour = 60 minutes12
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
13
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
14
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
Samuel is arranging books in shelves at their library. He has 80 books to arrange he needs to put the same number of books on each shelf, and he needs to use all of the books. Between 9, 10 and 11 shelves, which is his best choice for the number of shelves that he can use?
(Show the solution and do not use Division (optional) and use the Divisibility rules of numbers)
Answer:
10 shelves
Step-by-step explanation:
out of the other choices, 10 is most suitable to divide with 80
Let x = a bi and y = c di and z = f gi. which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x × (y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z)
The first one , the second one ,the fourth one are true.
What is a commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
1) x + y = y + x = a + c (b + d ) i true
2) ( xy )z = x (yz) = (a + bi)(c + di)( f + gi) true
3) x - y = a + bi - ( c - di ) = a - c + ( b- d )i
y - x = c + di - ( a+bi) = c-a +(d-b)i false
4) (x + y ) + z = x + ( y + z ) = a + c +f + (b +d + g)i true
5) (x - y ) - z = a + bi - ( c + di) - ( f + gi)
= a - c . f + ( b- d - g) i
x - ( y - z ) = a + bi - ( c + di - f - gi )
= a - c + f + ( b - d + g ) i
{ put the hypothesis into the equation and get the proof }
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Noah has 22 5 of a pound of rice in his cupboard. He also has 8 9 of that amount in his pantry. Which of the following equations could be used to determine how much rice he has in the pantry?
225/0.88*100%
255.68*100
25,568 pounds in pantry
The cost of a watermelon depends on its weight. Which of the following
shows this idea expressed in function notation?
Answer:
20 pounds
Step-by-step explanation:
i took the test trust me i got 2 points
Answer:cost(weight)
Step-by-step explanation:
A convenience store sells two brands of orange juice Brand A contains 11 fluid once and costs
$2.31. Brand B contains 15 fluid ounces and costs $2.70.
What is the difference in cost, in dollars, per fluid ounce between the two brands of juice
Answer:
$0.03
Step-by-step explanation:
2.31/11 =.21
2.70/15 =.18
.21-.18 = .03
It takes a machine at a seafood company 20 s to clean 3 1 ib of shrimp _ 3
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:
Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second
It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second
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Find the missing side lengths. Leave your answers as radicals in simplest form.
The missing side length of the right triangle are as follows;
v = 1 units
u = 2 units
How to find side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore,
tan 60 = opposite / adjacent
tan 60 = √3 / v
cross multiply
v = √3 / tan 6-
v = √3 / √3
v = 1
Hence,
sin 60 = opposite / hypotenuse
sin 60 = √3 / u
cross multiply
u = √3 / sin 60
u = √3 × 2 / √3
u = 2√3 / √3
u = 2
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Your friend won't get many stars like this! What changes would you make to the equation to help your friend collect all the stars? Why are those changes going to work
The required equation that represents the line of best fit is y = 2x + 4
Finding the equation of a line of best fit.A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.
Using the following points (4, 12) and (2, 8)
The equation of the line will be in the form y = mx + b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = y2-y1/x2-x1
Slope = 8-12/2-4
Sope = -4/-2
Slope = 2
Determine the y-intercept
Using the coordinate point (2, 8) and m = 2
8 = 2(2) + b
b = 8 - 4
b = 4
Hence the required equation that represents the line of best fit is y = 2x + 4
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Let f (x) be a polynomial function with a zero of multiplicity of 1 at 2 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function g of x equals the cube root of x minus 2 Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations. (5 points) Part B: Let h (x) be the piecewise defined function of h of x is the piecewise function of f of x if x is less than 0 and g of x if x is greater than or equal to 0 Are there any breaks in the domain of h (x)? Explain why or why not. (5 points)
The polynomial functions in their expanded form is given as follows. It is right to state that there are no breaks in the domain of h(x).
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
For instance, the polynomial 3x+4 has an exponent of 1.
Part A: F(x) has zero at 2 and multiplicity of 1; and
1 at the multiplicity of 2
f(x) = x-2) (x-1)²
= (x-2) (x² - 2x + 1)
= x³ - 4x² + 5x -2
Part B: h (x) = [tex]\left \{ {{x^3 -4x^2 + 5x -2; X < 0} \atop {\sqrt[3]{x-2} ; X\geq 0 }} \right.[/tex]
The domain of X is X ∈ R
Hence it is correct to state that there are no breaks in the domain of h(x).
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can someone help me really quick?
Answer:
Step-by-step explanation:
23 - (-2)
= 23 + 2
= 25
1) The mistake you made was to subtract 2 from 23 instead of subtracting -2 from 23.
2) Keep in mind the difference between the '-' used as a subtraction and the '-' used for indicating a negative number.
If you like, remember the mantra ' 2 negatives make a '+'.:-
2 - -4
= 2 + 4= 6.
