Answer:
No, the root 3 has multiplicity of 2.
Final answer:
Mariana is incorrect because the Fundamental Theorem of Algebra states that a third-degree polynomial must have three complex roots, and she has found only two real zeros.
Explanation:
Mariana is not correct in her assumption that the Fundamental Theorem of Algebra does not apply to the function ƒ(x) = x^3 − 4x^2 − 3x + 18. The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem guarantees that a polynomial of degree n has exactly n complex roots, though some of the roots may be repeated and not all of them may be real. In Mariana's case, the polynomial is of the third degree, so it should have three complex roots. She has found two real zeros, −2 and 3. There must be another root, which could also be real or complex. If all roots were real, she would see all three zeros on the graph. If the third root is complex, it will not appear on the real number graph that Mariana is using.
Which expression is equivalent to −2.1+(−5.9)+(−3.7) ?
−2.1−(5.9+3.7)
(2.1+5.9)+(−3.7)
(2.1+5.9+3.7)
−(2.1−5.9)+(−3.7)
Option A is correct. The equivalent expression is −2.1−(5.9+3.7)
Given the expression −2.1+(−5.9)+(−3.7)
Before we can determine the equivalent expression, we need to first know that:
- × - = ++ × - = -+ × + =+The given expression then becomes;
−2.1+(−5.9)+(−3.7) = -2.1 - 5.9 - 3.7
Factoring out the negative sign from the last two terms;
-2.1 - 5.9 - 3.7 = -2.1 - (5.9 + 3.7)
Hence the equivalent expression is −2.1−(5.9+3.7)
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14 less than 3 times a number is 5 more than half of the number
how do I solve -15=-4m+5
The solution to the equation -15 = -4m + 5 is m = 5.
We have,
To solve the equation -15 = -4m + 5, you can follow these steps:
- Step 1:
Start by isolating the variable term (-4m) on one side of the equation.
You can do this by subtracting 5 from both sides:
-15 - 5 = -4m
Simplifying, we get:
-20 = -4m
Step 2:
Divide both sides of the equation by -4 to solve for m:
-20 / -4 = -4m / -4
Simplifying, we get:
5 = m
Therefore,
The solution to the equation -15 = -4m + 5 is m = 5.
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(2x+3 2/5) + (5x -4/3
The warehouse already has 27 pallets of stock waiting to be unloaded, and the delivery van arrives with another 8. The warehouse has room for 32 pallets, how many extra pallets will there be?
There are 3 extra pallets will be there.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example,Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
We have.
The warehouse already has 27 pallets of stock waiting to be unloaded, and the delivery van arrives with another 8.
So, total pallets
= 27 + 8
= 35
Now, the number of extra pallets
= 35- 32
= 3 pallets
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two friends share 7 cookie equally. How many cookies does each friend get?
Answer: Each friend get 3.5 cookies.
Step-by-step explanation: Given that two friends share 7 cookie equally.
We are to find the number of cookies that each friend get.
We will be using the UNITARY method to solve the given problem.
Number of cookies shared by 2 friends equally = 7.
Therefore, number of cookies that one friend get will be
[tex]\dfrac{7}{2}=3.5.[/tex]
Thus, each friend get 3.5 cookies.
A gym membership costs $25 to join and $14 each month. Write and use an algebraic expression to find the cost of the gym membership for 6 months?
Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and section B had 20 students who had a mean score of 90. Overall, what was the approximate mean score for all the students on the quiz?
A. 84.3
B. 85
C. none of these
D. cannot be determined
Final answer:
The approximate mean score for all the students on the quiz, calculated by weighing the means by the number of students in each section, is 85.71, which rounds to 86. Thus, the best answer choice (B) from those provided is 85.
Explanation:
To find the overall mean score for all the students on the quiz, we need to weigh the mean scores by the number of students in each section. We do this by multiplying each section's mean score by the number of students in that section, then adding these products together, and dividing by the total number of students.
For Section A: 15 students × mean score of 80 = 1200 total points.
For Section B: 20 students × mean score of 90 = 1800 total points.
The total points for both sections is 1200 + 1800 = 3000 points.
The total number of students is 15 + 20 = 35 students.
To find the overall mean, we divide the total points by the total number of students:
3000 total points ÷ 35 students = approximately 85.71.
Therefore, the approximate mean score for all the students on the quiz is 85.71, which, when rounded to a whole number, is 86. The closest answer choice given is B. 85, so that would be the best selection from the available options.
Help me please I really don’t understand
An art teacher has 40 paint brushes.she divides them equally among her 4students. She finds8 more brushes and divides these equally among the students, as well. How many brushes does each student receive
Answer: The required number of brushes that each student receive is 12.
Step-by-step explanation: Given that an art teacher has 40 paint brushes.she divides them equally among her 4 students.
She finds 8 more brushes and divides these equally among the students, as well.
We are to find the number of brushes that each student receive.
The total number of brushes that divides among the 4 students is
[tex]n=40+8=48.[/tex]
Since there were 4 students, so the number of brushes that each student receive is
[tex]n_b=\dfrac{n}{4}\\\\\\\Rightarrow n_b=\dfrac{48}{4}\\\\\Rightarrow n_b=12.[/tex]
Thus, the required number of brushes that each student receive is 12.
A bear was climbing a tree. It took a few steps forward and then slipped a few steps backward. After taking 12 total steps of equal distance, it was back at its starting position. How many steps did the bear take in the forward and backward directions?
Answer: 6 steps forward and 6 steps backward
Hope this helped :D
What’s the answer to this question?
solve for A
7a + 2 = 3a + 14
a = ??
Explain how you can find the numbers of ninths in 2 5/9
Answer:
23 is the required answer.
Step-by-step explanation:
We are given a fraction of the form [tex]2\frac{5}{9}[/tex].
It is a mixed fraction.
We convert it into improper fraction.
The improper fraction is of the form [tex]\frac{(9\times2)+5}{9} = \frac{23}{9}[/tex].
This fraction can also be written as 23 multiplied [tex]\frac{1}{9}[/tex] times.
It is clear that the above fraction have 23 parts of ninth.
The parade had 127 floats. Thatis 34 fewer floats than last year. How many floats were in the parade last year?
Is also sort of math but how do you do celsius since I can't figure out how to do it since I'm American so I've never learned it in my school
to convert Fahrenheit to Celsius
subtract 32 then multiply by 5/9
example 80 degrees F would be (80-32=48, 48 *5/9 = 26.66) 27 degrees C
Before discarding, Carolee has 4 green cards, 3 red cards, 3 orange cards, and 1 gold card. If she discards the gold. Are, what percent of her remaining cards are red?
After discarding the gold card, Carolee has a total of 10 cards left. The calculation for the percentage of red cards among these is (3 red cards / 10 total cards) × 100, resulting in 30% of the remaining cards being red.
Explanation:The question asks about the percentage of the remaining cards that are red after Carolee discards the gold card. Initially, Carolee has 4 green cards, 3 red cards, 3 orange cards, and 1 gold card. After discarding the gold card, she has a total of 10 cards left (4 green + 3 red + 3 orange).
To find the percentage of the remaining cards that are red, we use the formula for percentage, which is (Part / Whole) × 100. In this case, the 'part' is the number of red cards, and the 'whole' is the total number of remaining cards.
Percentage of red cards = (Number of red cards / Total number of cards) × 100
= (3 / 10) × 100
= 30%
Therefore, 30% of Carolee's remaining cards are red.
If the value of "a" lies between −5 and 2 and the value of "b" lies between −7 and 1, what are the possible values for the product a· b?
The possible values for the product [tex]\( a \cdot b \)[/tex] are between -14 and 14, inclusive.
Here's the step-by-step calculation:
1. To find the minimum possible value, we multiply the smallest values of ( a ) and ( b ):
[tex]\( a = -5 \) and \( b = -7 \)[/tex]
[tex]\( a \cdot b = (-5) \cdot (-7) = 35 \)[/tex]
2. To find the maximum possible value, we multiply the largest values of ( a ) and ( b ):
[tex]\( a = 2 \) and \( b = 1 \)[/tex]
[tex]\( a \cdot b = 2 \cdot 1 = 2 \)[/tex]
So, the possible values for the product[tex]\( a \cdot b \)[/tex] are between -14 and 14.
The range of values for( a ) is from -5 to 2, and for ( b ) is from -7 to 1. To find the extreme values of the product [tex]\( a \cdot b \),[/tex] we multiply the smallest and largest values of ( a ) and ( b ).
For the minimum value, we take ( a = -5 ) and ( b = -7 ), which gives us [tex]( a \cdot b = 35 \).[/tex]
For the maximum value, we take ( a = 2 ) and ( b = 1 ), which gives us [tex]\( a \cdot b = 2 \).[/tex]
Therefore, the product[tex]\( a \cdot b \)[/tex] ranges from -14 to 14, inclusively.
complete question
If the value of "a" lies between −5 and 2 and the value of "b" lies between −7 and 1, what are the possible values for the product a· b?
An animal shelter spends $1.00 per day to care for each bird and $7.00 per day to care for each cat. Oliver noticed that the shelter spent $186.00 caring for birds and cats on Wednesday. Oliver found a record showing that there were a total of 36 birds and cats on Wednesday. How many birds were at the shelter on Wednesday?
What is the value of k in the function ƒ(x) = 112 - kx if ƒ(-3) = 121?
k =
factor out -1/4 out of -1/2x-5/4y
Graph the lines by finding the points of intersection with the axes (intercepts):
y=4x+8
Answer:
x − intersection is (__,__ ) .
y − intersection is (,__,__).
The x-intersection of y=4x+8 is at the point (-2,0) and the y-intersection is at the point (0,8).
Explanation:We want to find the points where the line y=4x+8 intersects the x and y-axis.
For the x-intersection, we set y=0.
So, 0=4x+8, which simplifies to x = -2. So, the x-intersection is at the point (-2,0).
For the y-intersection, we set x=0.
So, y=4*0+8, which gives y = 8. So, the y-intersection is at the point (0,8).
To find the x-intercept, set y=0 and solve for x:
0 = 4x + 8
x = -2
So, the x-intercept is (-2, 0).
To find the y-intercept, set x=0 and solve for y:
y = 4(0) + 8
y = 8
So, the y-intercept is (0, 8).
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the vertices of a triangle are A(-2,4), B (1,2), and C(-2,-2). reflect the triangle in the y-axis, and then rotate the image 90 degrees counterclockwise about the origin. what are the coordinates of the image?
The coordinates of the image of triangle ABC are A''(4, -2), B''(2, 1) and C''(-2, -2).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x).
Given that, he vertices of a triangle are A(-2,4), B (1,2), and C(-2,-2).
Reflect the triangle in the y-axis
The rule for a reflection over the y -axis is (x,y)→(-x, y)
Here, A(-2, 4)→A'(2, 4)
B (1,2)→B'(-1, 2)
C(-2,-2)→C'(2, -2)
Then rotate the image 90 degrees counterclockwise about the origin.
A'(2, 4)→A''(4, -2)
B'(-1, 2)→B''(2, 1)
C'(2, -2)→C''(-2, -2)
Therefore, the coordinates of the image of triangle ABC are A''(4, -2), B''(2, 1) and C''(-2, -2).
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(6^3)^2 =
A) 6^1
B) 6^5
C) 6^6
D) 6^9
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{(6^3)^2}\\\\\mathtt{= (6\times6\times6)^2}\\\\\mathtt{= (36\times6)^2}\\\\\mathtt{= (216)^2}\\\\\mathtt{= 216^2}\\\\\mathtt{= 216\times216}\\\\\mathtt{= 46,656}\\\\\mathtt{= 6^6}\\\\\mathtt{= 6\times6\times6\times6\times6\times6}\\\\\mathtt{= 36\times36\times36}\\\\\mathtt{= 1,296\times36}\\\\\mathtt{= 46,656}\\\\\\\huge\text{Therefore your answer should be:}\\\boxed{\mathtt{Option\ C.\ 6^6}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]There are 99 males and 121 females participating in a marathon what percent of the participants are females?
Answer: 55%
Work:
99 + 121 = 220
121 / 220 = 0.55 = 55%
Latrell has $8 to spend on postcards. He wants to buy one large postcard and some small ones. Write and solve an inequality to determine how many small postcards Latrell can purchase. Interpret the solution.
25m/s to miles/h
Can anyone solve it?
With explanation if you can
25 meters per second x 60 seconds = 1500 meters per minute
1500 meters per minute x 60 minutes per hour = 90,000 meters per hour
1 mile = 1609.34 meters
90000/1609.34 = 55.92 miles per hour
round answer to either 55.9 or 56 mph depending on what you need.
Simplify 10 • 2 • 2 • 30 500 1200 4800 5000
Processing ends successfully
Answer:
1200
Step-by-step explanation:
10 times 2 is 20
20 times 2 is 40
40 times 30 is 1200
answer: 1200
The width of a rectangle has been measured as 19.4mm correct to 1 decimal place.
What is the lower bound for the area of this rectangle?
The lower bound of the width of the rectangle is 19.35 mm. Without the length, we cannot determine the exact lower bound for the area of the rectangle. However, if we know the length, we can calculate it by multiplying the length by 19.35 mm.
Explanation:The lower bound of the width of the rectangle, measured to one decimal place, is slightly less than the measured value. Thus, the lower bound of the width would be 19.35 mm (since we are accurate to 1 decimal place). However, without information about the length of the rectangle, we cannot exactly determine the lower bound of the area of the rectangle.
But if we assume the length to be a certain value (let's say 'L'), the lower bound for the area (A) would be the product of this length and the lower bound of the width. So,
A = L*19.35 mm.
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can you help with the air freshener question?? And can you simplify the answer