One can determine the number of roots by seeing the degree of the given polynomial.
The number of roots can be determined by just seeing the highest power of the given equation.
1) for the equation x-4=0
here, the highest power of the equation is one. So, it will have one root.
What is the polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on, and non-negative integer exponentiation of variables.
Let's check it by simplifying x-4=0 which implies x=4
Hence, the equation has only one root namely x = 4.
2) Consider a quadratic equation,
10t^2-t-3=0
here, the highest power of the equation is two. So, it will have two roots.
Let's check it by simplifying using the middle term splitting method,
10t^2+5t-6t-3=0
5t(2t+1)-3(2t+1)=0
(5t-3)(2t+1)=0
t=-3/5 or t=-1/2
Thus, the equation has two roots.
Hence, one can determine the number of roots by seeing the degree of the given polynomial.
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A box contains 72 cups of fruit juice. one serving size is 12 cup. how many servings can be made from the fruit juice?
Answer:
6 servings
Step-by-step explanation:
Box = 72 cups
1 serving size = 12 cups
72 ÷ 12 = 6
hey can you please give me the answer to this?
The height of the tower is 452.66 ft
What is angle of elevation and depression?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
Given:
we have two angles one of which is angle of elevation and another angle depression.
Using trigonometric ratio,
tan ∅ = P / B
tan 32° = h / 425
0.624= h /425
h= 265.569 ft
again,
tan 29° = h(bottom of the tower) / 425
h(bottom of the tower) = 425 × tan 29°
h(bottom of the tower) = 235.581 ft
Thus, Height of tower = h(top of the tower) + h(bottom of the tower)
Height of tower = 265.569 + 235.581
Height of tower = 501.15 ft
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What is the total number of digits used when the first 2002 positive even integers are written?
Please help, 25 points.
The total number of digits used when the first 2002 positive even integers are written is 4 digits
How to find the number of sequence?Using arithmetic sequence,
nth term = a + (n - 1)d
where
a = first termd = common differencen = number of termsa = 2
d = 2
nth term = 2 + (2002 - 1)2
nth term = 2 + 4002
nth term = 4004
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Please answer the given question
there are total 64 is the answer if she puts 2 cookies in each packet
hope this helps u :)
Question 4 of 10
Which of the following is not a condition that must be met before you can use
the quadratic formula to find the solutions of an equation?
A. There can be no term whose degree is higher than 2.
OB. The coefficient of the x²-term can't be zero.
C. The coefficient of the x²-term must be positive.
D. One side of the equation must be zero.
The condition that must not be met before usage us that the coefficient of the x²-term must be positive.
Equations of quadratic functionThe standard quadratic function is given as;
ax²+bx + c = 0
From the equation shown above, the leading degree of the equation is 2. The following are condition that must be met before you can use
the quadratic formula to find the solutions of an equation.
There can be no term whose degree is higher than 2.The coefficient of the x²-term can't be zero.The condition that must not be met before usage us that the coefficient of the x²-term must be positive.
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The term at position n in a sequence is 3n
Work out the 4th term in this sequence.
(Hint: the 4th term is when n = 4)
Answer:
12
Step-by-step explanation:
3(4)=12
The 4th term of the sequence is 12.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.
Given:
sequence, S(n): 3n
Now, to find the 4th term of sequence we have to put n= 4.
So, the term of sequence
S(4) = 3(4)
s(4) = 12
Hence, the 4th term is 12.
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Helppp!!!
Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
The number of tiles Lynn needs to cover the floor with an area of 16.875 ft² is 17 tiles
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The floor measures 4 1/2 ft by 3 3/4 ft.
Hence:
Area of floor = 4 1/2 ft * 3 3/4 ft = 9/2 ft * 15/4 ft = 16.875 ft²
Each tile measures 1 square foot each, hence:
number of tiles needed = 16.875 ft² / 1 ft² per tile = 16.875 tiles ≅ 17 tiles
The number of tiles Lynn needs to cover the floor with an area of 16.875 ft² is 17 tiles
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If the long hand of a clock is 11 and short hand is 9what is the time .help please
Please do these questions for me separately(in the picture)
Based on the cost of each of the snacks in a s'more, the number that the summer camp counselor can make is E.10.
The total change in temperature on the surface of Mercury is C. 1,168°F.
What is the total s'mores that can be made?First, find out the cost of one s'more:
= (2 x 0.50) + 0.75 + (2 x 1.25)
= 1 + 0.75 + 2.50
= $4.25
The total s'mores that can be made is:
= 45 / 4.25
= 10 complete s'mores
What is the change in temperature?= 869 - (-299)
= 869 + 299
= 1,168°F
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Find the area of a rhombus.
4
30°
Answer:
[tex]13.86[/tex]
Step-by-step explanation:
you should see 2 triangles with angle 60 bounded by two equal sides of 4
[tex]=2(\frac{1}{2} (4)(4)sin 60)\\=13.86[/tex]
The amount of algae covering the Smith's backyard pond doubled every day until it was completely covered in algae on day $30$ of the month. On what day of that month was $75%$ of the pond algae-free?
The day of the month that was 75% of the pond algae-free is: on day 28 or third day.
75% of the pond algae-freeSince we were told the algae doubled every day until it was covered in algae on day 30 of the month.
Hence:
Day 30 (First day)= It was 100% covered.
Day 29 (Second day)=It was 50% covered.
Day 28 (Third day )=it was 25% covered, which will be the same as 75% pond algae-free.
Therefore the day of the month that was 75% of the pond algae-free is: on day 28 or third day.
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The complete question is:
amount of algae covering the Smith's backyard pond doubled every day until it was completely covered in algae on day 30 of the month. On what day of that month was 75% of the pond algae-free?
find the midpoint of the segment with end points (-2,-1) and (0,9)
Answer:
-1 , 4
Step-by-step explanation:
x = ( -2 + 0 ) ÷ 2
y = ( -1 + 9 ) ÷ 2
-2 ÷ 2 = -1
8 ÷ 2 = 4
( -1 , 4 )
What is the range of the function on the graph? O all real numbers Oall real numbers less than or equal to 1 O all real numbers less than or equal to 3 all real numbers less than or equal to 0
The range of the function on the graph is (c) all real numbers less than or equal to 3
How to determine the range?The missing graph is added as an attachment
From the graph, we have the following highlights
The highest y value is 3Other y values do not exceed 3This means that the range is (c) all real numbers less than or equal to 3
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Samuel bought presents for 40 cents, 50 cents, 60 cents, and 70 cents. How much money did he spend in all?
Answer:
$2.20
Step-by-step explanation:
100 cents= $1
70+60= 130. Move the decimal to the left twice to get $1.30.
50+40= 90 cents
90+30= $1.20+ the 1 dollar from before and you get $2.20
Answer: 220
Step-by-step explanation:
40+50+60+70= 220
Because the questions says in all we have to add it all together.
You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below.
Hot Chocolate Sales and Outside Temperatures
Sales ($) $100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Temperature (°F) 92° 88° 54° 62° 85° 16° 52° 65° 68° 89° 91°
how would you describe the correlation in the data? Explain your reasoning
Answer:
There is a negative correlation.
Step-by-step explanation:
The point on the scatter plot are downwards sloping. This implies that there is a negative relationship between the variables temperature and sales. Thus, there is a negative correlation.
find the area of the shaded regions.
Answer: [tex]7\pi[/tex]
Step-by-step explanation:
The area of the entire circle is [tex](\pi)(3^{2})=9\pi[/tex]
The area of each of the smaller circles is [tex](1^{2})(\pi)=\pi[/tex], so their combined area is [tex]2\pi[/tex].
By subtracting areas, we get the area of the shaded region is [tex]7\pi[/tex].
The ratio of vina's age to jill is 7:6.if vina is 4 years older than jill,how old is jill
jill is 24 years old.
What is ratio ?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls).The ratio of vina's age to jill is 7:6 .
Let vina's age =7x
let jill's age = 6x
If vina is 4 years older than jill.
Then , 7x - 6x = 4
x = 4
Now vina's age = 7x = 7 * 4 = 28 years
jill's age = 6x = 6 * 4 = 24 years.
Therefore, jill is 24years old.
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there are 400 beads of the same size. 35% are red. 2/5 of the remaining are blue. the rest are white. what fraction are there white beads?
Answer:
84/400
Step-by-step explanation:
First, divide 35 by 100 to get the decimal, 0.35. Then, multiply 0.35 x 400. You should get 140. Now the question says 2/5 of the remaining are blue. You need to multiply 2/5 x 140 to get 56. 56 are blue. So now subtract 56 from 140 to get 84. The answer (not in simplest form) is 84/400.
help me please maths
A. 64
B. 1/12
C. 1/64
D. 12
Answer:
Step-by-step explanation:
First, since they have the same base, you can join them. Because it is division, you have to subtract the exponents.
4^(-11/3 -(-2/3)) = 4^-9/3 = 4^-3
Negative exponents turn the base into a fraction and 4^3= 64
so the answer is C. 1/64
Which compares the medians of the data? the median for the students is 4 and the median for the teachers is 8. the median for the students is 2 and the median for the teachers is 3. the median for the students is 4 and the median for the teachers is 3. the median for the students is 2 and the median for the teachers is 8.
(B) The median for the students is 2 and the median for the teachers is 3, comparing the medians of the data.
What is a median?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data set. The main difference between the median and the mean in summarizing data is that the median is not skewed by a tiny fraction of exceptionally big or small values, and thus provides a better depiction of a "typical" value. Because income distribution can be distorted, median income may be a better approach to illustrate what a "normal" income is.Therefore, the median for the students is 2 and the median for the teachers is 3, comparing the medians of the data.
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Correct question:
Which compares the medians of the data?
(A) The median for the students is 4 and the median for the teachers is 8.
(B) The median for the students is 2 and the median for the teachers is 3.
(C) The median for the students is 4 and the median for the teachers is 3.
(D) The median for the students is 2 and the median for the teachers is 8.
Divide:
5 x minus 8 StartLongDivisionSymbol 45 x squared minus 42 x minus 48 EndLongDivisionSymbol
Which of the following represents the length of the rectangle?
9x - 48
9x - 23
9x - 6
9x + 6
The length of the Rectangle is 9x +6 , Option D is the right answer.
What is a Rectangle ?A rectangle is a polygon with four sides , four angles and four vertices , The opposite sides are parallel and equal .
An expression representing the area of Rectangle is given
One of the side is 5x -8
The other side = ?
As Area of Rectangle = Length * Breadth
It can be calculated by Dividing Area by Breadth
(45x² - 45x -48 ) / (5x -8)
= 9x +6
Therefore the length of the Rectangle is 9x +6 ,Option D is the right answer.
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Answer:
9x + 6
INCLUDED WHOLE PAGE!!
☆
EDGE2022; Good Luck :3!!!
For f(x) = x^2 and g(x) = x^2 + 2, find the following composite functions and state the domain of each
Answer:
[tex]composite \: function \: is \: given \: as \: in \: two \: forms \\ \\ f(g(x))and \: g(f(x)) \: therefore \: f(g(x)) =( x {}^{2} ) {}^{2} + 2 \\ whereas \: g(f(x)) = (x {}^{2} + 2) {}^{2} \\ domain of \: f(x) = x {}^{2} is( \infty - \infty ) \: and \: domain \: of \: g(x) = x {}^{2} + 2 \: is \: also \: ( \infty - \infty )[/tex]
A salesperson earns a commission based on the number and type of vehicle sold. A person selling 6 cars and 3 trucks earns $4,800. A person selling 8 cars and 1 truck earns $4,600. How much does a salesperson earn for selling 2 cars and 3 trucks?
$2,500
$2,700
$2,800
$3,000
An English teacher has equal numbers of fiction, literature, and poetry books.
Each day, she randomly selects one book to read from. She designs a
simulation to estimate the probability that the next three books she selects
are all literature.
Which simulation design could she use to estimate the probability?
The simulation design regarding the probability is:
Let 1, 3 = fiction.
Let 2, 4 = non fiction.
Let 5,6 = poetry
What is a simulation design?It should be noted that a simulation design us used to make a particular prediction.
In this case, a number cube can be used to estimate the probability.
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In which of the following intervals does the trigonometric inequality sec(x) < cot(x) always hold true.
The inequality for sec (x) < cot (x) is; π/2 < x < π
How to express trigonometric inequality?
We are given that;
We want to find the intervals that the trigonometric inequality sec (x) < cot (x) always hold true.
This can also be expressed as;
1/cos (x) < 1/tan (x)
Now, this can happen only in the quadrant where tan (x) is negative and cos x is positive which is in fourth quadrant where;
π/2 < x < π
The inequality for sec (x) < cot (x) is; π/2 < x < π
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Answer:
C on edge 22 for Pre-Calculus
Step-by-step explanation:
pi < x< 3pi/2
I retook the unit test, put C, and got a 100. I promise it's right
Raj and Aditi like to play chess against each other. Aditi has won 12 of the 20 games so far. They decide to play more games.
How many more games will Aditi have to win to have a 70% winning record?
12 + x = 0.70(20 + x)
x = x equals StartFraction 20 Over 3 EndFraction is approximately 6.67. ≈ 6.67
She will have to win 7 more games to have a 70% winning record.
How many more games will Aditi have to win to have an 80% winning record?
The linear equation that models this is .
Aditi would have to win more games to have an 80% winning record.
The linear model is 12 + x = 0.80(20 + x)
Aditi would need to win is 20.
How many more games does Aditi have to win?Given this linear model: 12 + x = 0.80(20 + x)
Take the following steps in order to determine the value of x:
Expand the bracket : 12 + x = 16 + 0.8x
Combine like terms: 16 - 12 = x - 0.8x
Add similar terms: 4 = 0.2x
Divide both sides by 0.2 : 4/ 0.2
x = 20
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Answer:
the first answer would be C and the second is B I think
Step-by-step explanation:
based off what I just did so 20 is the second answer aka B lol
What is the volume of this rectangular prism? A rectangular prism with a length of 6 and one-fourth foot, width of 14 feet, and height of 3 feet.
Answer:
V = 262.5 ft.
Step-by-step explanation:
Volume = length × width × height
6.25 × 14 × 3
6.25 × 42
262.5
Jake kept track of the number of minutes it took him to assemble sandwiches at his
restaurant.
Number of
sandwiches
Minutes
1
3
2
4
4
5
6
6
7
7
6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp
Answer:
6xp^24
Step-by-step explanation:
Basically, there is 24 6xp's which is 6xp^24.
Hope I explained well enough.
Counting by thousands, write five numerals from 1578 onwards.
Answer:
1578 + 1000 = 2578
2578 + 1000 = 3578
3578 + 1000 = 4578
4578 + 1000 = 5578
5578 + 1000 = 6578