The polynomial function in standard form that has the zeros listed. i and -i is x² +1 = 0.
What is polynomial function?A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.
The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Calculation for the polynomial function-
The general two degree/quadratic equation is given by-
ax² + bx + c = 0
Where a ≠ 0
If the two roots of the equation are x1 and x2.
Then the relation between roots and coefficients of the polynomial are -
The sum of the roots = (- coefficient of x)/(coefficient of x²)x1 + x2 = (-b)/a
The multiplication of the roots = constant/coefficient of x²x1.x2 = c/a
From the above two relation the general equation can be written as-
x² -(x1 - x2)x + x1.x2 = 0
Lets say x1 = i and x2 = -i
Substitute the values of x1 and x2 in the general equation
x² -(i - i)x + (i).(-i) = 0
x² - i ² = 0
x² + 1 = 0
Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.
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If a client is exercising for 150 minutes per week (30 minutes, 5 days per week), then a 10% increase in volume would result in how many minutes total per week
It takes 165 minutes per week if 10% increase in volume for an exercising client.
How much is the 10% increase in the volume?A client is exercising for 150 minutes per week. I.e., 30 minutes, 5 days per week.
So, 10% increase results,
30 minutes × 10% = 3
So, the increased minutes per day = 30 + 3 = 33 minutes/day.
How many minutes total per week results if a 10% increase in the volume?After the 10% increase, the minutes per day = 33 minutes
Since 5 days a week, he does exercise, the total minutes per week
= 33 × 5 = 165 minutes.
So, a 10% increase in volume would result in 165 minutes total per week.
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Which expression is equivalent to 21/15 - 915?
A. 12
B. 30 15
c. 125
D. 12 15
[tex]\textbf{Heya !}[/tex]
the denominators are equal, so subtracting these two fractions is a piece of cake:-
[tex]\sf{\cfrac{21}{15}-\cfrac{9}{15}}[/tex]
[tex]\sf{\cfrac{21-9}{15}}[/tex]
[tex]\sf{\cfrac{12}{15}}[/tex]
`hope it's helpful to u ~
work out the area of a rectangle with base, b = 20mm and perimeter, p = 50mm.
Answer:
100
Step-by-step explanation:
If the base is 20, then 2 of the sides must have a length of 20. This means that the TOTAL length of the remaining sides is 10. (20*2) + (10) = 50. If we divide that in half, we get 5. That is the side length of the remaining 2 sides. This means that 20 * 5 will give us the area (b*h).
Given,
base, b = 20mm &
perimeter, p = 50mm.
the area of the rectangle : (50 – 20 × 2) ÷ 2 = 5. 5 × 20 = 100 [tex]mm^{2}[/tex].
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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Given startlayout enlarged left-brace first-row startfraction x cubed minus 1 over x squared minus 1 endfraction, for x less-than 1 second row startfraction 3 over x minus 1 endfraction, for x greater-than-or-equal-to 1 endlayout. what is limit of f (x) as x approaches 1 minus? negative three-halves 0 three-halves dne
The limit of f(x) as it approaches -1 is given as 3/2
What is limit in mathematics?In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value
The unit is used to assign values to numbers at certain points where there are no defined values.
How to solve the limitwe have 3/x-1
We have to take the value of x here to be three as the equation tends to 1.
Then we apply it in the formula
3/3-1
= 3/2
Hence the limit of f(x) is given as 3/2
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there are four elevators in a building. Each elevator makes three stops, which do not have to be on consecutive floors or include the ground floor. For any two floors, there is at least one elevator that stops on both floors. What is the maximum number of floors that this building can have
The maximum number of floors that this building can have is 6
How to determine the maximum number of floors?The given parameters are:
Elevators = 4
Stops = 3
At least one elevator stops on 2 floors
The maximum number of floors is calculated as:
Maximum = Elevators * Stops/2
This gives
Maximum = 4 * 3/2
Evaluate
Maximum = 6
Hence, the maximum number of floors that this building can have is 6
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The sum of an integer and 7 more than the next consecutive integer is 66. find the integer
If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.
Given that the sum of an integer and 7 more than the next consecutive integer is 66.
Integer is a number that is written without a fraction component. It can be positive as well as negative.
let the first integer be x.
Consecutive integer will be x+1.
Sum of integer and 7 more than the next consecutive integer is 66.
Sum according to the given information=x+x+1+7
=2x+8
2x+8=66
2x=66-8
2x=58
x=58/2
x=29
Next integer=29+1-30.
Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.
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What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
The possible length of the third hallway is between 30 yards and 150 yards.
How to find the third length of a triangle?The hallway forms a triangle .
Therefore, using triangle inequality theorem, It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Hence,
90 + 60 > x
Where
x is the third side
x + 60 > 90
x + 90 > 60
Therefore, the possible length of the third hallway is between 30 yards and 150 yards.
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Answer:
D: between 30 yards and 150 yards
1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
Answer:
x = 7Step-by-step explanation:
1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
1 1/6 + x/12 = 1 3/4
1 1/6 - 1 3/4 = -x/12
-7/12 = -x/12
-7 = -x
x = 7
----------------
check
1 1/6 + (7/12 * 1/4) = 1 3/4
1 1/6 + 7/48 = 1 3/4
1 15/16 = 1 3/4
1 3/4 = 1 3/4
the answer is good
Thank you please
Solve the system of equations
:−5x−10y=−50
10x+8y=16
The solution is
x
=
,
y
=
Answer:
x=-4, y=7
Step-by-step explanation:
-5x-10y=-50...(1)
Multiply both sides by -1:
5x+10y=50
5x=50-10y
x=(50-10y)/5
Substitute x=(50-10y)/5 into second given eqaution:
10(50-10y)/5+8y=16
Cancel out common factor 5:
2(50-10y)+8y=16
100-20y+8y=16
-12y=16-100
-12y=-84
y=84/12
y=7
Substitute y=7 into equation (1)
-5x-10(7)=-50
-5x-70=-50
-5x=-50+70
-5x=20
x=-20/5
x=-4
HURRY PLEASE!!!!!!
Jarrett splits his bag of j jelly beans into two equal piles and gives one pile to his brother. He then gives his brother seven more beans. Write an algebraic expression to represent the number of beans his brother has?
Can someone please help me
Answer:-2.4+3.2t
Step-by-step explanation:
-3.6+1.2-1.9t+5.1t
= -2.4+3.2t
Round 5 358 708 to the nearest million
Answer:5 million
Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.
The science teacher has to write report cards for all her students. It takes 1/8 of an hour to complete one report card. How many report cards can the teacher complete in 14 hours?
Answer:
112
Step-by-step explanation:
If she takes 1/8 of an hour to complete one then she can finish 8 in 1 hour.
8 x 14 = 112
A single die is rolled twice. Find the probability of getting a 1 the first time and a 5 the second time. Express the probability as a simplified fraction.
The probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur.To find the probability of getting a 1 the first time and a 5 the second time:
Probability of getting 1 in 1st time = [tex]\frac{1}{6}[/tex]
Probability of getting 5 in 2nd time = [tex]\frac{1}{6}[/tex]
The probability of first rolling a 1, then a 5, will be = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{6}[/tex]
[tex]= \frac{1}{36}[/tex]
Therefore, the probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].
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A tank of water contains 35 liters of water that leaks 6 liters of water an hour another container contains 29 liters of water that leaks 3 an hour if no the the tank and container start leaking at the same time how long does it takes for both the tank and container to have the same amount of water
Answer:
Step-by-step explanation:
Let the # of liters in both containers = y when equality is reached.
Container 1: loses 6 liters / hour
Container 2: loses 3 liters / hour
Equation
35 - 6x = 29 - 3x
Solution
35 - 6x = 29 - 3x Subtract 29 from both sides
35 - 29 - 6x = 29 - 29 - 3x Combine
6 - 6x = - 3x Add 6x to both sides
6 - 6x + 6x = - 3x + 6x Combine
6 = 3x Divide both sides by 3
6/3 = 3x/3
2 = x
After 2 hours they should have the same amount of water.
35 - 6(2) = 35 - 12 = 23
29 - 3*2 = 29 - 6 = 23
Answer
After 2 hours have passed, both containers should have 23 Liters each.
Select the correct answer.
The parent function f(x)=√x is transformed to g(x) = 2f(x-3). Which is the graph of g(x)?
The function g(x) is a translation of 3 units to the right and a vertical dilation by scale factor k = 2 of f(x), the graphs of both functions can be seen in the image at the end.
Which is the graph of g(x)?We know that g(x) is a transformation of the parent function f(x) = √x, such that:
g(x) = 2*f(x - 3)
g(x) = 2*√(x - 3)
Then we can see that g(x) is a translation of 3 units to the right followed by a vertical dilation of scale factor 2 of the parent function f(x).
So to graph g(x) you first need to move the whole graph of f(x) 3 units to the right, and then apply a dilation vertically.
The graph of g(x) and f(x) can be seen in the image below:
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In order to avoid double counting, statisticians just count the __________________.
In order to avoid double counting, statisticians just count the final goods and services.
According to the statement
we have to find the procedure which is used by statisticians to avoid the double counting.
final goods and services are the type of way which is used to avoid the double counting.
In other words, statisticians count only the final results rather than the efforts.
So, In order to avoid double counting, statisticians just count the final goods and services.
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solve this two questions with explaining method also....
Answer:
6) Selling price = ₹ 1608
Labelled price = ₹ 2010
7) Profit percentage = 10.5%
Step-by-step explanation:
Finding the selling price:
6) Cost Price = ₹ 1200
[tex]\sf Profit = 33\dfrac{1}{3} \% * Cost\ price\\\\[/tex]
[tex]\sf = \dfrac{102}{300}*1200\\\\ = 102 * 4\\\\[/tex]
= ₹ 408
Selling price = Cost price + Profit
= 1200 + 408
= ₹ 1608
Let the labelled price = x
Discount % = 20%
(100-20)% of x = 1200 + 408
80% of x = 1608
[tex]\sf x = 1608*\dfrac{100}{80}\\\\[/tex]
x = ₹ 2010
Answer: Selling price = ₹ 1608
Labelled price = ₹ 2010
7) Let the Cost price = ₹ X
Marked price = (100 + 30)% of Cost price
[tex]\sf = \dfrac{130}{100}X\\\\ = 1.3 X[/tex]
Discount% = 15%
Selling price = (100 - 15)% of 1.3X
= 85% * 1.3X
= 0.85 * 1.3X
= 1.105X
[tex]\sf \boxed{\bf Profit \% =\dfrac{Selling \ price - Cost \ Price}{Cost \ price }*100}[/tex]
[tex]\sf = \dfrac{1.105X - X}{X}*100\\\\ = \dfrac{0.105X}{X}*100\\\\ = 0.105*100\\\\ = 10.5 \%[/tex]
GOOD AFTERNOON BRAINLIESTS! Please help me with this question! TYSM!
- xXIndieKidXx
Answer:
Domain: All real numbers ; Range: y> -3
Step-by-step explanation:
There are 3 pieces of glass that are cracked. if a rock is thrown by a lawn mower hits the window, what is the probability, that the rock hits a piece of glass that is cracked?
The chance or chance that the lawn mower will hit a chunk of glass that is already cracked is calculated with the aid of dividing the variety of glasses that are cracked by way of the full quantity of glasses. on this item, the unknown may be calculated through . The solution is, therefore, 0.20.
Opportunity is a measure of the chance of an event to arise. Many occasions cannot be predicted with overall reality. We are able to are expecting only the danger of an event to arise i.e. how likely they're to manifest, using it.
The possibility is the branch of arithmetic regarding numerical descriptions of how in all likelihood an occasion is to arise, or how possibly it's miles that a proposition is actual. The possibility of an occasion various between 0 and 1, where, roughly talking, 0 indicates the impossibility of the event and 1 shows reality.
The probability of an event can be calculated by possibility components via surely dividing the favorable range of effects through the full range of possible outcomes.
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Felix’s total credit card balance is described by the following function: f(p) = p(1.30). If Felix owes $2500, what is the total bill plus interest?
$3,250
$32,500
$325
None of the choices are correct.
The total bill plus interest on the credit card is $3,250
What is credit card?
Credit card gives its holder the opportunity to make purchases on credit such that amount spent and the interest that accrues thereon would be paid by the credit card holder at a future time.
In this case, the function shows the relationship between the amount owed and the interest so as to give the outstanding balance.
f(p) = p(1.30)
p=amount owed=$2,500
f(p)=$2,500*(1.30)
f(p)=$3,250
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Help me in this question please dont put wrong answers!
Step-by-step explanation:
Has greater balance = Heba
Has more debt = Nour
Read the "note" thing on there it says banks use Negative balances meaning the negative sign ( minus sign) to represent an account with debt which means an account that is owning money e.g -$11, -$15 etc.And they use positive balances meaning the positive sign to represent account that contains valuee.g $2, $7 etc( You might wonder why I didn't put a positive sign on it, the reason is because it's already a positive number so no need to add a positive sign (+) to it) ( BUT they can still add a positive sign to it but it isn't necessary )If you see any number or amount without a negative sign (-) then that number or amount is positive e.g 1, 2,3,4,5,6,11,14,17,20,100,8, $3, $15, $23 and so on..
Hope this helps.Good luck ✅.
Using the number line:
Heba has the greater account balance
Nour has the most debt.
What is a Number Line?A number line shows where a number lies according to the order. Values greater than 0 and are on the right side are greater than values and vice versa.
Given their balances, $29.17 is greater than -$11.99. Therefore, Heba has the greater account balance using the number line.
Since - indicates debt, Nour has the most debt.
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can someone please help mee (will give brainliest 20 points!!!)
[a] x = 175 - 7.5p
For a, we are isolating the x variable to one side of the equation.
0.4x + 3p = 70
0.4x = - 3p + 70
x = - 7.5p + 175
[b] x = 115
For b, we are solving for x when p = 8.
x = - 7.5p + 175
x = - 7.5(8) + 175
x = 115
Triangle \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the image of \triangle ABC△ABCtriangle, A, B, C under a rotation about the origin, (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.
From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).
What is the proof the above?Notice that the question states: △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,
under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,
△A'B'C' is in the same position with △ABC.
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Answer: D: 60 degrees
Step-by-step explanation:
khan
Sample Response: First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller. Which did you include in your answer? Check all that apply. Write the ratios as fractions. Find a common denominator. Compare the numerators to see that 4:10 is the smaller ratio
In the case above, the option that one need to include in your answer is to Find a common denominator.
What is Fraction in lowest terms?When the numerator and denominator of a fraction are known to not have common factor other than 1, then a person can say that the fraction in its simple form or say its in its lowest term.
Since there is a common numerator and the common denominator will be between 10 and 20. Since 10 is less that than 20, the common denominator will be 20 as both can divide it.
Hence, In the case above, the option that one need to include in your answer is to Find a common denominator.
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Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24.
Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses.
3 minus 16 d + 2 d = 24
Step 2 Simplify like terms.
3 minus 14 d = 24
Step 3 Subtract 3 from both sides of the equation.
Negative 14 d = 21
Step 4 Divide both sides of the equation by –14.
d = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half
Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over 2d, to get 3 minus 16 d + (negative three-fourths d) = 24.
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
In step 3, she should have added 3 to both sides of the equation to get Negative 14 d = 27.
In step 3, she should have first divided both sides by –14 to get 3 + d = 24
The error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
Simplifying linear equationsGiven the following equation as shown below
-3/8(-8-16d)+2d = 24
Step 1 Distribute -3/8 over the expression in parentheses
3 + 6d + 2d = 24
Simply the like terms
3 + 8d = 24
Subtract 3 from both sides of the equation.
8d = 24 - 3
8d = 21
d = 21/8
Hence the error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
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The graph of the function f(x) = (x +2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the r
Answer: The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
Step-by-step explanation:
The domain is the set of inputs, and the range is the set of outputs.
Answer: Option A
Step-by-step explanation
The domain is the set of allowed x inputs of a function.
We can replace x with any number we want to get some output for y = f(x)
This tells us the domain is the set of all real numbers.
-----------
The range is the set of numbers y such that
In other words, we can have y = -4 or y > -4
This is because y = -4 is the lowest output possible, as indicated by the vertex point.
number 68 is increased by 43%
Answer:
68 increased by 43% is 97.24.
Step-by-step explanation:
Multiply 68 by 1.43.
68×1.43=97.24
The answer is 97.24.
Hope this helps!
Answer:
97.24 Absolute change, And the actual difference is 97.24 - 68 = 29.24.
Step-by-step explanation:
What are the coordinates of the midpoint of the segment whose endpoints are C(−7, −10) and D(3, 9) ?
(−2, −0.5)
(−4, −1)
(−5, −9.5)
(−8.5, 3)
Answer:
(-2, -0.5)
Step-by-step explanation:
1. add the x-coordinates and then either divide by 2 or multiply by 1/2
2. add the y-coordinates and then either divide by 2 or multiply by 1/2
(-7+3)/2 = -2
(-10+9)/2 = -0.5
Have a blessed day!
Can someone please help me with this
Answer:
y = 0.5x
Step-by-step explanation:
y = rx
4.5/9 = 0.5
7/14 = 0.5
15/30 = 0.5
y = 0.5x