An nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).
As given in the question,
Number of zeros of the polynomial function N = 3
Real and complex zeros = 3, 2i , -2i
Function value f(-1) = 20
f(x) = k (x-3)(x-2i)(x+2i)
⇒f(x) = k(x-3)(x²-4i²)
⇒f(x) =k(x-3)(x²+4)
⇒f(-1) = k(-1-3)((-1)² +4)
⇒ 20 =k(-4)(5)
⇒k =-1
Now , f(x) = (-1)((x-3)(x²+4)
= (-1)(x³ -3x²+4x -12)
Therefore, nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).
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J. The Math Club found a company that will sell it t-shirts for $5.00 each, but there is a set-up fee of $50.
Montel heated a 12-cup pot filled with soup. He served bowls of soup to his family.
How can Montel find out how much soup his family ate?
He can find out by using mathematical operation - subtraction.
What are Mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as a ternary operation, is the mixed product.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
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fully factorise
[tex]12x^3 + 38x^2 - 14x[/tex]
Answer:
2x(2x + 7)(3x - 1).
Step-by-step explanation:
12x^3 + 38x^2 - 14x
= x(12x^2 + 38x - 14)
= 2x(6x^2 + 19x - 7)
To factor the expression in the parentheses we need 2 numbers whose product is (6 * -7) = - 42 and whose sum = +19.
These are +21 and - 2.
So, we write:
6x^2 - 2x + 21x - 7
= 2x(3x - 1) + 7(3x - 1)
= (2x + 7)(3x - 1)
So, the answer is 2x(2x + 7)(3x - 1).
Answer:
[tex]2x(3x-1)(2x+7)[/tex]
Step-by-step explanation:
[tex]12x^3+3x^2-14x\\[/tex]
Factor out common factor: (2x)
[tex]=2x(6x^2+19x-7)[/tex]
Factor [tex]6x^2+19x-7[/tex]
[tex]= 2x(3x-1)(2x+7)[/tex]
Hope this helps! :) Sorry for the late reply
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours. What was the average change in temperature per hour?
Enter your answer as a decimal.
The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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What is the volume of the following cone?
The volume of the cone, to the nearest whole number, is: 50 cm³.
How to Find the Volume of a Cone?The volume of a cone is defined as the amount of space it contains. The volume can be calculated using the formula:
Volume of cone = 1/3 × π × r² × h, where h is the height of the cone, and r is the radius of the cone.
Given the parameters:
Height of the cone (h) = 3 cmRadius of the cone (r) = 4 cmPlug in the values:
Volume of the cone = 1/3 × π × 4² × 3
Volume of the cone = 1/3 × π × 16 × 3
Volume of the cone = 16π
Volume of the cone = 50 cm³
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Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
Answer:
x = -3 and y = 6
Step-by-step explanation:
by plugging the function (y = 3x + 15) into the y value in the function (3x + 3y = 9), you can then solve to find that x = -3
After solving for the x-value, plug -3 into the easiest equation to solve for the y-value (y = 3x + 15) to then find that y = 6
This is method of solving is called substitution
Type the correct number
Cars
4
12
16
Trucks
5
10
15
25
Answer:
cars= 32 , trucks= 55
Step-by-step explanation:
add all the cars up then the trucks
who knows how to solve this! its geometry
Answer:
figure out how to get 180% from those 3 points
Step-by-step explanation:
I really need help you guys pleaseeee
1.998 x 10^27
Ordinary number
The representation of the number is 1.998 multiplied by 10^27
How to evaluate the expression?The expression is given as
1.998 x 10^27
The above mathematical representation is a number in scientific form and is already in its most simplified form
This means that the scientific form cannot be further simplified
However, the scientific number can be rewritten as a mathematical statement
Recall that, we have
1.998 x 10^27
The pronunciation of the above expression is:
1.998 multiplied by 10^27
And it is evaluated by
Moving the decimal point 27 places to the right.
This gives
1998000000000000000000000000
See that the above result does not have a proper representation compared to 1.998 x 10^27
Hence, the representation of the scientific number given as 1.998 x 10^27 is the 1.998 multiplied by 10^27
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Which of the following is true? ( not multiple choice)
Answer: A
180-130= <D
50=<D
50+70= 120
180-120=<B
60=<B
m<BCD= 70
m<DBC= 60
70-60=10
Answer:
О A = 10°
Step-by-step explanation:
∡ DBC = 180 - 130 = 50°
∡ DBC + ∡ CBD + ∡ BCD = 180°
50° + 70° + ∡BCD = 180°
∡BCD = 180° - (50°+70°)
∡BCD = 180° - 120°
∡BCD = 60°
Then:
∡BCD - ∡DBC = 60° - 50° = 10°
−14 = −21 +
C
11
Subract
Answer:
35
Step-by-step explanation:
The sum of the digits of a certain two-digit number is 11. When you reverse its digits you increase the number by 45. What is the number?
Answer:
6 and 9.
Step-by-step explanation:
PLS HELP!! DUE TODAY! Will give branliest to the best answer, 40 points!!
What is the slope of a line that is perpendicular to the line y = 18x + 5?
A. -8
B. -1/8
C. 1/8
D. 8
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:B. \:\: - \dfrac{1}{18} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation of a line is in its slope intercept form, that is :
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
The original equation is :
[tex]\qquad \tt \rightarrow \:y = 18x + 5[/tex]
by comparing the two equations we get slope (m) of this line equal to 18
we need to find the slope (n) of line perpendicular to this.
By the property of perpendicular lines, we know :
[tex]\qquad \tt \rightarrow \:m \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:18 \times n = - 1[/tex]
[tex]\qquad \tt \rightarrow \:n = - \cfrac{1}{18} [/tex]
So, slope of required line is -1/18
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: -1/18
Step-by-step explanation:
Let y=k₁x+b1 be the line. Given the perpendicularity of lines, the equation of the line perpendicular to the given line has the form:
[tex]\displaystyle\\y=-\frac{1}{k}x+b_1[/tex]
[tex]\displaystyle\\So,\ y=18x+5\\\\\Rightarrow\ -\frac{1}{18}[/tex]
tim and his sister drove 18 miles in 27 minutes. How long will it take them to drive 24 miles
It will take them 36 minutes to drive 24 miles.
What is unitary method?A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Because of this, the goal of this method is to determine values in reference to a single unit. For instance, we can use the unitary technique to determine how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Given Data
Tim and his sister drove 18 miles in 27 minutes.
They drove 1 mile in :
18 mile = 27 minutes
1 mile = [tex]\frac{27}{18}[/tex] minutes
1 mile = 1.5 minutes
For 24 miles,
1 mile = 1.5 minutes
24 miles = 1.5(24) minutes
24 miles = 36 minutes.
It will take them 36 minutes to drive 24 miles.
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What is the range of the function shown on the graph?
Check the picture below.
Given: 1 || m, p || q Prove: 21 = 22
Answer:
Proved.
Step-by-step explanation:
l // m and p is transversal.
∠1 ≅ ∠3 ----------(I) {Corresponding angles}
p // q and l is transversal.
∠3 ≅ ∠2 -------(II) {Corresponding angles}
From (I) & (II),
∠1 ≅ ∠2
Hence proved.
To prove ∠1 = ∠2
What are parallel lines?
In a plane, parallel lines are those whose distances between them are constant. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given: l II m and p II q
According to the properties of parallel lines
∠1 and ∠ 3 are equal because l II m therefore ∠1 and ∠ 3 are corresponding angles.
Since p II q therefore ∠3 = ∠2 { angles present on the same sides of the parallel lines called corresponding angles are equal }.
Thus since ∠1= ∠3 and ∠3=∠2 therefore we can say that ∠1 = ∠2.
Hence proved.
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Can u please answer this asap and thank you
Answer:
10 popcorn orders
Step-by-step explanation:
[tex]10 + 4.55 x = 8 + 4.75x \\ 4.55x - 4.75x = 8 - 10 \\ - 0.2x = 8 - 10 \\ - 0.2x = - 2 \\ x = \frac{ - 2}{ - 0.2} \\ x = 10[/tex]
What are the domain and range of this relation? pt3 last one pls help
In WXY, m/W = (10x + 17)°, m/X = (2x - 9)°, and m/Y = (3x + 7)°. Find m/Y.
Answer:
m∠Y = 40°
Step-by-step explanation:
The sum of the three angles of a triangle must equal 180°
Thus
m∠W + m∠X + m∠y = 180°
→ (10x + 17) + (2x - 9) + (3x + 7) = 180
→ 10X + 17 + 2X + 9 + 3X + 7 = 180
Collecting like terms
→ 10X + 2X + 3X + 17 - 9 + 7 = 180°
→ 15x + 15 = 180
Subtract constant 15 from both ssides:
→ 15x + 15 - 15 = 180 - 15
→ 15x = 165
Divide both sides by 15
→ 15x/15 = 165/15
→ x = 11
m∠Y = 3x + 7
m∠Y = 3 x 11 + 7
m∠Y = 33 + 7
m∠Y = 40°
Solve for b.
-14b + 1
4
<3 or b - 15 - 15b > 1
Write your answer as a compound inequality with integers, proper fr
fractions in simplest form.
or
Answer:
Step-by-step explanation:
Order 81%, 8/9, 0.79, and 9/11 from least the greatest.
Answer:
9/11, 8/9, 0.79, 81%
Step-by-step explanation:
i don't know how to explain but this is pretty much how you'd do it
(c) A total of 1800 students attend St. John's College. The ratio
of teachers to students is 1:25.
(i) How many teachers are there at the college.
Three-quarters of the students own laptop computers.
(ii) How many students DO NOT own laptop computers?
Answer: the number of teachers are 14.4 and the amount of students that don’t own laptops of 5400
Step-by-step explanation:
1. Ganymede is one of Jupiter’s moons. It takes Ganymede 7 days, 3 hours, and 15 minutes to make one rotation around Jupiter. How many hours does it take Ganymede to complete a full rotation? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
The number of hours it would take Ganymede to complete a full rotation is 171.25 hours.
What is the number of hours?The first step is to convert days to hours. A day is equivalent to 24 hours. In order to convert days to hours, multiply 7 by 24.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
1 day = 24 hours
24 x 7 = 168 hours
The second step is to convert minutes to hours, In order to do this, divide 15 by 60. Division is the process that is used to determine the quotient of two or more numbers.
60 minutes = 1 hour
15 / 60 = 0.25 hours
Now, add all the converted hours together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Total hours = 168 hours + 3 hours + 0.25 hours = 171.25 hours
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Help quickly please!
The equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) include C. 1 2/3x + 35 - 1 1/2x + 12
How to express the expression?It should be noted that an expression simply shows the relationship between the variables.
In this case, the value of the expression illustrated will be:
5(1/3x + 7) - 3(1/2x - 4)
= 5/3x + 35 - 3/2x + 12
= 5/3x - 3/2x + 35 + 12
= 10/6x - 9/6x + 47
= 1/6x + 47.
Therefore, the equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) will be 1 2/3x + 35 - 1 1/2x + 12. This was illustrated based on the information given as it has the final value of 1/6x + 47.
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Write the equation of the line that passes through the points (3,−8) and(−4,−9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
Step-by-step explanation:
Point slope form: y − y1 = m(x − x1)
First, we find the slope (m):
m = [tex]\frac{y2-y1}{x2-x12} = \frac{-8-(-9)}{3-(-4)} = \frac{1}{7}[/tex]
Now insert your points and slope into the form:
y + 9 = [tex]\frac{1}{7}[/tex](x+4)
solve y-59 equal to 80
Answer:
y=139
Step-by-step explanation:
add 59 to 80
I’ll mark you brainliest for a correct answer!!! I have been reeling over this question forever
answer the following questions for each set: (a) what are the limit points? (b) is the set open? closed? (c) does the set contain any isolated points?
a) limit point of a set A is 1
b) set A is neither open nor closed
c) all the element of set A are isolated point except -1 and 1
Let A={(−1)^n+2/n :n=1,2,3,.....} and B={x∈Q:0<x<1}
Answer the following questions for each set:
a) What are the limit points?
b) is the set open? closed?
c) does the set contain any isolated points?
a) the limit point of a set A are -1 and 1
-1 does not belong to set A
1 belong to set A
Therefore limit point of a set A is 1
b) A set is open if every point in is an interior point. A set is closed if it contains all of its boundary points
thus set A is neither open nor closed
c) a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S and there exists a neighborhood of x which does not contain any other points of S.
all the element of set A are isolated point except -1 and 1
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Pls help!!!: select all the expressions that are equivalent to (1/2) to the power of negative 3. a). -(1/2) to the power of 3 b).2 to the power of 3 c).(1/1/2 to the power of 3) d).1/8 e).8
Answer:
option (e) 8
Step-by-step explanation:
using identity
==>1/(a^(-x))=a^x()
=(1/2)^(-3)
=(2)^3
=2*2*2=8
option (e)
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