The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = [tex](x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.[/tex]
The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = [tex](x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]
A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2[/tex].
In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.
Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]
In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that [tex](x+1), (x-3), (x^2+4)[/tex]are the factors of the polynomial.
It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = [tex]x^2[/tex]+4 is a factor of the polynomial and it is included in the polynomial..
Learn more about polynomial:
https://brainly.com/question/17822016
#SPJ4
The length, width and height of a rectangular prism are in the ratio 3:2:1, respectively. What is the length of the prism if it has a volume of 48 cm3?.
The rectangular prism's dimensions are 3:2:1 in terms of length, breadth, and height. The prism's length can be computed as 24 cm using its volume, 48 cm3, as input.
Volume = Length × Width × Height
48 cm3 = L × 2 × 1
L = 24 cm
A rectangular prism is a solid 3D object that has six faces, eight vertices and twelve edges. The length, width and height of a rectangular prism can be expressed in a ratio of 3:2:1 respectively. Knowing this ratio and the volume of the prism, which is 48 cm3, it is possible to calculate the length of the prism. To calculate the length of the prism, first the volume of the prism must be expressed in terms of the length. This can be done by using the formula Volume = Length × Width × Height. Therefore, 48 cm3 = L × 2 × 1. Solving this equation for L gives the length of the prism as 24 cm. Therefore, the length of the rectangular prism with a volume of 48 cm3 and a ratio of 3:2:1 is 24 cm.
Learn more about volume here
https://brainly.com/question/16134180
#SPJ4
How do you solve y =- 2x 6?.
We can find the solution of y = -2x + 6 by graphing the equation by plotting the intercepts of the equation.
Here we can solve the equation by calculating the x and y intercepts of the equation.
This is done by equating the other coordinate to 0 to get the intercept.
For the x-intercept, we will take y to be 0 to get
-2x + 6 = 0
or, 2x = 6
or, x = 3
Hence one intercept will be (3 , 0)
For the y-intercept, we will let x be 0 to get
y = 6
Hence getting the other intercept to be (0 , 6)
Now we can plot the graph by simply plotting these points and drawing a straight line passing through it
To get any unique solution, another equation needs to be plotted and the intersection point of the 2 lines will give us the required answer.
To learn more about equations visit
https://brainly.com/question/30127282
#SPJ4
Complete Question
How do you solve y = -2x + 6?
Marshall spins a prize wheel with 4 segments of equal size, one of which is labeled "winner. "
Let X = the number of spins until Marshall wins a prize.
What is the probability that Marshall wins a prize on his 2nd spin?
Recall: P(X = k) = (1 – p)k–1p
Round to 4 decimal places
The probability that Marshall wins a prize on his second spin = 0.1875
Consider an event X = the number of spins until Marshall wins a prize.
Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.
So, the sample space n = 4
For given event x, the possible outcomes = 1
Using the formula of probability,
p = x/n
p = 1/4
p = 0.25
So, the probability of success p = 0.25
q = 1 - p
q = 1 - 0.25
q = 0.75
To find the probability that Marshall wins a prize on his 2nd spin.
Using formula, [tex]P(X = k) = (1 - p)^{k-1}p[/tex]
For k = 2,
[tex]P(X = 2) = (1 - 0.25)^{2-1}\times 0.25[/tex]
P(X = 2) = 0.75 × 0.25
P(X = 2) = 0.1875
Thus, the required probability is 0.1875
Learn more about the probability here:
https://brainly.com/question/30034780
#SPJ4
given 3x+2y=8 what equation represents the line parallel to the given equation and passes through the point (-2,5).
Answer:
y = -3/2 x + 2
Step-by-step explanation:
3x + 2y = 8
2y = -3x + 8
y = -3/2 x + 4
slope of given line = m = -3/2
Parallel lines have equal slopes.
Slope of parallel line through point (-2, 5), m = -3/2.
y = mx + b
m = -3/2
y = -3/2 + b
point: (-2, 5)
5 = (-3/2)(-2) + b
5 = 3 + b
b = 2
Equation: y = -3/2 x + 2
Alexis bought X boxes of cereal for $3 each and paid with a $20 bill. Which expression represents the total amount of change she should receive?
The expression that represents the total amount of change she should receive is y = 20 - 3x.
What is linear expression?An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.
The price of x boxes of cereal $3 each = 3x
Let y be the extra cash she paid
Total cash she paid = $20
Then we have
3x + y = 20
And for expression that represents the total amount of change she should receive
y = 20 - 3x
Thus, The expression that represents the total amount of change she should receive is y = 20 - 3x.
Learn more about linear expression.
https://brainly.com/question/30111963
#SPJ1
I DEF~GHF, find the value of x and y
Answer:
x = 8y = 35Step-by-step explanation:
Given similar triangles DEF and GHF, and side lengths DE = 6, EF = 10, GH = 21, FG = 28, you want the lengths of y=FH and x=FD.
ProportionCorresponding sides of similar triangles are proportional. This means ...
DE/GH = EF/HF = FD/FG
6/21 = 10/y = x/28
We can multiply by 28 to solve for x:
x = 28(6/21) = 8
Multiplying by 21y/6 will give the value of y:
y = (21/6)(10) = 35
The values of x and y are 8 and 35, respectively.
__
Additional comment
These are both 3-4-5 right triangles. The smaller is multiplied by 2; the larger is multiplied by 7 to give 6-8-10 and 21-28-35 triangles.
What is the solution of 7x 9 16?.
The solution to the equation 7x - 9 = 16 is x = 25/7. This can be achieved by using the addition property of equality and simplifying the equation.
The equation 7x - 9 = 16 can be solved by using The equation's solution can be changed by adding the same amount to either side of the equation, according to the addition property.
To both sides of the equation, add 9.
7x - 9 + 9 = 16 + 9
Simplify the equation.
7x = 25
Divide both sides of the equation by 7.
7x/7 = 25/7
Simplify the equation.
x = 25/7
Therefore, the solution to the equation 7x - 9 = 16 is x = 25/7.
Learn more about equality visit:
https://brainly.com/question/28293087
#SPJ4
Simplify the expression
using only positive exponents.
The expression is simplified to y⁹/12x². Option A
What are index forms?The index form of a number is simply described as a number written as an exponential expression.
It is described as a single number raised to another number.
Index forms are also described as standard forms and scientific notation.
From the information given, we have;
3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²
Now, expand the bracket of the denominator and multiply the values
3x^⁻⁴y⁵/2x⁶y⁻¹⁴
Divide the expression , we have;
3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)
To determine the quotient, subtract the exponents of the denominator from the numerators
3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)
Now, add or subtract the exponential values, we get;
-12 (x⁻²y⁻⁹)
y⁹/12x²
Hence, the value is y⁹/12x²
Learn more about index forms here:
https://brainly.com/question/15361818
#SPJ1
Fat food chain uing platic or tyrofoam in elling their product, make a 5 entence of the problematic ituation
Fast food chains that use plastic or styrofoam containers in selling their products are contributing to the global plastic pollution crisis. Styrofoam and plastic containers, which are not biodegradable, take up to 1000 years to decompose.
Every year, an estimated 8 million metric tons of plastic end up in the ocean, and the majority of it is from single-use plastic products such as those used by fast food chains. This plastic pollution is having a devastating effect on the environment, with marine life ingesting and becoming entangled in the plastic. In addition, the production of styrofoam and plastic containers is highly energy intensive and contributes to the emission of greenhouse gases. This is a problematic situation that needs to be addressed urgently.
The energy intensity of production for styrofoam and plastic containers can be calculated using the formula:
Energy Intensity (EI) = Energy Used (EU) / Output (O)
For example, if it takes 50 kWh of energy to produce a unit of output, the energy intensity of production would be 50 kWh/unit. This highlights the environmental impact of styrofoam and plastic containers, and the urgent need to reduce their use in fast food chains.
Learn more about Energy Intensity here:
https://brainly.com/question/27696379
#SPJ4
Ryan got 7/8 problems correct
on the test. Sam got 80%
correct. Who got a better
score?
Answer:
Ryan did
Step-by-step explanation:
7/8 is .875 which is about 87
To compare the score of Ryan and Sam, we need to convert the fractions to decimals.
Ryan got 7/8 problems correct, which is equivalent to 0.875 when expressed as a decimal.
Sam got 80% correct, which is equivalent to 0.8 when expressed as a decimal.
So, Ryan got a better score
Think about a plan carlo plan to build a grain bin with a radiu of 15ft. The recomended lant of the room i 25
The length x will be 23.994615468 ft or rounded approximately 24 feet.
Roof Length Calculation in FeetThe length x is the distance from the center of the roof to the edge of the roof.
Using trigonometry, we can find the length x by using the equation:x = 15 + (15 * tan(25°)) + 1
The tan(25°) can be found using a calculator or table. With a calculator, we get:tan(25°) = 0.466307658
Substituting this value back into the equation, we get:x = 15 + (15 * 0.466307658) + 1
x = 15 + 6.994615468 + 1
x = 23.994615468 ft
So, the length x = 23.994615468 ft, or approximately 24 feet.
The problem is about finding the length x, which is the distance from the center of the roof to the edge of the roof of a grain bin with a radius of 15 ft and a recommended slant of 25° for the roof. The roof is also required to overhang the edge of the bin by 1 ft. The length x was calculated using trigonometry and found to be approximately 24 feet.
Complete Problems (Question):
Carlos plans to build a grain bin with a radius of 15 ft. The suggested slant of the roof is 25°. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be? Give your answer in feet and inches.
Learn more about Grain Bin Height Calculation here:
https://brainly.com/question/30301560
#SPJ4
ABCD is a rhombus. If AB=26 and BD=20, find AE
In the given Rhombus ABCD, the measure of side AE = 27.85.
What is Area of a Rhombus?Verify that the two diagonals are parallel to one another. The diagonal lines are parallel. A rhombus is what it is. The parallelogram is a rectangle, rhombus, and square since the diagonals are all congruent and perpendicular to one another.
Area can be used to determine the area of a rhombus because it is a parallelogram, and its area can be determined from the length of its base and perpendicular height.
Here, we construct an alternate formula for the area of a rhombus that uses the lengths of its diagonals. Find the length of the other diagonal if one of the diagonals is 8 units long. We already know how to compute the area of a rhombus using its diagonals: Area = (1/2) (diagonal1 diagonal2) 256 = (1/2) (8 diagonal2).
AB = 26
BD = 20
BD/2 = 10
Using Pythagorean theorem:
[tex]AE = \sqrt{26^2 + 10^2}[/tex]
AE = 27.85
To learn more about rhombus refer to :
https://brainly.com/question/27870968
#SPJ1
Complete the statements describing the process of converting z = 2 + 3i to polar coordinates using technology.
Write the complex number as a point in the complex plane,
(2, 3pi)
(2, 3)
(3i, 2)
(-3, 2)
Substitute _ for a and _ for b.
Options for the first _:
2
2pi
3
3i
Options for the second _:
2
2i
3
3i
Using radians for θ, record the result ___ as your answer in polar coordinate form.
(3.606cos(.983), 3.606sin(.983))
(3.606, 0.983)
3.606
0.983
Answer:
The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:
Write the complex number as a point in the complex plane: (2, 3i)
Substitute a = 2 and b = 3 for the real and imaginary parts respectively.
Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).
To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:
Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.
Substitute a for the real part and b for the imaginary part.
Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.
Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.
Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.
It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))
Answer:
z = 2 + 3i
Step-by-step explanation:
What is partial sum limit?.
A partial sum limit is the sum of the series.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.
Learn more about Partial sum:
https://brainly.com/question/24249275
#SPJ4
greg has 128 books this is 4 times as many book as sarah
Answer:512
Step-by-step explanation:
How do you write eight more than a number?.
To write 8 more than a number, we use the mathematical operation of addition and the notation 8+ Number = N+8.
To write 8 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 8 + Number = N+8.
This notation means that we are adding 8 to a number, which results in N+8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+8.
Another way to write 8 more than a number is to use the phrase "8 plus a number". This phrase indicates that we are adding 8 to a number to get N+8.
Therefore, In short, to write 8 more than a number, we use the mathematical operation of addition and the notation 8 + Number = N+8. This means that we are adding 8 to a number, resulting in N+8. It can also be written as "8 plus N", indicating the same operation.
To learn more about arithmetic operations,
Visit; brainly.com/question/16679150
#SPJ4
pls help :(
y= _x +_
Find the equation of the line
hi, I'm no bot just in case...
the grapgh of the line shows y intercept of -9 and rate of change by 4
SoThe equation of the lline will be: [tex]y=4x-9[/tex]
The points O, P, Q and R all lie on the same line segment, in that order, such that the ratio of OP : PQ : QR is equal to 1 : 1 : 3. If OR = 10, find OQ.
Answer:
OQ = 4
Step-by-step explanation:
the ratios of the segments OP : PQ : QR = 1 : 1 : 3 = x : x : 3x ( x is a multiplier)
then
OP + PQ + QR = OR , that is
x + x + 3x = 10
5x = 10 ( divide both sides by 5 )
x = 2
Then
OQ = OP + PQ
= x + x
= 2x
= 2 × 2
= 4
What is the relationship between the sine rule and the sine ratio in a right triangle?.
The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.
What is the relationship between the sine rule and the sine ratio in a right triangle?.The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.
The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The sine law is can therefore be given as,
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.
To know more about sine rule , check out:
https://brainly.com/question/20839703
#SPJ4
I don’t really understand how to do this! Please someone helppp! The question is : What is the slope of the line?
At KFC, the kitchen taff baked 25 chicken leg and 50 wing. The taff had to prepare platter for an office lunch. If each platter will have the ame number of leg and wing, what i the greatet number of platter they can make?
So, each platter will have 25 legs and 25 wings.
To determine the greatest number of platters the kitchen staff can make, you need to find the least common multiple of 25 and 50. This is because each platter must have the same number of legs and wings, so you need to find the smallest number of legs and wings that can be divided evenly into both 25 legs and 50 wings.
The least common multiple (LCM) of 25 and 50 is 50. This means that the greatest number of platters the kitchen staff can make is 50/25 = 2 platters.
Therefore, each platter will have 25 legs and 25 wings.
To learn more about least common multiple
Visit; brainly.com/question/30060162
#SPJ4
Find the least frequent multiple of 25 and 50 to determine the maximum number of platters the kitchen staff can produce. Finding the fewest number of legs and wings that can be equally divided into 25 legs and 50 wings is necessary because each platter must have the same number of legs and wings.
25 and 50 have a least common multiple (LCM) of 50. The maximum amount of platters the kitchen staff is capable of producing is 50/25, or 2 platters.
Therefore, there will be 25 legs and 25 wings on each plate.
NEED TO FINISH BY 5!!! WILL MARK BRAINLIEST
Answer:
10 1/8
Step-by-step explanation:
25 3
8
+
-15 1
4
= (25 + -15) + (
3
8
+
-1
4
)
= 10 +
3
8
+
-1 × 2
4 × 2
= 10 +
3
8
+
-2
8
= 10 +
3 + -2
8
= 10 +
1
8
=
10 1
8
THE FIRST PERSON TO GET THIS RIGHT GETS 10 POINTS AND BRAINLIEST! MUST BE RIGHT AND IF THE ANSWER IS YES, THEN ALSO ANSWER WHAT IS THE CONSTANT OF PROPORTIONALITY
Answer:
No
Step-by-step explanation:
1. The population of the country Ghana was 24 658 823 in the year 2010. In the year 2020, Ghana Statistical Service gave an estimated number of people in the country Ghana a 31 072 940.
a. Find the difference in the two data provided.
b. Calculate the sum of the two data to the nearest thousand hundred.
a. the difference in the two data provided =31072940 - 24658823 = 6414117
b. the sum of the two data to the nearest thousand hundred = 31072940 - 24658823 = 55731763
nearest to Thousand hundred = 55730000
URGENT PLEASE HELP I NEED IT RN! THANKS
7. Critique Reasoning Julio states that he can use the SAS Triangle Congruence
Theorem to prove that two right triangles are congruent. He constructs two right
triangles to have congruent hypotenuses and one set of congruent legs. What does
Julio need to do in order to use the SAS Triangle Congruence Theorem? Explain your
reasoning
Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.
Julio needs to prove that the two triangles have congruent sides in order to use the SAS Triangle Congruence Theorem. This means that he needs to show that one side of one triangle is congruent to a corresponding side of the other triangle and the same applies to the other two sides. This can be done by using methods such as measuring the sides, using algebraic equations, or using geometric constructions.
According to Julio statement, he has already constructed two right triangles to have congruent hypotenuses and one set of congruent legs, which means he has already proved that one side of one triangle is congruent to a corresponding side of the other triangle (hypotenuse) and one set of legs are congruent.
Therefore, Julio need to prove the remaining side of the triangle congruent to the corresponding side of the other triangle. Once he proves this, he can use the SAS Triangle Congruence Theorem to state that the two triangles are congruent.
Learn more about SAS Triangle Congruence Theorem at,
https://brainly.com/question/18922904
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
9
Step-by-step explanation:
2x + 3y - 2
Putting x=1; y=3
(2x1) + (3x3) - 2
2 + 9 - 2
Now, according to BODMAS, we shall add first.
11 - 2
9
What is the solution of 3x 4y 12?.
(0,3) , (4,0) are two solution of equation 3x + 4y = 12.
An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equal sign (=), with the expressions on either side representing the same value.
Given Linear equation in two variables:
3x + 4y = 12 ----( 1 )
Substitute x = 0 , in equation ( 1 ) ,
3 × 0 + 4y = 12
=> 4y = 12
=> y = 12/4
y = 3
Therefore ,
( x , y ) = ( 0 , 3 )
Substitute y = 0 in equation ( 1 ) ,
3x + 4 × 0 = 12
=> 3x = 12
=> x = 12/3
x = 4
Therefore,
( x , y ) = ( 4 , 0 )
Required two solutions are ( 0 , 3 ) , ( 4 , 0 )
Therefore, (0,3) , (4,0) are two solution of equation 3x + 4y = 12.
To learn more about equation visit : brainly.com/question/29657983
#SPJ4
The volume of a cube is 8 in³. What is the length of one side?
Answer:
2 in
Step-by-step explanation:
If im not wrong, each side should be 2 inches, as it would have to be 2x2x2 for a volume of 8 inches cubed
A triangular tract of farm land has sides of length 2.1 miles, 1.8
miles, and 2.7 miles. If a bag of fertilizer covers 0.2 square
miles, how many bags of fertilizer are needed to cover the area
of the triangle? Round your answer to the nearest whole
number. NEED THIS ASAP TYSM
Answer: we would need 7 bags of fertilizer to cover the area of the triangle.
Step-by-step explanation:
To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.
The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7
The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35
Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75
Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.
What is the formula for the sum of exterior angles in a polygon?
The sum of a regular polygon's exterior angles will always equal 360 degrees.
What is exterior angles?Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).
Here,
The sum of the exterior angles of a regular polygon will always equal 360 degrees.
To know more about exterior angles,
https://brainly.com/question/28835566
#SPJ4
