Answer:
14
Step-by-step explanation:
because ab means 2(5), then add 4 you get your answer as 14
Which is the wrong one highlighted ?
Answer:
First step
Step-by-step explanation:
The right one is
[tex] {10}^{2} - {1}^{2} = 99 \\ \sqrt{99} = 3 \sqrt{11} [/tex]
If you have problems with mathematics you can text me if you want
The volume of a cylinder is given by the formula v=nr^2h where is r is the radius of the cylinder and h is the height
The volume of a cylinder is given by [tex]\pi 2x^{3} - \pi 5x^{2} -\pi 24x +\pi 63[/tex].
we know that
The volume of a cylinder is given by the formula v=nr^2h
where
r is the radius of the cylinder
h is the height of the cylinder
in this problem, We know that height of the cylinder is given by h = 2x + 7 and radius r = x-3
Substituting the given values in the above formula to get:
Volume = [tex]\pi .(x - 3)^{2} .2x+7[/tex]
[tex]= \pi (x^{2} - 6x + 9)(2x + 7)\\\\= \pi (2x^{3} - 5x^{2} -24x +63)[/tex]
Hence , the volume of a cylinder is given by [tex]\pi 2x^{3} - \pi 5x^{2} -\pi 24x +\pi 63[/tex].
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A system consists of two particles. At t = 0 one particle is at the origin; the other, which has a mass of 0. 50 kg, is on the y-axis at y = 6. 0 m. At t = 0 the center of mass of the system is on the y-axis at y = 2. 4 m. The velocity of the center of mass is given by (0. 75 m/s3) t2i^.
The total mass of the system which consists of two patches is1.25 kg.
The position vector of the center of mass of the system can be defined as the weighted normal of the position vectors of the two patches, with the weights being the millions of the patches.
Given that the position of the center of mass is on the y- axis at y = 2.4 m and the y- element of the haste of the center of mass is(0.75 m/ s3) t2, we know that the center of mass doesn't move in thex-direction. So, the position vector of the center of mass can be expressed as
Rcm = 2.4 i
The position vector of the first flyspeck is given as the origin, and the position vector of the alternate flyspeck is given as 6j. The total mass of the system is given by the following equation
m1 m2 = mtotal
m1 * R1 m2 * R2 = mtotal * Rcm
Where R1 and R2 are the position vectors of the first and alternate patches, independently, and m1 and m2 are their separate millions.
working the below equation for mtotal, we get
mtotal = m1 m2 = m2 *( R2/ Rcm)
mtotal = 0.5 *(6/2.4) = 0.5 *(2.5)
mtotal = 1.25 kg
Hence the total mass of the system is1.25 kg.
This question is deficient and should be written as
A system consists of two patches. At t = 0 one flyspeck is at the origin; the other, which has a mass of0.50 kg, is on the y- axis at y = 6.0 m. At t = 0 the center of mass of the system is on the y- axis at y = 2.4 m. The haste of the center of mass is given by(0.75 m/ s3) t2i. Find the total mass of the system. The aggregate mass of the system which consists of two patches is1.25 kg.
The position vector of the center of mass of the system can be defined as the weighted normal of the position vectors of the two patches, with the weights being the millions of the patches.
Given that the position of the center of mass is on the y- axis at y = 2.4 m and the y- element of the haste of the center of mass is(0.75 m/ s3) t2, we know that the center of mass doesn't move in the x-direction. So, the position vector of the center of mass can be expressed as
Rcm = 2.4 i
The position vector of the first flyspeck is given as the origin, and the position vector of the alternate flyspeck is given as 6j. The total mass of the system is given by the following equation
m1 m2 = mtotal
m1 * R1 m2 * R2 = mtotal * Rcm
Where R1 and R2 are the position vectors of the first and alternate patches, independently, and m1 and m2 are their separate millions.
working the below equation for mtotal, we get
mtotal = m1 m2 = m2 *( R2/ Rcm)
mtotal = 0.5 *(6/2.4) = 0.5 *(2.5)
mtotal = 1.25 kg
Hence the total mass of the system is1.25 kg.
This question is deficient and should be written as
A system consists of two patches. At t = 0 one flyspeck is at the origin; the other, which has a mass of0.50 kg, is on the y- axis at y = 6.0 m. At t = 0 the center of mass of the system is on the y- axis at y = 2.4 m. The haste of the center of mass is given by(0.75 m/ s3) t2i. Find the total mass of the system.
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The total mass of the system which consists of two particles is 1.25 kg.
The position vector of the center of mass of the system can be defined as the weighted average of the position vectors of the two particles, with the weights being the masses of the particles.
Given that the position of the center of mass is on the y-axis at y = 2.4 m and the y-component of the velocity of the center of mass is (0.75 m/s^3)t^2, we know that the center of mass does not move in the x-direction. So, the position vector of the center of mass can be expressed as:
Rcm = 2.4iThe position vector of the first particle is given as the origin, and the position vector of the second particle is given as 6j. The total mass of the system is given by the following equation:
m1 + m2 = mtotalm1 * R1 + m2 * R2 = mtotal * RcmWhere R1 and R2 are the position vectors of the first and second particles, respectively, and m1 and m2 are their respective masses.
Solving the above equation for mtotal, we get
mtotal = m1 + m2 = m2*(R2/Rcm) mtotal = 0.5*(6/2.4) = 0.5*(2.5) mtotal = 1.25 kgHence the total mass of the system is 1.25 kg.
This question is incomplete and should be written as:
A system consists of two particles. At t = 0 one particle is at the origin; the other, which has a mass of 0.50 kg, is on the y-axis at y = 6.0 m. At t = 0 the center of mass of the system is on the y-axis at y = 2.4 m. The velocity of the center of mass is given by (0.75 m/s3) t^2i. Find the total mass of the system.Learn more about center of a mass here: brainly.com/question/8662931
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an aquarium holds 42 gallons of water after two minutes the aquarium has three gallons of water in it how many more minutes will it
Answer:
After 7 minutes, both tanks have the same amount of water.
Step-by-step explanation:
Aerabella is planning her sweet 16 and wants to rent a DJ. She has at most $130 to spend.
* The rental of the DJ costs $50 for the day
* The DJ charges 0.75 per song
what is the greatest number of songs she can play at her sweet 16?
Make sure to use whole numbers only.
Using mathematical operations, the greatest number of songs Aerabella can play at her Sweet 16 party is 106.
How is the number determined?The number of songs Aerabella can play is determined by subtracting the fixed charge for the day from her spending budget and dividing the difference by the unit charge per song.
Subtraction and division operations are two of the four basic mathematical operations, including addition and multiplication.
The total spending budget = $130
The fixed rental charge for a DJ = $50
The charge per song (unit rate) = $0.75
The variable cost for the party = $80 ($130 - $50)
The number of songs Aerabella can play = 106.67 ($80 ÷ $0.75)
= 106
Thus, based on the mathematical operations of subtraction and division, and given the fixed cost of hiring a DJ, the highest number of songs Aerabella can play for her Sweet 16 party is 106.
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234 × 673 pls help I'm on my last remaining brain cell
Answer:
157482
Step-by-step explanation:
234 × 673 = 157482
Answer:
157,482
Step-by-step explanation:
Use a calculator.
What is the length of the midsegment of a trapezoid whose vertices are E(-7, 6), F(-2, 5), G(-2, 2), and H(-7, -4)?
The length of the midsegment of the trapezoid E(-7, 6), F(-2, 5), G(-2, 2), and H(-7, -4) found using the formula for finding the distance between two points on the coordinate plane is 6.5 units long
What is the formula for the distance between points (x₁, y₁), and (x₂, y₂), on the coordinate plane?The formula for the distance d between two points on the coordinate plane is; [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The midsegment of a trapezoid is the segment that joins or extends between the midpoints of the sides of the trapezoid that are not parallel.
The parallel sides are the sides that have the same slope;
Slope of the side EF = (5 - 6)/(-2 - (-7)) = -0.2
Slope of the side FG = (5 - 2)/(-2 - (-2)) = Undefined
Slope of the side GH = (-4 - 2)/(-7 - (-2)) = 1.2
Slope of the side EH = (-4 - 6)/(-7 - (-7)) = Undefined
The non parallel sides are EF and GH
The midpoint of EF = ((-7 + (-2))/2, (6 + 5)/2) = (-4.5, 5.5)
The midpoint of GH = ((-7 + (-2))/2, (2 + (-4))/2) = (-4.5, -1)
The length of the mid segment is therefore;
d = √((-4.5 - (-4.5))² + (5.5 - (-1))²) = 6.5
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 10 6
The area of the shaded region of the Frame if it's 2 units wide would be = 17.5 units²
How to calculate the area of the shaded region?From the given diagram, the shaded region is the framed rectangle, and the white part is the frame.
The frame is 2 units wide which shows to get sides of the shaded rectangle is thus;
Length = 10/2 = 5
width = 7/2 = 3.5
Therefore the area of that shaded region is calculated using the formula for area of a rectangle:
Area of a rectangle = l × w = 5× 3.5 = 17.5 units²
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Nathalia is shopping for a bank. She does not write checks or use
the ATM. She pays for lunch with her debit card 25 times each
month. Which bank is a better deal for Nathalia?
A. Tex-Bank is the better deal because the fees for
this bank for Nathalia is $3.50 per month.
B. Nation-Bank is the better deal because the fees
for this bank for Nathalia is $2.75.
C. Tex-Bank is the better deal because the fees for
this bank for Nathalia is $12.25 per month.
D. Nation Bank is the better deal because the fees
for this bank for Nathalia is $20.75.
Tex-Bank is the better deal because the fees for this bank for Nathalia is $12.25 per month.
What kind of account allows you to make withdrawals when you need cash and spend money instantly using a debit card or check?Savings account: A checking account makes it simple to access your money for daily transactions while also keeping it safe. Typically, customers may pay their bills or make purchases using a debit card or a cheque.There is a fixed fee of Rs. 10,000 per ATM if you use an ATM for more than ten hours in a month. In the event of White Label ATMs (WLAs), the bank providing the required amount of cash would be charged the penalty.To learn more about Tex-Bank refer to:
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A paper bag has seven colored marbles. the marbles are pink, red, green, blue, purple, yellow, and orange. list the sample space when choosing one marble.
1. s = {1, 2, 3, 4, 5, 6} 2. s = {purple, pink, red, blue, green, orange, yellow} 3. s = {g, r, b, y, o, p} 4. s = {green, blue, yellow, orange, purple, red}
The sample space when one marble is to be chosen is given as s = {purple, pink, red, blue, green, orange, yellow}
A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S." Events are a subset of the potential outcomes of an experiment. The results in a sample area could vary depending on the experiment. There are only a finite number of possible outcomes in discrete or finite sample spaces.
The sample space in the question has been listed according to the colors of the offered marbles. Finding the sample whose result is a specific stone is necessary. As a result, each color of the marble will be taken into account once. Therefore, the sample space becomes s = {purple, pink, red, blue, green, orange, yellow}
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Answer: its B
Step-by-step explanation:
True or false 20PTS
The required, if triangle ABC is isosceles, then AB≅BC is a valid statment.
In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
here,
A triangle with two sides and two congruent angles is called an isosceles triangle.
So, if triangle ABC is isosceles, then AB≅BC is a valid statement because the definition of an isosceles triangle states that two sides of a triangle are equal.
Thus, the required, if triangle ABC is isosceles, then AB≅BC is a valid statment.
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What is the quadratic function of 5 and 7?
The quadratic function of 5 and 7 is f(x) = x² - 12x + 35
Suppose the solution of a quadratic equation is a and b, the its quadratic function is:
f(x) = (x - a) (x - b)
f(x) = x² - ax - bx + ab
f(x) = x² - (a+b)x + ab
In the given problem, the solution of the quadratic equation is 5 and 7. Hence, its quadratic function is:
f(x) = (x - 5) (x - 7)
f(x) = x² - 5x - 7x + 35
f(x) = x² - 12x + 35
We can also find the function directly using the last row formula:
f(x) = x² - (a+b)x + ab
f(x) = x² - (5+7)x + (5)(7)
f(x) = x² - 12x + 35
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What is the slope of the line that passes through the points (2, 3)(2,3) and (0, 11)(0,11)? write your answer in simplest form.
The slope of the line that passes through the points (2, 3) and (0, 11) is -4.
Slope of line is calculated by the formula m = (y2-y1)/(x2-x1).
In this case, x1 = 2, y1 = 3, x2 = 0 and y2 = 11.
Plugging in the values gives us:
m = (11-3)/(0-2)
We can simplify this expression by multiplying the numerator and denominator by -1:
m = (-11+3)/(-2-0)
This simplifies to:
m = 8/-2
Finally, we can simplify the fraction to:
m = -4
Therefore, the slope of the line that passes through the points (2, 3) and (0, 11) is -4.
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The slope of the line that passes through the points (2, 3) and (0, 11) is -4
In this question we need to find the slope of the line that passes through the points (2, 3) and (0, 11)
We know that the formula for the slope of the line passing through points (x1, y1) and (x2, y2) is
m = (y2 - y1)/(x2 - x1)
Let (x1, y1) = (2, 3)
and (x2, y2) = (0, 11)
Using above formula the slope of the line that passes through the points (2, 3) and (0, 11) would be,
m = (y2 - y1)/(x2 - x1)
m = (11 - 3)/(0 - 2)
m = 8 / (-2)
m = -4
Therefore, the slope of the line is -4
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Find the rational number which when multiplied with -9/13 gives the product 45.
Answer:
-1/45
If this help please set brainliest.
Step-by-step explanation:
To find the number that when multiplied with -9/13 gives the product 45, you can divide 45 by -9/13. Dividing 45 by -9/13 is the same as multiplying -9/13 by the reciprocal of 45, which is -1/45. The reciprocal of a number is 1 divided by that number, so the reciprocal of 45 is 1/45.
Therefore, the number you are looking for is -1/45. When multiplied by -9/13, this number gives the product 45:
(-1/45) * (-9/13) = (-1 * -9) / (45 * 13) = 9/585 = 45
The number you are looking for is -1/45.
solve for x 6/9=x/6 please
The value of x in the algebraic equation '6/9 = x/6' is 4
What are algebraic equations?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants.
For example 5x+6 = x is an algebraic equation where 5 and 1 are the coefficient of x at the L.H.S and R.H.S respectively. And x is the variable.
in the equation 6/9 = x/6. This equation is an algebraic equation with fraction.
We solve by multiplying both side by the L.C.M which is 18
6/9× 18 = x/6 × 18
12 = 3x
divide both sides by 3
x = 12/3 = 4
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Help! Find the perimeter of the figure. Round to the nearest hundrest if nessary.
Answer: Your answer should be 10.8
Step-by-step explanation:
2.9+2.9+2.5+2.5
Pretty simple
Answer:
10.8 m
Step-by-step explanation:
To calculate the perimeter you must add up all the sides
= 2.5 + 2.5 + 2.9 + 2.9
= 10.8
12.
If two groups of numbers have the same mean, then
a. their standard deviations must also be equal.
b. their medians must also be equal.
c. their modes must also be equal.
d. other measures of location need not be the same
13.
The Sample Mean
a. can never be negative.
b. can assume any value between the highest and the lowest value in the sample.
c. can never be zero.
d. is always smaller than the mean of the population from which the sample was taken
If two groups of numbers have the same mean, then other measures of location need not be same. The Sample Mean is always smaller than the mean of the population from which the sample was taken.
Mean: It is the most commonly used measure of central tendency. It actually represents the average of the given collection of data. It is applicable for both continuous and discrete data.
Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:
If two groups of numbers have same mean that does not imply they will have same std deviation, median and mode. Even if two groups have same mean other measures may not be same because one group might be more or less scattered than the other group and though they may have same mean.
So the correct answer is option A.
Other measures of location need not be same.
2. Here, the correct option is option d. This is because when we calculate mean we basically take the average of each and every value in the given sample, which is bound to lie between the maximum and minimum value.
A mean can be zero if it has equal positive and negative numbers and a mean can be negative if it has more negative numbers. Again the mean of the sample is not always necessarily smaller than the mean of the population of which the sample is a part. Hence the first three options are incorrect
Therefore, the correct option is option d. Mean is always smaller than the mean of the population from which the sample was taken.
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Question #2:
-3x < 4y - 12
Line: Solid or Dashed?
Shade: Above or Below?
m=
b=
Are these points solution: (0,3)
(2,4)
<
(-1,-2)
Answer:
Line: Dashed
Shade: Below
m = -3/4
b = 3
(0,3) - False - No
(2,4) - True - Yes
(-1,-2) - False - No
Step-by-step explanation:
Given:
-3x < 4y - 12
Questions:
Line: Solid or Dashed?
Shade: Above or Below?
m=
b=
Are these points solution:
(0,3)(2,4)(-1,-2)Solve:
Inequalities that use '< or >' symbols are plotted with a dashed line. Due to that dashed line means the solution doesn't include the line itself.
< = Less than
> = Greater than
Inequalities that use '≤ or ≥' symbols are plotted with a solid line. Due to that solid line means the solution does includes the line itself
≤ = Less than or equal to
≥ = Greater than or equal to
Therefore, based on the given, the line is Dashed. Which also means the solution doesn't includes the line itself.
We also know that the given info with the inequalities of "<".
"<" Means Less than which means shade below. If it was "> " which means greater than you have to shade above.
To find the m and b we first have to know that;
y = mx + b
m = Slope
b = y-intercept
To find the Slope(m) and b(y-intercept) we first have to put -3x < 4y - 12 in slope-intercept form.
-3x < 4y - 12
y > -3/4x + 3
Hence,
m = -3/4
b = 3
To see if the following points {(0,3) (2,4) (-1,-2)} are solutions for -3x <4y-12
All we have to do is to substitute it in.
Starting with (0,3)
x = 0
y = 3
-3(0) < 4(3) - 12
0 < 0
False. 0 isn't less than 0- it equal to 0. Hence it isn't a solution to -3x < 4y - 12
Next (2,4)
x = 2
y = 4
-3(2) < 4(4) -12
-6 < 4
True. -6 is less than 4. Hence it is a solution to -3x < 4y - 12
Finally, we have (-1,-2)
x = -1
y = -2
-3(-1) < 4(-2) -12
3 < -20
False. 3 isn't less than -20. Hence it isn't a solution to -3x < 4y -12
RevyBreeze
the shorter leg of a right trialbe is 9cm shorter than the longer leb. the hypotenuse is 9cm onger than the longer leg. find the side lengths of the triable.
The side lengths of the triangle are 27 cm, 36 cm, and 45 cm.
Let x = length of the longer leg of the triangle
If the shorter leg of a right triangle is 9cm shorter than the longer leg, then
length of the shorter leg of the triangle = x - 9
If the hypotenuse is 9cm longer than the longer leg, then
length of the hypotenuse of the triangle = x + 9
Use Pythagorean theorem to solve for the side lengths of the triangle. Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
(x + 9)² = x² + (x - 9)²
Simplify the equation and solve for x.
(x + 9)² = x² + (x - 9)²
x² + 18x + 81 = x² + x² - 18x + 81
36x = x²
x² - 36x =0
x(x - 36) = 0
x = 36
length of the longer leg of the triangle = x = 36 cm
length of the shorter leg of the triangle = x - 9 = 36 - 9 = 27 cm
length of the hypotenuse of the triangle = x + 9 = 36 + 9 = 45 cm
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Suppose that y varies directly with x, and y=9 when x= -3.
(a) Write a direct variation equation that relates x and y
Equation: y = -3
The equation that relates x and y is y = -3x.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
y ∝ x
y = kx
Now,
When x = -3, y = 9
This means,
9 = -3k
k = -3
Now,
The equation is y = -3x
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(04.05 mc) remo needs to buy a countertop for a bathroom. he calculated the area as 10 square feet. the actual area is 9.5 square feet. what is remo's percentage error? (1 point) 0.5% 0.95% 5% 5.26%
The actual value is 9.5. So the percentage error is (0.5 / 9.5) * 100% = 5.26%.
To find the percentage error, we need to divide the difference between the measured value and the actual value by the actual value and multiply by 100%. In this case, the difference between the measured value and the actual value is 10 - 9.5 = 0.5. The actual value is 9.5. So the percentage error is (0.5 / 9.5) * 100% = 5.26%.
The percentage error tells us how much the measured value differs from the actual value as a percentage. In this case, the measured value (10 square feet) is 5.26% larger than the actual value (9.5 square feet).
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Remo's percentage error is 5.26%
In this question we have been given Remo calculated the area as 10 square feet.
And the actual area is 9.5 square feet.
We need to find Remo's percentage error
We know that the formula for the percentage error.
E = (V_o - V_a)/V_a × 100
where V_a is the actual value
V_o is the observed value
E is the percentage error
From given data: calculate area A_o = 10 square feet
actual area A_a = 9.5 square feet
So, Remo's percentage error would be.
E = (A_o - A_a)/A_a × 100
E = [(10 - 9.5)/9.5] × 100
E = 5.26%
Therefore, the percentage error is 5.26%
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what is the are of a sector when r=5/6 and theta= 2pi/3 raidians
Answer:
[tex]\displaystyle \frac{25\pi}{108}\text{units}^2[/tex]
Step-by-step explanation:
The area of a sector is [tex]\displaystyle A=\frac{r^2\theta}{2}[/tex] where [tex]r[/tex] is the radius of the circle and [tex]\theta[/tex] is the angle that is formed by the sector in radians:
[tex]\displaystyle A=\frac{r^2\theta}{2}=\frac{(\frac{5}{6})^2*\frac{2\pi}{3}}{2}=\frac{\frac{25}{36}*\frac{2\pi}{3}}{2}=\frac{\frac{50\pi}{108}}{2}=\frac{50\pi}{216}=\frac{25\pi}{108}\text{units}^2[/tex]
Find all the real and complex solutions of the polynomial equation. Be sure to show ALL work (4 points):
x3-2x2+9x-18=0
2, 3i, -3i are the real and complex solutions of the polynomial equation.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is x³-2x²+9x-18
x³-2x²+9x-18=0
Take the common terms from first two terms
x²(x-2)+9(x-2)
(x²+9)(x-2)=0
(x²+3²)(x-2)=0
x-2=0
x=2
and x²+3²=0
x=3i and x=-3i
Hence, 2, 3i, -3i are the real and complex solutions of the polynomial equation.
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What is data or other facts gathered to test an idea?
Data or other facts gathered to test an idea are called evidence. Evidence is information that is collected and analyzed to support or refute a hypothesis or theory.
It can come in many forms such as observations, measurements, or statistics, and it can be qualitative or quantitative in nature. The purpose of gathering evidence is to evaluate the validity and reliability of an idea or theory by testing it against the facts.
Evidence-based decision-making is the process of using the best available evidence to inform decisions. The goal of evidence-based decision-making is to make decisions that are based on the best available evidence, rather than relying on intuition, tradition, or personal experience.
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1) (6.4G) What percentage of the
model is shaded?
Answer:
66%
Step-by-step explanation:
If you count all the shaded blocks you get 10 to a total of 15 blocks
which simplifies down to 2/3
what is x+y=-2 in finding linear equations
The expression x + y = -2 is a Linear equation. Note that A linear equation is one whose solutions, when displayed on a graph, create a straight line. A linear equation is generally expressed as ax + by = c, where a, b, and c are constants and x and y are variables.
How can the above expression be re-written into the standard linear equation format?To rewrite the above expression, we must make "y" the subject of the expression after the similitude of y = mx + b Where m is the slope and b is the constant or intercept.
Hence the expression standardized is:
y = -x -2.
In the above case,
m = -1
b = -2.
In order to find the solution to the expression y = -x - 2, one would need to set x and y to any real values and find the pair of x and y that is consistent with the equation.
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The gift shop sold 4 times as much wrapping paper in december as in january. they sold 635 rolls over the two moths Draw a bar model to represent the number sold each month. write an equation to show the number represented by each box of the bar model. then find the number. how much wrapping paper was sold in december? explain how you know.
Answer:
5x = 635
x = 127
508 rolls of paper were sold in December.
Step-by-step explanation:
3
1. The function f (x) = x³ + 3x² + 3x + 2 can be
rewritten as f(x)=(x+2)(x2+x+1) The equation f(x)=0 has
only one real solution, -2. Which of these best explains
why the Fundamental Theorem of Algebra still holds true
for this polynomial function?
0= x² + x + 1 has exactly
two complex solutions.
0= x² + x + 1 has exactly
one complex solutions
f(0)-2 is false for the
function
f(0) = 2 is true for the
function
On solving the provided question, we can say that - the value of the following function f (x) = x³ + 3x² + 3x + 2 will be 9.
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
we have been provided with -
f (x) = x³ + 3x² + 3x + 2
so, x= 1
f(x) = 1+3+3+2 = 9
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use the binomial series to find the maclaurin series for the function. f(x) = 1 (1 + x)4. I know what the binomial series is, and I expanded, using the given information, into a polynomial, but I'm stuck with trying to turn the Maclaurin polynomial into a series with the sigma form.
[tex](1+ x)^{-4}[/tex] = 1-4x +10 x^2 +10 x^2 -20 x^3 +................. is the required maclaurin series for the function 1 / [tex](1+x)^{4}[/tex] . and explained in detailed as ;
we know that the maclaurin says that :
[tex](1+x)^{k}[/tex] = 1+ kx + k(k-1) x^2 /2! + k(k-1)(k-2) x^3/3! +.............
hence the value of k = -4 then on substituting we get,
[tex](1+ x)^{-4}[/tex] = 1+ (-4) x + (-4)(-4-1)x^2 /2 +..........
(1+ x)^{-4} = 1- 4x + 20 x^2 /2 - 120 x^3 /6 + ...........
(1+ x)^{-4} = 1-4x +10x^2-20x^3 +.........
hence the equation of maclaurin series for the function is
(1+ x)^{-4} = 1-4x +10 x^2 +10 x^2 -20 x^3 +.................
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Meg is a veterinarian. she found that 33% of the nine dogs she saw this week were boxers. Steve is also a veterinarian. he found that nine of the 27 dogs he saw this week were boxers. does each person need to find the part the whole or the percent? 
Meg needs to find the part And Steve needs to find the percent.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Meg is a veterinarian she found that 33% of the nine dogs she saw this week were boxers.
The whole is the entire number of dogs seen is 9dogs.
The percent is given as 33%.
Hence, she needs to find the part: this is how many (what part) of the 9 dogs she saw were boxers.
9×33%=3 dogs are boxers
This is 3 dogs of 9 were boxers.
Steve already knows the part 9 of the 27 dogs were boxers
Then he needs to find the percent, he can do using the next operation:
Percent = (part / whole) × 100 = (9/27)×100
= 33%
Hence, Meg needs to find the part And Steve needs to find the percent.
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