Find all the zeros of the equation. Need help finding the zeros.
-3 x^{4} } +27 x^{2} +1200=0
Final answer:
The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.
Explanation:
To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.
The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.
we can re-write our expression as:
-3a^2+27a+1200=0
-3(a^2-9a-400)=0
a^2-9a-400=0
factorizing the above we have:
a^2+16a-25a-400=0
a(a+16)-25(a+16)=0
(a+16)(a-25)
thus replacing back x^2 we have:
(x^2+16)(x^2-25)
=(x^2+16)(x-5)(x+5)
factorizing (x^2+16) we get
x^2=+/-√-16
x=+/-4i
thus the zeros of the expression are:
x=-5, x=5 , x=-4i, x=4i
Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side?
1. if a dozen eggs (12 eggs) are worth 3 cowry shells, how much would 6 dozen be worth?
a. 9 cowry shells
b. 36 cowry shells
c. 18 cowry shells
d. 15 cowry shells
2. I have 7 cowry shells. If a dozen eggs (12 eggs) cost 3 cowry shells, how many dozens can i purchase?
a. 21 dozen
b. 2 dozen
c. 9 cowry dozen
d. 3 dozen,
Which of these statements is true for f(x)....
Answer:
B. the y -intercept is (0,3)
Step-by-step explanation:
Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
A.) 2
B.) 6
C.) 10
D.) 13
The answer to this should be 13
Substitute the value of the variable into the expression and simplify
Substitute: |-2^2 + -3^2|
Simplify: |-2^2|= 4, |-3^2|= 9
Solve: 4 + 9 = 13
Given a = 5, b = -3, and c = -2, the absolute value of |c2 + b2| is calculated by squaring the values of c and b, adding them, then taking the absolute value, resulting in 13.
Explanation:The question asks us to evaluate the expression |c2 + b2|, given that a = 5, b = -3, and c = -2. The vertical bars indicate that we are dealing with the absolute value, which means we want the positive result of the expression inside the bars.
First, substitute the given values into the expression, we get |-22 + (-3)2| which is |4+9|.
Second, add the squares of c and b together to get 13.
Finally, since the absolute value of 13 is still 13, this is our answer, corresponding to option D.
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The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10
Final answer:
The value of y, which directly varies with x, is found by first determining the constant of variation when x = 9 and y = 5.4. Using this constant, we calculate the value of y for x = -10, resulting in y = -6.
Explanation:
The value of y directly varies with x, which means the relationship between x and y can be described by the equation y = kx, where k is the constant of variation. Since y = 5.4 when x = 9, we first find the constant of variation as follows: k = y/x = 5.4/9 = 0.6. Now, to find y when x is -10, we use the constant of variation k in the equation: y = kx = 0.6(-10) = -6.
The relationship between y and x is one of direct variation, represented by the equation y = kx, where k is the constant of variation. Given that y = 5.4 when x = 9, the constant k is calculated as 0.6. Applying this constant, when x = -10, the value of y is found to be -6. This process showcases the direct variation principle in determining y based on the given x values and the constant of variation.
A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. What is the area of the pentagon, rounded to the nearest tenth? 13.8 cm2 17.3 cm2 32.7 cm2 69.0 cm2
plz dont ask for a pic i cant put one
Answer:
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Step-by-step explanation:
Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
we have to find the area of pentagon.
Apothem=a=3 cm
Perimeter=s=21.8 cm
[tex]\text{Area of regular pentagon=}\frac{1}{2}\times apothem\times perimeter[/tex]
[tex]\frac{1}{2}\times s \times a[/tex]
[tex]=\frac{1}{2}\times 21.8\times 3[/tex]
[tex]=\frac{65.4}{2}=32.7 cm^2[/tex]
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Option 3 is correct.
Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?
Answer: The required equation of line BC is [tex] x=4.[/tex]
Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).
We are to find the equation of line BC.
We know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the line AB will be
[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]
Therefore, the equation of the line AB is
[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]
Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.
So, its equation will be of the form
x = constant.
Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have
[tex]x=4.[/tex]
Thus, the required equation of line BC is [tex] x=4.[/tex]
Larry has 62 nickels, 24 dimes, 17 quarters, and 11 fifty-cent pieces. How much money does he have?
A. $17.15
B. $16.30
C. $15.25
D. $16.75
Answer:
Larry has 1525 cents or 15.25 dollars.
Step-by-step explanation:
The following are the values for each of the coins:
1 Nickel=5 cents
1 Dime = 10 cents
1 Quarter = 25 cents
1 Fifity-cent = 50 cents
So the total value of the Larry's have is
Total money = 62*5 cents + 24*10 cents + 17*25 cents + 11*50 cents
Total money = 310 cents + 240 cents + 425 cents + 550 cents
Total money = 1525 cents
This is equal to 15.25 dollars.
Find the missing value to the nearest whole number of tan x° =0.9
We have to find the missing value to the nearest whole number of tan x° =0.9.
Since, tan x° =0.9
To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]
So, [tex] x^{\circ}=\arctan (0.9) [/tex]
Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,
[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]
So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].
Match each economic term with its description. Tiles There are no barriers to entry in the market. There is a single seller in the market. Three companies secretly enter into a price agreement. Every company in this market structure is aware of the actions of the other companies. Pairs monopoly arrowBoth oligopoly arrowBoth perfect competition arrowBoth collusion arrowBoth \
Each economic term is matched with its appropriate description as follows:
OLIGOPOLY || There are no barriers to entry in the market.
MONOPOLY || There is a single seller in the market.
COLLUSION || Three companies secretly enter into a price agreement.
PERFECT COMPETITION || Every company in this market structure is aware of the actions of the other companies.
There are no barriers to entry in the market is the match of - Oligopoly (The market is shared by many sellers )
There is a single seller in the market is the match of - Monopoly
Three companies secretly enter into a price agreement is the match for - Collusion
Every company in this market structure is aware of the actions of the other companies is the match for Perfect Competition.
greatest common factor of −27x2yz5 + 15x3z3
To estimate 179% of 41 by rounding use the expression
Answer:
To estimate 179% of 41 by rounding, use the expression
✔ 180%(40)
.
Using the distributive property, the expression is equivalent to
✔ (100%)(40) + (80%)(40)
.
179% of 41 is about
✔ 72
.
Step-by-step explanation:
What is the similarity ratio of a cube with volume 1,728m3 to a cube with volume 19,683m3?
A. 9:4
B. 4.9
C. 144:729
D. 729:144
A grid shows the positions of a subway stop and your house. The subway stop is located at (6,-2) and your house is located at (3,1) what is the distance to the nearest unit between your house and the subway stop?
A. 10
B. 9
C. 4
D. 3
A swing set is going to be placed over a region of mulch that is shaped like a trapezoid. The bases of the trapezoid have a length of 12 and 15 feet, and the perpendicular distance between the bases is 8.5 feet. What is the area of the region under the swing set? If necessary, round your answer to the nearest tenth.
Answer:
[tex]114.8\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
In this problem we have
[tex]b1=12\ ft[/tex]
[tex]b2=15\ ft[/tex]
[tex]h=8.5\ ft[/tex] ----> the height of the trapezoid is the perpendicular distance between the bases
substitute the values
[tex]A=\frac{1}{2}(12+15)(8.5)[/tex]
[tex]A=\frac{1}{2}(27)(8.5)=114.75\ ft^{2}[/tex]
Round to the nearest tenth
[tex]114.75=114.8\ ft^{2}[/tex]
Answer:
114.8 is the answer
Step-by-step explanation:
got it on edgen
Please help! Thanks!
An organization president conducts a survey to see where the next convention should be held. She uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey. An organization is conducting a survey to see where their next convention should be held. They use a list of their 1008 members listed in alphabetical order and selects every 10th member to participate in the survey Is this sample valid or not valid, and why? A not valid; Since 1008 divided by 10 is not a whole number, there are 8 members who are not accounted for. B not valid; The survey chooses only members of the organization. C valid; There is no bias in the survey. D not valid; The survey chooses only every 10th member.
Answer:
The correct option is:
Option: C
C valid; There is no bias in the survey.
Step-by-step explanation:
It is given that:
An organisation president uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey.
So, the sample used by her is a valid sample.
Since, she sets a random rule to choose the members to participate in the survey.
The sample used by her is unbiased.
( Since, the aim of our survey questions are to capture an unbiased opinion to capture the true sentiments of the survey taker )
Hence, the correct statement regarding her survey is:
C. valid; There is no bias in the survey
Claudia dumped her 200-penny coin collection on the floor and counted the number of pennies that landed heads up. Claudia repeated this process 5 times and had an average of 84 pennies landing heads up on each try. Which of the following statements is true?
If Claudia had repeated this process fewer times, the average number of pennies landing heads up would be closer to 100.
Each penny has a greater probability of landing heads up than tails up.
The theoretical probability of a penny landing heads up is
If Claudia had repeated this process more times, the average number of pennies landing heads up would be closer to 100.
A complex number, will, in general, have ____ fifth roots.
What is the blank?,
Arthur borrowed $380 for six months, with $67 monthly payments. How much interest will he pay on this loan?
Given is the borrowed amount = 380 dollars.
Repayment period = 6 months.
Monthly installments = 67 dollars.
After six months, total repaid amount would be sum of all six monthly installments i.e. 6 x 67 = 402 dollars.
The interest to be paid on this loan would be difference of total repaid amount and borrowed amount.
Interest paid = Repaid amount - Borrowed amount
Interest = 402 dollars - 380 dollars
Interest = 22 dollars.
So, he would pay 22 dollars as interest on this loan.
A circle could be circumscribed abut the quadrilateral below
Answer:
B. False.
Step-by-step explanation:
We have been given an image of a quadrilateral. We are asked to determine whether a circle could be circumscribed about the given quadrilateral.
We know that opposite angles of a cyclic quadrilateral are supplementary.
Let us check is this true for our given quadrilateral or not.
[tex]m\angle B+m\angle D=180^{\circ}[/tex]
[tex]80^{\circ}+60^{\circ}=180^{\circ}[/tex]
[tex]140^{\circ}\neq 180^{\circ}[/tex]
Now let us check other pair of angles.
[tex]m\angle A+m\angle C=180^{\circ}[/tex]
[tex]110^{\circ}+110^{\circ}=180^{\circ}[/tex]
[tex]220^{\circ}\neq 180^{\circ}[/tex]
Since opposite angles of our given quadrilateral are not supplementary, therefore, a circle could not be circumscribed about the given quadrilateral.
3. Some investments in the stock market have earned 12% annually. At this rate, earnings can be found using the formula A = P(1.12)n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $5000 is invested in the stock market at this annual rate of return, what is the expected total value after 20 years?
( Please show your work so I can understand how you got that answer! Thanks in advance! )
The sum of the squares of two consecutive positive even integers is 340. what are the integers?
Write this number in standard form.
1 x 1 + 8 x 1/100 + 9 x 1/1000,
If somebody uses 1 quart of blue paint each month in one year how many gallons of paint will they use
In the diagram below of right triangle ACB, altitude CD is drawn by hypotenuse AB. if AB= 36 and AC= 12, what is the length of AD?
The length of AD is 18 units.
To find the length of AD, we can use the fact that the altitude from the right angle of a right triangle divides the triangle into two smaller similar triangles.
Let's denote the length of AD as x.
Since triangle ADC and triangle CDB are similar to triangle ACB, we can set up the following proportions:
For triangle ADC:
AD / AC = CD / AB
For triangle CDB:
BD / AC = CD / AB
We already know that AC = 12, AB = 36, and CD = x. So, let's substitute these values into the proportions:
For triangle ADC:
x / 12 = CD / 36
For triangle CDB:
(36 - x) / 12 = CD / 36
Now, let's solve these equations:
From the first equation:
x / 12 = CD / 36
x = (12 * CD) / 36
x = CD / 3
From the second equation:
(36 - x) / 12 = CD / 36
36 - x = (12 * CD) / 36
36 - x = CD / 3
Now, let's solve for CD using the second equation:
36 - x = CD / 3
36 - (CD / 3) = CD / 3
36 = (2 * CD) / 3
CD = (36 * 3) / 2
CD = 54
Now that we have found CD, we can substitute it into the first equation to find x:
x = CD / 3
x = 54 / 3
x = 18
So, the length of AD is 18 units.
What is the x intercept for y=3x+4
NASA cameras film a rocket launcher vertically
miles is buying a chair that regularly costs $250. today the chair is on sale for 30% off. if the tax rate is 6%, what is the sale price of the chair including tax?
The sale price of the chair including tax is $185.5.
What is tax?In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Given that, Miles is buying a chair that regularly costs $250.
Today the chair is on sale for 30% off
So, the new cost is 250-30% of 250
= 250 - 30/100 ×250
= 250-75
= $175
The tax rate is 6%
Sale price = 175+6% of 175
= 175+6/100 ×175
= 175+0.06×175
= $185.5
Therefore, the sale price of the chair including tax is $185.5.
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As a pendulum swings , the angle (theta) that it makes with the vertical changes through its swing. The force of gravity pulling on the bob is given by F=mg sin (theta), where g is equal to 9.8m/s^2. If the mass of the pendulum is 0.01 kg, what is the force pulling on the pendulum when it makes a 22.5 degree angle with the vertical?
We have been given that the formula for the force of gravity pulling on the bob is given by [tex] F=m\times g\times sin(\theta) [/tex]), where g is equal to[tex] 9.8m/s^2 [/tex].
Now, we have been given that the mass of the bob of the pendulum is 0.01 kg and that the pendulum makes 22.5 degree angle with the vertical.
Thus, applying the given values in the formula of the given in the question, we get the formula to be:
[tex] F=m\times g\times sin(\theta)=0.01\times9.8\times sin(22.5^{\circ}) [/tex]
[tex] \therefore F\approx0.0375 [/tex] N