If x varies directly with y, then :
● Increase in x results in increase of y
● Decrease in x results in decrease of y
● It is represented by : x ∝ y
[tex]\mathsf{\bigstar\;\;If\;x\;varies\;directly\;with\;y\;then : \large\boxed{\mathsf{\dfrac{x_1}{x_2} = \dfrac{y_1}{y_2}}}}[/tex]
Here : x₁ = 6 and y₁ = 15 and x₂ = x₂ and y₂ = 20
Substituting the values we get :
[tex]\mathsf{\implies \dfrac{6}{x_2} = \dfrac{15}{20}}[/tex]
[tex]\mathsf{\implies x_2 = \dfrac{20 \times 6}{15}}[/tex]
[tex]\mathsf{\implies x_2 = 8}[/tex]
Answer : x = 8 when y = 20
Answer:
x = 8
Step-by-step explanation:
Given that x varies directly as y then the equation relating them is
x = ky ← k is the constant of variation
To find k use the condition x = 6 when y = 15
k = [tex]\frac{x}{y}[/tex] = [tex]\frac{6}{15}[/tex] = 0.4
x = 0.4y ← equation of variation
When y = 20, then
x = 0.4 × 20 = 8
Please answer this question for 25 points and brainliest!!
Answer:
64 cm²
Step-by-step explanation:
Suppose the original paper was x cm on a side. Then the original perimeter was 4x.
When the square is folded in half, two of the sides are now x/2, so the perimeter is ...
x + x/2 + x + x/2 = 3x
If 3x = 24 cm, then x = 8 cm.
The area of the original paper is ...
A = x² = (8 cm)² = 64 cm²
What is magma? a. The molten mixture of rock-forming substances, gases, and water from the mantle.. c. Hardened lava on the surface of the Earth. b. Liquid rock that reaches the surface. d. All of the above Please select the best answer from the choices provided A B C D
Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle
Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.
The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.
An arrow is shot vertically upward at a rate of 180ft/s. Use the projectile formula h=?16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. Round your answer(s) to the nearest tenth of a second.
The answer is:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time time equal to 7.94 seconds when the arrow was going down.
Why?To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.
Also, we are given some information, we need to substitute it and then use the quadratic equation.
The equation is:
[tex]h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0[/tex]
Substituting the given information we have:
[tex]-16t^{2}+vot-h=0[/tex]
[tex]-16t^{2}+180\frac{ft}{s} t-420=0[/tex]
We have a quadratic equation where:
[tex]a=-16\\b=180\\c=-420[/tex]
Now, using the quadratic equation to find the value or values of "t", we have:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94[/tex]
Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time equal to 7.94 seconds when the arrow was going down.
Have a nice day!
Answer:
3.3secs, 7.9secs
Step-by-step explanation:
We are looking for the number of seconds it takes the arrow to reach a height of 420ft. We are given the projectile formula h=−16t2+v0t, where h is the height, in feet, and t is the time, in seconds. We can substitute the initial velocity v0=180 and desired height h=420 to find
420=−16t2+180t
Rewriting this quadratic equation in standard form, we have
16t2−180t+420=0
Now that the equation is in standard form, at2+bt+c=0, we can identify the coefficients a=16, b=−180, and c=420. Substituting these into the quadratic formula, we have
t=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−180)±(−180)2−4(16)(420)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(16)=180±5520‾‾‾‾‾√32
The approximate values for t are
t=≈180+5520‾‾‾‾‾√327.9andt=≈180−5520‾‾‾‾‾√323.3
The arrow will go up and then fall down. As the arrow goes up, it will reach 420ft after approximately 3.3s. It will also pass that height on the way down at approximately 7.9s.
PLEASE HELP!!!!
Question: ⇒ An object is launched from the ground. The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched. When will the object hit the ground after it is launched?
⇒ Explain how you found your answer.
⇒ No spam answers, please!
⇒ No wrong answers, please!
Thank you!
Answer:
it would take 5 seconds for the object to hit the ground after launched.
////////////////////////////////////////////////////////////////////////////////
1st step: (turn the quadratic function to a quadratic equation by setting the equal to zero): 0 = -16t2 + 80t + 0
2nd step: t = 0 & t = 5
(t = 0 is the time of launch. t = 5 represents the 5 seconds it took to hit the ground after the object was launched.)
Answer:
The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds
PLEASE HELP
4. The table shows the probabilities of a response chocolate or vanilla when asking a child or adult. Use the formula for conditional probability to determine independence.
Chocolate | Vanilla | Total
Adults 0.21 0.39 0.60
Children 0.14 0.26 0.40
Total 0.35 0.65 1.00
a. Are the events “Chocolate” and “Adults” independent? Why or why not?
b. Are the events “Children” and “Chocolate” independent? Why or why not?
c. Are the events “Vanilla” and “Children” independent? Why or why not?
Answer:
a) Yes the events Chocolate and Adults are independent
b) Yes the events Children and Chocolate are independent
c) Yes the events Vanilla and Children are independent
Step-by-step explanation:
* Lets study the meaning independent and dependent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
# From the table:
- The probability of chocolate is 0.35
- The probability of vanilla is 0.65
- The probability of adults is 0.60
- The probability of children is 0.40
- The probability of chocolate and adults is 0.21
- The probability of chocolate and children is 0.14
- The probability of vanilla and adult is 0.39
- The probability of vanilla and children is 0.26
a.
∵ P(chocolate) = 0.35
∵ P(Adults) = 0.60
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(chocolate) · P(adults) = (0.35)(0.60) = 0.21
∵ P(chocolate and adults) = 0.21
∴ P(chocolate and adults) = P(chocolate) · P(adults)
∴ The events chocolate and adults are independent
b.
∵ P(chocolate) = 0.35
∵ P(children) = 0.40
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(chocolate) · P(children) = (0.35)(0.40) = 0.14
∵ P(children and chocolate) = 0.14
∴ P(chocolate and children) = P(chocolate) · P(children)
∴ The events chocolate and children are independent
c.
∵ P(vanilla) = 0.65
∵ P(children) = 0.40
∵ Two events are independent if P (A and B) = P(A) · P(B)
∵ P(vanilla) · P(children) = (0.65)(0.40) = 0.26
∵ P(vanilla and children) = 0.26
∴ P(vanilla and children) = P(vanilla) · P(children)
∴ The events vanilla and children are independent
Pasion wants to rent a car to take a trip and has a budget of $75. There is a fixed rental fee of $25 and a daily fee of $10. Write an inequality that would be used to solve for the maximum number of days for which Pasion can rent the car on her budget.
Answer:
The maximum number of days is 5
Step-by-step explanation:
Let
x ----> the number of days
y ---> the total cost to rent a car in dollars
we know that
The fixed rental fee plus the daily fee multiplied by the number of days must be less than or equal to Pasion's budget
so
The inequality that represent this situation is
[tex]25+10x\leq 75[/tex]
Solve the inequality for x
Subtract 25 both sides
[tex]10x\leq 75-25[/tex]
[tex]10x\leq 50[/tex]
Divide by 10 both sides
[tex]x\leq 5\ days[/tex]
therefore
The maximum number of days is 5
The system of equations shown below is graphed on a coordinate grid:
3y + x = 6
2y – x = 9
Which statement is true about the coordinates of the point that is the solution to the system of equations?
[ ] It is (–6, 4) and lies on both lines.
[ ] It is (–6, 4) and does not lie on either line
[ ] It is (–3, 3) and lies on both lines.
[ ] It is (–3, 3) and does not lie on either line.
WILL GIVE BRAINIEST FOR CORRECT ANSWER
First of all, for a point to be the solution to the system of equations, it must be located on both lines, since we are calculating the point at which the lines cross. Therefor, we can automatically discount B and D as the answers, which state that the point does not lie on either line. To see whether it is A or C we will have to solve the equations.
1. There are quite a few ways to approach solving the system of equations, however I will show the substitution method as it requires less modification of equations.
What we need to do is to isolate either x or y in one of the equations so that we can then substitute this value into the other equation. So for example if we take the first equation and isolate x:
3y + x = 6
x = 6 - 3y (Subtract 6 from both sides)
2. Now we can substitute this into the second equation (2y - x = 9).
when x = 6 - 3y:
2y - (6 - 3y) = 9
2y - 6 + 3y = 9
5y - 6 = 9 (Add 2y and 3y)
5y = 15 (Add 6 to both sides)
y = 3 (Divide both sides by 5)
From here, we can already see that the answer is C, since A has a y-value of 4, however if we were to completely solve the question we would do the following:
3. Now that we know the value of y, we can substitute this back into our equation of x = 6 - 3y to find x:
x = 6 - 3(3)
x = 6 - 9
x = -3
So, our solution is the point (-3, 3). It also has to lie on both lines to be a solution. Therefor C. It is (-3, 3) and lies on both lines, is the correct answer.
Answer:
The answer is C
(It is (−3, 3) and lies on both lines.)
Step-by-step explanation:
Katie invested $33,750 at 11.17% compounded continuously.
What will Katie's account balance be in 10 years?
Using the continuous compounding formula A = Pe^rt, Katie's account balance after 10 years will be approximately $103,204, with her initial investment of $33,750 at an annual interest rate of 11.17%.
Explanation:To calculate what Katie's account balance will be in 10 years, with an investment of $33,750 at 11.17% compounded continuously, we use the formula for continuous compounding:
A = Pert
Where:
A is the future value of the investmentP is the principal amount ($33,750)r is the annual interest rate (11.17% or 0.1117 as a decimal)t is the time in years (10 years)e is the base of the natural logarithm (approximately 2.71828)Plugging in the values we get:
A = $33,750 * e(0.1117 * 10)
Calculating the exponent:
A = $33,750 * e1.117
Calculating the future value:
A = $33,750 * 3.0579 (approximate value of e1.117)
A = $103,204
Katie's account balance after 10 years will be approximately $103,204.
Which expressions are equivalent to the one below? Check all that apply. log2 16 + log2 16 A. log2(28) B. 8 C. log 256 D. log2 256
The correct equivalent expression is D. [tex]\log_2{256}[/tex].
The given expression is:
[tex]\log_2{16} + \log_2{16}[/tex]
First, we need to simplify the given expression using properties of logarithms.
Using the property:
[tex]\log_b{m} + \log_b{n} = \log_b(m \times n)[/tex]
We can rewrite the given expression as:
[tex]\log_2{16} + \log_2{16} = \log_2{(16 \times 16)} = \log_2{256}[/tex]
Now we can analyze the options given:
A. [tex]\log_2{28}[/tex]: This is not equivalent because 28 is not the same as 256.
B. 8: This is not in logarithmic form and not equivalent to the simplified expression.
C. [tex]\log{256}[/tex]: This is not equivalent because the base here is 10 (common logarithm), while the given expression has a base of 2.
D. [tex]\log_2{256}[/tex]: This is correct because our simplified form is exactly [tex]\log_2{256}[/tex].
What's the difference between:
x≥0
And
Nonnegative integer.
?
Answer:
none, if x is an integerx may be a real number, hence not necessarily an integerStep-by-step explanation:
x ≥ 0 means x is non-negative, but it does not mean x is an integer. An additional restriction would need to be applied for x to be a non-negative integer.
Alexander throws a baseball straight up into the air with an initial vertical velocity of 48 ft/s
from an initial height of 3.4 ft. Which equation can be used to find the time, T, it takes for the
ball to reach the ground?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \\\\ ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{48}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{3.4}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf h(t)=-16t^2+48t+3.4\implies \stackrel{\textit{when it hits the ground}}{\stackrel{h(t)}{0}=-16t^2+48t+3.4}[/tex]
Check the picture below.
Stephanie is a goalie on her soccer team, which means she tries to block any shots her opponents take on goal. During a tournament, she blocked 15 shots but allowed 4 goals. For every goal Stephanie allowed, she blocked nearly shots.
A ferry takes several trips between points A and B. It moves at a constant speed of 0.35 miles/minute and takes the same route on each trip. The total duration of a round trip from point A to point B and back is 80 minutes, ignoring the time spent stopped at point B. If d is the ferry’s distance from point A in miles and t is the time in minutes, which equation models the ferry’s distance from point A for the duration of the trip?
Answer:
D. -|0.35t -14| +14
Step-by-step explanation:
The problem statement is asking for an expression for distance in miles, so the constants in the expression will be miles. In the time it takes to get to point B (40 minutes), the ferry has gone (0.35 mi/min)×(40 min) = 14 mi. Hence the maximum value of the function must be 14. The only function with that characteristic is the one of selection D.
How many solutions does the equation 5m − 5m − 12 = 14 − 2 have?
None
One
Two
Infinite
Answer:
None
Step-by-step explanation:
It simplifies to -12 = 12, which cannot be made true by any value of m.
Answer:
none
Step-by-step explanation:
Select the correct answer.
Which system of equations can be represented by this matrix?
Answer:
A) x + 2y = 4
3x + 4y -9z = 2
-x + 7z = 1
Step-by-step explanation:
The matrix form is
x y z
1 2 0 4
3 4 -9 2
-1 0 7 1
Here 0 represents no term in system.
So, the following system represents the above matrix.
x + 2y + 0z = 4 => x + 2y = 4
3x + 4y -9z = 2
-x + 0y + 7z = 1 => -x + 7z = 1
Therefore, the answer is A.
Can u guys please do this ratio question. THIS IS EXTREMELY URGENT
A tap is leaking water at a rage of 1L every 8 hours. How long will it take for the tap to leak a total of 300mL?
Answer:
I think 8 hours maybe if I wrong sorry
The time taken for tap to leak a total of 300mL is 2.4 hours.
Given information:A tap is leaking water at a rage of 1L every 8 hours.
Calculation of time taken:Since 1L = 1000 mL and it takes 8 hours
So for 300 mL it takes
[tex]= 300 \times 8 \div 1000[/tex]
= 2.4 hours
Learn more about the tap here: https://brainly.com/question/24489593
The area of a rectangle is 38.25 square yards and its base is 9 yards. What is the height? Do not round your answer.
h = ________ yd
Answer:
4.25 yards
Step-by-step explanation:
Area of rectangle = Base x Height
or
Height = Area of Rectangle ÷ Base
In this case, Area =38.25 sq yards and Base = 9 yards
Height = 38.25 ÷ 9 = 4.25 yards
Two linear equations are shown. What is the solution to the system of equations? (7, 4) (9, 7)
Answer:
[7, 13/3]
Step-by-step explanation:
Select the correct solution in each column of the table.
Solve the following equation.
Table included in image below:
Answer:
No of real solutions =1
No of extraneous solution =2
Real solution: x =3
Step-by-step explanation:
[tex]\frac{3}{x}-\frac{x}{x+6}=\frac{18}{x^2+6x}[/tex]
solving:
Taking LCM of x, x+6 and x^2+6 we get x(x+6)
Multiply the equation with LCM
[tex]\frac{3}{x}*x(x+6)-\frac{x}{x+6}*x(x+6)=\frac{18}{x^2+6x}*x(x+6)\\3(x+6)-x*x=\frac{18}{x(x+6)}*x(x+6)\\3(x+6)-x*x=18\\3x+18-x^2=18\\-x^2+3x+18-18=0\\-x^2+3x=0\\x^2-3x=0\\x(x-3)=0\\x=0 \,\,and\,\, x =3\\[/tex]
Checking for extraneous solution
for extraneous solution we check the points where the solution is undefined
The solution will be undefined. if, x=0 or x=-6 so both are extraneous solutions
Putting x =3
[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(0)}[/tex]
[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(3)}\\1-\frac{3}{9}=\frac{18}{9+18}\\1-\frac{1}{3}=\frac{18}{27}\\\frac{3-1}{3}=\frac{2}{3}\\\frac{2}{3}=\frac{2}{3}[/tex]
So, x=3 is real solution.
Now, Selecting answers from tables
No of real solutions =1
No of extraneous solution =2
Real solution: x =3
Number of Number of Real solutions
real solution Extraneous solution
1 1 x=3
Step-by-step explanation:Extraneous solution--
It is a solution which is obtained on solving the equation but it does not satisfies the equation i.e. after it is put back to the equation it does not occur as a valid solution.
True solution or real solution--
It is the solution which is obtained on solving the equation and is also a valid solution to the equation.
The equation is:
[tex]\dfrac{3}{x}-\dfrac{x}{x+6}=\dfrac{18}{x^2+6x}[/tex]
On taking lcm in the left hand side of the equation we get:
[tex]\dfrac{3\times (x+6)-x\times x}{x(x+6)}=\dfrac{18}{x^2+6x}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}=\dfrac{18}{x(x+6)}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}-\dfrac{18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x+18-x^2-18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x-x^2}{x(x+6)}=0\\\\i.e.\\\\3x-x^2=0\\\\i.e.\\\\x(3-x)=0\\\\i.e.\\\\x=0\ or\ x=3[/tex]
When we put x=0 back to the equation we observe that the first term of the left hand side of the equation becomes undefined.
Hence, x=0 is the extraneous solution.
whereas x=3 is a valid solution to the equation.
I don’t get this one
Answer:
Option A is correct.
Step-by-step explanation:
No of white cars: 25
No of blue cars : 17
Total number of white and blue cars = 25 + 17 = 42
No of silvers cars: 21
No of red cars: 9
Total number of silver and red cars = 21+9 = 30
No of white and blue cars more than silver and red cars
=Total number of white and blue cars - Total number of silver and red cars
=42 - 30
= 12 cars
So, Option A is correct.
Identify the exponent in the term –3x2. A. x B. 2 C. minus sign (–) D. 3
Answer:
B. 2
Step-by-step explanation:
Assuming the term is meant to look like this: -3x², then the answer is B.2. An exponent is a superscript (super means above, script means writing) that tells you to multiply something by itself.
In this case, -3x² means -3·x·x
If it was written as (-3x)², it would mean (-3x)·(-3x)
Answer:
2
Step-by-step explanation:
The exponent is raised to the power of any variable [smaller number].
I am joyous to assist you anytime.
A train arrives at a station and waits 2 min before departing. Another train arrives at the station 18 minutes later, repeating the cycle. Identify the probability that a train will be at the station when you arrive.
[tex]|\Omega|=20\\|A|=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}=10\%[/tex]
Answer:
1/10.
Step-by-step explanation:
The length of each cycle is 2 + 18 = 20 minutes.
During this time the train in stationary for 2 minutes.
So the probability of the train being at the station when you arrive is 2/20 = 1/10.
Suppose the population of a town is 2,700 and is growing 4% each year. Write an equation to model the population growth. Predict the population after 12 years
How do the graphs of the functions f(x)=[tex](\frac{3}{2})^x[/tex] and g(x)=[tex](\frac{2}{3})^x[/tex] compare?
{Explain your answer.}
Show your work!
Step-by-Step calculations required.
No spam answers, please!
Thank you!
Step-by-step explanation:
f(x) = (3/2)ˣ
g(x) = (2/3)ˣ
These are examples of exponential equations:
y = a bˣ
If b > 1, the equation is exponential growth.
If 0 < b < 1, the equation is exponential decay.
So f(x) is an example of exponential growth, and g(x) is an example of exponential decay.
Also, 2/3 is the inverse of 3/2, so:
g(x) = (3/2)^(-x)
So more specifically, f(x) and g(x) are reflections of each other across the y-axis.
Two fair dice are rolled.
What is the PROBABILITY that the FIRST lands on a 6 and the SECOND lands on an ODD number?
SHOW YOUR WORK! Use the sample space from question 8 to assist you! Write your answer in SIMPLIFIED FRACTION form.
Answer:
1/12
Step-by-step explanation:
There are two dices being rolled. A dice has six faces numbered from one to six. A fair dice means that the probability of each number to appear is equal. Thus the probability of any number showing up is:
P(a number appears on the dice) = how much times the number has been displayed on the dice/number of faces of the dice.
Since all numbers appear once, and there are six sides of a dice. therefore:
P(a number appears on the dice) = 1/6. Thus, P(6 appears on a dice) = 1/6.
As far as the odd numbers are concerned, there are three even numbers and three odd numbers on the dice. So P(odd number appears on the dice) = 3/6 = 1/2.
Assuming that the probabilities of both the dices are independent, we can safely multiply both the probabilities. Thus:
P(first dice lands on a 6 and second dice lands on an odd number) = 1/6 * 1/2 = 1/12.
Thus, the final probability is 1/12!!!
Based on the line of best fit estimate what the income might be for 2006
Answer:
190000 is the best answer in my opinion because by 2006 it is more then 160000 but it is less then 200000
Step-by-step explanation:
Find the missing factor. Write your answer in exponential form.
1^9 = 1^7 • = _
Answer:
[tex]1^2[/tex]
Step-by-step explanation:
The number 1 is called the base. When we multiply like bases, we add the exponents. So in order to get 1^9, we will multiply 1^7 by 1^2 because 7+2=9.
Answer:
The answer is [tex]1^{2}[/tex]
Step-by-step explanation:
Using the formula: [tex]a^{m}+a^{n}= a^{m+n}[/tex]
[tex]1^{9}=1^{7}*1^{2}=1^{7+2=9} =1^{9}[/tex]
please help will mark brainliest
The following dot plot shows the mass of each rock in Nija's rock collection. Each dot represents a different rock.
Answer:
10
Step-by-step explanation:
Each dot represents 1 rock.
There are 10 dots in the plot, so there are 10 rocks in the collection.
Given one zero of the polynomial function, find the other zeros.
f(x)=2x^3+3x^2-3x-2; -2
Answer:
{-1/2, 1}
Step-by-step explanation:
You can divide the given polynomial by the factor (x +2) to find the remaining quadratic. That can be factored in the usual way to find the remaining zeros, or other means can be used. Such "other means" include graphing and the use of the quadratic formula.
The first attachment shows the synthetic division of f(x) by (x+2). The quotient is 2x^2 -x -1, which factors as ...
2x^2 -x -1 = (2x +1)(x -1)
The zeros are the values of x that make these factors zero: -1/2, +1.
_____
My favorite way to find the roots of any higher degree polynomial is to use a graphing calculator. The second attachment shows that method.
We can find other zeros for the given polynomial by polynomial factoring or polynomial division. Upon dividing the given polynomial by (x+2), we get another polynomial. The zeros of this second polynomial can be found using the quadratic formula; getting the two zeros as x = 1 and x = -0.5.
Explanation:Given a polynomial [tex]f(x) = 2x^3 + 3x^2 - 3x - 2[/tex]and one of its zeros is -2; we can find the other zeros by polynomial factoring or polynomial division. First, divide the entire polynomial by (x+2) because -2 is one of the zeros. So we end up with 2x^2 - x - 1 = 0.
Now use the quadratic formula to find the remaining zeros: [tex]x = [-b\±\sqrt(b^2 - 4ac)] / (2a).[/tex]By substituting the constants from the factored polynomial equation, we will get [tex]x = [-(-1)\±\sqrt((-1)^2 - 4*2*(-1))] / (2*2) = [1\±\sqrt(1 + 8)] / 4.[/tex]This simplifies to [tex]x = [1\±\sqrt(9)] / 4 = [1\±3] /4.[/tex] Hence our two more zeros are x = 1 and x = -0.5.
Learn more about polynomial zeros here:https://brainly.com/question/29775881
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Complete the following exercises by applying polynomial identities to complex numbers.
Factor x2 + 64. Check your work.
Factor 16x2 + 49. Check your work.
Find the product of (x + 9i)2.
Find the product of (x − 2i)2.
Find the product of (x + (3+5i))2.
Please help, explanations and written work apprciated
1.)
=(x-8i)(x+8i)
x^2+8ix-8ix-64i^2
x^2-64i^2
x^2-64(-1)
x^2+64
2.)
=(4x-7i)(4x+7i)
16x^2+28ix-28ix-49i^2
16x^2-49i^2
16x^2-49(-1)
16x^2+49
3.)
=(x+9i)(x+9i)
x^2+9ix+9ix+81i^2
x^2+18ix+81(-1)
x^2+18ix-81
4.)
=(x-2i)(x-2i)
x^2-2ix-2ix+4i^2
x^2-4ix+4(-1)
x^2-4ix-4
5.)
=[x+(3+5i)]^2
(x+5i+3)^2
(x+5i+3)(x+5i+3)
x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9
x^2+6x+10ix+30i+25i^2+9
x^2+6x+10ix+30i+25(-1)+9
x^2+6x+10ix+30i-25+9
x^2+6x+10ix+30i-16
Hope this helps :)