The 3rd degree polynomial equation 2 x³ -16 = 0 has 1 real solution x₁=2 and two imaginary solutions x₂= -1 + √3 i and x₃= -1 - √3 i
The given equation is:
2 x³ -16 = 0
This is a 3rd degree polynomial equation.
Divide both sides by 2, we get:
x³ - 8 = 0
Add both sides with 8:
x³ = 8
Root characteristics: If a 3rd degree polynomial equation has the form
x³ = b
Then, it has 1 real solution and 2 imaginary complex conjugate solutions.
Furthermore,
x₁ = ∛b
x₂,₃ = ½.∛b (-1± √3 i)
Apply this to the given problem, we have:
x₁ = ∛8 = 2
x₂ = ½. 2 (-1 + √3 i) = -1 + √3 i
x₃ = ½. 2 (-1 - √3 i) = -1 - √3 i
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A die is rolled 200 times with the following results.
What is the theoretical probability of the given event?
P(3)
Answer:
You didn’t add the data chart. But I’ll try my best to help.
Step-by-step explanation:
If it landed on the same time multiple times than you will most likely land the same time again.
Seamus sees a good helmet that is 195 and on a 35% off discount. What is the original price?
The original price of the helmet is 300.
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Price of helmet = 195
Discount on helmet = 35% = 0.35
Let the original price be x.
Now since Price of helmet = 195
Thus, Original price = x - 0.35x = 0.65x
Hence we get
0.65x = 195
Dividing both the side by 0.65 we get
x = 195/0.65
Solving we get
x = 300
this is the required original price of the helmet.
Thus, the original price of the helmet is 300.
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Let g(x) = -x² + 4. What is the value of g at x = -3 and x = 1 ?
A. g(−3) = −5, g(1) = 3
B. g(-3) = 13, g(1) = 3
C. g(-3) = -5, g(1)=5
D. g(-3) = 13, g(1) = 5
Answer:3) Find the domain of each, express answers in interval notation x+1 a) f(x) = 3x +2 b) f(x)=. 5 x² - 4x-12 x+1 for x < -2 ... 1 a) g(x) = f(x+10) b) g(x)
Step-by-step explanation:
Please help me please help me please
Answer: (2,-2 )
Step-by-step explanation: That's where U is located on the Graph.
If QR = 5x, RS = x + 3, and QS = 9, what is QR?
The value of QR is 5
What is a line segment?A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.
From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S
Given the points;
QR = 5xRS = x + 3 QS = 9We have that;
QR + RS = QS
substitute the values
5x + x + 3 = 9
collect like terms
6x = 9 - 3
6x = 6
Make 'x' the subject
x = 6/ 6
x = 1
But QR = 5x = 5(1) = 5
Thus, the value of QR is 5
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The complete question;
If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?
how do you find the area of a circle
Answer: A=(pi)r^2
Step-by-step explanation:
multiply pi (3.14) times the radius to the power of 2.
Think About the Process At a little-known vacation spot, taxi fares are a bargain. A 63 mile taxi ride takes 81 minutes and costs $.56.70 You want to find the cost of a 31 - minute taxi ride. What unit price do you need?
The unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.
How to solve for the amount that would be needed for a 31 minute rideWe have the fare for 81 minutes to be $56. 70
Then we are to find the amount that would be needed for 31 minutes.
In order to get this value we would have to cross multiply
such that we would have
81 minutes = $56.70
31 minutes = ?
then 56 * 31 = 1736
1736 / 81
= 21.4 dollars.
Hence we would conclude that the unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.
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Solve for y and calculate the ACB. Using the picture below. Show all work
Applying the linear pair postulate:
y = 30
m<ACB = 160°
What is the Linear Pair Postulate?According to the linear pair postulate, the sum of two adjacent angles that form a linear pair is equal to 180 degrees.
Given the following:
m<ACB = (4y + 40)°
m<DCE = (y - 10)°
Angles ACB and DCE are a linear pair. Therefore:
m<ACB + m<DCE = 180°
Substitute
(4y + 40) + (y - 10) = 180
Solve for y
4y + 40 + y - 10 = 180
Combine like terms
5y + 30 = 180
Subtract 30 from both sides
5y + 30 - 30 = 180 - 30
5y = 150
Divide both sides by 5
5y/5 = 150/5
y = 30
Find m<ACB:
m<ACB = (4y + 40)°
Plug in the value of y
m<ACB = 4(30) + 40
m<ACB = 120 + 40
m<ACB = 160°
Thus, applying the linear pair postulate:
y = 30
m<ACB = 160°
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Simplify each number. 125 . 125¹/₃
[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]
Applying the laws of indices mentioned above,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]
= [tex]5^{3} .( 5 )[/tex] = [tex]5^{3 + 1}[/tex]
= [tex]5^{4} = 625.[/tex]
Thus, [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
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The circle represents a pizza.
Using only four straight slices
(straight lines) see if you can
make a pizza with 10 pieces
(pieces don't have to be the
same size or shape):
Answer:
Cross two lines then put one line above the point of intersection and below the point of intersection. straightforward though
What are the coordinates of G after it is translated LEFT 4 UNITS AND UP 3 UNITS?
this is a text
Answer:
The coordinates of G' after being translated is (-8,6)
Step-by-step explanation:
Find the original coordinates of G by looking at the graph. In this case it's (-4,3). Translate the changes: When you go to the left you are subtracting the x-axis from the original x-axis and when you go up you are adding the y-axis from the original y-axis so it would be -4 -4 is -8 and 3 + 3 is 6 so the new coordinates are (-8,6)
Let g(x)=3 x+2 and f(x)= x-2 / 3 . Find each value.
f(g(1))
The value for f(g(1)) = 1
What are the domain of the function f(g(1))?Given:
g(x) =3 x+2 and f(x)= x-2 / 3
f(x) = x-2 / 3
substitute x =1 into the function f(x). Then:
f(1) = 1-2 / 3
f(1) = -1/3
Now, the next step is to substitute f(1) into the function g(x)
g(x) = 3 x+2
g(f(1)) = 3 (-1/3)+2
g(f(1)) = 1
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Estimate 93% of 149.
Answer:
Convert 93% to decimal and round. "Of" means to multiply.
93% = 0.93 ≈ 0.9
0.9 × 150(estimate) ≈ 135
Thus, the estimate is 135
Hope this helps!
Given f(x)=x-4 and g(x)=x²-3x+ | algebraically determine all values of x such that f(g(x)) = g(f(x))
Step-by-step explanation:
When we plug in the values we get
[tex]f(g(x)) = ({x}^{2} - 3x + 1) - 4 \\ = {x}^{2} - 3x - 3 [/tex]
[tex]g(f(x)) = {(x - 4)}^{2} - 3(x - 4) + 1[/tex]
[tex] {x}^{2} - 3x - 3 = {(x - 4)(x - 4)} - 3x + 12 + 1 \\ {x }^{2} - 3x - 3 = {x}^{2} - 8x + 16 - 3x + 13 \\ \\ {x}^{2} - {x}^{2} - 3x + 8x + 3x - 3 - 16 - 13 = 0 \\ 8x - 32 = 0 \\ 8x = 32 \\ \frac{8x}{8} = \frac{32}{8} \\ x = 4[/tex]
pls help i don't understand
Find the AREA (base x height), in square microns, of a rectangular object with a width of 6,000 microns and a length of 2,000,000 microns.
Show your work and write your final answer in scientific notation.
The area of this rectangular object is equal to 12 × 10⁹ square microns.
Given the following data:
Length of rectangle, L = 2,000,000 microns.Width of rectangle, W = 6,000 microns.How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Substituting the given parameters into the formula, we have;
Area of a rectangle = 6,000 microns × 2,000,000 microns
Area of a rectangle = 12 × 10⁹ square microns.
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Find the measure of
Answer:
12
Step-by-step explanation:
See attachment for step-by-step instructions
A farmer, Sarah, has 54 hectares of hay to harvest. She hires a harvester
at £1200 a day. If Sarah can harvest 12 ha per day, what will it cost her to
harvest this hay?
One edge that is parallel to line segment FG is line segment ___.
Answer:
BC.
Step-by-step explanation:
Answer:
Line segment BC.
Step-by-step explanation:
Parallel lines are always the same distance apart at least. In this instance, FG and BC are parallel.
Which linear inequality is represented by the graph?
O y>_1/3x-4
Oy<_1/3x-4
Oy<_1/3x+4
Oy>_1/3x+4
answer is y ≤ [tex]\frac{1}{3}x (-4)[/tex]
Given that,
Area of shaded inequality below solid line is positive
and y-intercept of the solid line is equal to - 4
therefore,
The inequality must be
y ≤ [tex]\frac{1}{3}x (-4)[/tex]
In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables. When we solve linear inequality then we get an ordered pair. So basically, in a system, the solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system. Let us see an example to understand it.
the Linear inequality: 2x – y >1, x – 2y < – 1
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
here is given step to easily find the value of inequality:
Step 1: The inequality is already in the form that we want. That is, the variable y y is isolated on the left side of the inequality.
Step 2: Change inequality to equality. Therefore, y > x + 1y>x+1 becomes y = x + 1y=x+1.
Step 3: Now graph the y = x + 1y=x+1. Use the method that you prefer when graphing a line. In addition, since the original inequality is strictly greater than symbol, \Large{>}>, we will graph the boundary line as a dotted line.
Step 4: The original inequality is y > x + 1y>x+1. The greater than symbol implies that we are going to shade the top area or region.
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round the square root of 62 to 1 dp
Answer:
7.9
Step-by-step explanation:
yep
An online music store is having a promotion. Customers receive a $ 5 rebate if they buy any regular priced CD at $ 13 each. They can also recelve 15% off if they register as a store member.
c. Use your answer from part (b) to determine the amount a customer will save if she buys 5 CDs.
The amount a customer will save if she buys 5 CDs will be equal to $ 30.25
We are given that:
Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.
If a customer registers for the store member, he get a discount = 15 %.
Now, let the regular priced CD purchased be x and the application for store member be y.
So, the functions will become:
For rebate:
R (x) = 5 x
For discount:
M (y) = 15 % of x
M (y) = 0.15 x
Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x
If x = 5 ( number of CD)
= 6.05 ( 5)
= $ 30.25
Therefore, we get that, the amount a customer will save if she buys 5 CDs will be equal to $ 30.25
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Renting a roller rink for your birthday costs $150 plus $8 per person. The total charge
for your party was $294. Translate this information into an equation using a to
represent the number of guests at your party.
Answer:
294 - 150 divided by 8 = A
Step-by-step explanation:
So, we already know, that we have $294 as our total. If we subtract $150, we get $144. The final step would be to divide it by $8 and that would be 18. There is 18 guests at the party.
Hope it helped!
Write each equation in logarithmic form.
(1/3)³ = 1/27
The logarithmic form of the equation is [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex] .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log x The logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e. The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation [tex](\frac{1}{3})^3 =\frac{1}{27}[/tex] .
Taking log on both sides , we get
[tex]log(\frac{1}{3})^3 =log(\frac{1}{27})[/tex] ..(1)
Applying the property of logarithm which is given by [tex]log_ab=bloga[/tex] in equation (1) ,we get
[tex]3log(\frac{1}{3}) =log(\frac{1}{27})[/tex]
On rearranging the above equation , we get
[tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})} =3[/tex] ..(2)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\
[tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})}[/tex] can be written as [tex]log_{\frac{1}{3} }\frac{1}{27}[/tex] using property
Putting in equation (2) , we get
[tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex]
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Unit 2A sample work the distributive property
PLEASE HELP
Answer: 1b. 5x - 30, 1c. -8x - 32, -8x + 12, 1e. -6x + 21, 1f. 3( 3x - 9)
Step-by-step explanation:
You multiply the number outside of the parentheses by the numbers inside, if it's just an "x", you assume there's a 1 beside it, ex: 8(x + 2)... 8 multiplied by x will give you 8x, 8 multiplied by 2 will give you 16.
if the numbers are both negative when you multiply them it becomes a positive, ex: -8(x - 2)... -8 multiplied by x will be -8, and -8 multiplied by -2 will become positive 16.
But if one number is negative and the other is positive then the answer will be negative.
A group of friends wants to go to the amusement park. they have no more than $155 to spend on parking and admission. parking is $6.25, and tickets cost $20.50 per person, including tax. what is the maximum number of people who can go to the amusement park?
The maximum number of people who can go to the amusement park is 7 based on tickets cost of $20.50 per person
What is the total cost function for the amusement park?
The total cost is made up of cost of admission and parking and the tickets cost per person, which means that the total cost can be modeled as shown below based on the fact the number of persons that can attend is x
total cost=6.25+20.50x
total cost=155
155=6.25+20.50x
155-6.25=20.50x
148.75=20.50x
x=148.75/20.50
x=7(rounded to the nearest whole number)
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at a clothing store a pair of jeans costs 50$. Using a coupon, shanice can pay 20$ less than the original price. Determine the percentage off the original price the coupon represents. Show your work in the space provided. The coupon gives shanice _____% off the original price. HELP HELP
The coupon gives Shanice 40% off the original price, based on the coupon of $20 on an original price of $50
What is the price after having considered the coupon?
The price of the pair of jeans after having considered the coupon is the original price of $50 minus the $20 coupon
price after the coupon=$50-$20
price after the coupon=$30
However, the task at hand is to determine the coupon as a percentage of the original price
coupon as % of original price=$20/$50
coupon as % of original price=40.00%
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You jog at a rate of 6 miles per hour. Your friend is 55 feet ahead of you and jogs at a rate of 6.6 feet per second. Write and solve an inequality that represents the amounts of time, t , that your friend is ahead of you.
The inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to write and solve an inequality that represents the amounts of time your friend is ahead of you?The given parameters are
Your rate, r1 = 6 miles per hour
Your friend's rate, r2 = 6.6 feet per second
Distance apart = 55 feet
Convert your rate to feet per second, we have
Your rate, r1 = 6 * 1.47 feet per second
Evaluate
Your rate, r1 = 8.8 feet per second
To calculate the time that your friend is ahead of you, we use the following expression
r1 * t < distance apart + r2 * t
So, we have
8.8t < 55 + 6.6t
Collect the like terms
So, we have
8.8t - 6.6t < 55
Evaluate the like terms
So, we have
2.2t < 55
Divide both sides by 2.2
So, we have
t < 25
Hence, the inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds
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Round to the nearest hundredth, if necessary. Complete the statement. 30.9mm = in
The complete statement is 30.9mm = 1. 21 in
What is conversion of units?Conversion of units is simply the conversion between different units of measurement for a particular quantity.
Given the statement;
30.9mm = in
It is important to note that;
25. 4 millimeters = 1 inch
Then;
30. 9 millimeters = x inches
Cross multiply
x × 25. 4 = 30. 9 × 1
To make 'x' the subject
Divide both sides by 25. 4, we have;
x = 30. 9/ 25. 4
x = 1. 21 Inches
Thus, the complete statement is 30.9mm = 1. 21 in
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PLEASE HURRY THIS WAS DUE A HOUR AGO
What is the sum
-8 + 6 =
Answer:
-2
Step-by-step explanation:
Integer math!
Please help! The Great Wall of China built in the 7th century BCE, is about 1 x 10^4 miles long. The Panama Canal, built two thousand years later, is about 5 x 10^1 miles long. Write your answer in standard form.
The Great Wall of China is about what times long as the Panama Canal?
The number of times that the Great Wall of China is as long as the Panama Canal will be 2 × 10².
How to calculate the standard form?It should be noted that the Great Wall of China built in the 7th century BCE, is about 1 x 10⁴ miles long and the Panama Canal, built two thousand years later, is about 5 x 10^1 miles long.
Therefore, the number of times that the Great Wall of China is as long as the Panama Canal will be:
= 1 × 10⁴ / 5 × 10¹
= 2 × 10²
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