In linear equation, p(x) = -2x³ - 6x² - 12x - 8 is the equation of the cubic polynomial in standard form.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written
p(x) = a( x - x₁ ) ( x - x₂) ( x - x₃ )
Where a is the leading coefficient.
We know the three roots of the polynomial −2, 1 and 2.
p( x ) = a( x + 2) ( x + 1 ) ( x + 2 )
Since the y-intercept of the polynomial is y= - 8 when x=0
- 8 = a( 0 + 2 ) ( 0 + 1 ) ( 0 + 2 )
- 8 = a * 4
- 8 = 4a
a = -8/4
a = -2
The polynomial is
p( x ) = -2( x + 2) ( x + 1 ) ( x + 2 )
We must write it in standard form, so we have to multiply all of the factors as follows
p(x) = -2 ( x + 1 )² ( x + 1 )
p(x) = -2 ( x² + 4 + 2x ) ( x+ 1 )
p(x) = -2 ( x₃ + 3x² + 6x + 4 )
p(x) = -2x³ - 6x² - 12x - 8
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write the coordinate notation for the following:
rotation in the direction of 90°: (x,y) becomes (y,-x) rotation of (x,y) at 90 degrees counterclockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and counterclockwise results in (-x,-y) Rotating (x,y) in a 270° clockwise direction (-y,x).Upon 360-degree rotation, a point with the coordinates (x, y) is produced.
How is rotation calculated?
The number of central angles multiplied by the size of each central angle gives the angle of rotation between the two points or vertices: rotational angle =m = m
The term "order of rotation" refers to how many times a figure appears the same after a full 360-degree rotation. The angle of rotation can also be used to compute the order of rotation. A figure's rotational order can be determined using the angle of rotation (360°). A line segment rotates at a 180° angle.
Precession, nutation, and intrinsic rotation are the names of these rotations.
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which equation represents the line that passes through the points -3 7 and 9 -1
EXPLANATION
Given ordered pairs: (-3,7) and (9,-1)
(x1,y1) (x2,y2)
The equation that represents the line that passes through the points will be given as:
y = mx + b
First, we need to calculate the slope:
[tex]\text{Slope = }\frac{(y2-y1)}{(x2-x1)}=\frac{(-1-7)}{(9-(-3))}=\frac{(-8)}{(12)}=-\frac{2}{3}[/tex]Now, taking either one pair, we can calculate the value of b in this way:
[tex]7=-\frac{2}{3}(-3)\text{ + b}[/tex][tex]7=\frac{6}{3}+b[/tex]Simplifying:
[tex]7\text{ = }2\text{ + b}[/tex]Clearing b:
[tex]7-2=5=b[/tex]Finally, the equation will be:
[tex]y=-\frac{3}{2}x+5[/tex]
Solve
y (y- 8) = - 15
Answer:
y=5,3
Step-by-step explanation:
Companies also gather data on customer web use and preferences often without
their consent.
True
False
This is true, Companies also gather data on customer web use and preferences often without their consent.
What is data?
A set of discrete values called data is a collection of information that can describe amount, quality, fact, statistics, or just a series of symbols that can be further understood. A datum is a distinct state inside a collection of data. Typically, data is arranged into structures like tables that provide it additional context and meaning and can also be used as their own form of data in bigger structures. It's possible to use data as variables in a computation. Data can reflect both actual measures and abstract concepts. Data is employed often in practically every aspect of human organizational activity, including business and science. Stock prices, crime rates, unemployment rates, literacy rates, and census statistics are a few examples of data sets.
Companies sometimes gather data on customer web usage and preferences often without their consent. The main reason behind this dat collection is to suggest the best product or to show best advertisement based on the web usage and preferences.
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Square meters of ceiling | Number of tiles 1 | 10.75 10 | X what is the value of X?
We can find the number of tiles, using the next proportion:
[tex]\frac{1\text{ square meter}}{10\text{ }square\text{ meters}}=\frac{10.75\text{ tiles}}{x\text{ tiles}}[/tex]Solving for x:
[tex]\begin{gathered} 1\cdot x=10.75\cdot10 \\ x=107.5\text{ tiles} \end{gathered}[/tex]Whats the slope and y intercept of 21x+45y=-6
The line's equation is:
[tex]21x+45y=-6[/tex]To get slope and y-intercept, we have to re arrange this into slope intercept form, that is:
y = mx + b
Where
m is the slope
b is the y-intercept
Let's do this:
[tex]\begin{gathered} 21x+45y=-6 \\ 45y=-21x-6 \\ y=-\frac{21x}{45}-\frac{6}{45} \\ y=-\frac{21}{45}x-\frac{6}{45} \end{gathered}[/tex]So,
The slope is -21/45
y intercept is -6/45
In Ron's neighborhood, 5 out of every 6 families get a newspaper. Currently, 75 of the families get a newspaper. How many families are in Ron's neighborhood?
To solve this question we use the following ratio
[tex]\frac{No\text{of families that have newspaper}}{\text{Total number of families}}[/tex]No of families with newspaper = 5
No of families in the neighbourhood = 6
If the number of families currently with newspaper = 75 then,
[tex]\frac{5}{6}=\frac{75}{\text{total number of families in the neighbourood}}[/tex]Find the value of x.
20°
x = [?]°
(2x-8)°
Answer:
14
Step-by-step explanation:
the angle of 20° and the angle where it says (2x-8)° are the same.
Then find the number that substituted for x, multiplied by 2 and subtracted 8, gives 20°.
And it's 14.
Indeed:
([2×14]-8)° = 20°
HELP ASAP BRAINLEST + 100 POINTS PLEASE I AM DESPERATE EASY 7TH GRADE
A TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 10^10
9.7 x 10^5
4.85 x 10^10
4.85 x 10^5
Answer:
4.85 x 10^5
Step-by-step explanation:
First you want to find 5.6 x 10^5 into simplified form, which is 560000.
Then, you want to find 4.1 x 10^5 into simplified form, which is 410000.
Then you can add these numbers together to get 970000.
970000 into scientific notation is 9.7 x 10^5.
CORRECTION:
Answer should be based off of the AVERAGE viewers, not total.
Average viewers is 485000
485000 in scientific notation is 4.85 x 10^5
The average number of viewers over the two weeks are 4.85 x 10^5
A tv show had 5.6 x 10^5 viewers in the first week
and 4.1 x 10^5 viewers in the second week.
What is an average number:
This is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers.
To find the average number of viewers over the two weeks
Remove the decimal point.
5.6 x 10^5 write like this 560000
Similarly, 4.1 x 10^5 write like this 410000
Now, Solving the question
Therefore, the average will be
560000 + 410000
= 970000/2
=485000
=4.85 X 10^5
and 4.85 x 10^5
Thus , the average number of viewers over the two week 4.85 x 10^5
Give a Θ estimate of the number of addition operations that the following algorithm will execute: i←1 t←0 while (i≤n) t←t+i i←i+
The estimate of the number of addition operations that the algorithm will execute is:
Θ(2n).
What is the complexity of the given algorithm?The complexity of the given algorithm is an estimate of the number of operations that the algorithm will execute.
For an algorithm bounded by a loop such as this one, due to the command while (i≤n), the length of the loop is bound of the complexity of the algorithm, hence we can begin the complexity equation as follows:
Θ(n).
Inside the loop, for each iteration of the loop, that is, each value of i, two addition operations are made, adding i to t and incrementing the count control variable i by 1.
Due to the two addition operations inside on each iteration of the loop, 2 is multiplied inside the complexity, hence the estimate of the number of addition operations that the algorithm will execute is:
Θ(2n).
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LOLLL HELO HELP PLS PLS PLS
Answer: C
2 1/6 x 1 1/3 = 26/9 which = 2 8/9
Write the FOLLOWING algebraic expression in words1/3 a to the 3rd power
From the question we are to express the algebraic expression in words
[tex]\frac{1}{3}a^3[/tex]The algebraic expression can be written as
The product of one-third and the cube of a certain number, a
or
The cube of a certain number, a divided by 3
Other than the spots reserved for drivers with a disability, there are 285 parkingspots for monthly rentals and the rest are for hourly parking. How many spots arethere for hourly parking?
Given:
Total parking =1327
NO of spots for reserved for disabilities:
[tex]=12\times6[/tex][tex]=72[/tex][tex]No\text{ of spots for hourly parking=}1327-72-285[/tex][tex]No\text{ of spots for hourly parking=}970[/tex]1/3 (2x - 1) = z for x
We need to solve the equation shown below for x:
[tex]\frac{1}{3}(2x-1)=z[/tex]Using distributive propery, a(b - c) = ab - ac , we can simplify the left hand side:
[tex]\begin{gathered} \frac{1}{3}(2x)-\frac{1}{3}(1)=z \\ \frac{2}{3}x-\frac{1}{3}=z \end{gathered}[/tex]We isolate the term with x and then divide the other side by 2/3 to get x = something...
[tex]\begin{gathered} \frac{2}{3}x-\frac{1}{3}=z \\ \frac{2}{3}x=z+\frac{1}{3} \\ x=\frac{z+\frac{1}{3}}{\frac{2}{3}} \end{gathered}[/tex]To simplify it (reduce), we can divide both terms by (2/3) and simplify. Shown below:
[tex]\begin{gathered} x=\frac{z}{\frac{2}{3}}+\frac{\frac{1}{3}}{\frac{2}{3}} \\ x=z\times\frac{3}{2}+\frac{1}{3}\times\frac{3}{2} \\ x=\frac{3z}{2}+\frac{1}{2} \\ x=\frac{3z+1}{2} \end{gathered}[/tex]The final answer:
[tex]x=\frac{3z+1}{2}[/tex]Complete the following using all of the numbers
1, 2, 3, 4, 5, 6
to find the smallest even number
Must be in the format
____ - ____ (3 digit numbers only)
Answer:
Step-by-step explanation:
hdhdhdhdh
Answer:
The answer is
[tex]465 - 321[/tex]
Or;
[tex]456 - 312[/tex]
Question 1
A student went to the gas station to buy gasoline and a bag of potato chips. Gasoline was $2.31 per
gallon and potato chips were $1.25.
Part 1. Write a linear equation to model the total amount the student spent at the gas station,
where g represents the number of gallons of gasoline, and t represents the total amount of money
spent. Assume there is no tax.
Part 2. Suppose the student bought 16 gallons of gas. Find the total amount the student spent at
the gas station
Part 1. The linear equation is 2.31g + 1.25t = 0
Part 2. Total amount student spent at the gas station is $36.96
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
Part 1.
Here in question of part 1 it stated that
g = the number of gallons of gasoline
t = the total amount of money
So according to question, the linear equation will be
2.31g + 1.25t = 0
Part 2.
Given, 1g = $2.31
then, 16g = 16 * 2.31
= $36.96
Therefore, for Part 1. The linear equation is 2.31g + 1.25t = 0 and,
for part 2. Total amount student spent at the gas station is $36.96
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Can someone help me on this geometry assignment
Based on the triangle sum theorem, the measure of <RSP is: B. 49°
How to Apply the Triangle Sum Theorem?According to the triangle sum theorem, every triangle has a sum of 180 degrees when all its interior angles are added together.
Since lines PS and QR are parallel lines, therefore:
5y + 14 = 8y - 13 [alternate angles are congruent]
Solve for the value of y
5y - 8y = -14 - 13
-3y = -27
-3y/-3 = -27/-3
y = 9
(8y - 13) + 3x + (2x + 1) = 180 [triangle sum theorem]
8y - 13 + 3x + 2x + 1 = 180
8y - 12 + 5x = 180
Plug in the value of y
8(9) - 12 + 5x = 180
72 - 12 + 5x = 180
60 + 5x = 180
5x = 180 - 60
5x = 120
x = 120/5
x = 24
Measure of <RSP = 2x + 1 = 2(24) + 1
Measure of <RSP = 49°
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ANSWER PLS QUESTION ATTACHED
Answer:
40+80=a(exterior angle of a triangle is equal to the sum of two opposite interior angle)
c+95=a(same as above)
180-95=85(being straight angle)
b+40+85=180(sum of interior angles of triangle)
or,b=180-125
or,b=55
Answer:
a=120 b=60 c=25
Step-by-step explanation:
All digits in a dropdown number are different and one of its digits is the average of all its digits. It has at least two digits. For example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.1. Find the smallest dropdown number2. What are the smallest and largest 4-digit dropdown numbers? Please provide working out for a and b. Thanks.
a) 102 is the smallest of the dropdown number
b) 1025 is the smallest dropdown number
c) 9874 is the largest 4-digit dropdown number
Explanation:Given:
All digits in a dropdown number are different and one of its digits is the average of all its digits.
It has at least two digits.
To find:
a) the smallest dropdown number
b) the smallest and largest 4-digit dropdown numbers
a) From the information given, the numbers are at least two digits. This means the smallest of the digits from the dropdown is 2
We can't have 0 as the starting number because it will reduce the digits by 1. The list will start from the smallest to the highest since we are looking for the smallest number.
For two digits: 12, 13, 14, etc
We can only have a 2-digit number whose average is part of digits if the numbers are the same digit.
As a result, we will move to 3 digits.
For 3 dgits: 102, 103, 104, 105, etc
We will check if any of the above will have one of its digits as average
102: 1 + 0 + 2 = 3
Average = 3/3 = 1
One of the digits of this number is the average of the number.
Hence, 102 is the smallest of the dropdown number
b) To get the smallest 4 digit dropdown number, we will list from smallest to highest
For 4 digits: 1023, 1024, 1025, 1026, 1027, ...
We will check if any of the above will have one of its digits as average
1023: 1+0+2+3 = 6
Average = 6/4 = 1.5
1024: 1+0+2+4 = 7
Average = 7/4 = 1.75
1025: 1+0+2+5 = 8
Average = 8/4 = 2
One of the digits of this number is the average of the number.
Hence, 1025 is the smallest dropdown number
To get the largest 4-digit dropdown number, we will list from largest to smallest
For 4 digits: 9876, 9875, 9874, 9873, 9872, etc
We will check if any of the above will have one of its digits as average
9876: 9+8+7+6 = 30
Average = 30/4 = 7.5
9875: 9+8+7+5 = 29
Average = 29/4 = 7.25
9874: 9+8+7+4 = 28
Average = 28/4 = 7
One of the digits of this number is the average of the number.
Hence, 9874 is the largest 4-digit dropdown number
Hello! I'm stuck here. I've tried solving it and I'm not getting any of the answers.
We have the cost function C(d) and the revenue function R(d) as:
[tex]C(d)=10500+3.9d[/tex][tex]\begin{gathered} R(d)=d(14.5-0.00003d) \\ R(d)=14.5d-0.00003d^2 \end{gathered}[/tex]The profit can be defined as the difference between the revenue and the cost, so we can express it as:
[tex]\begin{gathered} P(d)=R(d)-C(d) \\ P(d)=(14.5d-0.00003d^2)-(10500+3.9d) \\ P(d)=-0.00003d^2+14.5d-3.9d-10500 \\ P(d)=-0.00003d+10.6d-10500 \end{gathered}[/tex]We can now evaluate it for d = 30,000 as:
[tex]\begin{gathered} P=-0.00003\cdot(30,000)^2+10.6(30,000)-10,500 \\ P=-0.00003\cdot900,000,000+318,000-10,500 \\ P=-27,000+318,000-10,500 \\ P=280,500 \end{gathered}[/tex]Answer: the profit for 30,000 units is $280,500 [Fourth option].
21 cookies are shared equally among 3 girls. How many
cookies does each girl receive?
Answer:7
Step-by-step explanation: you divide the amount of cookies by the amount of girls
21/3=7
helpppppppppppppppppp
Answer:
33
Step-by-step explanation:
3! karma :)
Joe owes John 16$ he tells
his four kids to pay off the dept.
How much will each kid
pay off?
Answer: $4
Step-by-step explanation:
First, why are you making yo kids pay yo debt?
Second 16/4=4
An advertiser rents a rectangular billboard that is 44 ft wide and 20 ft tall. the rent is $15 per square foot. for a billboard twice as tall, the advertiser has to pay $26,400. is this reasonable? explain.
Yes; when the height is doubled, the area is also doubled (option D)
Explanation:width of the billboard = 44 ft
height of the billboard = 20 ft
the rent per square ft = $15
for a billboard twice as tall, the advertiser has to pay $26,400
We need to find the area of the billboard = width × height
Area = 44 × 20
Area of the billboard = 880 ft²
The rent for the whole area of the billboard = $15 × 880
The rent for the whole area of the billboard = $13,200
when the height is doubled = 2(height)
new height = 2(20) = 40 ft
The new area = 44 × 40 = 1760 ft²
The rent for the new area of the billboard = $15 × 1760
The rent for the new area of the billboard = $26400
The result in our calculation is the same as the amount the advertiser payed.
new height = 2(old height)
new area = 2(old area)
26400 = 2(13200)
We can conclude: it is reasonable
Yes; when the height is doubled, the area is also doubled (option D)
what is 2(9n-1)+7n+6= -60
n = -2.56
Explanation:2(9n-1)+7n+6= -60
The first thing we do is expand the parenthesis:
2× 9n - 2×1 + 7n + 6 = -60
18n -2 + 7n + 6 = -60
collect like terms:
18n + 7n -2 + 6 = -60
25n + 4 = -60
Subtract 4 from both sides:
25n + 4 -4 = -60 - 4
25n + 0 = -64
25n = -64
divide both sides by 25:
25n/25 = -64/25
n = -2.56
help meeeeeeeeeeeeeeeeeeeeeee
thank you
By evaluating the square root function in x = 0 and x = 25/16 we will get:
f(0) = 0
f(25/16) = 5/4
How to evaluate the function?Here we have the square root function:
f(x) = √x
And we want to evaluate this in x = 0 and x = 25/16.
Evaluating in zero we get the same than you got:
f(0) =√0 = 0
Evaluating in x = 25/16 we will get:
f(25/16) = √(25/16)
Remember that the square root can be distributed under division, so:
√(25/16) = √(25)/√(16)
Now, we know that:
√25 = 5
√16 = 4
Then we can rewrite the quotient as:
√(25)/√(16) = 5/4
so f(25/16) = 5/4.
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write an equation of the line with the given slope, m, and y intercept (0,b)
Given Data:
[tex]\begin{gathered} m=\frac{1}{4} \\ b=0 \end{gathered}[/tex]The general equation of a line passing through a point of cordinates (x, y) can be written as,
[tex]y=mx+b[/tex]Therefore substituting for m and b, we can write, the line equation as,
[tex]y=\frac{1}{4}x+0[/tex]Thus the equation is, y = (1/4)x.
Answer:
y = 1/4x
hope this helps
Part A: Solve the equation 4(x + 5) = 9x + 4x − 34, and show your work. (5 points) Part B: Use this list of properties to justify each step of your math work. Justifications may be used more than once if needed
Find the average of the following set offractions (do not use decimals).{ 42, 1/8, 44, 5/8, 3/4 }
SOLUTION
The average of the 5 numbers become
[tex]\begin{gathered} \text{Average =}(\frac{42}{1}+\frac{1}{8}+\frac{44}{1}+\frac{5}{8}+\frac{3}{4})\text{ divided by 5} \\ \\ \text{Average = }\frac{336+1+352+5+6}{8}\text{ divided by 5} \\ \\ \text{Average = }\frac{700}{8}\text{ divided by 5} \\ \\ \text{Average =}\frac{700}{8}\times\frac{1}{5} \\ \frac{700}{40} \\ \\ \frac{70}{4} \\ \\ \frac{35}{2} \\ \\ \text{Average = 17}\frac{1}{2} \end{gathered}[/tex]AC Round your answer to the nearest hundredth. ? a А 3 70 B Show Calculator
We are given a right-angled triangle.
We are asked to find the length of the side AC
Recall from trigonometric ratios,
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]With respect to the angle 70°, the adjacent side is 3 and the opposite side is AC
