One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to
Need help geometry ^^^
Ken wants to build a table and put a border around it. The table and border must have an area of 3,276 square inches. The table is 36 inches wide and 72 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x?
4x^2 + 216x + 2,592 = 0
4x^2 + 216x − 684 = 0
2x^2 + 216x − 3,276 = 0
x^2 + 108x + 3,276 = 0
The quadratic equation that can be used to determine the thickness of the border, x is 4x² + 216x - 684 = 0
Which quadratic equation can be used to determine the thickness of the border, x?
From the question, we have the following parameters that can be used in our computation:
Length = 72
Width = 36
Border = x
Area = 3276
The area can be represented as
Area = (Width + 2x) * (Length + 2x)
Substitute the known values into the equation
(36 + 2x) * (72 + 2x) = 3276
Expand
4x² + 216x + 2592 = 3276
So, we have
4x² + 216x + 2592 - 3276 = 0
4x² + 216x - 684 = 0
Hence the quadratic equation is 4x² + 216x - 684 = 0
The function F(x) = 6x-2/5 is an example of a rational function.
A. True
B. False
The function F(x) = (6x-2)/5 is an example of a rational function.
Explanation:The function F(x) = (6x-2)/5 is an example of a rational function. A rational function is a function that can be expressed as the quotient of two polynomial functions, where the denominator is not equal to zero.
In this case, the function F(x) has a numerator of 6x-2 and a denominator of 5. Both the numerator and denominator are polynomial functions since they involve multiplication, addition, and subtraction of terms with x.
Therefore, the function F(x) = (6x-2)/5 is indeed a rational function, so the correct answer is True.
The function F(x) = (6x-2)/5 is an example of a rational function because it can be expressed as a ratio of two polynomials.
Function F(x) = (6x-2)/5 is an example of a rational function because it is a ratio of two polynomials. The numerator, 6x-2, is a linear polynomial, and the denominator, 5, is a constant polynomial.
To determine if a function is rational, we check if the function can be expressed as a quotient of two polynomials. In this case, F(x) is a ratio of a linear polynomial, 6x-2, and a constant polynomial, 5.
Therefore, the statement is True.
On his birthday newton was 14 years old and his father was 41 newton noticed that his age was his fathers age with the digits reversed how many years later with their ages next have their digits reversed
When the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
It is given that when Newton was 14 years old , his fathers age was 41 yrs.
We have to find out that at what age of Newton his fathers age will be reversed again ?
Solve for the value of x ; 10 x - 14 = 12x - 28 ?
The value of x will be 7.
Let's assume the tens place as x and one's place as y.
The actual number will be ; 10 x + y.
Reverse numbers pairs can be written as (10x+y) and (10y+x).
As the age of Newton's father is 41 yrs when he is 14 yrs old , so we have ;
(10x+y) - (10y+x) = 41–14 = 27
Hence , we can say that the age difference between Newton and his father is 27 years. This age difference will be same forever.
So ;
(10x+y) - (10y+x) = 27
and we have to find all values of x and y that will satisfy this equation.
⇒ (10x+y) - (10y+x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3
For all x’s and y’s who have their difference as 3 will answer the question. For example , (4,1) (5,2) (6,3) (7,4) (8,5) …. and so on.
Since Newton's father age today is 41 yrs.
The next age to satisfy the condition is 52 yrs.
This makes Newton’s age to be 52 - 27 = 25 which is the reverse of 52.
So , the answer of the question is that Newton should be of 25yrs , for his age to be the reverse of his father’s age.
Thus , when the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
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What is 51/4 ÷ 22/7 ? A. 1219/64 B. 219/64 C. 2 D. 12
B is correct :
5 1/4 = 21/4
2 2/7=16/7
21/4x7/16=147/64=2 19/64
What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?
-2/x+1
the / is a fraction symbol xxx
A baseball pitcher pitches a ball at the speed of 83 mph what conversion factors can be used to find the speed of the ball in feet per second
Answer: [tex]121.73\text{ feet per second}[/tex]
Step-by-step explanation:
Given : The speed of a baseball pitcher = 83 mph
or 83 miles per hour
Since , we know that
1 mile= 5280 feet
1 hour = 3600 seconds
Then, 83 miles per hour = [tex]\dfrac{\text{83 mile}}{\text{1 second}}=\dfrac{83\times5280\text{ feet}}{1\times3600\text{ seconds}}[/tex]
[tex]\approx121.73\text{ feet per second}[/tex]
Hence, the speed of the ball in feet per second = [tex]121.73\text{ feet per second}[/tex]
Lola takes the train from Paris to Nice. The distance between the two cities is about 921,000 meters. If the train travels at a speed of 307 kilometers per hour, how long will it take Lola to travel from Paris to Nice
Answer:
First,you need to convert 307km/hr into 85.2 meter per second.The formula for finding time is the distance divided by the speed.So,the answer is 10809 second,about 3 hours.
The graph represents this piecewise function
Answer:
Step-by-step explanation:
Given is a piecewise graph.
From the graph we find that the domain is [-3,1]
From [-3,-1) the line is slant passing through (-3,0)(-2,1)
Slope =change in y/change in x = 1
Equation is y = x+3
Thus the function is x+3 for -3≤x<-1
and 5, -1≤x≤1
Write a conditional that multiplies the value of the variable pay by one-and-a-half
HELP ME PLEASE!
Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. Peter and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image below:
Image depicts a mirror on the ground between a person and a house. The mirror is 6 feet away from the person and 30 feet away from the house.
What is the height of the house?
By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.
According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.
The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).
Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:
Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house
5 feet / 6 feet = Height of the house / 30 feet
Now, cross-multiply to solve for the height of the house:
5 feet * 30 feet = Height of the house * 6 feet
Height of the house = (5 * 30) / 6
Height of the house = 150 / 6
Height of the house = 25 feet
Therefore, the height of the house is 25 feet.
What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.
Consider the equation [tex] x^6+6x^3+5=0 [/tex].
First, you can use the substitution [tex] t=x^3 [/tex], then [tex] x^6=(x^3)^2=t^2 [/tex] and equation becomes [tex] t^2+6t+5=0 [/tex]. This equation is quadratic, so
[tex] D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1 [/tex].
Then you can factor this equation:
[tex] (t+5)(t+1)=0 [/tex].
Use the made substitution again:
[tex] (x^3+5)(x^3+1)=0 [/tex].
You have in each brackets the expression like [tex] a^3+b^3 [/tex] that is equal to [tex] (a+b)(a^2-ab+b^2) [/tex]. Thus,
[tex] x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1) [/tex]
and the equation is
[tex] (x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0 [/tex].
Here [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex] and you can sheck whether quadratic trinomials have real roots:
1. [tex] D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25} <0 [/tex].
2. [tex] D_2=(-1)^2-4\cdot 1=1-4=-3<0 [/tex].
This means that quadratic trinomials don't have real roots.
Answer: [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex]
If you need complex roots, then
[tex] x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2} [/tex].
A model rocket is launched with an initial upward velocity of 32 m/s. The rocket's height h (in meters) after t seconds is given by the following.
h=32t-5t^2
Find all values of t for which the rocket's height is 10 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
0.33 and 6.07
Step-by-step explanation:
How would you represent 3 quarter notes as a fraction?
12 sixteen notes have a nice day
simplify the expression. 7m^2+6.5n-4n+2.5m^2-n
A.) 1.5m^2+4.2n
B.)4.2m^2+1.5n
C.)1.5m^2-4.2n
D.)4.2m^2-1.5n
What are the rules for adding and subtracting negative numbers?
How many lines of symmetry does a regular octagon have?
Syreeta wants to buy some cds, each costing $14, and a dvd that costs $23. she has $65 to spend. write an equation to find how many cds she can buy
Answer:
14x+23y=65
Step-by-step explanation:
let cds=x and dvds=y
14x+23y=65
Simplify.
Square root of 121m^8n^4
A. 11mn
B. 11m^2n^2
C. 11m^4n^2
Answer:
B
Step-by-step explanation:
no
The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3
a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?
b) The first quartile for the wind speed data set is?
Find the constant sum for an ellipse with foci F1 (0, -12), F2 (0, 12) and the point on the ellipse (9, 0).
I don't understand how we do this PLEASE help me!!!
28 = (45 + KL)/2
56 = 45+ KL
KL = 56-45
KL = 11
Find the surface area of the sphere.
Round to the nearest hundredth.
The student came to the conclusion that the system has infinitely many solutions, which is not correct. Describe the error was the student work being shown.
The equation of the straight line of slope 3 passing through the point (2, 5) may be written as
WILL GIVE A BRAINLIEST PLEASE HELP!!!
Use the formula below to find the 6th term in the geometric sequence.
a(n)=(5)x(3/2)n-1
A.
5
B.
15/2
C.
1,215/32
D.
3,645/64
Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. If /,/, /, and /, solve for x.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
The base of a pyramid covers an area of 13.3 acres (1 acre = 43,560 ft2) and has a height of 473 ft. if the volume of a pyramid is given by the expression v = bh/3, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.
Work the following pricing problems for services rendered. (For all calculations use hundredths.)
Labor time = 8 hours
Overhead rate = 65%
Retail price of parts = $98.70
Total cost of job = $242.58
What is hourly rate for labor?
a=27.67
b=13.32
c=10.90
d=117.08
Answer:
10.90
Step-by-step explanation: