What is the sum of the given polynomials in standard form?
(x2 – 3x) + (–2x2 + 5x – 3)
The expression 2x+13/2x+6-3x-6/2x+6 is equivalent to
Luisa draws a regular nonagon and rotates it about its center. which angle measures can luisa rotate the regular nonagon through to map it onto itself? select each correct answer. 40° 80° 90° 120° 160° 180°
Answer: [tex]40^{\circ}[/tex]
Step-by-step explanation:
Given: A regular nonagon with 9 sides.
For a regular nonagon, it maps onto itself 9 times during a rotation of 360°.
Mow, the angle at Lusia can rotate the regular nonagon through to map it onto itself=[tex]\frac{360}{\text{number of sides of regular polygon}}=\frac{360}{9}=40^{\circ}[/tex]
A shape is said to has rotational symmetry if it maps onto itself under rotation about a point at its center. The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°.A shape that maps onto itself after rotation, has a rotation symmetry
The angles of rotation that would map the nonagon onto itself are:
[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]
A regular nonagon has nine equal sides i.e.
[tex]\mathbf{n = 9}[/tex]
The angle at the center of the nonagon is:
[tex]\mathbf{\theta = 360}[/tex]
So, the angle of rotation symmetry is:
[tex]\mathbf{\alpha = \frac{\theta}{n}}[/tex]
This gives:
[tex]\mathbf{\alpha = \frac{360}{9}}[/tex]
[tex]\mathbf{\alpha = 40}[/tex]
This means that, the nonagon would map onto itself, when rotated at 40 degrees.
Other angles of rotation symmetry must be a multiple of 40
i.e.
[tex]\mathbf{\alpha = 40, 80, 120, 160, 200, 240, 280......}[/tex]
Using the above list of angles, the angles of rotation that would map the nonagon onto itself are:
[tex]\mathbf{40, 80, 120\ and\ 160}[/tex]
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Given triangle ABC ~ triangle XYZ, what is the value of cos(Z)
Answer:
cos(Z) = 12/13
Step-by-step explanation:
Given that the triangles ABC and XYZ are similar (their corresponding angles are congruent and the corresponding sides are in proportion), then cos(Z) is equal to cos(C).
From the picture attached:
cos(C) = adjacent/hypotenuse
cos(C) = 12/13
Final answer:
Without additional information about triangle XYZ or its similarity ratio to triangle ABC, it is impossible to provide the exact value of cos(Z).
Explanation:
The question involves finding the value of cos(Z) in a triangle similar to triangle ABC. When triangles are similar, their corresponding angles are equal. However, without additional information such as side lengths or other angle values, it's not possible to calculate the exact value of cos(Z). But in general for any triangle, the value of cosine for any angle can be found using the cosine formula or by using the ratio of the adjacent side to the hypotenuse in a right triangle. For non-right triangles, one could utilize the Law of Cosines to determine the cosine of the included angle.
Teo makes a necklace of x wooden beads at .50 each and 6 glass beads at 1.25 each. The average cost of the beads in the necklace is .75. What is an equation that will model this solution?
w = 13, x = 9, y = 1.9, z = 0.5 x + 20 – 1
A. 28
B. 19
C. 30
D. 32
The value the given expression x + 20 – 1 is, the solution is A. 28.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
w = 13, x = 9, y = 1.9, z = 0.5
x + 20 – 1
Since X Is 9 ,
You're Problem Would Now Be
= 9 + 20 - 1
Then You Subtract 20
And 1 Which Will Give You 19
Then , You're Left With 9 + 19
Which Is 28.
Hence, the solution is A. 28.
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investment historically have doubled every 9 years if you start with $2000 investment how much money would you have after 45 years
Answer: $64000
Step-by-step explanation:
The exponential equation for growth in function with growth factor 'b'in time 't' is given by :-
[tex]y=Ab^x[/tex] , where A is the initial value.
Given : The initial value : [tex]A=\$2000 [/tex]
Growth rate = [tex]b=2\text{ every 9 years} [/tex]
Time periods in 45 years :[tex]t=\dfrac{45}{9}=5[/tex]
Then , the exponential equation for growth for t=5 is given by :-
[tex]y=2000(2)^{5}=64000[/tex]
Hence, the money you would have after 45 years = $64000
Georgia, a florist, charges 10.95 per flower bundle plus a 15 delivery charge per order. If Charlie orders 8 bundles of flowers and has them delivered,how much does Georgia charge Charlie
Joy drove 120 miles the first day of her trip. She drove 60 mph on the following days. What is the beginning amount (b) in the linear model
A) 30 miles
B) 60 miles
C) 90 miles
Or
D) 120 miles
Answer:
120
Step-by-step explanation:
Building a is 160160 feet shorter than building
b. the total height of the two buildings is 14801480 feet. find the height of each building
1/3 + 1/6 in simplest form
Which expression forms an equation with the given expression?
24 - 5 * 2 = ______
A. (5 + 3) * 2
B. 2(6 + 1)
C. 5 * 8 - 2
D. 4 * 9 + 2
Use properties of addition and subtraction to evaluate the expression. −38−11−22 Enter your answer in the box.
What is (-1+8i)(-8+8i)
simplify i^31 (click photo for options)
Five less than twice what negative number squared is 157?
Using algebraic equation, the negative number that is squared is: -9.
What is an Algebraic Equation?An algebraic equation can be used to find an unknown value, by making the unknown value the variable.
Let the negative number that would be squared be represented by the variable, x. Thus, we have -x². Therefore:
2x² - 5 = 157
2x² = 157 + 5
2x² = 162
x² = 162/2
x² = 81
x = √81
x = -9
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What are the solutions to the equation? 5x^3 =405x
what are potential roots of p(x) = x4 + 22x2 – 16x – 12
Answer:
±1, ±2, ±3, ±4, ±6 and ±12
Step-by-step explanation:
The potential roots are obtained as following:
potential roots = factors of the constant term / factors of leading coefficient
The constant term is -12, its factors are ±1, ±2, ±3, ±4, ±6 and ±12
The leading coefficient is 1, its factors are ±1
Therefore the potential roots are ±1, ±2, ±3, ±4, ±6 and ±12
The running back for the bulldogsame football team carried the ball 9 times for a totall loss of 15 3/4 yards find the average change in field position on each run
What are three collinear points on line l?
points A, B, and F
points A, F, and G
points B, C, and D
points B, F, and G
Points A, F, and G are three collinear points on line l.
[tex]\boxed{ \ The \ Answer \ is \ B \ }[/tex]
Further explanationLet us consider the definition of collinear.
Collinear
Collinear points represent points that lie on a straight line. Any two points are always collinear because we can constantly connect them with a straight line. A collinear relationship can occur from three points or more, but they don’t have to be.
Noncollinear
Noncollinear points represent the points that do not lie in a similar straight line.
Given that lines k, l, and m with points A, B, C, D, F, and G. The logical conclusions that can be taken correctly based on the attached picture are as follows:
At line k, points A and B are collinear. At line l, points A, F, and G are collinear. At line m, points B and F are collinear. Point A is placed at line k and line l.Point B is placed at line k and line m.Point F is located at line l and line m.Points C and D are not located on any line.Hence, the specific answer to this key question is undoubted, i.e., points A, F, and G.
Note:
All points can, also, be said to be coplanar. This is because the three lines intersect with each other and lie on a planar surface.
Coplanar
Coplanar points represent a group of points that lie on the same plane, i.e. a planar surface that extends without end in all directions. Any two or three points are always coplanar, but four or more points might or might not be coplanar.
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Answer: B
Step-by-step explanation:
Suppose that a compensation professional would like to calculate the median salary. he orders four salaries as follows: $20,000, $22,000, $24,000, $26,000. what is the median salary for this data set?
The median salary for the given data set of four salaries ($20,000, $22,000, $24,000, and $26,000) is calculated by averaging the two middle values ($22,000 and $24,000), resulting in a median of $23,000
To calculate the median salary from an ordered data set, you first need to determine if the number of data points is even or odd. In this scenario, there are four data points: $20,000, $22,000, $24,000, and $26,000. As the number of data values is even, the median is the average of the two middle values.
Steps to Calculate Median Salary
Arrange the salaries in ascending or descending order. This step is already completed, as the salaries are presented in order: $20,000, $22,000, $24,000, $26,000.Find the two middle salaries since the number of data points is even. In the given data set, the two middle salaries are $22,000 and $24,000.Calculate the average of these two middle salaries. Add $22,000 and $24,000 to get $46,000, then divide by 2 to obtain $23,000. This value is the median salary for the data set.Therefore, the median salary for this data set is $23,000
Please check!
Mary has been hired as a receptionist. She is paid a flat rate of $150 each week and earns an additional $12.50 for every hour that she works. If her goal is to make $575 in one week, which equation will help Mary determine the number of hours she must work?
Plz help!! Which of the following is not equivalent to the ratio 12/4 A. 6/2 B. 36/12 C. 24/16 D. 240/80
PLEASE HELP!!!!!!!!!!!!!! AND THANK YOU :-) 15 POINTS A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.
(?) = 4500 (?) (?)
W= (?) (?) (?)
Answer: [tex]w+s=4500[/tex]
[tex] w=1.25s[/tex]
Step-by-step explanation:
Let w be the number of bottles of water and let s be the number of bottles of soda.
Since , the manager needs to buy a total of 4,500 drinks.
Then , we have [tex]w+s=4500[/tex]
Also, the they have 25% more water than soda.
Since 25%=0.25
Then, [tex]w=s+0.25s=s(1.25)[/tex]
[tex]\Rightarrow\ w=1.25s[/tex]
Hence, the system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.
[tex]w+s=4500[/tex]
[tex] w=1.25s[/tex]
For the linear equation, x + y - 1 = 0, determine a corresponding value of y for the x-value of -6.
x + y-1 = 0
if x = 6
replace x with 6 to get
6 +y-1 =0
subtract 6 from each side
y-1 =-6
add 1 to each side
y = -5
How do you find the x and y intercepts of x^2+x-2/x^2-3x-4?
James age in years is five more than two timed kevin's age. If James is 19 years old , how many years old is kevin?
Final answer:
Kevin is 7 years old. The problem is solved by setting up an equation 19 = 2K + 5, subtracting 5 from both sides to get 14 = 2K, and then dividing by 2 to find Kevin's age.
Explanation:
The question asks us to find Kevin's age given that James's age is five more than two times Kevin's age and that James is 19 years old. To solve this, we'll set up an equation based on the information provided.
Let K represent Kevin's age. According to the problem, we have:
James's age = 2 × Kevin's age + 5
Since James's age is 19, we can write:
19 = 2K + 5
To solve for K, we first subtract 5 from both sides of the equation:
14 = 2K
Then, we divide both sides by 2 to isolate K:
K = 7
Therefore, Kevin is 7 years old.
Which statement is the correct interpretation of the inequality –2 > –8?
On a number line, −2 is located to the right of –8.
On a number line, −2 is located to the left of –8.
On a number line, −2 is located to the left of 0 and –8 is located to the right of 0.
On a number line, −2 is located to the right of 0 and –8 is located to the left of 0.
the correct interpretation of the inequality –2 > –8 is On a number line, −2 is located to the right of –8.
is 0.12112111211112 a rational number ?
Answer: The given number is NOT rational.
Step-by-step explanation: We are given to check whether the number 0.12112111211112 . . . a rational number or not.
We know that
if the digits after the decimal in a number are either repeating or terminating, then the number is rational.
The given number is
[tex]x=0.12112111211112 . . .[/tex]
We can see that the digits after the decimal are neither repeating nor terminating.
Therefore, the given number is NOT rational.
Scott earns $25 an hour at his job as a landscaper. His boss Danny gives him $10 per day for lunch. Scott works thirty hours per week (He works Monday thru Friday, for six hours each day). An expression for determining how much Scott gets paid per week might be written as follows:
25 h + 10 d
Identify each part of this expression and explain what it represents, and which numbers should be substituted for which variables in order to calculate how much Scott earns per week. Do you think this is the best expression to use for this application? Why or why not?