Answer: 30ft
Step-by-step explanation:
NEED HELP ASAP - Algebra 2 - 50 Points
Write a reasonable equation in the form g(x) = a(x - h)^2 for g(x) below.
Explain why your equation is reasonable.
The parabola g(x) is reasonable because it can be derived of parabola f(x) by rigid transformations.
How to generate the image of the parabola by rigid transformation
Parabolas are represented by second order polynomials in vertex form, whose definition is shown below:
y - k = C · (h - k)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.In this problem we must create the expression for the image of the parabola by means of rigid transformations, that is, transformations that change the parabola without changing Euclidean distances. Most common rigid transformations are listed below:
TranslationReflectionDilation / ContractionRotationThe procedure is summarized below:
Shift the parabola 3 units right. (Horizontal translation)Shift the parabola 2 units up. (Vertical translation)Reflect the parabola about the line y = 2. (Reflection)Enlarge the parabola horizontally by a factor of 0.5. (Dilation)Now we proceed to apply the rigid transformations in that order:
Step 1
y = f(x) → y = f(x - 3)
y = x² → y = (x - 3)²
Step 2
y = f(x - 3) → y - 2 = f(x - 3)
y = (x - 3)² → y - 2 = (x - 3)²
Step 3
y - 2 = f(x - 3) → y - 2 = - f(x - 3)
y - 2 = (x - 3)² → y - 2 = - (x - 3)²
Step 4
y - 2 = - f(x - 3) → y - 2 = - f[0.5 · (x - 3)]
y - 2 = - [0.5 · (x - 3)]²
Finally, we proceed to plot both parabolae by help of a graphing tool.
To learn more on parabolae: https://brainly.com/question/21685473
#SPJ1
Which description best matches the graph below? Please explain why you chose the answer. I will mark you brainliest.
Gill walks for a minute away from home for several minutes, and then turns toward home and walks for a few minutes. He stops when he knows and they talk for a few minutes. Then he starts walking away from home.
Hence option C is correct.
What is a graph?
In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The items correspond to mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.
Given graph represents the y-axis is the distance from home and the x-axis is the number of minutes.
There are 4 straight lines in the graph
The first line is increasingly and represents Gill walking away from home.
The second line is decreasing and represents Gill walking toward home.
The third line is parallel to x-axis. It means he stands a point for a few minutes.
The fourth line is increasingly and represents Gill walking away from home.
Hence option C is the correct option.
To learn more about graph, click on the below link:
https://brainly.com/question/14936256
#SPJ1
find the sum of these polynomials. (4x^2+3x-1) + (x^2-5x-6)=
The sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
we will add the coefficients of the same degree terms.
(4x^2+3x-1) + (x^2-5x-6) = (4x^2+x^2) + (3x-5x) + (-1-6) = 5x^2-2x-7
Therefore, the sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
To learn more about Polynomials:
https://brainly.com/question/4420925
David wants to rent a bicycle for a couple of hours to explore the city. The price of the bike rental, (P), depends on the time the bike was out, (t). The price consists of a base charge of $8 and a variable hourly cost. The graph of the function is shown below.
Answer:
The hourly charge is $4 per hour for the first 3 hours.
The rate then drops to $2 per hour until the end of the 6th hour.
The hourly rate drops further to $1 per hour between the 6th and 10th hours.
The maximum price of the bike rental is $30.
Step-by-step explanation:
The slope of the graph corresponds to the hourly rate for the bike rental.
During the first three hours of the bike rental, the price increases by $4 each hour.
Between the 3rd and 6 th hours, the slope of the graph is 2, which means the hourly rate of the bike rental is $2 per hour.
Between the 6th and 10th hours, the rate is $1 per hour.
After the 10th hour, the price, P, stops increasing. The maximum price of the bike rental is $30.
what is the answer for this question? Answer ASAP
The value of the expression as a fraction in its simplest form is 2/7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 ÷ ( 5/2 x (2 x (1(3/5) - 2/5) - 1) )
Step 1:
Removing the parenthesis.
We will solve (1(3/5) - 2/5) first.
8/5 - 2/5 = 6/5
1 ÷ ( 5/2 x (2 x 6/5 - 1) )
Step 2:
Solve this (2 x 6/5 - 1)
12/5 - 1 = 7/5
1 ÷ ( 5/2 x 7/5)
Step 3:
Solve (5/2 x 7/5)
5/2 x 7/5 = 7/2
1 ÷ 7/2
Step 4:
1 ÷ 7/2
= 1 x 2/7
= 2/7
Thus,
The value of the expression is 2/7.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
2 step equations
3f + 1 = 10
Answer:
3f = 9
Step-by-step explanation:
[tex]3f + 1 = 10 \\ 3f = 10 - 1 \\ 3f = 9 \\ f = \frac{9}{3} \\ f = 3[/tex]
Answer:
[tex] \sf \: f = 3[/tex]
Step-by-step explanation:
Given equation,
→ 3f + 1 = 10
Now the value of f will be,
→ 3f + 1 = 10
→ 3f = 10 - 1
→ 3f = 9
→ f = 9 ÷ 3
→ [ f = 3 ]
Hence, the value of f is 3.
Determine the value of y, if x is 5.
y = x² - 6
Answer:
19
Step-by-step explanation:
if x=5
y=x^2 - 6
y= 5^2 - 6
y= 25- 6
y=19
How do you write an equation of a line in slope intercept form when given a graph of a line?
We can write an equation of a line in slope intercept form when given a graph of a line by using the equation y = mx + c.
There are various forms in which an equation is present. Based on the given equation or graph values, we can determine the form we should use. The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
We first see the point where the line cuts the y-axis, then we calculate the slope of the line using the formula,
Slope= Δy/Δx
Once we get these values, we can substitute them in the equation for our final answer.
Read more about Slope-intercept form from:
https://brainly.com/question/27469757
#SPJ4
please help me w this
Answer:
Opposite Sides are perpendicular (only correct answer)
Step-by-step explanation:
Not every parallelogram has diagonals that are perp to each other (form right angles.
How do you find the quotient of a division fraction?
Take the reciprocal of the second fraction, and Multiply it by the first fraction. later reduce the resultant fraction to its lowest terms.
The quotient of a fraction is the whole number that is obtained when we simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.
The quotient can also be the solution to a division problem involving two fractions. That division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient.
The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator.
Consider an example:
2 3/7=3 *2/7 =3 + 2/7
3 is the quotient
2 is the remainder
7 is the divisor
23 is the dividend
To know more about the quotient of a division fraction:
https://brainly.com/question/2110934
#SPJ4
What is an example of no solution?
As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.
What is infinite solution?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".
What is an infinite number?
There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.
The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.
Learn more about infinite solution
brainly.com/question/29093214
#SPJ4
4.
What is the solution of the system of equations?
y = –4x + 10
y = –2x – 6
Eva deposited $50 in an account earning 10% interest compound annually to the nearest cent how much interest will she earn in 2 years
Answer:
For 10% interest, you can multiply the original number by 1.1.
$50 x 1.1 = $55 after one year
$55 x 1.1 = $60.50 after two years
$60.50 - $50 = $10.50
In 2 years, Eva will earn $10.50 in interest.
please this is due tonight and its for a test I did this all day
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An unfair comparison between two numbers or other mathematical expressions is referred to as an inequality. It is most frequently used when comparing the sizes of two numbers on a number line. The attachment contains the graph for each inequality or equation.
What is graph?A graph is a graphical representation of statistical data or the functional relationship of variables. Graphs can highlight broad trends in the quantitative behaviour of data, which is useful for forecasting. They can, however, be inaccurate and occasionally deceptive as mere approximations.
Most graphs have two axes: one for independent variables and one for dependent variables. A broken-line graph is the most common type of graph, with time serving as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
Learn more about inequality
https://brainly.com/question/28823603
#SPJ1
Write an equation in slope-intercept form to represent the linear relationship shown in the table.
The equation in y = 2x + 8 for the given coordinates.
What is the slope-intercept form of a line?Finding the equation of a straight line in the coordinate plane is done using the slope-intercept form. A straight-line's equation will be that relationship that:
any place on the line's coordinates must meet.
Any point that is not on the line will not have coordinates that satisfy.
Given coordinates
x -2 -1 0 1
y 4 6 8 10
equation is given by y = mx + c
m is the slope and c is y-intercept
let x₁ = -2, x₂ = -1
y₁ = 4, y₂ = 6
m = (y₂ - y₁)/(x₂ - x₁)
m = (6 - 4)/(-1 - (-2))
m = 2
so y = mx + c
substitute value of m
y = 2x + c
at x = 0 and y = 8
8 = 2(0) + c
c = 8
equation of line y = mx + c
y = 2x + 8
Hence the equation is y = 2x + 8.
Learn more about slope intercept;
https://brainly.com/question/29146348
#SPJ1
the complete question is in image.
The diameter of a circle is 25 cm. what is the radius of the circle? a. 5 cmb. 12.5 cm c. 25 cm d. 50 cm
The radius of the circle is 12.5 cm. So the option b is correct.
In the given question, the diameter of a circle is 25 cm.
We have to find the radius of the circle.
The radius of a circle is the distance a circle's centre from any point along its perimeter. Usually, "R" or "r" is used to indicate it. In almost all calculations containing spheres, this quantity is essential. In terms of radius, a circle's area and circumference are also calculated.
The distance from any circular object's centre to its outermost border or boundary is measured in terms of radius. A radius is a property of not only circles but also spheres, semi-spheres, cones with circular bases, and cylinders with circular bases.
The given diameter = 25 cm.
Now the radius = diameter/2
Radius = 25/2
Radius = 12.5 cm
So the option b is correct.
To learn more about radius of the circle link is here
brainly.com/question/28946570
#SPJ4
Derek has $82 in his bank account. There is a service fee of $5.50 charged every month. For 6 months, Derek deposits $11.25 in the account. If he doesn’t make any other deposits or withdrawals, how much is in the account after 11 months?
After 11 months, Derek would have $89 in his account
How to calculate the amount of money that Derek would have in his account after 11 months?Derek has $82 in his account
The bank charges a service fee of $5.50 each month
For 6 months Derek deposits $11.25 in his account
Therefore the amount of money in his account after 11 months can be calculated as follows
82 + 11.25(6)
82 + 67.5
= 149.5
The service charge for the entire 11 months is
= 5.50(11)
= 60.5
The money in the account is
149.5-60.5
= 89
Hence Derek has $89 in his account after 11 months
Read more on account here
https://brainly.com/question/5960760
#SPJ1
A certain blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments. Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
Which equation can be used to find d, the number of days it will take before both bloggers have the same number of followers?
21 days it will take before both bloggers have the same number of followers
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given a blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments.
y=460-6d
Where d represents the number of days
Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
y=128+10d
We need to find equation to find the number of days it will take before both bloggers have the same number of followers
460-6d=128+10d
Add 6d on both sides
460=128+16d
Subtract 128 on both sides
460-128=16d
332=16d
d=20.75=21
Hence, 21 days it will take before both bloggers have the same number of followers
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Daniel can spend no more than 40 dollars at the fair. If admission into the fair is 10 dollars and the rides cost 1.50 each write and Wolfe an inequality that represents the greatest number of rides Daniel can go on?
The inequality that represents the greatest number of rides that Daniel can go is 1.50x + 10 ≤ 40
How to solve for the inequalityFrom the question we would have the inequality that would be written as
1.50x + 10 ≤ 40
admission is 10 dollars
cost of rides is 1.50 dollars
So, the equation would be -
1.50x + 10 ≤ 40
we are to solve for the value of x. Such that we would have
1.5x ≤ 40 - 10
1.5x ≤ 30
divide through by 1.5
x = 30 / 1.5
x = 20
Proof
Hence we would have
1.5 * 20 = 30 + 10 = 40
Read more on inequalities here: https://brainly.com/question/24372553
#SPJ1
use words to write 114.674
Answer: one hundred + fourteen point six hundred + seventy four
Step-by-step explanation:
Answer:
One hundred and fourteen point six seven four
When solving a system of equations, which of the following is a possible outcome? select all that apply. explain why you chose this answer! please help I will mark you brainliest.
Answer: When solving a system of equations, the following are possible outcomes:
Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Option A,B,C are possible outcomes.
A: Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
B: Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
C: Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Step-by-step explanation:
How do you find out if a number is a multiple of 8?
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8. So we can check the last three digits of a number to know whether they are a multiple of 8.
A multiple of 8 is a number that can be evenly divided by 8 without a remainder. To determine if a number is a multiple of 8, you can divide it by 8 and check if the quotient is an integer (a whole number with no remainder).
For example, to check if the number 96 is a multiple of 8, you can divide 96 by 8 and the quotient is 12, which is an integer, so 96 is a multiple of 8.
Another way to check if a number is a multiple of 8 is to check if the last three digits of the number are 000 or divisible by 8. This is because 8 is a power of 2 (2^3=8), and any number that is a multiple of 8 will be divisible by 2^3, which means it must have 3 trailing zeroes.
A more general method to check if a number is a multiple of any number is by using the modulo operator, which returns the remainder of a division. If x is a multiple of y, then x mod y = 0. Therefore, you can use x % 8 == 0 to check if x is a multiple of 8.
To know more on divisibility rule
https://brainly.com/question/28811818
#SPJ4
NEED HELP ASAP!!!!!!!
Select all the ordered pairs that are solutions to 3x - y = 1.
A. (-2,-7)
B. (-1,-4)
C. (0, 1)
D. (3,8)
E. (4,2)
Answer:
A, B, and D
Step-by-step explanation:
Substitute all the coordinates into the equation. (x, y)
3(-2) - (-7) = 1
-6 - (-7) = 1
1 = 1
3(-1) - (-4) =1
-3 - (-4) = 1
1 = 1
3(0) - (1) = 1
0 - (1) = 1
-1 does not equal 1
3(3) - (8) = 1
9 - (8) = 1
1 = 1
Which phrase represents this expression? (30 - 10) × 5
A. 5 times the difference of 30 and 10
B. 5 times the difference of 10 and 30
C.the difference of 30 and the product of 5 times 10
D.the difference of the product of 5 times 10 and 30
Answer:
Step-by-step explanation:
A - Since there are parenthesis on 30 and 10, you would want to find the difference between 30 and 10 first, and then multiply it by 5, hence getting you 5 times the difference of 30 and 10.
An equilateral triangle and an isosceles triangle share a common side. What is the measure of∠ABC?
The unknown angle in the triangle is as follows:
∠ABC = 112 degrees.How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
An equilateral triangle is a triangle that has all it sides and angles equal to each other. Each angle of an equilateral triangle is 60 degrees.
An Isosceles triangle is a triangle that has two of it sides and angles equal to each other. The base angles of an isosceles triangle are equal and the two legs are equal.
Therefore, let's use these principle to find the ∠ABC.
∠DBC = 60 degrees
∠ABD = 180 - 64 - 64 = 180 - 128 = 52 degrees
Hence,
∠ABC = 52 + 60 = 112 degrees.
learn more on triangles here: https://brainly.com/question/30246787
#SPJ1
Ellen Andrzejewski purchased the car in the ad for $7775. She made a down payment of $775.00. She financed the remainder at $331.16 per month for 24 months. What is the APR?
474 is the Annual percentage rate (APR).
What is APR in plain English?
If you have a balance on your credit card, you will pay an annual percentage rate (APR) of interest. The cost of borrowing money is what you pay in interest on a credit card. The interest rates on credit cards are often expressed as an annual rate. The yearly percentage rate is used to describe this (APR).
Certain credit cards feature variable APRs, which means that your rate may increase or decrease over time.
$331.16 * 24 + 775 - 7775 = 947.84
She over paid $ 947.84
24 months equals two years.
947.84/2 = 473.92 ≈ 474
Learn more about Annual percentage rate (APR)
brainly.com/question/12571149
#SPJ1
Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly. How much would Katherine need to invest, to the nearest ten dollars, for the value of the account to reach $960 in 16 years?
Katherine need to invest $432.4 for the value of the account to reach $960 in 16 years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly.
We know that;
⇒ [tex]A = P e^r^t\\[/tex]
Let the invest amount = x
Here, The amount = $960
And, The time = 16 years
And, Rate = 5.8% = 0.058
So, We can formulate;
⇒ [tex]A = P e^r^t\\[/tex]
⇒ [tex]960 = P * e^{0.058 * 16} \\[/tex]
⇒ 960 = P × 2.22
⇒ P = 960 / 2.22
⇒ P = $432.43
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Graph work
Y=Mx+C
NEED ASAP
WILL GIVE BRAINILY TO FIRST CORRECT ANSWER
Answer: y = 6x + 20, or E = 6t + 20
Step-by-step explanation:
Taking two points on the graph, (10, 80) and (30, 200), you can find the slope ("E") with the equation (y2-y1)/(x2-x1), which when plugged into the formula would be (200-80)/(30-10) = 120/20 = 6. To get your "t", you would plug this back into the formula y=mx+b along with any point on the graph, which would be:
80 = 6(10) + b
80 = 60 + b
b = 20
So the final equation should be y = 6x + 20
Kayden has a collection of 120 coins. How many coins represent 5% of his collection?
Since , solution of percentage problem is Kayden has a collection of 120 coins, the number of coins that represent the 5% of his collection is 6.
What is a percentage?A percentage is a way to express a number as a fraction of 100.To calculate percentage increase, subtract the original value from the new value and divide by the original value. To calculate percentage decrease, subtract the new value from the original value and divide by the original value.
Here,
As given by the question , the total number ko coins Kayden has in his collection is , 120 coins.
To know how many of his coins represent 5%, we can calculate ,
5% of 120 coins
= 5/100 * 12
= 6 coins
To learn more about percentage calculations visit:
brainly.com/question/29541337
#SPJ1
hellppppp meeee pleasseee
Answer: -1/4
Step-by-step explanation:
Answer: the answer to your question I believe is d= -1/4 = -0.25