Main answer: Transformations of basic functions depend on the changes made to their variables.
Supporting answer :Functions can be transformed in different ways. The variable a modifies the vertical stretch or compression of a function. A negative value of a produces a reflection over the x-axis. The variable b is used to modify the horizontal stretch or compression of the function. A negative value of b produces a reflection over the y-axis. The variable h translates the graph to the left (h > 0) or to the right (h < 0). Lastly, the variable k translates the graph up (k > 0) or down (k < 0).
Know more about Functions here:
https://brainly.com/question/26896273
#SPJ11
Eliana puts $20.50 in her savings account every week for 25 weeks leading up to Christmas. How much money does she have to spend on Christmas presents?
Answer: $512.50
Step-by-step explanation:
Eliana saved for 25 weeks and put $20.50 in her savings account every week. We will use multiplication to help us solve.
$20.50 * 25 weeks = $512.50
Ans$w3r:
The answer is $512.50
Step By Step Explanation:
25 weeks x $20.50 = $512.50
what is standard form of quadratic equation
Answer:
y = ax
[tex]y = {ax}^{2} + bx + c[/tex]
Let’s begin with a 30°-60°-90° triangle. A 30°-60°-90° triangle with a hypotenuse of 2 units is shown.
If another right triangle contains a 30° or a 60° angle but is a different size, what can you say about the side lengths of that triangle in terms of the given triangle? Explain your answer.
The side lengths of the new right triangle can be determined by the ratio of the given triangle.
What is triangle?A triangle is a three-sided polygon with three straight sides that are connected at three corners. It is one of the most basic shapes in geometry and is found in many areas of mathematics. Triangles can be classified according to their angles, sides, and size. They can be equilateral, isosceles, or scalene, depending on the size of their angles and sides. Triangles are used in a variety of fields, including architecture, engineering, construction, art, and design.
The side opposite the 30° angle will always be half the length of the hypotenuse, while the side opposite the 60° angle will always be equal to the square root of three times the length of the side opposite the 30° angle. This means that if the hypotenuse of the given triangle is 2, then the side opposite the 30° angle will be 1 and the side opposite the 60° angle will be √3.
Therefore, for any other right triangle containing a 30° or a 60° angle, the side length can be found by multiplying the side length of the given triangle by the same ratio. For example, if the hypotenuse of the new triangle is 6, then the side opposite the 30° angle will be 3 and the side opposite the 60° angle will be 3√3.
In conclusion, for any right triangle containing a 30° or a 60° angle, the side lengths can be determined by multiplying the side lengths of the given triangle by the same ratio.
To know more about triangle click-
https://brainly.com/question/309896
#SPJ1
A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the parabola?
D: (–∞, ∞); R: [7, ∞)
D: (–∞, ∞); R: (–∞, 7]
D: (–∞, 7]; R: (–∞, ∞)
D: [7, ∞); R: (–∞, ∞)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
The polynomial x² - 6x + 4y - 19 = 0 has domain and range along D: (–∞, ∞); R: (–∞, 7], the foci is at (3, 6), it's directrix and axis of symmetry are y = 8 and x = 3 respectively
What is a PolynomialA polynomial is an equation made up of constants, such as integers and algebraic operations, and variables (sometimes referred to as coefficients) (such as addition, subtraction, multiplication, and division). The quantity of terms it contains determines what it is. Quadratic equations, cubic equations, and quartic equations are typical examples of polynomials.
In the given problem, the polynomial is
x² - 6x + 4y - 19 = 0
4y = -x² + 6x + 19
The domain of this function is;
domain = (-∞, ∞)
The range of the function is all possible values along the y - axis
range = (-∞, 7]
The focus is along (3, 6)
The directrix of the polynomial is y = 8
The axis of symmetry is x = 3
Learn more on polynomial here;
https://brainly.com/question/26497045
#SPJ1
which function below has a great rate of change
None of the functions listed have a great rate of change.
What is rate of change?Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.
Function (a) is a linear equation, and its rate of change is constant. Function (b) is a linear equation, and its rate of change is also constant. Function (c) is a set of coordinates, so it does not have a rate of change.
To know more about rate of change click-
https://brainly.com/question/25184007
#SPJ1
Determine the domain of the graph
You need to look at the graph and identify where the x-axis is located.
In this graph Domain is {-2,2,4,6}
How to determine the domain of a graph?To determine the domain of a graph, you need to look at the graph and identify where the x-axis is located.
The domain of a graph is the set of all possible x-values for which the graph is defined.
In other words, it is the set of all x-values that the graph will plot.
For example, if the x-axis of the graph is between 0 and 10, then the domain of the graph is the set of all numbers between 0 and 10, including 0 and 10.
The domain of a sine wave graph is all real numbers. This is because the sine wave graph is periodic and repeats itself over and over again.
In this graph domain is {-2,2,4,6}
To learn more about domain of a graph, visit
brainly.com/question/29183673
#SPJ1
A recipe uses 4 cups of milk to make 24 servings. If the same amount of milk is used for each serving, how many servings can be made from two gallons?.
The servings can be made from two gallons is 192 serving
From the question, we know that 4 cups of milk equals to 24 servings.
4 cups = 24 serving
To solve total serving which can be made from two gallons of milk, we have to convert unit from gallon into cup, so it can be multiplied with the amount of serving
1 gallon equals to 4 quarts .....(1)
1 quart equals to 2 pints ..........(2)
From info no. 1 and 2, we can know that
1 gallon = 4 x 2 = 8 pints ..........(3)
Next, 1 pint equals to 2 cups ...........(4)
Since 1 gallon equals to 8 pints from information no. 3, we combine information no. 3 and information no. 4 to convert gallon to cup.
1 gallon = 8 x 2
= 16 cups ....................(5)
For 2 gallon, we just simply multiply info no 5
2 gallon = 16 x 2 cups
= 32 cups .................(6)
In the case of 4 cups can make 24 serving, Total number of serving can be calculated with info no. 6
Number of serving = 32 / 4 x 24 = 8 x 24 = 192 serving
Learn more about gallon at
https://brainly.com/question/19638640
#SPJ4
Solve the following...
[tex]\sf 2+x =-9[/tex]
Answer:
x is equal to -11Step-by-step explanation:
Since adding a negative to a positive is inverse subtracting, use this as an advantage and act as if you're subtracting to get the result, or output value, -9.
Hope this helps! :)
Answer:
[tex] \sf \: x = - 11[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ 2 + x = -9
Then the value of x will be,
→ 2 + x = -9
→ x + 2 = -9
→ x = -9 - 2
→ [ x = -11 ]
Hence, the value of x is -11.
Is 0 and 3 a function?
Answer:
Yes it is!
Step-by-step explanation:
Hope it helps!
Answer: If I'm correct it's 3
Step-by-step explanation:
0 + 3 = 3
I need the sender to 2x4 x x3
Answer: two times four times three ( or if you meant 3x) then three x
Step-by-step explanation:
A pet aardvark that regularly sells for $125.70 is on sale for 30% off. Find the sale price of the aardvark someone please tell me i only got 10 mins for this
Answer: $87.99
Step-by-step explanation: ($125.70) x (1 - 0.30)
= $87.99
Answer: $87.99
Step-by-step explanation:
Use Is/Of=%/100
Step 1: Plug in Points
Aardvark=$125.70 is on sale for 30% off
is/125.70=30/100 ---> 125.70(30)/100=$37.71
Step 2: Subtract Discount to Original Price
125.70-37.71=$87.99
5x^3 + 8x^2 +2x^1 + 7 if x = 10
Answer:
5,827
Step-by-step explanation:
substitute x = 10 into the expression
5(10)³ + 8(10)² + 2(10) + 7
= 5(1000) + 8(100) + 20 + 7
= 5000 + 800 + 27
= 5,827
PLEASE HELP 100 POINTS
A line has a slope of 5/3 and passes through the point (4,6). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{5}{3}[/tex] , then
y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation
to find c substitute (4, 6 ) into the partial equation
6 = [tex]\frac{5}{3}[/tex] (4 ) + c = [tex]\frac{20}{3}[/tex] + c ( subtract [tex]\frac{20}{3}[/tex] from both sides )
[tex]\frac{18}{3}[/tex] - [tex]\frac{20}{3}[/tex] = c , so
c = - [tex]\frac{2}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← equation of line
What is midpoint formula Class 9?
In class 9, the midpoint formula is a mathematical formula used to find the midpoint of a line segment given the coordinates of its two endpoints. The midpoint formula is:
(x, y) = ( (x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint.
For example, if the coordinates of the two endpoints of a line segment are (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x, y) = ( (3 + 7) / 2, (4 + 10) / 2)
(x, y) = (5, 7)
So the midpoint of the line segment with endpoints (3, 4) and (7, 10) is (5, 7)
The midpoint formula is used in class 9 to find the midpoint of a line segment in coordinate geometry. It's a simple way to find the point which is exactly in the middle of two given points. It can be used to find the center of a circle if we know the coordinates of two points on the circumference.
Read more about the Midpoint formula:
brainly.com/question/28443113
#SPJ4
π
A sector with a central angle measure of
(in radians) has a radius of 12 cm.
6
||
π
6
What is the area of the sector?
r = 12 cm
Therefore , the solution to the given problem of surface area is the sector's area is 12 square centimeters.
What is surface area ?Surface is a unit used to describe how much overall space a object's surface occupies. A three-dimensional shape's surface area is equal to the sum of its surroundings. The overall surface region of a tri shape is referred to as surface area. The surface area of a cube with six square faces can be calculated by adding up each face's specific area. As an alternative, you can identify the box's measurements using the formula below: Surface (SA) is equal to two times two times two. The total amount of space that a three-dimensional shape takes up is used to determine its surface area.
Here,
The parameters in this case are:
Radius, r = 12 Angle, x = /6
The sector's geographic area is
A = (1/2) × r^2x
We thus have:
A = (1/2) × 12^2 * π/6
Evaluate
A = 12π
Therefore , the solution to the given problem of surface area is the sector's area is 12 square centimeters.
To know more about surface area visit:
https://brainly.com/question/2835293
#SPJ1
Consequently, the sector's area is 12 square centimeters in which the parameters are Radius, r = 12 Angle, x =π /6 .
what is circle ?A circle is created when every place in the line that is a specific distance apart from another point does so (center). As a result, it is a curve made up of points that are spaced apart from one another in the plane. It is rotationally symmetric the about center at all angles. Every pair of endpoints in the plane that make up a circle are uniformly distributed out from the "center" and form a closed, two-dimensional object. A specular symmetries line is produced by a line that passes through the circle. It is rotationally equal about the center at all angles.
given
The parameters are as follows:
Radius, r = 12 Angle, x =π /6
The sector's geographic area is
A = (1/2) × r^2x
We thus have:
A = (1/2) × 12^2 * π/6
Evaluate
A = 12π
Consequently, the sector's area is 12 square centimeters in which the parameters are Radius, r = 12 Angle, x =π /6 .
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
Evaluate (-6)^8/(-6)^5.
Answer:
[tex] \sf \: {( - 6)}^{3} = - 216[/tex]
Step-by-step explanation:
Given problem,
→ (-6)⁸/(-6)⁵
Let's evaluate the problem,
→ (-6)⁸/(-6)⁵
→ 1679616/-7776
→ (1679616) ÷ (-7776)
→ -216
→ (-6)³
Hence, the answer is (-6)³.
Which of the following tables represent a proportional relationship?
Answer: The answers are A and B because when you divide all the numbers you get 6. It is not C and D because when you get different quotients.
Step-by-step explanation:
A. 6/1=6
12/2=6
18/3=6
24/6=6
36/6=6
———————————————————————————————————————
B.14/-4=-3.5
7/-2=-3.5
-14/4=-3.5
-21/6=-3.5
According to the Polygon Interior Angles Sum Theorem, the sum of the interior angle measures of an n-sided convex polygon is (n−2)·180°. Write an equation setting this expression equal to the given angle measure. Then solve for n.
The equation will be represented as angle = (n - 2) × 180.
The value of n is 2.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since the sum of the interior angle measures of an n-sided convex polygon is (n−2)·180°.
An equation setting this expression equal to the given angle measure will be:
angle = (n - 2) × 180
Angle = 180n - 360
The value of n will be:
180n - 360 = 0
180n = 360
Divide
n = 360/180
n = 2.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
A.
In which graph is y a direct variation of .x?
ABCD
Previous
B.
C.
D.
The option D is correct. The line is going through the origin.
What is graph?A graph is a mathematical structure used to model relationships between objects. It is composed of a set of vertices (also called nodes) and a set of edges, which connect the vertices. The vertices represent the objects and the edges represent the relationships between them. Graphs can be used to model a wide variety of real-world systems, such as networks of roads, social networks, and biological networks. There are many different types of graphs, including undirected graphs, directed graphs, weighted graphs, and bipartite graphs. Graphs are used in a variety of fields such as computer science, mathematics, engineering and operations research. They are used for solving complex problems such as routing, scheduling, clustering and many more. Graph algorithms are also used in machine learning and data mining.To learn more about graph refer :
brainly.com/question/19040584
#SPJ1
Question 7 of 25
f(x)=√x-4. Find the inverse of f(x) and its domain.
O A. f¹(x) = x² + 4; x≥0
OB. f¹(x) = (x+4)²; x≥-4
O c. f¹(x) = x² + 4; x ≥-4
O D. f¹(x) = (x+4)²; x≥0
The inverse of the function f(x) and its domain include the following: D. f⁻¹(x) = (x + 4)²; x ≥ 0.
What is an inverse function?In Mathematics, an inverse function simply refers to any type of function that is typically generated by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = √x - 4
y = √x - 4
x = √y - 4
√y = x + 4
Taking the square of both sides of this inverse function, we have:
f⁻¹(x) = (x + 4)²
For the domain of this function, we have:
f(x) = √x - 4
When x= 0, we have:
f(0) = √0 - 4
f(0) = 0.
Read more on inverse function here: brainly.com/question/23626757
#SPJ1
10) Find the value of the term in the arithmetic sequence. (an = a₁ + (n − 1)d)
-
16, 7, -2, -11, -20,... (10th term)
a10= - 74
a10 = -56
a10 = -65
a10= - 83
The value of the term in the arithmetic sequence is -65. Option C
How to determine the term of the arithmetic sequenceThe general formula for the nth term of an arithmetic sequence is expressed as;
an = a₁ + (n − 1)d
Given the sequence;
16, 7, -2, -11, -20,...
The common difference is determined as = second term - first term
= 7 - 16
= -9
The first term, a = 16The common difference, d = -9Now, substitute the values, we get;
a10 = 16 + (10-1)-9
expand the bracket, we get;
a10 = -6 + 9(-9)
multiply the values, we have;
a10 = 16 -81
Subtract the terms
a10 = -65
Thus, the value is -65
Learn more about arithmetic sequence here:
https://brainly.com/question/6561461
#SPJ1
Nine times the sum of a number and 8 is equal to 4
The answer is 9x+8=4
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: Nine times the sum of a number and 8 is equal to 4
let the number be x then we have as per question
9x+8=4
x=-4/9
Hence, The required equation is 9x+8=4
Learn more about linear equations here:
https://brainly.com/question/545403
#SPJ1
AI's Auto Shop charges $149 for parts and $53 per hour of labor for a repair job. Edna's Engine Repair charges a flat fee of $280 for the same job.
a. Write a system of equations to represent the situation.
b. Graph the system of equations.
c. Which shop is cheaper if the job takes 2 hours? 3 hours?
Answer:
AI's Auto Shop: y = 149 + 53x
Edna's Engine Repair: y = 280
Explanation:
The system of equations represent the costs of the two different repair shops. The first equation, y = 149 + 53x, represents the total cost of AI's Auto Shop. The variable x represents the number of hours of labor required, and the variable y represents the total cost. The second equation, y = 280, represents the flat fee charged by Edna's Engine Repair.
The graph of the system of equations would show two lines, one for each equation. The line for AI's Auto Shop would have a slope of 53 and a y-intercept of 149, representing the cost of parts and hourly labor. The line for Edna's Engine Repair would be a horizontal line at y = 280, representing the flat fee charged.
When the job takes 2 hours, AI's Auto Shop would charge $149 + $53*2 = $255 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be cheaper.
For a job that takes 3 hours, AI's Auto Shop would charge $149 + $53*3 = $308 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be more expensive.
A man deposited ghc 1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
Calculate the
a.simple interest for the 4 years
b.amount at the end of the 4 types
a. The simple interest for 4 years would be $960.
b. The amount at the end of the 4 years would be $2160.$
A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
a. For calculating simple interest for the 4 years
We have been given data as:
Principal (P) = $1200
Rate of Interest (R) = 20%
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
The simple interest for 4 years would be:
⇒ 1200 x 20% x 4 = 960
b. For calculating the amount at the end of the 4 years
The amount at the end of the 4 years would be:
1200 + 960 = 2160
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ1
I Bet you can't answer
"5(2x+4)-3(-6-x)"
answer this with full formula
also expand simplify them
Answer:
13x+38
Step-by-step explanation:
help plssssssssssssssssssssss
Answer:
28
Step-by-step explanation:
a² + b² = c² where c is the hypotenuse (8)
a² + 6² = 8²
a² + 36 = 64
a² = 64 - 36
a² = 28
take square root of both sides
a = square root 28
Travis had a box of 61 french fries. He gave 14 french fries to each of f friends. Which expressions shows how many french fries he had left after giving some to his friends? A. 61 + f × 14 B. 61 - f × 14 C. (61 + f) × 14 D. (61 - f) × 14
Answer: B
Step-by-step explanation: 61 - (f x 14) would give us the number of french fries he had left over
Which graph shows a linear equation?
The correct option is A.
The linear equation y = 2x + 1 is shown in Graph A.
The equation of a straight line's shape with slope and y-intercept is as follows:
y = mx + b
where
y is equal to a point's y-coordinate on a line.
m is the line's slope.
The point on the line whose y-coordinate is y has the x-coordinate of x.
B is the line's y-intercept, or b.
As opposed to y = mx + b, y = 2x + 1
As we can see, the
m = 2 slope
b = 1 as the y-intercept
The graph that crosses the y-axis at the point where y = 1 is only option A, as shown by the intercept value.
For such more question on Linear equation.
https://brainly.com/question/26310043
#SPJ4
Note the correct question would be as bellow,
Which graph shows the linear equation y = 2x + 1
Why is a line of longitude called a meridian Class 6?
A line of longitude is called a meridian because it connects the North and South poles and forms a circle around the Earth, like the sun's meridian path during the day.
A line of longitude is an imaginary line that circles the Earth and runs in a north-south direction. It is measured in degrees and divides the Earth into two equal halves, the Eastern Hemisphere and the Western Hemisphere. This line is called a meridian because it is derived from the Latin word meridies which means mid-day or noon. The sun's path across the sky during the day follows a meridian from the North Pole to the South Pole, and this is what inspired the term "meridian" to describe the line of longitude.
learn more about longitude here
https://brainly.com/question/4749704
#SPJ4
What is this for math 1
Yes, it showed you the fomula
Answer: 64x^6y^3