What are the transformations of y= -4(x-5)^3+6 from the parent function y=x^3.
A parent function is the most fundamental function that still satisfies the criteria for a specific type of function. When considering the linear functions that make up a family of functions, for instance, the parent function would be y = x. The simplest function is this linear one.
What is linear function?An uninterrupted line represents the graph of a linear function. The following form represents a linear function. a + bx = y = f (x) (x).Two variables—one independent and one dependent—make up a linear function. Both X and Y are considered independent and dependent variables.The words "linear function" in mathematics are used to describe two different but related ideas: A polynomial function of degree 0 or 1 with a graph that is a straight line is known as a linear function in calculus and fields related to it.A straight line can be visualised on the coordinate plane using a linear function. A linear function is demonstrated by the equation y = 3x - 2 because it depicts a straight line in the coordinate plane.To learn more about linear function refer to:
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emma has 0.5 lb of sugar. How much water would she add to make the following concenstractions? Tell Emma how much syrup she would have each case. 50% syrup
To make the concentration of 50% syrup,
she needs to add 0.5 lb of sugar.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."
Given:
Emma has half a pound of sugar.
To make the concentration of 50% syrup:
Let n be the required amount.
In decimals, 50% is 0.5.
Applying the percentage formula;
we get,
[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]
Applying cross multiplication,
we get,
[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]
0.5 = 0.5(n + 0.5)
1 = n + 0.5
n = 1 - 0.5
n = 0.5 lb.
Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.
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How to explain how you add fractions.
Example: Add 1/4 + 2/4
Solution: Let us add these fractions using the following steps.
Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)
Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4
Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4
help me with my geometric homework goving 25 points plsss
Using the proportions of the side lengths of the pair of similar triangles, we have:
1. x = 35
2. x = 20; y = 23.3
3. x = 11
4. x = 9
5. x = 10
What are the Sides of Similar Triangles?Triangles that are similar to each other, will have side lengths that are proportional to each other.
Therefore, using proportions, we would have:
1. x/14 = 40/16
Cross multiply:
16x = 40 * 14
16x = 560
x = 560/16
x = 35
2. x/12 = 15/9
9x = 12 * 15
9x = 180
x = 20
y/14 = 15/9
9y = 210
y = 23.3
3. (x + 5)/24 = 36/54
Cross multiply:
54(x + 5) = 36 * 24
54x + 270 = 864
54x = 864 - 270
54x = 594
x = 11
4. 20/28 = 15/(2x + 3)
Cross multiply:
20(2x + 3) = 28 * 15
40x + 60 = 420
40x = 420 - 60
40x = 360
x = 9
5. 24/28 = x + 8 / 3x - 9
Cross multiply:
24(3x - 9) = 28(x + 8)
72x - 216 = 28x + 224
72x - 28x = 216 + 224
44x = 440
x = 10
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All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
An explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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21. A rectangle has an area of 24 square inches. Let W be the
width (in inches), L be the length (in inches), and A be the
area (in square inches).
a. Sketch three possible rectangles of area 24 square inches.
b. Which of the symbols W. L. and A are variables? Explain.
Which of the symbols W, L. and A are constants? Explain.
Three possible rectangles of area 24 square inches are:
A rectangle with width 6 inches and length 4 inches
A rectangle with width 8 inches and length 3 inches
A rectangle with width 4 inches and length 6 inches
How to explain the areaIt should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.
In this case, W and L are variables and A is a constant.
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4. [0/2 Points]. DETAILS
(b) g(g(3))
Use f(x) = 5x - 4 and g(x) = 2x2 to evaluate the expression.
(a) f(f(2))
how do i solve this?
Answer:
324
Step-by-step explanation:
To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.
To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324
What song form is the song. "Shameless" by Billy Joel written in?
A. Verse-chorus-bridge
B. AABA
C. ABACA
D. Verse-chorus
Solve the right triangle ABC, where C = 90°. Give angles in degrees and minutes. a = 18.7 cm, c = 46.4 cm
b= ? cm (Round to nearest tenth as needed) A= ?°?'(Round to nearest minute as needed) B=?°?'(Round to nearest minute as needed)
Answer:
To solve a right triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the two smaller sides equals the square of the largest side. In this triangle, we have:
a^2 + b^2 = c^2
Plugging in the values we have:
18.7^2 + b^2 = 46.4^2
Solving for b, we have:
b = √(46.4^2 - 18.7^2)
b = √(2159.36 - 349.69)
b = √1809.67
b = 42.6 cm (rounded to the nearest tenth)
Next, we can use the tangent function to find angles A and B:
tan(A) = a/b = 18.7/42.6 = 0.439
A = tan^-1(0.439) = 24° 26' (rounded to the nearest minute)
And, using the Pythagorean theorem:
c^2 = a^2 + b^2 = 18.7^2 + 42.6^2 = 346.69 + 1809.67
B = 90° - A = 90° - 24° 26' = 65° 34' (rounded to the nearest minute)
So the solution is:
a = 18.7 cm
b = 42.6 cm
c = 46.4 cm
A = 24° 26'
B = 65° 34'
C = 90°
Step-by-step explanation:
On a road trip to central Florida, you average 35 miles per hour while driving within city
borders and 60 miles per hour while driving on the highway (not in the city.) The trip was 995 miles long. You were in city borders for 4 hours longer than on the highway. Let C be the time, in hours, you spent driving in the city. Let H be the time, in hours, you spent driving on the highway. Find the sum C + H
The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
What is distance?Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.
Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.
Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation
Distance = Speed × Time
to solve for the time spent in both city and highway.
For time spent in city:
35 mph × C = 995 miles
C = 995 miles/35 mph = 28.43 hours
For time spent in highway:
60 mph × H = 995 miles
H = 995 miles/60 mph = 16.58 hours
Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
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Write equivalent expressions.
-4y+8
Select all that apply.
A: -4(y-2)
B: -4(-2+4y)
C: (2-y)4
D: 4(-y+8)
A and C are equivalent expressions for a given expression.
What does an expression mean?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is -4y+8.
Given options are:
A. -4(y-2)
By simplifying it we will get -4(y-2) = -4y+8
So, both are equivalent.
B. -4(-2+4y)
By simplifying it we will get -4(-2+4y) = 8-16y
So, both are not equivalent.
C. (2-y)4
By simplifying it we will get (2-y)4 = 8-4y
So, both are equivalent.
D. 4(-y+8)
By simplifying it we will get 4(y-8) = 4y-32.
So, both are not equivalent.
A, and C are equivalent expressions for a given expression.
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These two triangles are congruent.
b
B
6 cm
1049
12 cm
9 cm
A
47°
'R
29°
29°
12 cm
с
P
a)
What is the size of angle Q?
Since the triangles are congruent. Then The size of angle Q is 47°
Congruent Angle:
Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.
Here is a list of rules for the congruence of angles.
1. The only condition for two angles to be congruent is if the measurements of the angles agree.
2. The lengths and orientations of the two sides of this congruent angle are not important.
According to the Question:
It is given that :
B = 6 cm, 12 cm and 9 cm
A = 47°
R' = 29°
If the triangle is congruent, then all the three sides and angles will be same.
Therefore,
Angle Q = Angle A
Therefore, Angle Q = 47°
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Solve for x in the equation −6x+18=−6. Place the steps for solving this equations in order.
Answer:
x=4
Step-by-step explanation:
-6x = -6-18
-6x = -24
-6x/-6 = -24/-6
x =4
Find the complex number given arg(z+1) =pi/6 and arg(z-1)=(2*pi)/3
Answer:
Therefore, z = 1 + i.
Step-by-step explanation:
Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.
Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).
Using the argument values given, we have:
arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.
arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.
From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:
a = (z + 1 + z - 1)/2 = 1
b = (z + 1 - z - 1)/2 = 1
Therefore, z = 1 + i.
Solve for y
Y-18=b
Need help please.
Answer:
y = 18 + b
Step-by-step explanation:
Add 18 to both sides
y = 18 + b
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 7000 equation 1
0.1a + 0.11b = 730 equation 2
Where:
a = amount invested in the account that earns 10% interest
b = amount invested in the account that earns 11% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.1
0.1a + 0.1b = 700 equation 3
Subtract equation 3 from equation 2
0.01b = 30
Divide both sides of the equation by 0.01
b = 30 / 0.01
b = 3000
Substitute for b in equation 1:
a + 3000 = 7000
a = 7,000 - 3000
a = 4000
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BUDGET
Income
Expenses
Rent
Groceries
Utilities
Total Expenses
Net income
Instruction
Class Activity 1
January February March
$2200
$1200
$125
$69.51
$2200
$1225
$110.1
$82.71
$2200
$1225
$79.16
$73.04
1) Bold and center align the column headings and "merge and center" the title.
2) Format all numbers with "$" to 2 decimal places.
3) Calculate totals for each type of expense and for each month. Also, calculate a grand total for all 3 months of
expenses.
4) Calculate net income for each month (total income minus total expenses).
Class Activity (Contd.)
5) Add another column to calculate the percentage of total expenses for each category by
dividing each category's total by the grand total.
6) Create two different unique charts. Each chart must represent different information on the
table.
7) Each chart must be on a different Excel page and each page tab must be labelled
according to the chart.
Here are the steps to complete the budget, as described in the instructions:
Bold and center align the column headings:Highlight the column headings (Income, Expenses, Rent, Groceries, Utilities, Total Expenses, Net Income)Right-click and select "Format Cells"In the "Font" tab, select "Bold" and "Center" alignClick "OK"How to merge and center the title:Type the title "BUDGET" in cell A1Highlight cells A1 to G1Right-click and select "Merge and Center"The title will now be centered across the entire rowFormat all numbers with "$" to 2 decimal places:Highlight the cells containing numbersRight-click and select "Format Cells"In the "Number" tab, select "Currency" and set decimal places to 2Click "OK"Calculate totals for each type of expense and for each month:
To calculate the total expenses for each month, add up the amounts in the Rent, Groceries, and Utilities columnsFor example, in January the total expenses would be $125 + $69.51 + $82.71 = $277.22To calculate the grand total expenses for all 3 months, add up the total expenses for each monthFor example, the grand total expenses would be $277.22 + $110.10 + $73.04 = $460.36Calculate net income for each month:
To calculate the net income for each month, subtract the total expenses from the total incomeFor example, in January the net income would be $2200 - $277.22 = $1922.78Add another column to calculate the percentage of total expenses for each category:
Create a new column to the right of the Utilities columnLabel this new column "Percentage of Total Expenses"In the first cell of this column, divide the value in the Rent column by the grand total expenses and multiply by 100For example, in January the calculation would be =($125/$460.36)*100 = 27.11%Copy this formula down to the last row of dataCreate two different unique charts:
Go to the "Insert" tab and select the type of chart you want to create (e.g. bar chart, pie chart, line chart, etc.)Highlight the data you want to include in the chartClick the "Insert" button to create the chartRepeat the process to create a second chart on a different Excel pageLabel each page tab according to the chart:
Right-click on the first chart's page tab and select "Rename"Type in a descriptive label for the chart (e.g. "Expense Breakdown Chart")Repeat the process for the second chart page tab.Read more about budgets here:
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AIR 2021) Four functions are shown.
Which function is linear?
The option B is a linear function. The solution has been obtained by using the properties of a linear function.
What is a linear function?
A function is referred to as linear if it can be represented on a graph as a straight line. Typically, the highest degree of this polynomial function is 1 or 0. Despite the fact that linear functions can be expressed in both calculus and linear algebra.
We are given four functions.
It is clearly visible that option A is not a linear function because the degree of the function is 2.
Option B is a linear function because we obtain a straight line on the graph.
Also, option C is not a linear function because the degree of the function is greater than 1.
Similarly, option D is also not a linear function because it's graph is not a straight line.
Hence, option B is a linear function.
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What is the product of 4 and 1 3/8?
Answer:5.5
Step-by-step explanation:
Please help!
Carolina has two bank accounts, a checking account and a savings account. She has a total of $180 in both accounts. She has $30 more in her savings account than she has in her checking account. How much does Carolina have in her savings account? How much does she have in her checking account?
Answer:
$105
Step-by-step explanation:
Let x be the amount of money Carolina has in her checking account. Then, her savings account has x + $30. The total amount of money in both accounts is $180, so we can write the equation:
x + (x + $30) = $180
Expanding the left-hand side:
2x + $30 = $180
Subtracting $30 from both sides:
2x = $150
Dividing both sides by 2:
x = $75
Therefore, Carolina has $75 in her checking account and $75 + $30 = $105 in her savings account.
pls help!!
Which of the following is the inverse function of the image below?
PLEASE HELP (IMAGE ATTACHED)
the answer I get is -8+35x over 5x
But what does it simplify to?
Answer:
(-8 + 35x) / 5x or -8 / 5x + 7 (same)
Step-by-step explanation:
(-32x^8 + 140x^9) / 20x^9 =
= -32x^8 / 20x^9 + 140x^9 / 20x^9 =
= -8 / 5x + 7 =
= (-8 + 7 * 5x) =
= (-8 + 35x) / 5x
P.S. you can also simplify this, but only when the value of x is knownwhat is 5x+3 Please HELP ME
Answer: I believe that the answer is 8x.
Step-by-step explanation:
My explanation is that since x equals a random value, we can still add 5 and 3 to get 8.
I hope this helps!
Help me with this question….
The number that is most likely an irrational number is given as follows:
D. 4.279458105...
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
For this problem, the option D gives the irrational number, as it is the lone non-repeating decimal. For the others, we have that:
Option A: 26 is the repeating decimal part.Option B: 3 is the repeating decimal part.Option C: due to the large number of zeros, the number is the exact decimal 2.8.More can be learned about rational and irrational numbers at brainly.com/question/5186493
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find angle AED
please help
The angle AED of arc AD of the circle is calculated to be equal to 8100/πr
How to evaluate for the angle AED of arc length AD of the circleWe shall use the formula:
arc length = (arc angle/360) × 2 × π × radius
where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.
If AD = 45 and r the radius, we evaluate the arc angle m ∠AED as follows:
(arc angle/360°) × 2 × π × r
by cross multiplication;
arc angle AED = (360 × 45)/2πr
2 can divide 360° to give;
arc angle AED = (180 × 45)/πr
arc angle AED = 8100/πr
Therefore, the angle AED of arc AD of the circle is calculated to be equal to 8100/πr
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Please helpppppp!!!!
Answer:
x(f)- this is the correct answer
Carole is paid a monthly salary of $2011.10. Her regular workweek is 35 hours.
(a) What is Carole's hourly rate of pay?
(b) What is Carole's gross pay for May if she worked 73/4 hours overtime during
the month at time-and-a-half regular pay?
Para cercar un terreno rectangular de 24 m? se emplearon 20 m de malla de alambre, (cuánto mide el largo del terreno
we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.
If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:
2L + 2W = 20
L × W = 24
From the first equation, we can solve for L in terms of W:
2L = 20 - 2W
L = 10 - W
Substituting this into the second equation, we get:
(10 - W) × W = 24
Expanding the brackets, we get: 10W - W² = 24
Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0
We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0
So the possible solutions for W are: W = 6 or W = 4
If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.
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Complete Question
To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?
Find the value of x for the following
Answer:
x = -4°
Step-by-step explanation:
We know that,
→ Sum of angles of straight line is 180°.
Now we have to,
→ Find the required value of x.
Forming the equation,
→ (54°) + (7x + 154°) = 180°
Then the value of x will be,
→ 7x + 154° + 54° = 180°
→ 7x + 208° = 180°
→ 7x = 180° - 208°
→ 7x = -28°
→ x = -28° ÷ 7
→ [ x = -4° ]
Hence, the value of x is -4°.
Answer: I think x = -4
Step-by-step explanation: I used a calculator.
Which of the following is equivalent to the radical expression below, when the
denominator has been rationalized and x > 5?
10/
√x-√x-5
OA. 2(√x + √x - 5)
B. 2(√x + √x + 5)
Oc. 2(√x - √x+5)
OD. 2(√x - √x - 5)
Answer:
option (A).
Step-by-step explanation:
The equivalent expression to the given radical expression, when the denominator has been rationalized and x > 5, is 2(√x + √x - 5), or option (A).
