Answers
The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function
[tex]h(x) = 6x + 66x^2 + 17[/tex].
What are expressions in standard form?A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].
The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.
The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.
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Related Questions
Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
Answers
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer:
You are distributing (multiplying) the three to all the terms in the parentheses.
Start:
3(x-2) = 4x + 2
Next:
3x - 6 = 4x +2
After that simplify:
-8 = x
Hope this helps!
Answer:
3x - 6 = 4x + 2 x = -8Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The property we use,
→ Distributive property.
The equation is,
→ 3(x - 2) = 4x + 2
Then the value of x will be,
→ 3(x - 2) = 4x + 2
→ 3(x) - 3(2) = 4x + 2
→ 3x - 6 = 4x + 2
→ 3x - 4x = 2 + 6
→ -x = 8
→ [ x = -8 ]
Hence, the value of x is -8.
{ 4.82/ 7 } 358.9 / 7 Quotient
Answers
Answer:
51.2
Step-by-step explanation:
By dividing :0
17. Name the polyhedron that can be constructed using the given net. Assume squares and equilateral triangles were used to form each net. a. b.
Answers
The polyhedron that can be constructed using this net is a triangular pyramid.
A triangular pyramid is a polyhedron that has four faces, with one of the faces being a square and the other three faces being equilateral triangles. The given net shows a square in the center, with three equilateral triangles attached to each of its sides. When the net is folded along the edges, the square becomes the base of the pyramid and the three equilateral triangles become the sides of the pyramid. Therefore, the polyhedron that can be constructed using this net is a triangular pyramid.
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VI. Solve for roots using the Quadratic Formula: A.
4x 2
−9x+2=0
B.
2x 2
−7x−1=0
Answers
The roots of equation A are 2 and 0.25.
The roots of equation B are 3.14 and -0.64.
To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:
x = (-b ± √(b² - 4ac)) / (2a)
Where a, b, and c are the coefficients of the equation.
For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:
x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8
This gives us two possible values for x:
x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25
Therefore, the roots of equation A are 2 and 0.25.
For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:
x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4
This gives us two possible values for x:
x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64
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Find the sum of the polynomials (ax^2+2x-5) and (-2ax^2+a) and evaluate that sum when a=7 and x=-5
Answers
Answer:
29+3374=32483 that is the solution for the question
hope this helps <3
2
A geometric sequence is shown below.
Which function describes this sequence?
5, 11, 29, 83, ...
Answers
These values match the given sequence, so the function that describes the sequence is:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
What is the meaning of the word "function"?According to one definition, a function is a relationship between a number of inputs where each input has exactly one output.
To find the function that describes the given geometric sequence, we need to find the common ratio r. We can do this by dividing any term in the sequence by the previous term:
11/5 = 2.2
29/11 = 2.63636...
83/29 = 2.86206...
We can see that the common ratio is increasing, which suggests that the sequence is not a perfect geometric sequence. However, the differences between the ratios are getting smaller, so we can approximate the sequence as a geometric sequence with a changing common ratio.
Let's use the first two terms of the sequence to find an initial approximation for the common ratio:
r ≈ 11/5 = 2.2
Then, we can write the nth term of the sequence as:
an = 5(2.2)ⁿ⁻¹
However, we noticed that the common ratio is increasing, so we need to adjust our formula to account for this. Let's try a formula where the common ratio is a linear function of n:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
Plugging in n = 1, 2, 3, and 4, we get:
a1 = 5(2.2 + 0.8182(1))⁰ = 5
a2 = 5(2.2 + 0.8182(2))¹ ≈ 11
a3 = 5(2.2 + 0.8182(3))² ≈ 29
a4 = 5(2.2 + 0.8182(4))³ ≈ 83
These values match the given sequence, so the function that describes the sequence is:
an = 5(2.2 + 0.8182n)ⁿ⁻¹
where n is the index of the term in the sequence.
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Mary wins £400.
She gives 50% to her mother.
Mary gives 20% to her sister.
She keeps the rest.
Work out how much each person receives.
Answers
Answer:
Mother: £200, Sister: £80, Mary: £120
Step-by-step explanation:
Mary has a total of £400 to start off with.
In order to calculate the amount she gives to her mother, we must multiply 400 by .5 (the decimal equivalent of 50%), which leaves us with £200 to her mother.
Do the same with her sister; multiply 400 by .2 (the decimal equivalent of 20%), which leaves us with £80.
To figure out what she is left with, £400 - 200 - 80 = £120. Mary is left with £120.
Mary will have £120 with her, her mother will have £200 and her sister will have £80.
What is percentage?Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.
Given that, Mary won £400.
She gave 50% to her mother, 20% to her sister and rest she kept with herself,
So,
The amount her mother got =
50% of £400 = 1/2 × 400 = 200
Therefore, her mother got £200.
The amount her sister got =
20% of £400 = 1/5 × 400 = 80
Therefore, her sister got £80.
The amount Mary have = 400 - (200+80) = 400 - 280 = £120
Hence Mary will have £120 with her.
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Math question 12 help
Answers
Answer:
It's neither of them. The function is neither odd nor even
what is 1+1-5/34x + 14y+7
Answers
Answer:
[tex] - \frac{5x}{34} + 14y + 9[/tex]
Step-by-step explanation:
Just making sure. If the way the equation is written is
[tex]1 + 1 - \frac{5}{34} x + 14y + 7[/tex]
then yeah, that's the answer. If it's formatted differently, send a comment so that I could give you the proper answer.
PLUMBING A plumber charges $50 to visit a house plus $40 for every hour of work. Define a variable and write an
expression to represent the total cost of hiring a plumber.
Answers
The expression to represent the total cost of hiring a plumber is y = 50 + 40x
How to determine the expression to represent the total costFrom the question, we have the following parameters that can be used in our computation:
Charges = $50 for visiting
Rate = $40 every hours
Represent the number of hour with x and the total charge with y
Using the above as a guide, we have the following:
y = Charges + Rate * x
Substitute the known values in the above equation, so, we have the following representation
y = 50 + 40x
Hence, the equation is y = 50 + 40x
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These charts show state sales tax as of 2015. Alabarna Florida Georgia Hawaii Idaho Indiana lowa Kentucky Idaho State Mississippi Hawaii Wisconsin 4% 6% 4% 4% 6% 7% 6% 6% Louisiana Maryland Michigan Mississippi 4% 6% 6% 7% New York North Dakota Oregon Pennsylvania 6% 5% 8 Students from various states are attending a marching band conference. Each uniform costs $135 before state sales tax is added. Complete the table to show the total cost of uniforms with tax, for each group of students. Number of Students 10
5
15 Rhode Island South Carolina South Dakota Vermont West Virginia Wisconsin Wyoming 7% 6% 4% Total Cost of Uniforms
Answers
Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:
State Number Total Cost
of Students (After-tax)
Idaho 10 $1,431.00
Mississippi 5 $722.25
Hawaii 15 $2,106.00
Wisconsin 8 $1,134.00.
How is the total cost for each group determined?The total cost for each group of students from the four states can be determined by multiplication.
The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.
The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.
Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.
The price before state sales tax of each uniform = $135
Relevant Taxes and Number of Students:
State Number of Students Sales Tax Rate
Idaho 10 6%
Mississippi 5 7%
Hawaii 15 4%
Wisconsin 8 5%
State Number Total Cost Total Cost
of Students (Before tax) (After-tax)
Idaho 10 $1,350 $1,431.00 ($135 x 10 x 1.06)
Mississippi 5 $675 $722.25 ($135 x 5 x 1.07)
Hawaii 15 $2,025 $2,106.00 ($135 x 15 x 1.04)
Wisconsin 8 $1,080 $1,134.00 ($135 x 8 x 1.05)
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Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 440 miles. The speed of the plane was 150 mph faster than the speed
of the car. Find the speed of the plane.
Answers
By forming and solving the equations we know that the speed of the plane was 220 mph.
What are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal.
A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.
like 3x + 5 = 15, for instance.
Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.
So, d = rt.
t = d/r
The distances are equal.
140/r = 440/(r + 150)
Cross multiply:
140(r + 150) = 440r
140r + 21,000 = 440r
300r = 21,000
r = 70
70 + 150 = 220 mph
Therefore, by forming and solving the equations we know that the speed of the plane was 220 mph.
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Colleen has a wooden board that is 12 3/4 feet long. She cuts the board into three pieces. Two of the pieces are both 4 7/12 feet long.
How long is the other piece of Colleen's board?
Answers
Answer:
Step-by-step explanation: I don’t know
The__________of an angle is the point where the sides of the angle intersect
Help please<3
Answers
A geometric sequence is shown below.
5, 11, 29, 83, ...
Which function describes this sequence?
Answers
The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.
Which function describes this sequence?Remember that the recursive formula for a geometric sequence is:
f(n) = r*f(n - 1)
Where r is the common ratio.
Here we have the terms:
5, 11, 29, 83
To get the value of r, take the quotient between consecutive terms:
r = 11/5 = 2.2
r = 29/11 = 2.63
r = 83/29 = 2.86
We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.
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A parking garage in Quincy, IL charges $6.00 for the first hour and $2.00 for each additional hour or part of an hour. What is the maximum number of hours that you can park in the garage if you wish to pay no more than $14?
Answers
The maximum number of hours that you can park in the garage if you wish to pay no more than $14 is 5 hours.
Here's how to calculate it:
Start with the first hour charge of $6.00.Subtract this from the maximum amount you want to pay ($14) to get $8 remaining.Divide this remaining amount by the cost of each additional hour ($2) to get the number of additional hours you can park. $8/$2 = 4 additional hours.Add the first hour to the additional hours to get the maximum number of hours you can park. 1 + 4 = 5 hours.Therefore, the maximum number of hours you can park in the garage if you wish to pay no more than $14 is 5 hours.
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Prove that the medial triangle of a given triangle ABC
has sides parallel to and half the length of the sides of triangle
ABC.
Answers
The medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.
To prove that the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC, we can use the following steps:
Draw triangle ABC and label its vertices as A, B, and C.
Find the midpoints of the sides of triangle ABC. Let's call these midpoints D, E, and F.
Draw the medial triangle DEF, connecting the midpoints of the sides of triangle ABC.
We need to prove that the sides of triangle DEF are parallel to the sides of triangle ABC. To do this, we can use the fact that the midpoints of the sides of a triangle divide the sides into two segments of equal length.
Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.
We can also use the fact that if two lines are parallel and the corresponding angles are equal, then the corresponding sides are also parallel.
Since AD = DB and BE = EC, we know that angle ADB = angle BEC and angle BDE = angle CEF.
Therefore, we can conclude that the sides of triangle DEF are parallel to the sides of triangle ABC.
To prove that the sides of triangle DEF are half the length of the sides of triangle ABC, we can use the fact that the midpoints of the sides of a triangle divide the sides into two segments of equal length.
Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.
Therefore, we can conclude that the sides of triangle DEF are half the length of the sides of triangle ABC.
So, the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.
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pls asap i need this
Answers
The simplest form of the given expression x will be 42.
What is polynomials?Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial.
When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
Here we assume that no of suitcases be x
So, 7/24 = x/144
24x = 1008
x = 42.
Hence the simplest form of the given expression x will be 42.
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At the beginning of spring, Shaniece planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall. The sunflower then began to grow at a rate of 0.5 inches per week. How tall would the sunflower be after 10 weeks? How tall would the sunflower be after ww weeks?
Answers
The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.
What do you mean by expression?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. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
To calculate the height of the sunflower after 10 weeks, we can use the formula:
=>height = starting height + growth rate * time elapsed
where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.
So the height after 10 weeks would be:
=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches
Therefore, the sunflower would be 30 inches tall after 10 weeks.
To calculate the height after w weeks, we can use the same formula:
=>height = 25 + 0.5 * w
So the height after w weeks would be:
=>height = 25 + 0.5 * w inches
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1. There are 220 seventh-grade students. To estimate the number of students who preferred the turkey club, write the proportion who preferred the turkey club.
Answers
The correct answer to this question is 7/220. To calculate this answer, divide the number of students who preferred the turkey club (7) by the total number of seventh-grade students (220). The fraction form of this answer is 7/220, the decimal form is 0.0318, and the percentage form is 3.18%.
What is proportion?Proportion is a mathematical concept that compares two values, which can be the same or different, using division. It is used to identify the relationship between two or more values. It can also be used to compare the parts of a whole or to compare two different wholes. Proportions can be expressed as a fraction, a decimal, or a percentage.
This answer can be used to estimate the number of students who preferred the turkey club. To do this, multiply the total number of seventh-grade students (220) by the proportion (7/220). This calculation results in 7 students. In other words, approximately 7 of the 220 seventh-grade students preferred the turkey club.
The proportion 7/220 can also be used to estimate the number of students who preferred the turkey club if the total number of seventh-grade students changes. For example, if the total number of seventh-grade students increases to 250, the estimated number of students who preferred the turkey club can be calculated by multiplying the new total (250) by the proportion (7/220). This calculation results in 8 students.
Therefore, the correct answer to the question is 7/220.
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A tabletop in the shape of a trapezoid has an area of 6,731 square centimeters. Its longer base measures 127 centimeters, and the shorter base is 85 centimeters. What is the height?
Answers
Answer:
[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]
Step-by-step explanation:
We are given that,
Length of the base = 127 centimeters
Width of the base = 85 centimeters
Area of the trapezoid shaped base = 6,731 square centimeters.
Since, we know,
[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]
So, we get,
[tex]6731=\frac{127+85}{2}\times Height[/tex]
i.e. [tex]6731=\frac{212}{2}\times Height[/tex]
i.e. [tex]6731=106\times Height[/tex]
i.e. [tex]Height=\frac{6731}{106}[/tex]
i.e. Height = 63.5 centimeters
Hence, the height of the tabletop is 63.5 centimeters.
Two families attended a baseball game the first family bought three bags of popcorn in for souvenir cups which totaled $40 that second family but eight bags of popcorn in for souvenir cups which totaled $60 how much did one bag of popcorn cost
Answers
Two families attended a baseball game bought popcorns and souvenir, the cost of each pack of popcorn is $4 and cost of each pack of souvenir is $7.
An expression that depicts the relationship between two or more variables and numbers is called an equation. The provided information can be represented as, using equations:
let x be the price of popcorn and y be the price of souvenir.
First family:
[tex]3x+4y=40[/tex](equation 1)
Second family:
[tex]8x+4y=60[/tex] (equation 2)
We have a system of 2 equations with 2 variables.
3x + 4y = 40
8x + 4y = 60
We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.
from equation 2,
[tex]8x+4y=60\\4y=60-8x[/tex]
divide both sides by 4
[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=15-2x[/tex]
now putting the value of y in equation 1
[tex]3x+4(15-2x)=40\\3x+60-8x=40\\-5x=-20\\x=4\\[/tex]and [tex]y=7[/tex]
Hence, the cost of popcorn is $4 and cost of souvenir is $7.
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You bought water bottles to sell and spent a total of $50. You sell each bottle for $2. Which graph shows how many bottles you have to sell to earn back the money spent on water?
Answers
The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.
How to find the graph ?The number of bottles that need to be sold to earn back the amount spent on water is :
= Total spent / profit per bottle
= 50 / 2
= 25 bottles
Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.
Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.
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The height of a pole is 27 feet. A snake is curled up at a distance of 20 ft from the foot of
the pole. The snake looks at the top most point of the pole. Find the angle of elevation
made by the snake and the top of the pole. Round to the nearest tenth of a degree.
The angle of elevation is _____ degrees.
Help
Answers
The angle οf elevatiοn is 63.4 degrees.
What is angle οf elevatiοn?Angle οf elevatiοn is the angle between the hοrizοntal line οf sight and an οbject abοve the οbserver. It is measured with an angle starting frοm the hοrizοntal line and increasing in the upward directiοn. It is alsο knοwn as the angle οf elevatiοn οr inclinatiοn. The angle οf elevatiοn is used in navigatiοn, astrοnοmy and trigοnοmetry.
Tο find the angle οf elevatiοn, we can use the fοrmula fοr finding angles in a triangle. This fοrmula states that the sum οf all angles in a triangle is 180 degrees. Tο sοlve fοr the angle οf elevatiοn, we need tο begin by first finding the length οf the οppοsite side οf the triangle. This is dοne by subtracting the distance οf the snake frοm the fοοt οf the pοle frοm the height οf the pοle.
Therefοre, the length οf the οppοsite side οf the triangle is 7 feet. Nοw, we can use the tangent fοrmula tο sοlve fοr the angle οf elevatiοn. This fοrmula states that the tangent οf an angle is equal tο the length οf the οppοsite side divided by the length οf the adjacent side.
Let's find the angle of elevation.
tan ∅ = opposite / adjacent
where
∅ = angle of elevation
Therefore,
tan ∅ = 27 / 20
∅ = tan⁻¹ 1.35
∅ = 53.471144633
∅ = 53.5 degrees
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Determine the coefficient and the degree of each term in the polynomial. 8x^(2)+6x+8
Answers
The coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0
The coefficient of a term in a polynomial is the number that is multiplied by the variable. The degree of a term is the exponent of the variable. In the polynomial 8x^(2)+6x+8, there are three terms:
- The first term is 8x^(2). The coefficient of this term is 8, and the degree is 2.
- The second term is 6x. The coefficient of this term is 6, and the degree is 1.
- The third term is 8. The coefficient of this term is 8, and the degree is 0 (since there is no variable).
Therefore, the coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0.
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Perform long division on the following, please show work:
a) 33.143 / 100
b) 175.876 / 0.01
Answers
a) 0.33143; b) 17586.76
a) 33.143 / 100
33.143 ÷ 100
= 0.33143
b) 175.876 / 0.01
175.876 ÷ 0.01
= 17586.76
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15 POINTSSS!!!!!!! HELP A GIRL OUTTTTTTTT
Answers
The function that represents an exponential growth would be = f(X) = 0.3 ( 1.05) ^x. That is option C.
What is an exponential growth?An exponential growth of a function is defined as the growth that shows increase rates with respect to a given time.
There are two types of exponential functions: exponential growth and exponential decay.
The function that shows an exponential growth has the formula = f (x) = b^x, when b > 1.
From the examples given in the options above, the correct option that represents the exponential growth is f(X) = 0.3 ( 1.05) ^x. Thai so because 1.05 is greater than 1.
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20% tip, 8% tax sales. Total $23. 04, what is the pretax?
Answers
For a 20% tip, 8% tax sales. Total $23. 04, we can say that The pre-tax cost is $19.20.
Let x be the pre-tax cost of the sales. Then we can set up the equation:
x + 0.20x + 0.08x = 23.04
Simplifying and solving for x, we get:
1.28x = 23.04
x = 23.04 / 1.28
x = 18
Therefore, the pre-tax cost of the sales is $18. However, we need to add the 20% tip and 8% tax to this amount to get the total cost of $23.04. The tip is $3.60 (0.20 * 18) and the tax is $1.44 (0.08 * 18), which when added to $18 gives us a total cost of $23.04.
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What are the Big Ideas or Focal Points in the mathematics
curriculum in grades 6?
Answers
The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System. 3. Expressions and Equations. 4. Geometry. 5. Statistics and Probability.
1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.
2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.
3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.
4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.
5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.
These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.
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