3. Laurie uses yellow and white tiles to create a pattern.
a) Make a table of values to show the number of yellow tiles in relation to the figure number.
b) Describe the relationship between the number of yellow tiles and the figure number.
c) Develop an expression and an equation to model the number of yellow tiles. Explain what each part of the equation represents.
d) How many yellow tiles are in Figure 24?
e) Which figure number has 176 yellow tiles? Verify your answer.
f) Is it possible to have a figure with 54 yellow tiles? Show how you know.
Answers
a) Figure 1 2 3
Number of tiles 8 12 16
b) The number of tiles is 8 more than 4 times of 1 less than the number of figure.
c) The equation of model the number of yellow tiles is y = 4x + 4.
d) The number of tiles in figure 24 is 100.
e) Figure 43 has 176 yellow tiles.
f) No.
What is an 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. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given that
the number of yellow tile in figure 1 is 8.
The number of yellow tile in figure 2 is 12.
The number of yellow tile in figure 3 is 16.
(a) The table is
Figure 1 2 3
Number of tiles 8 12 16
(b)
The number of tiles increase at a constant rate.
The rate is (12 - 8) = (16 - 12) = 4
The relation with the figure and number of tiles is
The number of tiles is = 4 + (the number of figure - 1)4
C)
Assume that y represents total number of tiles.
x = Number of figure
Rewrite "The number of tiles is = 4 + (the number of figure - 1)4" in term of x and y:
y = 8 +(x - 1)4
y = 8 + 4x -4
y = 4x + 4
d) Putting x = 24 in y = 4x + 4
y = 4×24 + 4
y = 96 + 4
y = 100
e)
Putting y = 176 in y = 4x + 4
176 = 4x + 4
Subtract 4 from both sides:
172 = 4x
Divide both sides by 4
x = 43
f)
Putting y = 54 in y = 4x + 4
54 = 4x + 4
Subtract 4 from both sides:
50 = 4x
Divide both sides by 4
x = 50/4
The value of x is not a whole number. Thus it is not possible that a figure has with 54 yellow tiles.
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Related Questions
find the volume of the Rectangular prism given below the length is is 10 cm the width is 3.2 cm and the height is 1.5 cm
Answers
Answer:
44.8
Step-by-step explanation:
Volume = Length * Height * Width
Volume = 10 * 1.5 * 3.2
Volume = 44.8cm
what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answers
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
Answers
well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25[/tex]
There are two investment options:
• Option 1: An initial investment of $5 that increases by 50% every year.
.
• Option 2: An initial investment of $0.01 that doubles every year.
Part A:
Write an equation for each option to model the value A of the account after x years
Part B:
Explain which investment will eventually have the greatest value.
Answers
Option 1: An initial investment of $5 that increases by 50% every year
as after 20 years, it amounts to a greater value.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
The given situations can be modeled as a geometric sequence.
Option A :
a₁ = 5, r = 1.5.
We know Sₙ = a₁(rⁿ - 1)/(r -1).
Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).
Sₙ = 5(1.5ⁿ - 1)/(0.5).
Let us see for n = 20, 20th year.
S₂₀ = 5(1.5²⁰ - 1)/(0.5).
S₂₀ = 5(3324.25)/(0.5).
S₂₀ = 33242.5.
Option B :
a₁ = 0.01 and r = 2.
Sₙ = 0.01(2ⁿ - 1)/(1).
S₂₀ = 0.01(2²⁰ - 1)/(1).
S₂₀ = 10,485.75
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An approximate solution to an equation is found using this iterative process.
Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1
a)
(i) Work out the value of x₂
(ii) Work out the value of x₃
b) Work out the solution to 6 decimal places.
Answers
a) The values are given as follows:
i) x1: -0.5.ii) x2: -0.280125.b) The solution of the equation is of: -0.25410169644.
How to obtain the solution to the equation?The equation in this problem is given as follows:
y = (x³ - 1)/4.
The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.
Then the values are given as follows:
x1 = -1 -> attributed.x2 = ((-1)³ - 1)/4 = -0.5.x3 = ((-0.5)³ - 1)/4 = -0.28125.x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.More can be learned about iterative solution methods at https://brainly.com/question/13718918
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What is the surface area of the cube shown below?
Answers
Answer:
150 in^2
Step-by-step explanation:
It is a cube...it has six equal sides
the surface area of one side is 5 x 5 = 25 in^2
there are six .... so 6 x 25 = 15o in^2
Edited: should be in^2 not cm^2 as originally posted...wrong units
Answer:
150
Step-by-step explanation:
To find the surface area of a cube, you do 6a^2. That would mean it is 150.
The time spent by a customer at a checkout counter has mean 4 minutes and standard deviation 2 minutes.
a. What is the probability that the total time taken by a random sample of 52 customers is less than 180 minutes?
b. Find the 30th percentile of the total time taken by 52 customers.
Answers
The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.
μ=Population mean=4
σ=Population standard deviation=2
n=Sample size=50
The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.
The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.
The sum S's sample distribution has a mean and standard deviation of n and n, respectively.
The z-score is the value decreased by the mean, divided by the standard deviation
z = ( x -μS ) / √σS
= 150 - 50(4) / √ 50(2)
= 3.54
Using the appendix's normal probability table, get the relevant probability,
P(S < 150 ) = P(Z< -3.54)
= 0.0002
=0.02%
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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Select all the points of intersection between the graphs of the functions f(x)=(x+5)(x-2)and g(x)=(2x + 1)(x-2)
Select all that apply
a: (-5,0)
b: (-1/2,0)
c: (-2, -12)
d: (2,0)
e: (4, 18)
f: (5, 30)
Answers
The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.
What is a function?
A function is defined as a relation between a set of inputs having one output each.
We have,
f(x) = ( x + 5 ) ( x - 2 )
g(x) = ( 2x + 1 ) ( x - 2 )
To find the points of intersection between the two functions we must equal the function.
f(x) = g(x)
( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )
( x - 2 ) gets canceled
x + 5 = 2x + 1
5 - 1 = 2x - x
4 = x
x = 4
This means that at x =4 the function f(x) and g(x) intersect.
we can see that at x = 4 both the functions have the same value.
f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2
f(x) = 18
g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )
= 9 x 2
g(x) = 18
Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.
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Find the sum of the arithmetic series where n = 50, a = 9, and t50 = 331.
Answers
Solution
Given series is [tex]$5+11+17+\ldots .+95$.[/tex]
Thus,
[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]
Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]
What is arithmetic series?
The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.
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A local bank charges a $31-per-check overdraft protection fee. On June 5, Lewis has $932.77 in his account. Over
the next few days, the following checks were submitted: June 6, $791.29, $340.50, and $208.35; June 7, $428.61;
and June 8, $113.3. How much will he pay in overdraft fees?
Answers
Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.
Step-by-step explanation:
To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:
overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)
= 932.77 - 2082.05
= -1149.28
Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.
Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.
Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?
Answers
The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.
What is the confidence interval?In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.
We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.
α = (1 - 0.90)/2 = 0.05.
Now, we have to find z in the Ztable as such z has a p-value of 1 - α.
So it is z with a pvalue of 1 - 0.05 = 0.95 = 1.96.
Now, find the margin of error M as such,
M = z×(sigma/√n).
5 = 1.96×(16/√n).
5√n = 31.36.
n = 39.9.
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Box contains 160 fruits. of the total number of fruits in the box 30% are apples. 25% of the remaining fruits in the box pears and the rest of the fruits in the box are oranges. how many oranges are in the box?
Answers
Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.
Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)−4?
Answers
Answer:
the range of the graph would move down by 4 units.
Step-by-step explanation:
f(x) is the original/basis equation
g(x) is the translation equation
-4 does not have any x's attached to it, so it would affect the range, or the y of the equation
for example:
f(x) = 2x + 8
if you subtracted 4 from that it would be:
f(x) = 2x - 4, so the range would be affected
Adrian Alvarez Munoz
Write Expression from Context $(m x+ b)
Dec 12, 8:15:06 PM
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Angel is saving up to buy a new video game. He already has $ 30 and can save an additional $ 8 per week using money from his after school job. How much total money would Angel have after 5 weeks of saving? Also, write an expression that represents the amount of money Angel would have saved in w weeks.
Total savings after 5 weeks:
Total savings after w weeks:
Answers
The expression that represents the amount of money Angel would have savings in w weeks is 30+8w
The total amount of money saved after 5 weeks is $70
Which algebraic expression is required for Angel's total savings?
The required algebraic expression considers the amount she has saved already which is $30 and her potential to save $8 per week, for w number of weeksSystems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Total savings=30+8w
Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks
total savings=30+(8*5)
total savings=30+40
Total savings=$70
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if 25% of tolla's sallary is birr 135.75, what is the amount of his full salary?
Answers
If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.
Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.
This is the amount of Tolla's full salary.
LOL
full salary = 135.75 / 0.25
Plugging in the values, we get:
full salary = 135.75 / 0.25 = 543
So Tolla's full salary is $543.
There is 14 feet of fencing available to enclose a rectangular region. For what
Answers
The maximum area is 12.25 square feet
How to determine the maximum areaFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 14 feet
This means that
P = 2(l + w)
So, we have
2(l + w) = 14
Divide by 2
l + w = 7
Make l the subject
l = 7 - w
The area is calculated as
A = lw
So, we have
A = (7 - w)w
Expand
A = 7w - w²
Differentiate and set to 0
7 - 2w = 0
So, we have
w = 3.5
Substitute w = 3.5 in A = (7 - w)w
A = (7 - 3.5) * 3.5
Evaluate
A = 12.25
Hence, the area is 12.25 square feet
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Complete question
There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum
Consider the interval AC that has been graphed on the number plane. Find the length of interval AC, rounding your answer to two decimal places.
Answers
By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.
What is the distance formula?The distance formula is given as:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Give the example of two decimal rounding off.
Here are two examples of rounding off to two decimal places:
12.3456 rounded to two decimal places is 12.35
0.678 rounded to two decimal places is 0.68
Plugging in the coordinates of the two points, we get:
Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)
= sqrt(6^2 + (-9)^2)
= sqrt(36 + 81)
= sqrt(117)
= approximately 10.8
Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.
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Factorise fully the following:
4x² + 28x³
Answers
Answer: 4x^2(7x+1)
Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.
Answer:4x^2(1+7x)
Step-by-step explanation:
4x^2(1+7x)
A box of chocolates contains 24 chocolates. Ten of the chocolates have cherry centers. All chocolates appear the same.
Two chocolates are selected. Find the probability of each of the following. (Round your answers to four decimal places.)
(a) both have cherry centers
(b) one has a cherry center and one does not
Answers
The probability of selecting chocolate such that:
(a) both have cherry centers: 0.1630
(b) one has a cherry center and one does not: 0.507
In this question, we have been given a box of chocolates contains 24 chocolates.
n(S) = 24
Ten of the chocolates with cherry centers.
n(A) = 10
So, the number of chocolates with no cherry centers are:
n(B) = 14
We need to find the probability of selecting chocolate such that
(a) both have cherry centers
P = (10/24)(9/23)
P = 90/552
P = 15/92
P = 0.1630
(b) one has a cherry center and one does not
P = 2*(10/24)(14/23)
P = 0.507
Therefore, the probability of selecting chocolate:
(a) both have cherry centers
P = 0.1630
(b) one has a cherry center and one does not
P = 0.507
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answers
42% x 530=222.6
Rounded: 223
what is the measure of AB in O below?
Answers
The measure of AB in the figure is C. 100 degree
How to find the measure of ABThe measure of AB in the figure is the length of arc, this is given by the formula
given angle / 360 * 2πr
However, the measure in degree is equal to the angle given which is 100 degree.
The size or the measure of the angle is same at any point within same lines that formed the angel AB.
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the values f(x) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1. which of the following statements must be true?
Answers
The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
Given :
the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.
Function :
In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and a co - domain.
x sufficiently close to 1 means x → 1
but x ≠ 1.
so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞
Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
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Connor is driving to a concert and needs to pay for parking. There is an automatic fee
of $8 just to enter the parking lot, and when he leaves the lot. he will have to pay an
additional $2 for every hour he had his car in the lot. How much total money would
Connor have to pay for parking if he left his car in the lot for y hours? How much
vould Connor have to pay if he left his car in the lot for t hours?
Answers
The solution is
a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours
b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Let the second equation be represented as B
Now , the value of A is
The automatic fee for parking = $ 8
The additional fee for parking every hour = $ 2
So , for x number of hour , the additional parking fee = 2x
And , the total parking fee including x hours = automatic fee for parking + additional parking fee
Substituting the values in the equation , we get
The total parking fee including x hours = 8 + 2x
Now , when x = y hours
The total parking fee including y hours A = 8 + 2y
And , when x = t hours
The total parking fee including t hours B = 8 + 2t
Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours
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Therefore, in area or a circles given by the formula.
A. the circumference, or 2π²
B. the radius, r
C. half the radius, or 1/2 r
D. half the circumference, or s r
Answers
Area or a circles given by the formula = radius , r
What is area?
The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
For the circle or area given by the formula is radius ,r.
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MULTIPLE CHOICE PRACTICE
9. For the function defined by the equation y=2 x²-10, which of the following represents the output when the input is -3 ?
(1) 6
(3) -10
(2) 8
(4) -28
10. If a function is defined by the equation y=-5 x+1 and the domain is the set {-2,0,2,4\}, which set below represents the range of the function?
(1) {11,12,13,14}
(3) {-10,-1,9,19}
(2) {-19,-9,1,10}
(4) {51,53,55,57}
11. A function is given by the set: {(-6,2),(-4,7),(0,5),(2,-4),(5,2),(7,5)}. Which of the following gives a pair of inputs that have the same output?
(1) -6and -4
(3) -4 and 2
(2) 5 and 7
(4) 0 and 7
Answers
Answer:
answer for no.10 is {11,12,13,14}
Step-by-step explanation:
According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
USE EFFICIENT METHODS Determine whether Δ D E F P ≅ ΔP Q R.
D(-7,-3), E(-4,-1), F(-2,-5), P(2,-2), Q(5,-4), R(0,-5)
Find the side lengths of each triangle.
A) D E=√13, P Q=√13, E F=2 √5, Q R=√13, D F=√29, P R=√13
B) D E=√13, P Q=√13, E F=√5, Q R=√26, D F=√29, P R=√13
C) D E=√13, P Q=√13}, E F=2 √5, Q R=√26, D F=2 √29, P R=√13
D) D E=√13}, P Q=√13, E F=2 √5, Q R=√26, D F=√29, P R=√13
Answers
The side lengths of each triangle are given as follows:
D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]
How to obtain the side lengths of each triangle?The side lengths of each triangle are given by the distances between the vertices.
These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.
Suppose two points in the coordinate plane with notation given as follows:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Then the distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus the side lengths are given as follows:
DE: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]PQ: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]EF: [tex]\sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}[/tex]QR: [tex]\sqrt{5^2 + 1^2} = \sqrt{26}[/tex]DF: [tex]\sqrt{5^2 + 2^2} = \sqrt{29}[/tex]PR: [tex]\sqrt{2^2 + 3^2} = sqrt{13}[/tex]Meaning that option D is correct.
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Hello can you help me with this question
Part A: Without using a graphing calculator, which equation could be represented by the accompanying graph?
A) y= x^2-2
B) y =2^-x
C) y= -2^x
D) y= 2^x
Answers
Answer:
Step-by-step explanation:
A
Stem and leaf plots
And box
Pls help I have no idea what this is
Answers
Answer:
13
Step-by-step explanation:
The box plot ends at 13.
Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.
Consider r (x) = StartFraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline EndFraction, where a, b, c, and d are positive integers and b < d. What value does r(x) approach as x approachesInfinity?
0
StartFraction a Over c EndFraction
StartFraction b Over d EndFraction
Infinity
Answers
The value of r(x) approaches as x approaches Infinity is; 0
How to find the limit of a function?Limit is defined as the value that a function approaches for the given input value.
We have been given a function;
r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction
We can rewrite this function as;
r(x) = (axᵇ + 8)/(cx^d)
where a, b, c, and d are positive integers and b < d.
We need to find the value of r(x) approach as x approaches Infinity.
This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]
Now, we find the value of limit for given function;
[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]
This simplifies to;
[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)
Thus;
[tex]\lim_{x \to \infty} r(x) = 0[/tex]
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Monique wants to rent online movies. Movies Plus charges a one-time free of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. Write and solve an equation to determine m, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same.
__; m = __ movies
Answers
The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let the no. of movies be 'm' and the total cost is 'C'
Movies Plus charges a one-time fee of $20 plus $5 per movie
which is, C = 5m + 20.
Movies-To-Go charges $7 per movie
which is, C = 7m.
Now, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.
∴ 7m = 5m + 20.
2m = 20.
m = 10.
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