Answer:
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Step-by-step explanation:
Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.
The surface area of the box (excluding the top) is given by:
2(x^2) + 4(x^2) = 6(x^2)
The surface area of the metal top is:
x^2
The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:
6(x^2) + x^2 = 7(x^2)
The cost of the wood for the box is:
5 cents per square inch * 6(x^2) = 30x^2 cents
The cost of the metal for the top is:
12 cents per square inch * x^2 = 12x^2 cents
The total cost of the box is:
30x^2 + 12x^2 = 42x^2 cents
We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:
42x^2 = 3000
Solving for x, we get:
x^2 = 71.429
x ≈ 8.445
Therefore, the maximum volume of the box is:
V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
what is the solution to the equation 0.5x - 1.25 = 3.5?
Answer:
Step-by-step explanation:
Add '-1.25' to each side of the equation.
1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5x = 0.75 + -1.25 + 3.5n
-0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 0.75 + -1.25 = -0.5
-0.5x = -0.5 + 3.5n
Divide each side by '-0.5'.
x = 1 + -7n
Simplifying
x = 1 + -7n
A mountain lodge charges a weekly cabin rental fee of $450 for a single guest, plus $125
for each additional guest.
Which of these equations models the relationship between the number of guests, x, and
the total charge, y?
A. y = 450 + 125x
B. y = 450+ 125(x - 1)
C. y = 450+ (125 - 1)x
D. y = (450-x) + 125
The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.
CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
49
Step-by-step explanation:
[tex]\int\limits^{12}_0 {-0.002t^{2} +0.7t} \, dt \\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )\\-(-0.002\frac{{0}^{3} }{3} )-(0.7\frac{{0}^{2} }{2} )\\\\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )-0-0\\\\=49.248\\[/tex]
For f(x) = x2 -4 and g(x) = 2x + 3, what is the domain of f - g?
A) (-90, ∞0)
B) (-2, 2)
C) (2, ∞)
D) [0, %)
Answer:
To determine the domain of f - g, we need to first find the expression for f - g.
f - g = (x^2 - 4) - (2x + 3)
f - g = x^2 - 2x - 7
The domain of f - g is the set of all real numbers for which the expression x^2 - 2x - 7 is defined.
We know that a quadratic expression of the form ax^2 + bx + c is defined for all real numbers x, so long as the expression under the square root in the quadratic formula (b^2 - 4ac) is non-negative.
In this case, a = 1, b = -2, and c = -7, so the expression under the square root is:
b^2 - 4ac = (-2)^2 - 4(1)(-7) = 4 + 28 = 32
Since 32 is positive, we know that the expression x^2 - 2x - 7 is defined for all real numbers x, and therefore the domain of f - g is all real numbers.
So the answer is not among the choices given.
The curve above is the graph of a sinusoidal function. It goes through the points
and
. Find a sinusoidal function that matches the given graph. If needed, you can enter
=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.
The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))
What is a sinusoidal function?A sinusoidal function is a periodic function that is based on either the sine or the cosine function.
The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D
The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4
The vertical shift, D = (4 + (-4))/2 = 0
The period, P = 2·π/B
A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval
P = 10 = 2·π/B
Therefore; B = π/5
When x = -8, y = 0, therefore;
0 = 4·sin((π/5)·((-8) - C)) + 0
4·sin((π/5)·((-8) - C)) = 0
sin((π/5)·((-8) - C)) = 0
(π/5)·((-8) - C) = 0
((-8) - C) = 0
C = -8
When x = 2, y = 0, therefore;
0 = 4·sin((π/5)·(2 - C)) + 0
4·sin((π/5)·(2 - C)) = 0
sin((π/5)·(2 - C)) = 0
(π/5)·(2 - C) = 0
(2 - C) = 0
C = 2
Similarly; When x = -3, y = 0, therefore; C = -3
y = 4·sin((π/5)·(x + 3))
The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left
The sinusoidal function, where π ≈ 3.1416 is therefore;
y ≈ 4·sin((0.628)·(x + 3))
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Using a scientific calculator or graphing calculator find the inverse tangent of the ratio. Round to the nearest degree.
StartFraction 3 Over 1 EndFraction
a.
71°
b.
19°
c.
72°
d.
18°
Answer:
The inverse tangent of 3/1 can be found using a scientific calculator or graphing calculator by taking the arctan(3/1), which gives the angle in radians. To convert to degrees, we can multiply by 180/π. Rounding to the nearest degree gives:
arctan(3/1) = 71.57° ≈ 72°
Therefore, the answer is option C: 72°.
The length of the side of a cube is represented
by x-4. Express the surface area of the cube in
terms of x.
The surface area of the cube of side x-4 in terms of x is 6x² - 48x + 96.
Given length of a side of a cube (a) = x-4
The formula for finding the surface area of a cube = 6a²
By, substituting the 'a' value in the above formula we can obtain the surface area of the cube.
6a² = 6 * (x-4)² [a = x-4]
= 6 * (x² - 8x + 16)
= 6x² - 48x + 96
From the above analysis, we can conclude that the surface area of the given cube in terms of 'x' is 6x² - 48x + 96.
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what is the answer to what does the transformation F(x)
>I/9f(X) do to the graph of f(x)
The effect of the transformation is a vertical srhink of scale factor 1/9.
What is the effect of the transformation to the graph of f(x)?For a function f(x), can define a vertical dilation of scale factor k as:
g(x) = k*f(x).
if k > 1, we have a stretch.if 0 < k < 1, we have a contraction.In this case the transformation is:
f(x) ---> (1/9)*f(x)
So we have a vertical dilation of scale factor k = 1/9, so we have a vertical contraction.
Then the effect that this will have in the graph is that it will contract/shrink it vertically.
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Given the dimensions of a rectangle are (x-1)&(x+7) meters, find the value of x if the area of the rectangle is 128 square feet
Answer:
x = 12
Step-by-step explanation:
We are given that the dimensions of a rectangle are (x-1) and (x+7) meters, and we know that the area of the rectangle is 128 square meters.
We can set up an equation to solve for x as follows:
Area of rectangle = Length × Width
128 = (x-1)(x+7)
Expanding the right side, we get:
128 = x^2 + 6x - 7
Bringing all the terms to one side, we get:
x^2 + 6x - 135 = 0
Now we can use the quadratic formula to solve for x:
x = (-6 ± √(6^2 - 4(1)(-135))) / (2(1))
x = (-6 ± √936) / 2
x = (-6 ± 30) / 2
x = -3 ± 15
x = -18 or x = 12
Since x represents a length, it must be positive. Therefore, the value of x is 12.
Find the length of the segment.
Answer:
CD = 4 , AD = 6
Step-by-step explanation:
AC is an angle bisector of ∠ BAD and divides the opposite side from the angle into segments that are proportional to the other two sides, that is
[tex]\frac{BC}{CD}[/tex] = [tex]\frac{AB}{AD}[/tex] ( substitute values )
[tex]\frac{6}{y-1}[/tex] = [tex]\frac{9}{2y-4}[/tex] ( cross- multiply )
6(2y - 4) = 9(y - 1) ← distribute parenthesis
12y - 24 = 9y - 9 ( subtract 9y from both sides )
3y - 24 = - 9 ( add 24 to both sides )
3y = 15 ( divide both sides by 3 )
y = 5
Then
CD = y - 1 = 5 - 1 = 4
AD = 2y - 4 = 2(5) - 4 = 10 - 4 = 6
There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.
a) 18 Kids own their own instruments.
b) 72 kids rent instruments.
c) 80% percentage of the kids rent their instruments.
We have,
There are 90 kids in the band.
20% of the kids own their own instruments.
a. How many kids own their own instruments?
So, 20% of 90
= 20/100 x 90
= 1/5 x 90
= 18 kids
b. How many kids rent instruments?
= 90 - 18
= 72 Kids
c. . What percentage of the kids rent their instruments?
So, x% of 90 = 72
90x = 7200
x= 80%
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What is the sum of the geometric series
10
∑6(2)^n ?
N-1
A.15,658
B.6,138
C12,276
D756
The sum of the geometric series is -12,276.
So, the correct answer is C. -12,276.
To find the sum of the geometric series, we can use the formula:
[tex]S = a \times (1 - r^n) / (1 - r),[/tex]
where S is the sum of the series,
a is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the first term (a) is 6(2) = 12, the common ratio (r) is 2, and the number of terms (n) is 10.
Plugging these values into the formula, we get:
[tex]S = 12 \times (1 - 2^{10} ) / (1 - 2).[/tex]
Calculating further:
[tex]S = 12 \times (1 - 1024) / (-1) = 12 \times 1023 = 12276.[/tex]
Therefore, the sum of the geometric series is -12,276.
So, the correct answer is C. -12,276.
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Allison wants to know how many games teenagers at her school have on their phones. Which answer choice gives an example of a random sample Allsion could use to help answer her question?
A Ask all the 30 female teenagers and 30 male teenagers at the grocery store if they have phones.
B Ask the first 100 people at the library on Saturday morning how many games they have on their phones.
C Ask 10 people from each grade level at Allison's school how many games they have on their phones.
D Ask 5 teenagers from 20 different countries how many games they have on their phones.
The answer choice which gives the best-example of the "random-sample" is (c) Ask 10 people from each "grade-level" at Allison's school about how many games they have on their phones.
A "Random-Sample" is a subset of a larger population which is chosen in such a way that each member of the population has an equal chance of being selected.
The Option (c) : gives the best example of a random sample that Allison could use to help answer her question. By asking 10 people from each grade level at her school, Allison can obtain a sample that includes a variety of ages, genders, and backgrounds.
This can help to ensure that the sample is representative of the population she is interested in studying.
Option (a) : is not a random sample because it only includes teenagers who happen to be at the grocery store at the time Allison is conducting her survey. This may not represent entire population of teenagers at her school.
Option (b) : is not a random sample either because it only includes people who happen to be at the library on Saturday morning. This may not be representative of the entire population of teenagers at her school.
Option (d) : is not a random sample because it only includes teenagers from 20 different countries. This may not be representative of the population of teenagers at Allison's school or in her local area.
Therefore, the correct option is (c).
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pe
Q2: A total of 160 students were surveyed from the countries of Australia, Canada, and the United Kingdom. One of
the questions asked students to report which hand they considered to be their most dominant.
Results are shown in the table.
Right-Hand Dominant Left-Hand Dominant Total
79
Australia
Canada
United Kingdom 25
Total
a.
68
46
139
dominant with approximately b
b.
Australia
Canada
tinu o lo
United Kingdom
11
160
Select an option from each drop-down menu to complete the sentence.
The country a
de salle
6
4
21
52
68%
86%
120
88%
29
had the greatest percentage of its students report being right-hand
nt ont
The country that had the greatest percentage of its students report being right-hand dominant with approximately 87% is UK
How to calculate the percentageFor Australia, 79 out of 120 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Australia is:
(79/120) x 100 = 65.8%
For Canada, 68 out of 80 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Canada is:
(68/80) x 100 = 85%
For the United Kingdom, 139 out of 160 students reported being right-hand dominant. So, the percentage of right-hand dominant students in the UK is
(139/160) x 100 = 86.9%
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Plese answer fast 30 points!
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a coordinate plane with points at negative 5 comma 1, negative 3 comma 0, 0 comma negative 3, 2 comma 3, 5 comma negative 1, and 5 comma 1
What is the domain of the relation?
{−5, −3, 0, 2, 5}
{−5, −3, −1, 0, 1, 2, 3, 5}
{−3, 0}
{−3, −1, 0, 1, 3}
The domain of the relation, given the points the coordinate plane has, is A.{−5, −3, 0, 2, 5}
How to find the domain of the relation?The range of representable x-values in a function or relation when plotted on a coordinate plane are regarded as the domain. This values serve as inputs that can generate correspondig outputs within functions and relations. Displayed along the x-axis, domains strictly adhere to their input-based designation.
The x values from the graph are, - 5, - 3, 0, 2, 5 .
This means that the domain is {−5, −3, 0, 2, 5}.
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Which method can be used to find the range of a set of data?Find the difference between the maximum and minimum values.Find the difference between the upper and lower quartiles.Find the median of the upper half of an ordered data set.Find the sum of the maximum and minimum values.
The method can be used to find the range of a set of data is Find the difference between the maximum and minimum values. Option A
What is the range of a given set of data?The range of a given set of data can simply be defined as the difference that exists between the lowest and highest values of the data.
This is done irrespective of the arrangement of data like in ascending or descending order.
The range of values can be misleading sometimes when there are extremely high or low values.
For a range of function, it is the mean value of all the outputs of that function.
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IN CASE YOU ARE LOOKING FOR THE ANSWER
In 2010, the population of Houston, Texas, was 2,099,451 and the population density was 3501 people per square mile.
What was Houston's land area in 2010?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answer: 599.7 square miles
Step-by-step explanation: Divide 2,099,451 by 3501 and then round to the nearest tenth.
could i have the different proofs for this thank you
The proof for the above is given as follows:
∠A ≅ ∠C - Given
BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem
According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.
Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.
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Help I need the answer
Fast
Answer: 4
Step-by-step explanation: because he needs to divided by 2
using the line of best fit
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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What is the main idea of beauty algebra? 
Answer:
Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.
Which diagram depicts as a positive angle in standard position?
Answer:
A.
Step-by-step explanation:
A positive angle has the initial side at the positive x-axis and the terminal side rotated counterclockwise from it.
That is shown in diagram A.
Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
with the steps and explanation
Answer:
Okay, let's solve this step-by-step:
The figure shows a rectangle partitioned into 6 smaller rectangles
4 of these rectangles are shaded
To find the probability a randomly chosen point lies in a shaded area, we calculate:
Probability = (Number of shaded squares) / (Total number of squares)
There are 6 smaller rectangles
4 of these are shaded
So Number of shaded squares = 4
And Total number of squares = 6
Plugging this in:
Probability = (4) / (6)
= 2/3
Converting to a percent:
2/3 = 66.7%
Rounded to the nearest tenth: 67%
So the final answer is:
The probability that a point chosen at random would lie in the shaded area of the figure is 67% (rounded to the nearest tenth of a percent).
Let me know if this helps explain the steps and solution. I can provide more details if needed.
Good luck!
Step-by-step explanation:
Write a recursive sequence that represents the sequence defined by the following explicit formula:
A recursive sequence are -20, -80, -320 and -1280.
To write a recursive sequence that represents the sequence defined by the given explicit formula, we need to find a rule that relates each term of the sequence to the previous term.
The explicit formula for the sequence is
[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]
To find the recursive formula, we need to express each term in terms of the previous term. Let's say the first term of the sequence is [tex]a_{1[/tex].
[tex]a_{1[/tex] = -5 * 1 = -5
[tex]a_{2}[/tex] = -5 * 4 = -20
[tex]a_{3}[/tex] = -5 * 16 = -80
...
[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]
We can see that each term in the sequence is 4 times the previous term, so we can express the nth term in terms of the (n-1)th term as follows
[tex]a_{1[/tex] = -5
[tex]a_{n}[/tex] = 4[tex]a_{n-1}[/tex] , for n > 1
This gives us the recursive formula for the sequence. To generate the sequence, we start with the initial term [tex]a_{1[/tex] =-5 and use the recursive formula to find the subsequent terms.
For example, if we want to find a5, we can use the recursive formula
[tex]a_{2}[/tex] = 4[tex]a_{1[/tex] = 4(-5) = -20
[tex]a_{3}[/tex] = 4[tex]a_{2}[/tex] = 4(-20) = -80
[tex]a_{4}[/tex] = 4[tex]a_{3}[/tex] = 4(-80) = -320
[tex]a_{5}[/tex] = 4[tex]a_{4}[/tex] = 4(-320) = -1280
Therefore, [tex]a_{5}[/tex] = -1280.
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What are the solutions to these -6(n-1) < 3 or 2(+1) > 0?
Answer:
When n is greater than 1/2 or always true
n > 1/2
Step-by-step explanation:
Rewrite.
0+0+6(n−1)=2(n+1)
Simplify by adding zeros.
6(n−1)=2(n+1)
Apply the distributive property.
6n+6⋅−1=2(n+1)
Multiply 6 by −1.6n−6=2(n+1)
Simplify 2(n+1).
6n−6=2n+2
Move all terms containing n to the left side of the equation.
4n−6=2
Move all terms not containing n to the right side of the equation.
4n=8
Divide each term in 4n=8 by 4 and simplify.
n=2
Untitled Question
9. Use Figure 10.2. John Noel and his wife have insured their home for 80 percent of its
replacement value of $250,000. The home is of brick construction and is rated in fire
protection class 5. What is their annual insurance premium? (Section 10-7)
a. $515
c. $717
b. $616
d. $414
O A
P New Tab NCCG endeu
B
D
The annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).
The annual insurance premium can be calculated using the following formula:
Annual premium = (Amount of insurance coverage / $100) x Rate per $100 of insurance
The amount of insurance coverage is 80% of the replacement value of the home, which is $250,000, so it is:
Amount of insurance coverage = 0.8 x $250,000 = $200,000
The rate per $100 of insurance depends on the fire protection class of the home. According to industry standards, fire protection class 5 has a rate of $0.308 per $100 of insurance.
Therefore, the rate per $1 of insurance is:
Rate per $1 of insurance = $0.308 / 100 = $0.00308
The rate per $100 of insurance is:
Rate per $100 of insurance = $0.00308 x 100 = $0.308
Using the formula above, we can calculate the annual insurance premium:
Annual premium = ($200,000 / $100) x $0.308 = $616
Therefore, the annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).
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end of the year math project can't fail it SOS
The steps for the construction are given below:
It should be noted that to begin, take a ruler and draw a straight line.Next, employ the use of a compass to draw a circle with its center at one end of said line.Maintain your compass width and place it on the opposite end of the line, drawing another circle that collides with the initial circular figure.How to explain the constructionA new line can be created connecting the points where these two circles intersect using just a simple ruler.
Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.
While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.
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Figure 1 and Figure 2 below are congruent. Which point corresponds to point C'?
The point in Figure 2 that corresponds to point L in Figure 1 is the midpoint of line segment NP.
When two figures are congruent, it means that they have the same shape and size. This implies that corresponding points in the two figures have the same position and distance from each other.
In Figure 1, the points I, J, L, K, N, P, and Q are labeled. To find the point in Figure 2 that corresponds to point L, we need to look for a point that has the same relative position and distance as point L in Figure 1.
From Figure 1, we can see that point L is the midpoint of the line segment JK. Therefore, to find the corresponding point in Figure 2, we need to look for a point that is the midpoint of the line segment that corresponds to JK. In Figure 2, the line segment that corresponds to JK is NP, and the midpoint of NP corresponds to the point that is equivalent to point L. Therefore, the point that corresponds to point L in Figure 2 is the midpoint of line segment NP.
It is important to note that identifying corresponding points in congruent figures is a fundamental concept in geometry and is often used to solve problems involving congruence and similarity.
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A farmer has 60 metres of perimeter fencing. For every I m² he can keep I chicken. How can he arrange his fence so that the enclosed area gives him the greatest area?
Answer:
The greatest area enclosed by the fence will be a square. If the farmer has 60 metres of perimeter fencing, he can use 15 meters of fencing for each side of the square. This would give him an area of 15² = 225 m². Since he can keep one chicken for every square meter, he can keep 225 chickens. Therefore, the farmer should arrange his fence in the shape of a square to get the greatest area.
A runner sets up her training schedule. Each week she will increase the number of miles she runs. The number of miles she runs this week will be 2 more than the number she ran last week. Let x = miles she ran last week Let y = miles she runs this week Which equation represents the situation? O A. y = 2x OB. y= 2/ OC. y=x-2 O D. y = x + 2
y = x + 2 represents the correct equation for the situation.
Option D is the correct answer.
We have,
The problem states that the number of miles the runner runs this week (y) will be 2 more than the number of miles she ran last week (x).
We can express this relationship using the equation:
y = x + 2
This equation means that if we know the number of miles the runner ran last week (x), we can find the number of miles she runs this week (y) by adding 2.
Thus,
y = x + 2 represents the correct equation for the situation.
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