A fence is to be built to enclose a rectangular area of square feet. The fence along three sides is to be made of material that costs ​$ per foot. The material for the fourth side costs ​$ per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.

By using the concept of equation of line in slope intercept form, it can be obtained that

a)  x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   y- intercept is 20

   This means, Priya had $20 before buying any comics

b) Slope = -4

   This means Priya's money has been decreasing by $4 after buying        one comics    

c)  Equation of line

     y = -4x + 20

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

x represents the number of comic books Priya buys at the store

y represents the amount of money (in dollars) Priya has after buying the comic books.

a)From the figure, it is clear that x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   From the figure, it is clear that y- intercept is 20

   This means, Priya had $20 before buying any comics

b) The line passes through (5, 0) and (0, 20)

    Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4

     This means Priya's money has been decreasing by $4 after buying

    one comics

c) Equation of line

   y - 0 = -4(x - 5)

   y = -4x + 20

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Complete Question

The figure has been attached-

The equation of line d that is perpendicular to line c is: y = 7/3x - 2/3.

Perpendicular lines have slope values, whose product is equal to -1, that is, they are negative reciprocals to each other. An equation in slope-intercept form is often written for a line as y = mx + b, where m = slope and b = y-intercept.

The slope of y - 3/7x + 4 is -3/7. The negative reciprocal of -3/7 is 7/3. Therefore, the slope (m) of the perpendicular line d is 7/3.

Substitute m = 7/3 and (x, y) = (2, 4) into y = mx + b to find the value of b (y-intercept of the line):

4 = 7/3(2) + b

4 = 14/3 + b

-14/3 + 4 = b

(-14 + 12)/3 = b

-2/3 = b

b = -2/3.

To write the equation of line d, substitute m = 7/3 and b = -2/3 into y = mx + b:

y = 7/3x - 2/3

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option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .

Given:

points (1,0) and (3,4)

line equation is y - y1 = m(x-x1)

y - 0 = 4-0/3-1(x - 1)

y = 2(x-1)

y = 2x - 2

2x - y =2.

The vertex of the given upward parabola is in the first quadrant so the coefficient of [tex]x^{2}[/tex]  must have positive values.

so y = [tex]x^{2} -2x+1[/tex]

Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Equation of a line:

y = 2x  - 3

y = 2 x 0 - 3 = -3

y = 2 - 3 = -1

y = 2 x 2 - 3 = 4 - 3 = 1

Table

x   0     1     2

y  -3    -1     1

The graph of the straight line is given below.

Thus,

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

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The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.

What is a sequence?

A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.

We are given a sequence 8, 5,2, -1,.....

Now the first term of the sequence is 8 and common difference is -3.

As the difference between 2 consecutive terms is same, the given sequence is arithmetic.

now substituting this in the standard equation

we get,

t(n) = a+ (n-1)d

t(n)= 8+(n-1)(-3)

t(n) = 8-3n+3

t(n) = 11-3n                           (1)

Now we have to find the 5th, 6th, 7th term of the sequence

We substitute n=5, n=6, n=6 in equation 1

We get

t(5) = 11-3(5)

t(5) = 11-15

t(5) = -4

And,

t(6) = 11-3(6)

t(6) = 11-18

t(6) = -7

And,

t(7) = 11-3(7)

t(7) = 11-21

t(7) = -10

Hence the next three terms are -4, -7, -10.

The equation is t(n) = 11-3n

The 100th term would be given as

t(100)  = 11-3(100)

t(100)  = 11-300

t(100) = -289

Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289

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77 is the sum of their integers  squares .

What in math is an integer?

Let the numbers be ( n - 1 ), n , ( n + 1 )

according to question

  ( n - 1 ) (n) ( n + 1 ) = 8( n + n - 1 + n + 1 )

  n( n² - 1 ) = 8(3n)

   ( n² - 1 ) = 24

    n²= 25

    n = 5

since n is positive integer n = 5

thus required numbers are 4,5,6

4² + 5² + 6² = 77

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The total number of pages that he read will be 210 pages.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Based on the equation given, the equation to represent Amir's information will be:

y = 35 × x

y = 35x

Jesse's equation will be:

y = 30(x + 1)

Then, we'll equate both equations together. This will be:

35x = 30(x + 1)

35x = 30x + 30

35x - 30x = 30

5x = 30

x = 30/5

x = 6

Therefore, the number of pages read will be:

y = 35x

y = 35 × 6

y = 210 pages.

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The algebraic expression is C(5) =2.5 * 5 + 1.4 and the total cost is $13.9

From the question, the equation of the total sales amount is given as

Equation = 2.3q + 1.4

Where q represents the number of days

Rewrite as

Cost = 2.3q + 1.4

Express the equation as a cost function

So, we have the following representations

C(q) = 2.3q + 1.4

When the number of days is 5, we have

q = 5

Substitute the known values in the above equation So, we have the following equation

C(5) =2.5 * 5 + 1.4

Evaluate the products

C(5) = 12.5+ 1.4

Evaluate the sum

C(5) = 13.9

Hence, the total cost for the 5 days is $13.9

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Answer; the  Negative of 12 is -12

Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12  

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven

Let the number of days be d.

Let the number of miles be m.

The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.

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Answer:

$72 / hr

Step-by-step explanation:

$36 / (1/2 hr ) =  $72 per hour

Answer:

P=(2.25 x 10^4)(1 + 0.051)(1 +0.051)

Step-by-step explanation:

Answer:

1368

Step-by-step explanation:

let 3rd game be x

151+183+x=1702

334+x=1702

x=1702-334

x=1368

The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

According to some of the laws of indices, we have;

[tex]\dfrac{1}{x^n} =x^{-n}[/tex]

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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As per the unitary method, the cost of 8 bottles is $6.48

Unitary Method:

Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.

Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.

Let x be the cost of one bottle.

so, based on the unitary method we can written the situation as,

15 bottles = costs $12.15

Therefore, the cost of one bottle is.

x = 12.15/15

x = 0.81

So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,

Then we get,

=> 8 x 0.81

=> 6.48

Therefore, the cost of 8 bottles is $6.48

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Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)

The complement of set A is { 3, 6, 13, 14, 17, 19}

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).

U = {2,3,6,9,10,13,14,17,19}, A =  {2,9,10}

set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' =  { 3, 6, 13, 14, 17, 19}

In conclusion the complement of set A is  { 3, 6, 13, 14, 17, 19}

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Answer:

y+6 =-2(x-5)

Step-by-step explanation:

The question is asking for the equation of the line

The equation for point-slope form is always written as y-y₁=m(x-x₁)

y₁ and x₁ are the points given to you in this order (x₁, y₁)

so x₁=5 and y₁=-6

Now you plug in all the numbers you have into the point slope form

y- (-6)= -2(x-5)

When you subtract a negative (a double negative you get a positive)

y+6=-2(x-5)

Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).

Notes:

For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be

y-2=-2(x-1)

Assuming the question is : "how much does 1 box of blueberries cost?"

After he bought 5 boxes of blueberries and 3 watermelons, he was left with $16.50

Therefore, 5 boxes of blueberries and 3 watermelons cost $60.50 - $16.50 = $44

We are given the cost of 1 watermelon is $8.30

Therefore, 3 watermelons cost $8.30 x 3 = $24.90.

-> 5 boxes of blueberries cost $44 - $24.90 = $19.10

-> 1 box of blueberries cost $19.10 : 5 = $3.82

Answer:

If your trying to find the total of the 5 boxes of blue berries the answer is

$19.10

Step-by-step explanation:

60.50 - 16.50 = 44$ meaning he spent that much.

8.30 x 3 = 24.9

19.10 + 24.9 = 44

hope this helps

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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Answer:

Step-by-step explanation:

Arithmetic Sequence

Answer:

  (a)  Arithmetic Sequence

Step-by-step explanation:

You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.

An arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.

The graph shows an Arithmetic Sequence.

__

Additional comment

A graph of a geometric sequence would show points that lie on an exponential curve.

Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

Answer:

T = 52

Step-by-step explanation:

The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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Given the average profits on the different cell phone models, the expected value of profit to be earned on all models is $57.55

The expected value of the profit on these models of cell phones can be found based on the number of customers who choose the model and the profit of that model.

The expected value of the profit on all the models is:

= ∑ ( percentage of customers x Profit per model)

= (Percentage of customers model A x Profit from model A) + (Percentage of customers model B x Profit from model B) + (Percentage of customers model C x Profit from model C) + (Percentage of customers old collection x Profit from old collection)

= (25% x 60) + (33% x 75) + (32% x 40)  + ( (1 - 25% - 33% - 32%) x 50)

= $57.55

Options for this question are:

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The letters for XYZ are in the wrong order.

The correct statement should be [tex]\triangle TUV \cong \triangle ZYX[/tex]

============================================

Further Explanation:

The order of the letters matters when writing congruence statements.

The claim is that [tex]\triangle TUV \cong \triangle XYZ[/tex]

The first two letters of each are "TU" and "XY" in that order.

But notice how TU has a single tickmark, while XY has a double tickmark. The two sides are clearly different.

--------

Instead, the statement should be: [tex]\triangle TUV \cong \triangle ZYX[/tex] because of the following three facts:

Notice that:

The Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.

The distance between Jose's house and school is 1.85 miles.

The school is 2.34 miles from the nearest library, which is 1.91 miles away from Jose's house.

Total distance = Jose’s home to school + school to library

Total distance = 1.85 + 2.34

Total distance =  4.19 miles.

Thus, the Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.

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The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

According to the question,

We have the following information:

The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.

Let's take the second side to be x feet.

So, we have the following sides:

First side = (x+2) feet

Third side = (2x-5) feet

Perimeter = 49

x+x+2+2x-5 = 49

4x-3 = 49

Adding 3 on both the sides:

4x = 49+3

4x = 52

Dividing by 4 on both the sides:

x = 52/4

x = 13 feet

First side = 2+13

First side = 15 feet

Third side = 2*13-5

Third side = 26-5

Third side = 21 feet

Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

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