A rectangular field bordering a river is to be enclosed with 600 m of fencing. No fence is needed along the riverbank. What equation represents the maximum area enclosed by the fence?

a is correct

Question 1 (1 point )If y varies directly as x and y = 15 when x = 12, find y when x = 32. The value of y when x = 32 is 40.How to solve direct variation problems?A direct variation is a function that can be expressed in the form y = kx, where k is a nonzero constant. Two quantities x and y are said to be in direct variation if they satisfy this relationship. To solve direct variation problems, you can use the following formula: y = kx, where k is the constant of variation.The solution to the problem is given below:Given:y varies directly as xx = 12, y = 15To find:y when x = 32Formula:Since y varies directly as x, we have:y = kxLet's substitute x and y values in the above equation:15 = k × 1215/12 = kk = 5/4Thus, the equation of the direct variation is: y = (5/4) xTo find the value of y when x = 32, substitute 32 for x:y = (5/4) × 32y = 40Therefore, y = 40 when x = 32. Hence, the option (a) is correct.

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Answer:

To find the pressure that the box exerts on the ground, we need to divide the force by the area of the base:

pressure = force / area

We are given that the force is 4.5 kN and the area is 1.1 m². However, we need to convert the force from kilonewtons to newtons before we can divide by the area:

force = 4.5 kN = 4,500 N

Now we can plug in the values:

pressure = 4,500 N / 1.1 m² = 4,090.91 N/m²

To express the pressure in kilonewtons per square meter, we need to divide by 1,000:

pressure = 4.09091 kN/m²

Rounding to 2 decimal places, we get:

pressure ≈ 4.09 kN/m²

Therefore, the pressure exerted by the box on the ground is approximately 4.09 kN/m².

Answer:

V = (4/3)π(4^3) = 256π/3 cubic units

The criteria that we could use to prove the congruency that ΔABC ≅ ΔDEC is;

Vertical Angles are Congruent. We could then use AAS to prove that ΔABC ≅ ΔDEC

There are different triangle congruency postulates namely:

SSS: Side Side Side Congruency Postulate

SAS: Side Angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

We want to prove that ΔABC ≅ ΔDEC

Now, from the given image, we see that we are given 2 congruent sides.

However, angle ECD is congruent to angle DCA because they are vertically opposite angles and vertical angles are congruent.

Thus, the triangles are congruent by AAS Congruency postulate.

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We can calculate the percentages according to the amounts provided in the prompt, and then make a number line to illustrate each percentage as follows:

a) The price of the book decreased by 20%.

$15.00             $12.00

  |-----------------|------->

      100%            80%

b) The percentage decrease in the number of students who take the bus to school is 25%.

200               150

  |-----------------|------->

     100%            75%

Calculating percentages involves finding a portion of a whole expressed as a fraction of 100. To calculate a percentage, divide the part by the whole and then multiply the result by 100.

For example, if 20 out of 100 students are absent, the percentage of absent students is:

(20/100) x 100 = 20%.

With that in mind, we can conclude that we have correctly answered this question.

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Answer:

2

Step-by-step explanation:

PEMDAS

(-3+4)2

(1)2

2x1=2

The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

Given that the tοtal number οf bοοks that sοld in a week is 288.

The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.

Assume that the number οf histοry textbοοks sοld was x.

The number οf chemistry textbοοks sοld was (x-72)

The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.

Accοrding tο the questiοn:

2x - 72 = 288

Add 72 frοm bοth sides:

2x - 72 + 72 = 288 + 72

2x = 360

Divide bοth sides by 2:

x = 360/2

x = 180

The number οf histοry textbοοks sοld was 180.

The number οf chemistry textbοοks sοld was (180-72) = 108.

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By using the scale diagram, the height of this person in meters is equal to 1.6 meter.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Based on the information provided about the lorry, the lorry is approximately 11.2 m in length and 14 cm on a scale diagram. Therefore, the height of the person in meters can be calculated as follows;

1 centimeter = 11.2/14

1 centimeter = 0.8 meter.

Height of the person in meters = 0.8 meter × 2

Height of the person in meters = 1.6 meter.

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Answer:

x = 0 y = 7/5

The median increases by 0.5 and the mean decreases by 4.375

What are median and mean?

Median and mean are measures of central tendency that are commonly used in statistics. The median is the middle value in a sorted list of numbers. To find the median, you need to arrange the numbers in order from lowest to highest (or highest to lowest) and then find the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers. The mean is the average of all the numbers in a list. To find the mean, you need to add up all the numbers in the list and then divide by the total number of values. It is calculated by summing up all the values and dividing the result by the total number of values. The mean is influenced by outliers and extreme values in the data.

(a) The median is the middle value in a sorted list of numbers. In the original list, the median is 547. If the number 605 is changed to 549, then the new list becomes:

381, 465, 496, 537, 547, 589, 604, 549

Now the median is the average of the two middle values, which are 547 and 549. Therefore, the median increases by:

(549 + 547)/2 - 547 = 0.5

So, the median increases by 0.5.

(b) The mean is the average of all the numbers in a list. In the original list, the mean is:

(381 + 465 + 496 + 537 + 547 + 589 + 604 + 605) / 8 = 527.5

If the number 605 is changed to 549, then the new list becomes:

381, 465, 496, 537, 547, 589, 604, 549

The mean of this new list is:

(381 + 465 + 496 + 537 + 547 + 589 + 604 + 549) / 8 = 523.125

Therefore, the mean decreases by:

527.5 - 523.125 = 4.375

So, the mean decreases by 4.375

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The correct solution of the expression 5a² -25bˣ is 5(a² - 5bˣ)

From the question, we have the following parameters that can be used in our computation:

5a² -25bˣ

The expression is already in its simplest form in terms of combining like terms.

However, we can still look into factoring the expression

To do this, we can factor out the greatest common factor of 5 and rewrite the expression as follows:

5a² -25bˣ = 5(a² - 5bˣ)

This is the factored form of the expression, where the greatest common factor of 5 has been factored out.

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The explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.

To calculate the population for any year between 1930 and 1975, we can simply substitute the corresponding year for t in the equation. For example, if we want to calculate the population in 1950, we can substitute t = 1950 in the equation.

Therefore, [tex]P(1950) = 0.00004(1950)^1.9 + 1 = 0.0035 + 1 = 1.0035[/tex].

This is the population in 1950. In conclusion, the explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.

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Answer:

16 litres = 100% of the tank capacity

x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)

To solve for x, we can cross-multiply and simplify:

16 * 75 = 100x

1200 = 100x

x = 12

Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.

Answer:

= 12 liters.

Step-by-step explanation:

16*3/4 =48/4.

= 12

Step-by-step explanation:

The correct order of the functions in decreasing order of their periods is:

y = -10sin(pi/5 - 2pi)

y = 2/3cot(pi/4)+6

y = 5csc(3x)+6

y = 1/2tan(5pi/6 + pi)

y = -3cos(x+2pi)

Note: The periods of trigonometric functions are determined by the coefficient of the independent variable (x in this case). The period of y = asin(bx + c) or y = acos(bx + c) is 2pi/b, and the period of y = atan(bx + c) or y = acot(bx + c) is pi/b. The period of y = acsc(bx + c) or y = asec(bx + c) is 2pi/|b|.

The equation with y as the subject is y = x^m / (4x^n - 2)

To solve for y as the subject of the equation, we need to isolate y on one side of the equation. Here's how we can do it,

First, we can rearrange the equation to get all the y terms on one side:

4x^n y - 2y = x^m

Next, we can factor out y from the left-hand side,

y(4x^n - 2) = x^m

Finally, we can divide both sides by (4x^n - 2) to isolate y,

y = x^m / (4x^n - 2)

Therefore, the equation with y as the subject is:

y = x^m / (4x^n - 2)

where m and n are the constants given in the original equation.

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The given question is incomplete, the complete question is:

Hence , write down the equation with y as the subject ( in terms of x ). The value of m and q must be indicated. equation 4x^ny -2y - x^m = 0, m and n are constant

Based on the information in the image, we can infer that the correct four-digit code is: 4321

To find the four-digit secret code we must observe the image carefully, especially the intertwined lines. What we must do is follow the direction of the lines in the order from A to D to identify which number the line of each letter matches.

According to the above we can infer that the lines of each letter coincide in the following way with the numbers:

So according to the image, the four-digit secret code would be 4321.

Note: This question is incomplete. Here is the complete information:

Attached image

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y varies directly as x means

[tex]y=kx[/tex]

y varies inversely with z means

[tex]y=k\div z[/tex]

therefore

[tex]y=(kx^2)\div z[/tex]

k=constant of variation

[tex]6=(k9^2)\div 27[/tex]

[tex]6=(k81)\div27[/tex]

[tex]6=3k[/tex]

divide both sides by 3

[tex]2=k[/tex]

the constant of variation is 2

If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:

What is equation ?

A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.

y = k * (x^2) / z

where k is the constant of variation.

We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:

6 = k * (9^2) / 27

Simplifying, we get:

6 = k * 3

k = 6 / 3

k = 2

Therefore, the constant of variation is 2.
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Answer:200

Step-by-step explanation:

A+B=25

A^2+B^2= 225

we use short multiplication formulas:

(A+B)^2=A^2+B^2+2AB

and solve the equation

25^2=225+2AB

625=225+2AB

625-225=2AB

400=2AB

AB=200

Answer: SA=5183.62788

Step-by-step explanation:

A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788

~Find the radius- 30 divided by 2= 15 so radius =15

1) In the first line item - the Sales Price, Percent Saved and Percent Paid are given.

To work out the Original Price, we can state that: if 20% off the value of x = 800 what is x, (where x is the Original Price)?
If 20% is taken off the value of x, we need to find the original value of x before the discount was applied. We can set up the following equation:

x - 20% of x = 800

Simplifying by factoring out x on the left side, we get:

x * (1 - 20%) = 800

Converting 20% to a decimal, we get:

x * (1 - 0.20) = 800

Simplifying, we get:

x * 0.80 = 800

Dividing both sides by 0.80, we get:

x = 1000

Therefore, the original value of x before the 20% discount was applied is $1000.

Since the Original price is $1000, and the Sales price is $800, that means the Amount of Discount ($) is:

Original Price - Sales Price

= $1,000 - $800
= $200

Thus, the discount value for the Television is $200and the original price is $1000.


2) With regard to the sneakers, Original Price was $80 and the percent saved is 25%.The percentage saved is 75%.

Thus, the Sales Price = Original Price - (Original Price * Percent Saved)
Sales Price = 80 - (80 * 25%)
Sales Price = 80 - 20
Sales Price = $60

Since $20 was removed form the Original Price, that means the Amount of Discount ($) is $20.

3)

For the Video Game, we know the Sales Price and the Percent Paid, which is 90%.
That means $54 = 90% of x, where x is the Original Price.

To find x,
54 = 0.9x
x = 54/0.9
x (Original Price) = $60
Thus, the Original Price of the Video Game is $60.

Since Original Price = $60; and
Sales Price = $54
Amount discounted = Original Price - Sales Price
Amount discounted = 60-54
Amount discounted = $6
As a percentage of the Original Price $6 is: 6/60 * 100

= 10%


4) For the MP3 player, we know that that the Sales Price = $51.60 which is 60% (Percent Paid) of the Original Price. We also know that the Percent saved is 40% of the Original price.

Thus, if $51.6 is 60% of the original price, we can use the following proportion to find the original price:

60% = $51.6 / original price

To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 60%, which is 100% / 60%, or 5 / 3:

original price = $51.6 / (60%)

original price = $51.6 / (0.60)

original price = $86

Therefore, the original price before the 60% reduction was $86.

Amount of Discount = Original Price - Sales Price
= 86 - 51.6
= $34.4

Thus, Original Price and Amount of Discount for the MP3 Player are $86.00 and $34.40 respectively.


5)

For the book, we know that the Amount of Discount is $2.60 which is 80% (Percent Paid) of the Original Price.
If $2.6 is 20% of the original price, we can use the following proportion to find the original price:

20% = $2.6 / original price

To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 20%, which is 100% / 20%, or 5:

original price = $2.6 / (20%)

original price = $2.6 / (0.20)

original price = $13

Therefore, the original price before the 20% reduction was $13.
Since Original price = $13 and Discount given is $2.60, Thus,

Sales Price = Original Price - Discount Given
Sales Price = 13- 2.60
Sales Price = $ 10.40

Note that the percentage saved (discount) =
2.6/13 * 100

= 20%

Thus, the Percentage Saved  = 20%.

6)
For the Snack Bar, we know that the Sales Price is $1.70 and the Amount of Discount is $0.30. This means that the Original Price  =

Sales Price + Discount Given = 1.7 + 0.3

Original Price = $2.00


To find what percent 0.3 is of 2, we can use the following proportion:

x/100 = 0.3/2

where x is the percent we want to find.

To solve for x, we can cross-multiply and simplify:

2x = 30

x = 15

Therefore, $0.3 is 15% of $2 which is the percent saved.

If the percent saved is 15%, then the percent paid is:

100 - 15
= 85%

Thus, the percent paid is 85% of the Original Price.


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(d) The value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3 is 6. (e) The value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3 is -2.

(d) k=6 (e) k=-2

The vertex form of a quadratic function is given as;

f(x) = a(x-h)² + kf(x) = a(x−h)²+k, with vertex (h, k)

∴ for the quadratic equation y=x²+kx+9, the vertex is given by;

x = -b/2a = -k/2 ∴ k = -2x, using x=-3k = -2x = 6,

thus the vertex of the parabola y=x²+6x+9 lies on line x = -3

(e) Similarly, for the quadratic equation y=kx²+3x+4, the vertex is given by;

x = -b/2a = -3/2k ∴ k = -2x/3, using x=3k = -2x/3 = -2(3)/3 = -2,

thus the vertex of the parabola y=-2x²+3x+4 lies on the line x = 3

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m= y2-y1/x2-x1

m= 5-5/2+6= 0

Answer: The slope is equal to zero

Step-by-step explanation:

Find the slope of (-6,5) and (2,5)

First subtract the x coordinates 2 and -6

which equals 8

Next subtract the y coordinates 5 and 5

which equals o

Then you get 8/0 and when you simplify you get 0, so the slope is zero.

The volume of the prism with height h is h times the volume of the prism with height 1 unit.

If the original prism has a volume of V and a height of 1 unit, then the volume of the prism with height h is given by:

Bh = (V)(h)

where B is the area of the quadrilateral base.

The volume of the prism with height h is h times the volume of the original prism. So, we can compare the volume of the two prisms by looking at their volume ratios:

Volume ratio = Volume of prism with height h / Volume of original prism

= Bh / (V)(1)

= Bh / V

= h

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The equation that represents the variation is given by F = 42m/p

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

F varies directly as m and inversely with p, hence:

F ∝ m/p

Let k represent the constant of proportion. Therefore:

F= k*m/p

F = 36 when m = 6 and p = 7. Hence:

36 = k*6 / 7

k = 36 * 7 / 6

k = 42

The equation is F = 42m/p

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The range of values of x that satisfy the inequality 0 ≤ x < 6 is the set of all real numbers between 0 (inclusive) and 6 (exclusive), i.e., the interval [0, 6).

The inequality 0 ≤ x < 6 can be interpreted as follows: x can take on any value between 0 and 6, including 0 but not including 6. This means that x can be any number greater than or equal to 0 and less than 6. In other words, the range of values for x that satisfy this inequality is the set of all real numbers in the interval [0, 6), where the square bracket indicates that 0 is included in the interval (i.e., 0 is a valid value of x) and the round bracket indicates that 6 is excluded from the interval (i.e., 6 is not a valid value of x). This interval can be visualized as a number line with a closed circle at 0 and an open circle at 6, indicating that 0 is included in the range of values for x but 6 is not.

Therefore, any value of x between 0 and 6 (excluding 6) satisfies the inequality 0 ≤ x < 6.

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The new monthly salary after two increases of 6.9% and 15% is 2867.

The new monthly salary after two increases is calculated as follows:

First Increase:

The initial salary of 2332 increases by 6.9%. This is calculated by multiplying the salary by the percentage increase, i.e. 2332 x 0.069 = 160.68. The new salary after the first increase is 2332 + 160.68 = 2492.68.

Second Increase:

The salary after the first increase of 2492.68 is further increased by 15%. This is calculated by multiplying the salary by the percentage increase, i.e. 2492.68 x 0.15 = 373.90. The new salary after both increases is 2492.68 + 373.90 = 2866.58.

Rounded to the nearest dollar, the new monthly salary after both increases is 2867.

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We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. Adrian ran 90 yards during the last football game.

Let's define the variables we will use in this problem:

r: the number of yards Reggie ran during his previous personal best.

m: the number of yards Monte ran during the last game.

a: the number of yards Adrian ran during the last game.

From the problem statement, we know that:

Reggie ran for 180 yards during the last game, which is 40 more yards than his previous personal best: r + 40 = 180.

Monte ran 50 more yards than Adrian during the same game: m = a + 50.

Monte ran the same amount of yards Reggie ran in one game for his previous personal best: m = r.

We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. To solve for a, we need to use the information we have to create an equation that relates a to the other variables.

From the equation r + 40 = 180, we can solve for r by subtracting 40 from both sides: r = 180 - 40 = 140.

Substituting m = r into the equation m = a + 50, we get: r = a + 50.

Now we can substitute the value of r we found earlier into this equation: 140 = a + 50.

Solving for a, we subtract 50 from both sides: a = 90.

Therefore, Adrian ran 90 yards during the last football game.

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Based on the information in the table, the graph shows a diagonal going down from left to right.

To graph in a Cartesian plane we must be clear that it is a tool to graph the coordinates. The first number of the coordinate corresponds to the x-axis (horizontal) and the second number corresponds to the y-coordinate (vertical). According to the above, we can infer the graph would look like this (image attached). This graph corresponds to a function because it is a constant, in this case it is a diagonal line that descends from left to right.

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Answer:

[tex]130m^{2}[/tex] , [tex]65.000 rs[/tex]

Step-by-step explanation:

Given Length = 15m
Given Breadth = 12m

Since there is a 1m gap between the sides,

Actual Length = 15 - 2 = 13m
Actual Breadth = 12 - 2 = 10m

From here find the Area:

L * B = AR of a cuboid , so

13 x 10 = [tex]130m^{2}[/tex] is the Area

for every [tex]m^{2}[/tex] it is 500 rupees, so for [tex]130m^{2}[/tex] ,

130 * 500 = 65,000 rupees.