The fish population in a certain lake rises and falls according to the formula F= 1000(30 + 17+ - 12) Here F is the number of fish at time t, where t is measured in years since January 1, 2002, when the fish population was first estimated. (a) On what date will the fish population again be the same as on January 1, 2002? (b) By what date will all the fish in the lake have died?

The equation of the line in standard form of (2/3)x + 3 = 6y - 15 is 2x - 18y = -54.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.

Given the equation (2/3)x + 3 = 6y - 15, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

(2/3)x + 3 = 6y - 15

(2/3)x - 6y = -15 - 3

(2/3)x - 6y = -18

Multiplying both sides by 3 to have integer coefficients.

3[(2/3)x - 6y] = 3(-18)

2x - 18y = -54

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Step-by-step explanation:

12c-4c-9d+d

8c-8d..........

Answer:

8c - 8d

Step-by-step explanation:

Combine like terms..

12c-9d-4c+d

8c - 9d + d

then combine the other like terms then you will get

8c - 8d

Answer:

5n - 10 = 15.

Step-by-step explanation:

If the number is n then 5 times it is 5n.

10 less than this is 5n - 10.

So, the equation is

5n - 10 = 15.

After solving each system, 5x + y = 0, 5x + 2y = 30, the values of x and y are calculated to be -6 and 30 respectively.

The given equations are considered linear equations as the highest power of the variables in these equations is one.

By rearranging the first equation, the value of y can be found to be,

5x + y = 0

y = -5x

Putting the calculated value of y in the second equation,

5x + 2y = 30

5x + 2(-5x) = 30

5x - 10x = 30

-5x = 30

x = 30 / -5

x = -6

To solve for y, put x = -6  in the first equation as follows,

5x + y = 0

5(-6) + y = 0

-30 + y = 0

y = 30

Hence, the values of x and y in these systems are calculated to be -6 and 30 respectively.

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Answer:

0.029

Step-by-step explanation:

The answer

Based on the construction information, the unit rates will be 62, 65, and 63.

So, Rosk Construction's unit rate is 62. This is due to a=62w.

Fosbert's Construction has a unit rate of 65 because:

Therefore the unit rate is 65

Then,

Durable B Construction will have a unit price of 63.

This is due to:

Therefore, based on the construction information, the unit rates will be 62, 65, and 63.

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The correct question is given below:

Three competing subcontractors are reporting their average work output to a large project leader for a new housing development. Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units. Equation from Rosk Construction: a=62w Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew. Forsbert's contracting Number of Full Weeks, w 2 4 6 Area (square feet), a 130 260 390

Answer: (3/2, -2)

Step-by-step explanation:

basically average of the x's and y's

6+-3/2 and -2+-2/2

which gives

(3/2, -2)

Comparing the unit price of each bag of fries, the large bag of fries, which costs $0.014825 per gram, has the lower cost per gram than the other bag.

Unit price is defined as the price or the cost per unit of the item. The importance of the unit price is that it allows the buyer to understand how the total price has been calculated. Unit price can be solved by dividing the total cost to the total amount of the item.

unit price = total cost/total amount

Solving for the unit price of each bag of fries:

small bag : unit price = $1.39/80 grams = $0.017375/gram

large bag : unit price = $1.69/114 grams = $0.014825/gram

$0.014825 < $0.017375

large bag < small bag

Hence, the large bag which costs $0.014825 per gram has the lower cost per gram.

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According to the question, the given data for the clearance rack is as written below:

Regular price of the clearance rack = $[tex]$ 45.99[/tex]

Sales tax = [tex]7.25[/tex] percent

As per the question, multiply the given marked percentage with the regular price to get the exact value.

Therefore, Marked price(in $) = [tex]45.99X0.35 = 16.10[/tex]

Now, subtract the calculated price from the regular price:(in $)[tex]45.99-16.10 = 29.89[/tex]

Multiply the regular price with the sales tax: [tex]29.89X0.0725 = 2.17[/tex]

Add the tax price with the calculated regular price to know the register price: [tex]29.89+2.17=32.06[/tex]

Therefore, [tex]32.06[/tex] is the amount for the shirt ring up for at the register.

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The cost to get 3 small greeting cards and 2 large greeting cards is $15.75 and the it cost to get xx small greeting cards and yy large greeting cards is equals to $1.65(xx) + $5.40(yy)

To find out the cost of three small greeting card we need to multiply the cost of one small greeting card with 3 which equals to $4.95

To find out the cost of two large greeting card we need to multiply the cost of large greeting card with two which equals to $10.80

To find out the cost to get 3 small greeting cards and 2 large greeting cards we need to add $4.95 and $10.80 which equals to $15.75

As explained above to find the cost to get xx small greeting cards and yy large greeting cards we need to multiply with their respective unit price which equals to $1.65(xx) + $5.40(yy)

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this is a proportional relationship that can be written as:

P = 5,184*S

Top see this, just take the quotient between the number of pixels and the number of square inches of each screen, and let's see if we get the same value for the given rows.

31,104/6 = 5,184

For the next row we have:

373,248/72 = 5,184

And so on, you will get the same quotient for the 3 rows, then we can conclude that yes, this is a proportional relationship that can be written as:

P = 5,184*S

Where P is the number of pixels and S is the number of square inches.

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First, he convert the terms into a positive sign, then he replaces the terms, then he used additive and division property for equality.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Ilya was rewriting expressions using the parameters. His work is flawless this time around.

The steps of the solution are given below.

1) 3x - 12 + 7 - 5x = 91

2) 3x + -(12) + 7 + (-5x) = 91

In the 2nd step, he converts all the terms with a positive sign.

3) 3x + (-5x) + (-12) + 7 = 91

In the 3rd step, he places the like terms closer.

4) (3+-5)x + (-12) + 7 = 91

In the 4th step, he took common from the first two terms.

5) -2x + (-5) = 91

6) -2x + 5 + (-5) = 91 +5

In the 6th step, he used the additive property for equality.

7) -2x = 96

8) (-1/2) × (-2x) = 96 × (-1/2)

And in the 8th step, he used division property for equality.

9) x = - 96/2

10) x = - 48

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The area in square inches of triangle is 36.75.

Given,

∠A ≅ ∠P

Tan A = tan P

6/8 = x/14

X= 21/2

Area = 1/2 * 7*21/2

= 36.75 square

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base. Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

Hence, the area in square inches of triangle will be 36.75

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Answer:

Step-by-step explanation:

Perimeter of rectangle = 2(Length+Breadth)

Length= (2+x)ft

Breadth= 3ft

Perimeter= 28ft

P=2(L+B)

[tex]28 = 2((2 + x) + 3) \\ 28 = 2(2 + x + 3) \\ 28 = 2(5 + x) \\ 28 = (2 \times 5) + (2 \times x) \\ 28 = 10 + 2x \\ [/tex]

Collect like terms

[tex]28 - 10 = 2x \\ 18 = 2x \\ \\ \frac{18}{2} = \frac{2x}{2 } \\ \\ 9 = x \\ x = 9[/tex]

Checking

P= 2(L+B)

[tex]28 = 2((x + 2) + 3) \\ 28 = 2((9 + 2) + 3) \\ 28 = 2(9 + 2 + 3) \\ 28 = 2(14) \\ 28 = 2 \times 14 \\ 28 = 28[/tex]

Confirmed

1.) 64 dollars

2.) 145 dollars

3.) -110 dollars?

4.) -50 solldars

54 + 10 = 64

60+85=145

-180+70=-110

37-87=-50

Answer:

Step-by-step explanation:

Okay so the first question you need to add because the store is giving a refund to Clare of $10. The second question you need to subtract $60 from $85. The third one you need to add again 180+ 70. The final problem you need to subtract 87 from 37 (Just know you will get a negative number) I hope this helps you! :D

Based on the ratio and the measurement on the scale drawing, Elena's bed's actual measurements are 200 cm by 150cm.

The scale is given as 1 is to 50.

This means that every centimeter on the drawing is 50 actual centimeters for the bed.

The dimensions are:

= 4 x 50 = 200 cm

= 3 x 50 = 150 cm

Remaining part of the question:

The ratio is 1 to 50

In conclusion, the actual measurements are 200 cm by 150 cm.

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The solution of the inequality expression is -2 ≤ x ≤ 5

The inequality expression is given as

|2x - 3| ≤7

Remove the absolute bracket

So, we have

2x - 3 ≤ 7 and 2x - 3 ≥ -7

Add 3 to both sides of the inequalities

2x ≤ 10 and 2x ≥ -4

Divide to both sides of the inequalities by 2

x ≤ 5 and x ≥ -2

Rewrite as

-2 ≤ x ≤ 5

Hence, the solution of the inequality expression is -2 ≤ x ≤ 5

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The equation of the line r is y = ₋(10/9)x ₊ 7.

Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form

equation of line q is y = ₋10/9x ₊ 2

it's already in slope intercept form.

hence slope is:

m = (₋10/9) from the above the equation.

we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.

y = mx ₊ b

₋3 = ₋10/9 (9) ₊ b

₋3 = ₋10 ₊ b

b = 7

plug the y intercept back into the equation to get our final answer.

y = ₋(10/9)x ₊ 7

hence  we get the equation of the line r as y = ₋(10/9)x ₊ 7.

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The required coordinate of b is given as (-7, 4 ).

Given that,

To determine the coordinate of b  if M is the midpoint of AB. A(1, -4) and M(-3 ,0).

The midpoint is that point the line whose distance from both the ends of the line is equal.

Here,

We have given two coordinates one of the endpoints of AB and the other is midpoint M i.e. A(1, -4) and M(-3, 0).

Definition of midpoint says,

x = [x₁ +  x₂] / 2 ; y = [y₁ + y₂] / 2

x₁ = 1, x = -3 , y₁ = -4, y = 0

now,

-3 = [1 + x₂] / 2 ; 0 = [-4 + y₂] / 2

x₂ = -6 - 1 ; y₂ = 0 + 4

x₂ = -7 : y₂ = 4

Thus, the required coordinate of b is given as (-7, 4 ).

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Answer:

3 1/6

Step-by-step explanation:

Hope this helps you :)

Answer:

3 1/6.

Step-by-step explanation:

4 1/2 - 1 1/3

= 9/2 - 4/3

= 27/6 - 8/6

= 19/6

= 3 1/6.

So, the statement we are provided with is that,

A classmate says that the systems consisting of

x = 0, y = 0 and, z = 0 has no solution.

This statement is clearly wrong, and we look at the points/ conditions that make this statement completely invalid.

Firstly, a system cannot have only zeros like here. In this case, we have zeros for all three terms (x, y, and z).

Secondly, there will be only one answer for this system, which will be a non-zero value or no answer.

Hence one variable is at least not equal to zero for a proper system.

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The product of the irrational numbers 4√21 and 9√6 in simplest radical form is 108√14.

In this problem we must find the product of two radical numbers, whose procedure has to be done by radical properties and other properties:

4√21 × 9√6                           Given

4√(3 × 7) × 9√(2 × 3)             Definition of multiplication

(4√7 × √3) × (9√2 × √3)       Root square of a product

(4√7 × 9√2) × (√3 × √3)       Associative property

36√14 × 3                              Definition of power / Root square of a product

108√14                                  Associative property / Definition of multiplication / Result

The statement is poorly formatted. The correct form is shown below:

What is the product of 4√21 and 9√6 in simplest radical form?

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The value of the unknown variable x in the equation x² + 5² = 13² is 12.

The use of numbers and words in the same mathematical equation is considered as an algebraic expression.

We can calculate the square of a number by multiplying the number by itself.

Therefore, the square of 5 is equal to 5 multiplied by 5 which is equal to 25.

While the square of 13 is equal to 13 multiplied by 13 which is equal to 169.

So to find the value of x, we can rearrange the given equation as:

x² = 13² - 5 ²

x² = 169 - 25

x² = 144

As x² is equal to 144, we can calculate the value of x by taking the square root of the value of 144.

Therefore,

x= √144

x= 12

Hence, the value of the unknown variable x in this equation is 12.

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Answer: c=110.25

Step-by-step explanation:

[tex]r^2+21r+c\\r^2+(2)(r)(10.5)+(10.5)^2=\\(r+10,5)^2\\Hence,\\c=(10.5)^2\\c=(10.5)(10.5)\\c=110.25[/tex]

Answer:

output = -23

Step-by-step explanation:

if x = -2

output = x - 3 - 18 = -2 - 3 - 18 = -23

3. Both triangles are congruent by ASA congruence theorem.

4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.

If two triangles have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent by ASA congruence theorem.

If two triangles have two pairs of corresponding congruent angles and a pair of corresponding non-included congruent sides, then both triangles are congruent by AAS congruence theorem.

3. Both triangles are congruent by ASA congruence theorem.

4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.

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Answer:

√34

Step-by-step explanation:

it would be radical 34.