Derive linear equations what is the y intercept of the line b=

0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.

In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.

To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.

In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.

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The product of 6 √12 and 2√14 in simplest radical form is 24 √42 .

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

We have to find the product of 6 √12 and 2√14 in simplest radical form.

So,   6 √12 x  2√14

= 12 x √12 x √14

= 12 x 2√3 x √14

= 24 x √3 x √14

= 24 √42

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Answer:

The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).

Step-by-step explanation:

Hi,

We need to convert both measurements to the same unit (either km or meters) and then subtract:

Reminder:

1 km = 1000 m

=> 10 km = 10 * 1000 = 10000 m

=> 3 km 500 m = 3 * 1000 + 500 = 3500 m

Now we can subtract:

10000 m - 3500 m = 6500 m

The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).

Good luck!

follow the order

[tex]\pi /2[/tex] should be in between 0 and [tex]\pi[/tex], therefore it should be right in the middle. every 90 degrees, the circle increases by [tex]\pi /2[/tex] as well.

Arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.

An arrangement is a way of organizing or arranging a set of objects in a specific order or sequence.

When arranging the tiles in 3 rows of 4, there are more possible ways to create rectangular arrays using the tiles. For example, you could create a 4x3 array, a 3x4 array, a 2x6 array, a 6x2 array. These different arrays can be useful in a variety of mathematical contexts, such as exploring multiplication and division.

Therefore, arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.

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The equation where F(x) = G has no solution (x). By graphing the functions, the answer has been discovered.

The creation of a relevant function's graph is the first step in the graphing process. If a curve reflects the function at a given point, the curve at that point satisfies the function equation.

We are given two functions as f(x) = (3x + 2) and g(x) = (3x - 5)

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the f(x) function and the blue line represents the g(x) function.

From the graph, it is clear that the two lines are parallel, therefore they will never meet.

Hence, there is no solution where F(x) = G(x).

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Question: Graph the following functions and determine where F(x) = G(x). Select all that apply.

f(x)=(3x+2) and g(x)=3x-5

Answer:

The graph will shift 5 units to the left

Answer:

True

Step-by-step explanation:

Having a budget keeps your spending in check and makes sure that your savings are on track for the future. Budgeting can help you set long-term financial goals, keep you from overspending, help shut down risky spending habits, and more.

The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.

Household refers to a single dwelling unit occupied by a family or other group of people who share common living arrangements. This includes a home, apartment, condominium, or other dwelling. Households can be single-family, multi-family, or even a group of unrelated people. They are typically headed by one or more adults, and may include children, elderly family members, and other dependents.

The total number of households surveyed is 1000 and is represented by the circle outside the two others. The circle on the left represents the number of households with an Aggie fan and it is 670. The circle on the right represents the number of households with a Longhorn fan and it is 450. The circle in the middle represents the number of households with an Aggie or a Longhorn fan and it is 90.

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Step-by-step explanation:

volume = π · r^2 · h

volume = π · 3^2 · 5

volume = π · 9 · 5

volume = π · 45

Answer : 45π

Answer:

Below

Step-by-step explanation:

Slope,m, is the 'x' coefficient =  -1   for this line   y = -x+4-2

Answer: Krysti's mistake was ordering only 12 small T-shirts when she should have ordered more. To figure out how many small T-shirts she should have ordered, we can start by finding out how many classmates wanted small T-shirts:

60% of 25 classmates = 0.60 x 25 = 15 classmates

So, 15 classmates wanted small T-shirts. If Krysti had ordered one small T-shirt for each of these classmates, she would have needed 15 small T-shirts. However, Krysti only ordered 12 small T-shirts, which means she is short by 3 shirts.

To avoid this mistake, Krysti should have double-checked her calculations and made sure that the number of small T-shirts she ordered matched the number of classmates who wanted small T-shirts.

Step-by-step explanation:

Answer:

C 38.1 ft hope this helps

Do know trig? you'll find out that AB is Hypotenuse and we also know the Adjacent side if you don't please take a look at the image below and the cos alpha is equal to Adjacent side/Hypotenuse = AC/AB so AB is Adjacent side/cos alpha

Answer:

D.

Step-by-step explanation:

Answer:

the answer for the problem is D.

Answer:

[tex]1 - 25xy2256xx28( [/tex]

Marginal cost refers to the additional cost of producing one more unit of a product or service.

Marginal cost is the cost of producing one additional unit of a good or service.

In math, marginal cost refers to the additional cost of producing one more unit of a product or service. It is calculated by taking the change in total cost divided by the change in quantity produced.

Marginal cost is an important concept in economics and is used to determine the optimal level of production to maximize profits.

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Answer:

= 12q² - 3

Step-by-step explanation:

3(-4q² - 1)

= -12q² - 3

The coordinate notation for a clockwise rotation of 180° about the origin include the following: (x, y) → (-x, -y).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Generally speaking, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:

(x, y) → (-x, -y)

Where:

In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise direction.

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The man's daily wage is given as follows:

$42.

The man's daily wage is obtained applying the proportions in the context of the problem.

The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:

24/8 = $3 per hour.

Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:

7/5 x 3 = 21/5 = $4.2 per hour.

The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:

10 x 4.2 = $42.

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The man's daily wage is $42.

We know that the woman works 8 hours per day and gets $24 per day, then her hourly pay is the quotient between these two values.

$24/8 = $3 per hour.

And we also know that their wages per hour are in the ratio 7: 5.

Then the man's hourly pay 7/5 times the hourly pay of the woman, then we just need to solve the product below:

(7/5)*$3 = x

(7/5)*$3 = $4.2

And the man works for 10 hours, then the daily wage is 10*$4.2 = $42.

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Average cost per square foot to build a fast-food restaurant is $238 .

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.

Given,

Area of the restaurant = 4000 sqft

Total average cost to build the restaurant

= $952000

Average cost of per sqft

= 952000/4000

= $238

Hence, $238 is the average cost per square foot to build a fast-food restaurant.

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As the total of Rita and Shova's current ages is 20, they are both 20 years old.

A mathematical strategy for resolving proportional and ratio issues is called the unitary method. Finding the value of one unit of an amount and using that value to calculate the value of additional units is what this process entails. The foundation of the unitary approach is the idea that if two quantities are equal, then their ratios must also be equal. For instance, if five apples cost $10, then the expense-to-apple ratio is 10/5 = 2. This ratio can be used to calculate the price of a varied quantity of apples.

given

According to the issue statement, Rita was three times as old as Shova when her age and Shova's current age were equal.

R - (S - R) Equals 3(S - R) (S - R)

When we simplify this solution, we obtain:

2R = 4S - 2S

2R = 2S

R = S

As a result, we are aware that Rita and Shova are both currently the same age.

Additionally, we are aware that their combined current ages are 40 years.

R + S = 40

R = S, so we can change S in the second equation to R:

R + R = 40

2R = 40

R = 20

Rita is currently twenty years old. Since R = S, Shova is 20 years old at the moment.

As the total of Rita and Shova's current ages is 20, they are both 20 years old.

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Answer:

AC = 14.9

BC = 10.5

Step-by-step explanation:

The triangle is a isosceles right triangle with ∠B = 90o, ∠A = ∠C = 45o.

Therefore AB = BC = 10.5

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, which is AC.

AC^2 = AB^2 + BC^2

AC^2 = 2AB^2

AC^2 = 2(10.5)^2

AC^2 = 220.5

AC = √220.5 = 14.85 or 14.9

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

First, square both sides.

[tex]\left(\sqrt{3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}}\, \right)^2= 3^2[/tex]

[tex]3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6} = 9[/tex]

This eliminates the square root over the entire left side of the equation.

Next, multiply both sides by 6 to get rid of the fraction on the left side.

[tex]6\left(3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}\right) = 6( 9)[/tex]

[tex]6(3) + \left(4 + \sqrt{x+3} \, \right)^2 = 6(9)[/tex]

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54[/tex]

Then, subtract 18 from both sides to isolate the squared term.

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54\\\underline{-18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 18}[/tex]

[tex]\left(4 + \sqrt{x+3} \, \right)^2 = 36[/tex]

Now, we can square root both sides.

[tex]\sqrt{\left(4 + \sqrt{x+3} \, \right)^2} = \sqrt{36}[/tex]

[tex]4 + \sqrt{x+3} = \pm 6[/tex]

Remember to use apply the even root property, so that the right side (6) is positive or negative (indicated by the plus or minus sign).

Next, subtract 4 from both sides.

[tex]4 + \sqrt{x+3} = \pm 6 \\ \underline{-4\ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 4}[/tex]

[tex]\sqrt{x+3} = \pm 6 - 4[/tex]

Then, square both sides to get rid of the square root on the left side.

[tex]\left(\sqrt{x+3}\right)^2 = (\pm 6 - 4)^2[/tex]

[tex]x+3 = 2^2[/tex]    OR    [tex]x+3 = (-10)^2[/tex]

We can see that there are two resulting expressions, each of which we can solve individually.

[tex]x+3 = 4[/tex]    OR    [tex]x+3 = 100[/tex]

[tex]\boxed{x = 1}[/tex]                 [tex]\boxed{x\ne97}[/tex]

The reason that x = 97 is crossed out is because when we plug that x-value back into the original equation, it does not come out to be true. Therefore, 97 is an extraneous solution.

Also, see the attached image for another solution (that implores another method).

Answer:

  x = 1

Step-by-step explanation:

You want to solve for x:

  [tex]\sqrt{3+\dfrac{(4+\sqrt{x+3})^2}{6}}=3[/tex]

At any stage where there is a root, you isolate the radical and raise both sides of the equation to a power sufficient to eliminate the radical. Repeat as necessary.

The radical is already on one side of the equation by itself, so we simply square both sides:

  [tex]3+\dfrac{(4+\sqrt{x+3})^2}{6}=9\\\\(4+\sqrt{x+3})^2=6^2\qquad\text{subtract 3, multiply by 6}\\\\|4+\sqrt{x+3}|=6\qquad\text{take the square root}[/tex]

At this point, we note that the sum cannot be negative, so the absolute value bars are irrelevant. Isolating the radical and squaring both sides, we can finish the solution.

  [tex]4+\sqrt{x+3}=6\\\\\sqrt{x+3}=2\qquad\text{subtract 4}\\\\x+3=4\qquad\text{square both sides}\\\\\boxed{x=1}\qquad\text{subtract 3}[/tex]

This is the only solution, as the attached graph shows.

__

Additional comment

Generally, the square root symbol means the positive square root. That is, √z is usually considered to be non-negative.  This is why we use ±√z when we want both signs of the root.

In this problem, the only root we're taking as part of the solution is the root of a square. The possibility of a negative value for the term being squared is handled by using the absolute value brackets: √(z²) = |z|.

For solving these using a graphing calculator, we like to rewrite the equation to the form f(x)=0. That way, the solutions are the x-intercepts.

The following conclusions can be made regarding the given graph -

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is the graph of a straight line as shown in the image.

Only one single graph of a straight line is given. We cannot compare it, so we will analyze its meaning itself.

        {m} = (0 - 2.4)/(0.8 - 0)

        {m} = -2.4/0.8

        {m} = - 3

Therefore, the following conclusions can be made regarding the given graph -

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The translation of the polygon is 6 units to the left

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the polygon be represented as ABCD

Now , the coordinates of the polygon is given as

The coordinate of A = A ( 1 , 3 )

The coordinate of B = B ( 3 , -1 )

The coordinate of C = C ( 7 , -1 )

The coordinate of D = D ( 5 , 3 )

Now , the translated polygon is having the coordinates as

The coordinate of A' = A' ( -5 , 3 )

The coordinate of B' = B' ( -3 , -1 )

The coordinate of C' = C' ( 1 , -1 )

The coordinate of D' = D' ( -1 , 3 )

So , the translation rule is ( x , y ) → ( x - 6 , y )

And , the figure is translated 6 units to the left

Hence , the translation is 6 units to the left

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The monthly principle is $1000

Biweekly pay describes when employees are paid every other week on a specific day of the week. For example, if you want to establish a biweekly pay schedule, you might choose to pay your employees every other Friday. Since every calendar year has 52 weeks, this results in a total of 26 paychecks per year.

Since there are 4 weeks In a month

bi-week = 4/2 = 2 weeks

therefore the monthly principle = 500× 2 = $1000

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Answer:

Below

Step-by-step explanation:

x = original amount of fabric

2/9 * x = amount of cut fabric

8/9 * ( 2/9 * x) = amount of fabric used

8/9 * 2/9 * x =   ( 8 *2) / ( 9 * 9) * x = 16 / 81  x

 she used 16/81  of her fabric