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big ideas math

To solve many simultaneous linear equations, use the substitution method in algebra.

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.

The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x+y=7 and x-y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage.

There are three steps in the substitution technique:

Therefore, the answer is x= -2 and y= -8.

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At the optimal level where the present worth of cost is $3 million, the B/C ratio is 0 that is present worth of cost that optimizes the benefit/cost ratio.

To find the present worth of cost that optimizes the benefit/cost ratio, we need to solve the given equation:

(PW of benefits)² - 18 * (PW of cost) + 54 = 0

Let's solve this equation to find the present worth of cost.

By rearranging the equation, we have:

(PW of benefits)² = 18 * (PW of cost) - 54

Taking the square root of both sides, we get:

PW of benefits = √(18 * (PW of cost) - 54)

To optimize the benefit/cost ratio, we want to find the value of PW of cost that minimizes the denominator. In this case, we can consider the derivative of the benefit/cost ratio with respect to the PW of cost and set it equal to zero to find the minimum value. Taking the derivative of the benefit/cost ratio with respect to the PW of cost, we get:

d(B/C) / d(PW of cost) = -18 / (PW of benefits)

= -18 / √(18 * (PW of cost) - 54)

Setting the derivative equal to zero, we have:

-18 / √(18 * (PW of cost) - 54) = 0

Solving this equation, we find that PW of cost = $3 million.

Therefore, the present worth of cost for the project that optimizes the benefit/cost ratio is $3 million. To calculate the B/C ratio at the optimal level, we substitute the value of PW of cost into the equation:

(PW of benefits)² - 18 * (PW of cost) + 54 = 0

(PW of benefits)² - 18 * 3 + 54 = 0

(PW of benefits)² = 0

PW of benefits = 0

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Corresponding angles on parallel lines have equal measure

The value of x is 105 degrees

From the complete question (see attachment for figure), we have the following parameters:

Angle ABC = x

Angle CDE = 75

Because lines AB and CD are parallel lines, and lines BC and DE are also parallel lines.

It means that:

Angle ABC + Angle CDE = 180

Substitute x for Angle ABC, and 75 for Angle CDE

x + 75 = 180

Subtract 75 from both sides of the equations

x + 75 - 75 = 180 - 75

Evaluate like terms

x = 105

Hence, the value of x is 105 degrees

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a) The interest on the loan using exact interest and ordinary interest is as follows:

b) The difference between exact interest and ordinary interest amounts is d. $10.38.

Exact Interest is interest based on a period of 365 days.

Ordinary interest is interest based on a period of 360 days.

Loan amount = $35,000

Loan period = August 6 to December 14 (130 days)

Interest rate = 6%

Interest = $35,000 x 6% x 130/365

= $747.95

Interest = $35,000 x 6% x 130/360

= $758.33

Difference = $10.38 ($758.33 - $747.95)

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Answer:

(5.5,3)

Step-by-step explanation:

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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yt is anser 4325

Step-by-step explanation:

3 dollars and 60 cents

6% of 60 is 3.60

Answer:

26 gm

Step-by-step explanation:

Tin is   1   out of (9+1)   = 1/10 th

1/10th * 260 gm  =   26 gm

Then the equation of the parallel line which is parallel to the given line y = -4x - 5 and passing through the point (1, -5) will be y = -4x - 1.

When the distance between the lines is constant then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.

The equation is given below.

y = -4x - 5

The slope of the given line is negative 4. Then the equation of the parallel line will be given as,

y = -4x + c

The parallel line is passing through the point (1, -5). Then we have

-5 = -4(1) + c

-1 = c

Then the equation of the parallel line which is parallel to the given line y = -4x - 5 and passing through the point (1, -5) will be y = -4x - 1.

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Answer:

x=5 y=130

Step-by-step explanation:

27x-5 and 11x-5 = 180

27x-5 + 11x-5 = 180

38x- 10= 180

38x= 190

x=5

11(5)-5 = 50

50 + y= 180

y= 130

Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

choose the third one because a third one look like talking about the degrees and length

Answer:

67

Step-by-step explanation:

Answer.

67°

Step-by-step explanation:

the two lines are parallel so,

angle on line XY 67° is alternate angle on BD so, angle will be opposite angle y.

therefore, angle y= 67°

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Transportation has become an essential part of our daily lives. It has transformed over time and has improved access to transportation services, increased connectivity, and intermodal options.

To meet the various transportation needs, different modes of transportation have evolved, including water, air, rail, 3PL, cross-docking, truck, intermodal, and pipeline. Each mode of transportation has unique characteristics and advantages. In this regard, matching the following transportation characteristics with the appropriate mode of transportation is necessary.

The most capable mode of transportation is the water mode of transportation. It has the highest capacity and can transport a vast amount of goods over long distances. It can transport large, heavy, and bulky goods that are difficult to transport by other modes of transportation. The mode of transportation that provides the most accessibility is the truck mode of transportation. It can reach almost any location as it can travel on roads and highways. It offers door-to-door service, which means that it can pick up the goods from the sender and deliver them to the receiver. The most reliable mode of transportation is the rail mode of transportation. It is not affected by traffic or weather conditions, which means that it can transport goods on time. It also has a low risk of accidents or delays, which makes it a reliable mode of transportation.

The fastest mode of transportation over a long distance is the air mode of transportation. It is the quickest mode of transportation as it can travel at high speeds and can cover long distances in a short time. This makes it ideal for transporting goods that need to be delivered urgently. The mode of transportation that has the lowest per-unit cost is the water mode of transportation. It is the most cost-effective mode of transportation as it can transport a large number of goods at once, which reduces the cost per unit.

Match the following descriptions with the appropriate transportation intermediary. The transportation intermediary that consolidates LTL shipments into FTL shipments is cross-docking. It takes small shipments from multiple companies and consolidates them into larger shipments. The transportation intermediary that is a nonprofit cooperative that arranges for members' shipments is 3PL.The transportation intermediary that brings shippers and carriers together is the intermodal mode of transportation. It provides an intermodal network to connect different modes of transportation to transport goods efficiently.

The transportation intermediary that purchases blocks of rail capacity and sells it to shippers is rail transportation. It makes it easier for shippers to transport goods using the rail mode of transportation.

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Answer:

(-2,3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. convert 2/7

2/7 = 6/21

2. convert 1/3

1/3 = 7/21

3. add 6/21 and 7/21

6/21 + 7/21 = 13/21

4. subtract 13/21 from 21/21

21/21 - 13/21 = 8/21

5. reduce

8/21 is already in the lowest form

The next step to find the y intercepts is the substitute the value of m2 and coordinate of point P in the equation of the line intercepts from equation y= mx + b and then solve for b in each equation.

Bernie wants to write equations in the form of y=mx+b where m stands for slope. The line passing through the point P and that is perpendicular to the s and parallel to the line r.

we are aware that if two lines are parallel then the slopes are equal.

So, m1=m2

and if two lines are perpendicular then product of slopes equal to -1

m1×m2=-1

the y intercepts are the point of intersection between the straight line.

y = mx +b and the y axis. The y intercepts value of y when x=0.

The next step to find the y intercepts is the substitute the value of m2 and the coordinate of point P in the equation of the line intercept from equation y=mx +b and then solve for b in each equation.

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Answer:

495cm²

Step-by-step explanation:

Find the area of all the shapes and then add them together I believe...

Answer:

468 Square Centimeters

Step-by-step explanation:

Surface area can be calculated by adding the areas of each face on a prism:

please let me know if the answer or explanation is incorrect, hope this helps :)

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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The two different mathematical models derived from the Fibonacci's rabbits problem are the Fibonacci sequence and the matrix multiplication model.

The two different mathematical models that can be derived from the Fibonacci's rabbits problem are:

1. Fibonacci sequence:

Start with the initial values of the rabbit population, typically 0 and 1.

Apply the recursive formula F(n) = F(n-1) + F(n-2) for n ≥ 2, where F(n) represents the nth Fibonacci number.

To find any term in the sequence, calculate the sum of the two preceding numbers.

For example, F(0) = 0, F(1) = 1, F(2) = F(1) + F(0), F(3) = F(2) + F(1), and so on.

Continue this process until you reach the desired term in the sequence.

2. Matrix multiplication model:

Create matrices A, B, and C to represent the rabbit population and transformations.

Matrix A: [F(n), F(n-1)] representing the rabbit population at time n.

Matrix B: [[1, 1], [1, 0]] representing the transformation matrix.

Raise matrix B to the power of (n-1) because the first multiplication is already accounted for with matrix A.

Multiply matrix A with B^(n-1) to obtain matrix C, representing the rabbit population after n time periods.

The value F(n) is the first element of matrix C.

Both models provide different perspectives on the growth of the rabbit population. The Fibonacci sequence emphasizes the iterative nature of the problem, while the matrix multiplication model provides a more direct and efficient approach by leveraging matrix operations. These models can be used to calculate Fibonacci numbers and understand the growth pattern of various populations beyond just rabbits.

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Answer:

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=15;x+y=6

Rewrite equations:

x+y=6;2x+3y=15

Step: Solvex+y=6for x:

x+y=6

x+y+−y=6+−y(Add -y to both sides)

x=−y+6

Step: Substitute−y+6forxin2x+3y=15:

2x+3y=15

2(−y+6)+3y=15

y+12=15(Simplify both sides of the equation)

y+12+−12=15+−12(Add -12 to both sides)

y=3

Step: Substitute3foryinx=−y+6:

x=−y+6

x=−3+6

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=3

Answer:

x = 3, y = 3

Step-by-step explanation:

Given the 2 equations

2x + 3y = 15 → (1)

x + y = 6 → (2)

Multiplying 2) by - 2 and adding to (1) will eliminate x

- 2x - 2y = - 6 → (3)

Add (1) and (3) term by term to eliminate x

y = 3

Substitute y = 3 into either of the 2 equations and solve for x

Substituting into (1)

2x + 3(3) = 15

2x + 9 = 15 ( subtract 9 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

D 10/18

Step-by-step explanation:

when you divide the top and bottom by 2, you get 5/9 which is 5:9 not 5:8

Answer:

10 out of 18 as it is giving 5:9

Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Step-by-step explanation:

To find all the factors of a number, multiply all the prime factors of the number in all possible solutions.

Answer:

slope = -1, y-intercept = is n/a. The line is vertical since the y intercept was not given.

Answer:

c. goemon does not trust his rescuers.

Step-by-step explanation:

goemon said it might be poison.

he was cautious about eating the food.