Determine the length of the line segment shown.

graph of line segment from negative 6 comma negative 5 to 0 comma 3

100 units
25 units
10 units
8 units

a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative​ slope, indicating a decrease. The function representing the highway miles has a positive​ slope, indicating an increase.

b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.

Given

The function y =-1518x + 144.068 represents the railroad miles.

While the function y =-360.5x + 155.18models the number of highway miles.

For each function, x is the number of years after 1995.

The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.

Therefore,

-1518x + 144.068=  -360.5x + 155.18

-1518x+360.5x = 155.18-144.068

1157.5x             = 11.112

                x      = 9

Then,

1995 - 9 = 1986

It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.

A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.

To learn more about mile, refer;

https://brainly.com/question/23245414

#SPJ13

The measure of the angle PRS is given as follows:

m<PRS = 45º.

As stated in this problem, these following angles are given:

MRQ and and QRN form a ray, hence they are supplementary angles.

For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:

142 + x = 180

x = 180 - 142

x = 38º.

The entire diagram forms an angle of 360º, hence:

142 + 38 + 90 + m<MRS = 360º.

270 + m<MRS = 360º

m<MRS = 90º.

The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:

The diagram is given by the image at the end of the answer.

More can be learned about measures of angles at https://brainly.com/question/25716982

#SPJ1

Answer: Solve 5x=(2x+3)

Step-by-step explanation:

The line given passes through two points. These are (-6,0) and (0,-8).

Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.

The slope between two points (x1,y1) and (x2,y2) can be found using the formula:

If we replace our values:

To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.

This number is clearly 3/4. Because

Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.

If we graph this:

Answer: [tex]\angle 2=83^{\circ}[/tex]

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]

This means that [tex]5x+2=3x+40=97[/tex].

Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]

Answer:

The total T can be described as

[tex]T = (B+(B*.15))+1[/tex]

The system of equations has one solution, so it is consistent and independent, the correct option is C.

Here we have the system of equations:

x = 5

y = 6

-x - y + z = 0

By replacing the first and second equations into the third one, we get:

-5 - 6 + z = 0

-11 + z = 0

z = 11

So the solution is (5, 6, 11)

So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).

Then the correct option is C.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer: Undefined

Step-by-step explanation:

There is not enough information to complete the task.

Answer:

Jonathan and Seth

Step-by-step explanation:

multiple the laps by 2 youll get the minutes

Marsha must claim for itemized deductions.

Given,

Last year's gross income is $56,800.

Medical expenses = $4900

State and local income taxes paid = $3100

The mortgage interest paid = $1940

Charitable contributions = $530

Non-reimbursed work expenses = $1200

Standard deduction = $5700

The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670

And the Standard deduction is $5700.

Which is, $11,670 - $5700 = $5970 lesser.

Therefore, Marsha must claim for itemize deductions rather than the standard deductions.

Learn more about itemized deductions and standard deductions at

https://brainly.com/question/12530643?referrer=searchResults

#SPJ4

When 2 to the power of hundred is divided by 5 it show s remainder of 1

2 to the 100th power is solved as follows

2 ^ 100 = 1.2676506 * 10^30

This is solved using a calculator and the solution means that

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2   (2 multiplying itself till the number of 2's are up to 100)

This gives the value = 1.2676506 * 10^30

Division of the  2^100, by 5

2^100 / 5

2^1 / 5 remainder =2

2^2 / 5 remainder = 4

2^3 / 5 remainder = 3

2^4 / 5 remainder = 1

2^5 / 5 remainder = 2

2^6 / 5 remainder = 4

2^7 / 5 remainder = 3

2^8 / 5 remainder = 1

2^9 / 5 remainder = 2

2^10 / 5 remainder = 4

2^11 / 5 remainder = 3

It can be seen that it generates a pattern which is

The pattern counts in 4's. If we follow the pattern and count to 2^30

= 100 / 4

= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1

This is to say

2^97 / 5 remainder = 2

2^98 / 5 remainder = 4

2^99 / 5 remainder = 3

2^100 / 5 remainder = 1

Hence 2^100 divided by 5 will give a remainder of 1

Read more on exponents: https://brainly.com/question/109611

#SPJ1

My first step is to draw a picture

We know that the length is 2 times the width

L = 2w

We are given a width of 4.6 yards

L = 2(4.6) = 9.2 yards

We can find the area by using the formula

A = l*w

A = 9.2 * 4.6

A =42.32 yd^2

Answer:

Angle VSR + Angle SRU = 180° (corresponding angles, sum of angles on a straight line = 180°)

(5x + 4) + (44 + x) = 180

6x + 48 = 180

6x = 132

x = 22

Answer: 26

Step-by-step explanation:

[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]

Answer:

A D

Step-by-step explanation:

An A is 90% to 100% A B is 80% to 89% A C is 70% to 79% A D is 60% to 69%

It depends on the number of decimal points of the values from which we get the average.

Normally it must be rounded to the nearest tenth, 17.3

Answer:

no solutions

Step-by-step explanation:

2x - y = 3 → (1)

- 4x + 2y = 5 → (2)

multiply (1) by 2 and add to (2)

4x - 2y = 6 → (3)

add (2) and (3) term by term

0 + 0 = 11

0 = 11 ← not possible

this indicates the system has no solution

The largest possible value in the list is 35.

What is mean, median and mode?

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.

Given: There is a list of 11 positive integers.

Has a mean of 10, a median of 9 and a unique mode of 8.

Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).

If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.

The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.

The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.

Therefore, the largest possible value of an integer in the list is, 35.

To know more about mean, median and mode, click on the link

https://brainly.com/question/14532771

#SPJ4

Answer:

y = 1/2x - 5

Step-by-step explanation:

The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.

ANSWER:

STEP-BY-STEP EXPLANATION:

In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people

solving for x:

As per the concept of division, they sold 271 cookies boxes per day and there are 6 cookies are remained.

Division:

Division means splitting of a large group into smaller groups such that every group will have an equal number of items.

There are four parts of the division, which are dividend, divisor, quotient, and remainder.

Given,

The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each.

Here we need to find the number of boxes sold per day.

Through the given question we know that,

Number of cookies per day = 3,258

Number of cookies in one box = 12

So, the dividend is 3,258 and the divisor is 12.

So, the number of boxes per day is illustrated using the following diagram.

Based on these, there are 271 boxes are sold per day with 6 remaining cookies.

To know more about Division here.

https://brainly.com/question/21416852

#SPJ1

You have to convert the following number into a fraction:

This is a periodic decimal number, which explicitely is 0.68888888....

In order to convert this number to a fraction you proceed as follow:

You put 0.68 and not 0.688 because to do the convertion you need only the first periodic number (that is, only the first 8). The key is to put in the numerator the complete number as whole number, that is, 68. To this number you subtract the whole part of the decimal number, this whole part is 0 because of the 0.688. Then, in the numerator you have 68 - 0. In the denominator you write a number composed only by 9's. The number of 9 numbers is determined by the number of digits of the first number in the numerator. That is two 9 numbers

Given the system of equations:

x + y - z = 4 eq.(1)

3x + 2y + 4z = 17 eq.(2)

-x + 5y + z = 8 eq.(3)

Add the equations 1 and 3

so,

x + y - z + ( -x + 5y + z ) = 4 + 8

x + y - z - x + 5y + z = 12

6y = 12

y = 12/6 = 2

Substitute with y at eq. (1)

So,

x + 2 - z = 4

x - z = 4 - 2

x - z = 2 eq. (4)

Substitute with y at eq.(2)

3x + 2 * 2 + 4z = 17

3x + 4 + 4z = 17

3x + 4z = 17 - 4

3x + 4z = 13 eq.(5)

solve the equations (4) and (5) together

x - z = 2

3x + 4z = 13

Multiply [ x - z = 2 ] by 4

4x - 4z = 8

3x + 4z = 13

Add the last two equations

4x - 4z + 3x + 4z = 8 + 13

7x = 21

Divide both sides by 7

x = 21/7 = 3

So, x = 3 and y = 2

Substitute with the values of x and y at the equation [ -x + 5y + z = 8 ]

So,

-3 + 5 * 2 + z = 8

solve for z

-3 + 10 + z = 8

z = 8 + 3 - 10

z = 11 - 10 = 1

So,

x = 3 , y = 2 and z = 1

We need to convert 40 degrees to radians:

Then, we need to use the next equation:

Solve it:

Hence, 40 degrees is equal to 2/9π radians.

The equation of line is y = -x + 6

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

The given point are (5, 1) and (7, 11)

We know, the equation of line is,

y = mx + b

where, m = slope

            b = y-intercept

First, find slope i.e m

we know the formula of slope (m) = (y2 - y1) / (x2 - x1)

The points, (x1, x2) = (5, 1) and,

                   (y1, y2) = (7, 11)

put these values in slope formula,

m = (11 -7) / (1 - 5)

   = 4 / -4

m = -1

we get the slope is -1

Next, find y-intercept i.e 'b'

for that, take any one point I'm taking (5, 1) and put these in equation ,

y = mx + b

1 = -1 * 5 + b

1 = -5 + b

b = 6

Now, put slope (m) and y-intercept (b) value in ,

y = mx + b

we get,

y = -x + 6

Hence, the equation of line is y = -x + 6

To read more about Equation of line.

https://brainly.com/question/18831322

#SPJ9

The next three terms for the pattern will be 12, 48, 192 and 768.

It is important to note that a pattern is used to show the sequence of events.

In this case, the first term of a pattern is 12 and the pattern follows the rule "multiply by 4."

This will be:

First term = 12

Second term = 12 × 4 = 48

Third term = 48 × 4 = 192

Fourth term = 768

Learn more about pattern on:

brainly.com/question/27033681

#SPJ1

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The sum of interior angles of a polygon is:

CONCLUSION:

The final answer is:

The starting number of Michael's thought is 96

From the question, the given parameters are:

The above sequence of statements can be represented as

x * (100÷8) + 6.50 = 1206.5

Where x represents the number

So, we have

x * (100÷8) + 6.50 = 1206.5

Evaluate the quotient

x * 12.5 + 6.50 = 1206.5

Subtract 6.50 from both sides

x * 12.5 = 1200

Divide both sides by 12.5

x = 96

Hence, the initial number is 96

Read more about equations at

https://brainly.com/question/21405634

#SPJ1

According to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.

Given :

Blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8.

The formula of z-score is used to determine the probability that their mean blood pressure will be less than 127. The formula of z score is given by:

[tex]z = \frac{\frac{x - m}{\alpha } }{\sqrt{n} }[/tex]

Now, substitute the values of known terms in the above equation.

[tex]z = \frac{\frac{127 - 125}{8} }{\sqrt{100} }[/tex]

[tex]z = \frac{\frac{2}{8} }{10} }[/tex]

Further, simplify the above expression.

z = 2.5

P(z < 2.5) = 0.9938

So, the probability is 99.38%.

Therefore, according to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.

To learn more about probability refer here:

https://brainly.com/question/25870256

#SPJ1