Sheila had a piece of rope that was 62.41 centimeters long. She cut pieces 8.95, 3.17, and39.77 centimeters long from the rope. How many centimeters of the rope did Sheila have left?

Answer:

y = -0.5x + 6, Domain [0,12] and Range [0, 6]

Step-by-step explanation:

The slope in a linear function represents the rate of change. Since the amount of snow is decreasing (indicating a negative slope) at 0.5 inches an hour, our slope would be -0.5.

Our y intercept, 6, would be the starting amount of snow. At 0 hours, no snow has been melted.

Our domain is [0,12] these are the x values from where at zero there is 6 inches of snow and at 12 there is 0 inches of snow.

Finally, our range is [0,6]. Since there cannot be no more than 6 or less than 0 inches of snow, our range is [0,6]

Hope this helped!

Answer: For number 8, x=6. For number 9, x=7. For number 10, x=15

Step-by-step explanation:

#8:

Angle 16x-6 corresponds to the 90 degree angle. Therefore, they are equal.

16x-6=90

Add six: 16x=96

Divide by 16: x=6

#9

Angle 12x-4 and angle 10x+10 correspond. Therefore, they are equal.

12x-4=10x+10

Subtract 10x: 2x-4=10

Add four: 2x=14

Divide by 2: x=7

#10

Angles 7x and 5x+30 are alternate exterior angles. Therefore, they are equal.

7x=5x+30

Subtract 5x: 2x=30

Divide by 2: x=15

Answer:

The correct answers are:

• The system has one solution.

• The lines intersect.

Step-by-step explanation:

We are given system of linear equations as:

y=x-4--------(1)

and 3 y-x= -7----------(2)

on substituting the value of 'y' from equation (1) into equation (2) we have:

3(x-4)-x=-7

⇒ 3x-3×4-x=-7

⇒ 3x-x= -7+12

⇒  2x=5

⇒

also putting the value of x into equation (1) we have:

• Hence, we get a unique value of x and y on solving the system of  linear equations.

             Hence, the system has one solution.

• the slope for line y=x-4 is 1  ( since on comparing the equation with y=mx+c; where m denotes the slope of line and c is the y-intercept)

                y-intercept is -4

            but the slope of line 3y-x = -7 i.e.

          hence the slope of second line is: .

                  and y-intercept is .

• They represent different lines.

• the lines intersect at the point

Answer and explanation:

Given : Equations and

To find : Which statements about the system are true? Check all that apply.

Solution :

First we solve the system of equations,

 .....(1)

 ......(2)

Substitute y from (1) in (2),

Substitute the value of x in (1),

1) The system has one solution i.e.

2) The system has solution which means it is not parallel lines.

Writing equation in slope from,

where m=1 and c=-4

where and c=-4

3) Both lines have different slopes.

4) Both lines have the same y-intercept.

5) The equations represent the different lines.

6) The lines intersect at

Answer: $ 16,000 profit

Step-by-step explanation:

Given the following :

Profit when economy is strong = 50,000

Profit when economy is moderate = 10,000

Loss when economy goes into recession = 50000

Resulting probabilities of the three probable occurrences are:

Probability of strong economy; p(strong) = 30/100 = 0.3

Probability of moderate; P(moderate) = 60/100 = 0.6

Probability of recession; P(recession) = 10/100 = 0.1

Expected profit :

Summation of the product of each probability and its accompanying profit or loss.

P(strong) × profit of strong = 0.3 × 50000 = 15000

P(moderate) × profit of moderate = 0.6 × 10000 = 6000

P(recession) × loss on recession = 0.1 × 50000 = 5000 = - 5000 ( loss)

Expected profit :

$(15,000 + 6000 - 5000) = $16,000 profit

Answer:

Step-by-step explanation:

In a right-angled triangle, the tangent ratio of an acute angle = the ratio of the length of the opposite side to the length of the adjacent side.

Lets say angle A= 150 degrees (obtuse)

• to find its corresponding acute angle, we need to subtract 150 from 180 degrees, that is, 180-150= 30 degrees.

• Considering a right triangle where angle B=30 degrees. now assuming that the opposite side of angle B has a length of 7 while the adjacent side has a length of 25.

So, the tangent ratio of angle B= the ratio of the length of the opposite side to the length of the adjacent side.

So far we have:

• tan B = opposite/adjacent = 7/25

and because angle A is obtuse, its tangent ratio is the negative of the tangent ratio of its corresponding acute angle.

• So, tan A = -tan 30 = -1/√3 or approximately -0.577.

Step-by-step explanation:

first of all

tan(x) = sin(x)/cos(x)

that is the tangent ratio.

so, the question is also, what happens to sine and cosine for obtuse angles.

remember the trigonometric triangle inside the circle.

sine is the up/down leg (up = positive, down = negative), cosine is the left/right leg (and extension of the leg; of left from the center = negative, if right from the center = positive).

so, for an obtuse angle (90° < angle <= 180°) sine is still up and therefore positive, but cosine is left from the center and therefore negative.

for that reason tan(angle) = sin(angle)/cos(angle) is negative.

in fact, it is -tan(180 - angle).