Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1).

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

Learn more about system of inequalities click;

https://brainly.com/question/29785389

#SPJ1

Answer:

Step-by-step explanation:

Corresponding sides of congruent figures are congruent. We can use this fact to find x:

  KL = XY

  3x +9 = 129

  3x = 120 . . . . . subtract 9

  x = 40 . . . . divide by 3

__

Similarly, corresponding angles of congruent figures are congruent. This means ...

  ∠J = ∠W

  (2y +2)° = 122°

  y +1 = 61 . . . . . . divide by 2°

  y = 60 . . . . . . subtract 1

The correct answer is C) 54.34°.

Answer:

Mr. Shim would record the number +10 or 10 for Ben because of the word "more".

For Gail, Mr. Shin would record the number -8 because of the word, "less''.

Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.

I hope this helps better

Answer:

Step-by-step explanation:

\(m=\frac{1}{5}\)       (gradient same as line \(y=\frac{1}{5} x+9\))

Equation of line in point-slope form \(y-y_1=m(x-x_1)\):

  \(y-(-2)=\frac{1}{5} (x-(-2))\)       ( used \(m=\frac{1}{5}\), point (-2,-2)  )

        \(y+2=\frac{1}{5} (x+2)\)

     \(5y+10=x+2\)                  (multiplied both sides by 5)

             \(5y=x-8\)                  (subtracted 10 from both sides)

              \(y=\frac{1}{5} x-\frac{8}{5}\)                 (divided both sides by 5)

Solution: Equation in slope-intercept form is

              \(y=\frac{1}{5} x-\frac{8}{5}\)

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

36 is a multiple of 12

2 is a prime number

2 is a factor of 64

Step-by-step explanation:

This prompt is about Parallel and Skewed Lines. With regard to the attached image:

A pair of skew lines are two lines that do not cross and do not share the same plane. Skew lines are lines that run in entirely opposite directions, similar to "random" lines.

Skew lines are lines that are in distinct planes and never parallel or meet. Parallel lines, on the other hand, are lines that are in the same plane but never meet. Parallel lines, in other words, must exist in two planes; they are parallel inside the same plane.

Learn more about the skew line:
https://brainly.com/question/2603508
#SPJ1

Answer:

x > 3

Step-by-step explanation:

-17x + 2 < -10x - 19

_____________

.Subtract 2 from both sides.

-17x + 2 - 2 < -10x - 19 - 2

____________________

.Simplify.

-17x < -10x - 21

__________________

.Add 10x to both sides.

-17x + 10x < -10x - 21 + 10x

____________________

.Simplify.

-7x < -21

_________________

.Multiply both sides by -1 (reverse the inequality).

(-7x)(-1) > (-21)(-1)

______________________

.Simplify.

7x > 21

_______________________

.Divide both sides by 7.

7x/7 > 21/7

_____________________

.Simplify.

x > 3

\(\qquad\qquad\huge\underline{{\sf Answer♪}}\)

If the given triangles are congruent, then their corresponding sides are equal as well ~

So, let's use this condition

\(\qquad \sf  \dashrightarrow \:2y + 5 = 3y + 2\)

\(\qquad \sf  \dashrightarrow \:3y - 2y = 5 - 2\)

\(\qquad \sf  \dashrightarrow \:y = 3\)

and

\(\qquad \sf  \dashrightarrow \:2x + 7 = 15\)

\(\qquad \sf  \dashrightarrow \:2x = 8\)

\(\qquad \sf  \dashrightarrow \:x = 4\)

Answer:

  B = 80°

  b = 11.343

  c = 11.518

Step-by-step explanation:

Given side a=2 and angle A=10° in a right triangle with the right angle at C, you want to know the measures of B, b, and c.

The sum of angles in a triangle is 180°, so we have ...

  10° +B +90° = 180°

  B = 180° -100°

  B = 80°

This mnemonic is intended to remind you ...

  Sin = Opposite/Hypotenuse

  sin(10°) = 2/c

  c = 2/sin(10°) ≈ 11.343

and

  Tan = Opposite/Adjacent

  tan(10°) = 2/b

  b = 2/tan(10°) ≈ 11.518

The calculations are shown in the attachment.

The approximated area of the shaded region is 92.54 square units

From the question, we have the following parameters that can be used in our computation:

The area of the shaded region in the figure is calculated as

Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2

Using the given dimensions, we have

Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2

Evaluate

Shaded region = 92.54

Hence, the shaded region is 92.54 square units

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

300/1500, 1/5, or 20%

Step-by-step explanation:

There are 1500 students total, but only 300 engineering students. We can represent this as a fraction: 300/1500. When reduced it comes out to 20%.

The value that is not reasonable for the true mean weight of the residents of the town is 193 pounds

Given that the mean weight is 187 pounds with a margin of error of 3 pounds, we can construct the interval as follows:

Mean weight - Margin of error = 187 - 3 = 184 pounds

Mean weight + Margin of error = 187 + 3 = 190 pounds

So, the reasonable range for the true mean weight of the residents of the town is between 184 and 190 pounds.

Now, let's evaluate the options to identify the value that falls outside this reasonable range:

A. 170 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

B. 188 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

C. 193 pounds - This value falls above the upper limit of the reasonable range (190 pounds). Therefore, it is not a reasonable value for the true mean weight.

D. 186 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

E. 182 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

From the options provided, the value that is not reasonable for the true mean weight of the residents of the town is 193 pounds.

Learn more about Margin of Error here:

https://brainly.com/question/16981466

#SPJ1

Answer: x= −16

Step-by-step explanation:

Answer:

 0

Explanation:

Given expression:

\(\sf 6 - (1 \times 4) -2\)

Use BODMAS method:

brackets, order, division, multiplication, addition, subtraction

First simplify variables inside brackets

\(\sf 6 - (4) -2\)

Then simply use subtract integers

\(\sf 0\)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's get it done using Bodmas Rule ~

\(\qquad \sf  \dashrightarrow \: 6 - (1 \times 4) - 2\)

\(\qquad \sf  \dashrightarrow \: 6 - (4) - 2\)

\(\qquad \sf  \dashrightarrow \: 6 - ( 4 + 2)\)

\(\qquad \sf  \dashrightarrow \: 6 - 6\)

\(\qquad \sf  \dashrightarrow \: 0\)

We will get the end result 0, on simplification ~

The statement "there exists x ∈ S ∖ m" means that there exists an element x that belongs to the set S but does not belong to the set m. In other words, x is an element that is present in S but is not present in m.

The phrase "m ⊊ m ∪ {x} ∈ X" states that the set m is a proper subset of the set m ∪ {x}, and this union belongs to the set X. This implies that the set m ∪ {x} contains all the elements of m along with the additional element x.

The phrase "a contradiction" indicates that the statement or assumption being made leads to a logical inconsistency or contradiction. In this context, the contradiction arises from the fact that the assumption that x is not in m contradicts the statement that m ∪ {x} is a proper superset of m.

Overall, the given statement implies that the existence of an element x in S, which is not in m, leads to a contradiction when considering the relationship between m and m ∪ {x}.

For such more question on contradiction

https://brainly.com/question/30459584

#SPJ8

Answer:

6

Step-by-step explanation:

I did the work but like where did that cube go lol

Answer:

1/6 would be the answer because you multiply

1/2 x 1/2 x 1/2 = 1/6

5.   2 by 2 by 1 would work

Step-by-step explanation:

I will assume that we are trying to find the slope between (2,-6) and (-9,-6)

The slope's equation ⇒  \(\frac{y2-y1}{x2-x1}\)

Let's set the variables:

    (x1, y1) --> (2, -6)

    (x2, y2) --> (-9, -6)

Now let's plug them in:

 \(Slope = \frac{-6--6}{-9-2} =\frac{0}{-11} =0\)

Thus the slope of the line is 0.

Hope that helps!

Answer:

C number of binders because the teacher would have to order binders depending on how many students there are.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

yes it have same equation

The value of m ∠ABD will be;

⇒ ∠ ABD = 50°

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

In the diagram, the parallel lines are cut by transversal BC.

And,  BD bisects ∠ABC and m∠3 = 80.

Now,

Since, The parallel lines are cut by transversal BC.

Hence, We get;

⇒ ∠ 3 + ∠ 2 = 180°

⇒ 80° + ∠ 2 = 180°

⇒ ∠ 2 = 180 - 80

⇒ ∠ 2 = 100

And, We have;

⇒ ∠ 2 = ∠ ABC

⇒ ∠ ABC = 100°

Since, BD bisects ∠ABC.

Hence, We get;

⇒ ∠ ABD = 100 / 2

⇒ ∠ ABD = 50°

Thus, The value of m ∠ABD = 50°

Learn more about the parallel lines visit:

https://brainly.com/question/26961508

#SPJ1

Answer:

Option B: The largest diffrence is in Year 4 (negative difference, but it is the largest)

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

For more question on journey visit:

https://brainly.com/question/31381474

#SPJ8

Answer:

Step-by-step explanation:

Given that:

Dinner time =

Answer:

m-1: 31 degrees & m-4: 149 degrees

Step-by-step explanation:

we can start with im very bad at explaining but will try my best.

Step 1:

look at what you're given and remember the rules and principles of finding angles. so were given m-6. when having parallel lines with a perpendicular line the opposing side of the intercept will be the same. meaning that if m-6 is 149 then its opposing side, m-8, will have the same degree. but we know that with straight lines are 180 degrees so now that we have that out of the way we can move to step 2

Step 2:

you have the given and the rules to go with, so now we will begin to apply it. like i was saying a line is 180 degrees, and when we put a line through that we end up having different degrees. although theres an intercept the line is still 180 degrees. so to find the aligning angle we just have to subtract the given angle by our own knowledge.

180-149=31 this aligns with everything in this. there are only 2 angles necessary. 149 and 31, all we have to do now is plug it in.

M-5: 31 degrees

m-6: 149 degrees

m-7: 31 degrees

m-8: 149 degrees

Step 3:

all those annoying angles we just got through, guess what, all you have to do is apply those same angles with m1-m4

M-1: 31 degrees

M-2: 149 degrees

M-3: 31 degrees

M-4: 149 degrees

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

For more such questions on implicit differentiation visit:

https://brainly.com/question/25081524

#SPJ8

Answer: 100

Step-by-step explanation:

Sub in 5 for b in the expression

\(4b^2\\4(5)^2\)

You must do the exponent first as it comes before multiplication in the order of operations

\(4(5)^2\\4(25)\)

Now multiply

\(4(25)\\100\)