The graphs of f(x)= x³ + x² - 6x and g(x) = e^x-3-1 have which of the following features in common?

A. Range
B. X-intercept
C. Y-intercept
D. End behavior

Using percentage error, the error factor is ± 2.15 inches and the smallest size is 40.85 inches and largest size is 45.15 inches.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

The formula of percentage error is given as

P.E = [(actual value - estimated value) / actual value] × 100

Since we know the percentage error and actual value, we can find the difference or actual error by;

5 / 100 = x / 43

0.05 = x / 43

x = 2.15

The increase of decrease in size is by a factor of ± 2.15

The smallest size = 43 - 2.15 = 40.85 in

The largest size = 43 + 2.15 =  45.15 in

The smallest and largest size are 45.15 and 40.85 inches respectively

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Answer: 1/2

Step-by-step explanation:

The amount of milk remaining after the milk is sold to the customer and hotel is 18 liters.

Given is that a milkman had 31 liters of milk in the can. He sold 11 liters to a customer and 2 liters to a hotel.

Assume that the remaining milk in the container is denoted by [x]. Then, we can write -

[x] = Total milk - {milk sold to customer + milk sold to can}

[x] = 31 - {11 + 2}

[x] = 31 - 13

[x] = 18

Therefore, the amount of milk remaining in the can is 18 liters.

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Answer:

Below

Step-by-step explanation:

edited:  FOR QIII   (I didn't see that part)

Remember for a right triangle  S-O-H-C-A-H-T-O-A

   Tan is OPPOSITE LEG / ADJACENT LEG

   make the right triangle with legs 3 and 4  ( in quadrant III)

      then the hypotenuse is 5

         sin = opp/ hyp =  - 3/5

            cos = -  4/5

                csc = 1/sin = - 5/3

                   sec = 1/cos = - 5/4

                       cot = 1/tan = 3/4

Answer:2

Step-by-step explanation:

car, and arc, however ar is also a word, not distinctly though.

Answer:

  (a)  -2

  (b)  y -120 = -2(x -10)

  (c)  y = -2x +140

  (d) 2x +y = 140

Step-by-step explanation:

Given a graph with y-intercept 140 and x-intercept 70, you want the slope and various equations describing the graph.

The line drops from a y-value of 140 to 0 as x increases from 0 to 70. The slope is ...

  m = rise/run = -140/70 = -2

The slope of the line is -2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

We have a line with slope -2 that goes through the point (10, 120), so we can write the equation as ...

  y -120 = -2(x -10)

In part (a) we identified the y-intercept as 140, so we can write the equation as ...

  y = mx + b . . . . . line with slope m and y-intercept b

  y = -2x +140 . . . . . . line with slope -2 and y-intercept 140

The slope-intercept equation can be converted to standard form by adding the opposite of the x-term to both sides.

  y +2x = -2x +2x +140 . . . . . 2x added to both sides

  2x +y = 140 . . . . . . . . . standard form equation of the line

The equations whose graphs encompass a region are thus provided. when the region's area is 301.5

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. The simplest technique is to multiply the room's length and width. The floor surface area for a rectangular room is equal to the length times the width. The formula for this is area = length x width (A = lw).

Given

g(x) = x²

x = 0

x = 3

We must determine the area using the functions f(x) and g(x), which are provided.

ₐ∫ᵇ (f(x) + g(x)) dx

₀∫³ (x² + 15(x + 5)) dx

₀∫³ (x²dx  + ₀∫³15(x + 5)) dx

(x³/3) + 15x²/2 + 75x

₀[x³/3]³ + ₀[15x²/2 + 75x]³

[(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]

27/3 + 15(9/2) + 75(3)

9 + 15(4.5) + 7

76.5 + 225

301.5

The equations whose graphs encompass a region are thus provided. when the region's area is 301.5

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Answer:

Step-by-step explanation:

10(a)+5(c)=310

a= number of adult

c= number children

Answer:

206 ft

Step-by-step explanation:

Each wire is a hypotenuse of a right triangle in which the height of the tower is one leg and the distance from the anchor of the wire to the base of the tower is the other leg.

Leg 1: 200 ft

Leg 2: 50 ft

Hypotenuse: x

200² + 50² = x²

x² = 40,000 + 2,500

x² = 42,500

x = √42,500

x = 206

Answer: 206 ft

The equation that represents the graph that gives the number of servings, y, in x pints of frozen yogurt is: y = 3x.

A proportional relationship graph is a straight line graph that passes through the point of origin, (0, 0), which has an equation that can be expressed in the slope-intercept form as y = kx.

"k" is the constant of proportionality, which is the ratio of y to x. k = y/x.

Given the graph above, we need to find the constant of proportionality, k. To do this, use the coordinates of one point on the graph, say (1, 3):

Constant of proportionality, k = y/x = 3/1

k = 3

To write the equation that gives the number of servings, y, in x pints of frozen yogurt, substitute k = 3 into y = kx:

y = 3x

The equation is: y = 3x.

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Answer:

the correct answer is 3

hope it is right

The answer to the expression is 3

The value of x in the parallel lines is 102 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angle, linear angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the value of x using the angle relationships.

Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal.

Therefore,

x = 102 degrees(alternate exterior angles)

Alternate exterior angles are congruent.

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The Area of given figure is 48.28 unit² (Approx.)

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

We are Given Length of parallel lines are 13 , 6 respectively

Diameter of semi-circle = 6

Height of parallelogram = 8

Area of given figure

Radius of semi-circle = Diameter of semi-circle / 2

Radius of semi-circle = 6 / 2

Radius of semi-circle = 3

Area of given figure = [1/2][Sum of parallel line][Height] + [πr² / 2]

Area of given figure = [1/2][13 + 6][8] + [(3.14)(3)² / 2]

Area of given figure = 42 + 6.28

Area of given figure = 48.28 unit² (Approx.)

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Part (a)

The compound interest formula is

A = P*(1+r/n)^(n*t)

where,

For option 1, we have these values:

Plug them into the formula to get:

A = P*(1+r/n)^(n*t)

A = 4000*(1+0.018/4)^(4*3)

A = 4221.4270078004

A = 4221.43

The account balance after three years is $4221.43

Then subtract off the deposit to find the interest made.

i = A - P

i = 4221.43 - 4000

i = 221.43

Answer: Option 1 pays $221.43 in interest.

====================================================

Part (b)

If n heads to infinity, then the compound interest formula is replaced with the continuously compounded interest formula.

That formula is

A = P*e^(r*t)

where the new item 'e' is a special constant.

e = 2.718...

It's similar to how pi = 3.14...

Most calculators have an "e" button, so it's best to let the calculator handle the decimal digits of "e".

For option 2, we have:

So,

A = P*e^(r*t)

A = 4000*e^(0.015*3)

A = 4184.11143963493

A = 4184.11

and,

i = A - P

i = 4184.11 - 4000

i = 184.11

Answer: Option 2 pays $184.11 in interest.

Option 1 is the better choice.

Graphing these equations can help find the solution to the system by unique solution, no solution and infinite number of solution.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given

Graphing these equations can help find the solution to the system by,

There are three possible outcomes when two equations with two variables are considered in a two-dimensional plane.

1.Unique solution: A point will be where the graphs of the two lines connect.

The One equation's coefficient of variation and constant will not be proportionate to another equation's coefficient of variation and constant.

2. No Solution: The two lines run parallel to one another.

While constants are not proportional, the coefficient of variables of one equation will be related to the coefficient of variables of another equation.

3, Infinite number of Solution: The two lines will coincide.

One equation's coefficient of variation and constant will be proportional to another equation's coefficient of variation and constant.

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The compositions of the functions are given as follows:

The domain and the range of the functions are given as follows:

The representation of the composite function is that the output of the inner function works as the input to the outer function, as follows:

(f ∘ g)(x) = f(g(x)).

Hence, at x = 0, the composite function is given as follows:

(f ∘ g)(0) = f(g(0)) = f(1) = 0.

At x = 1, the composite function is given as follows:

(g ∘ f)(0) = g(f(0)) = g(1) = -2.

The definitions of the domain and of the range of a function are given as follows:

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Answer:

$7.25.

Step-by-step explanation:

To find the cost of Wilson's bus ticket, we first need to determine how many additional miles he traveled beyond the first 10 miles. Since the ticket price was $0.50 per 1/2 mile, we can divide the number of additional miles by 0.5 to find the number of additional 1/2 miles. For example, if Wilson traveled 12 miles, he would have traveled 2 miles beyond the first 10 miles. Dividing 2 by 0.5, we get 4, so he would have traveled an additional 4 1/2 miles.

Once we know the number of additional 1/2 miles, we can multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket. For example, if the ticket price was $0.50 per 1/2 mile and Wilson traveled an additional 4 1/2 miles, the cost of the additional portion of the ticket would be 4.5 * $0.50 = $2.25.

Finally, we can add the cost of the initial portion of the ticket, which was $5.00 for the first 10 miles, to the cost of the additional portion to find the total cost of the ticket. For example, if the initial portion of the ticket was $5.00 and the additional portion was $2.25, the total cost of the ticket would be $5.00 + $2.25 = $7.25.

In conclusion, to find the cost of Wilson's bus ticket, we need to divide the number of additional miles he traveled beyond the first 10 miles by 0.5 to find the number of additional 1/2 miles, multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket, and then add that amount to the cost of the initial portion of the ticket to find the total cost.

Answer:$11.00

Explanation:22-2=20

20÷5=4

4÷2=2

2×$5.00=$10

additional 2 miles

2×$0.50=$1

so

$10+$1=$11.00

An equation whose solution is the number of months, m, it takes for the account balance to reach $2000 would be the initial balance minus the monthly rent times the number of months equals $2000.

$4800-$400m=$2000

Given:

initial balance : $4800

removed from the account each month for rent : $400

Since the account starts with $4,800 and decreases by $400 each month, there will be 4800−400m dollars left in the account after m months have passed.

The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is

4800−400m=2000.

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Answer:

x= 12

Step-by-step explanation:

Y[tex]\alpha[/tex] X

Let the constant be k

For the proportionality sign to be gone,a constant has to be introduced.

Since y varies directly,the constant ( k) will multiply x

Y= kx

Substitute for x=6 and y=36 to find k

36=6x

x = 36/6 = 6

To find the value of x,substitute for k = 6 and y = 72

72= 6x

x = 72/6

x=12

Answer:

-3

Step-by-step explanation

x^3+(5x+y)2

-1^3=-1

-1 x -1 x -1 = -1

(5x+y)2

(5(-1)+(4)2

(-5+(4))2

(-1)2 = -2

Bring -1 down from -1^3

-1-2=-3

You answer is -3

By solving the given expression we get sinα as a final result.

What is tanx in terms of sinx and cosx ?

Tanx can be defined as the ratio of sinx and cosx and tanx can be defined by ratio of opposite side and adjacent side also.

Given expression,

secα / (cotα+tanα)

secα can be written as 1/cosα

cotα = cosα/sinα

tanα = sinα/cosα

so,

by substituting we get,

(1/cosα ) / ((cosα/sinα) + (sinα/cosα) )

(1/cosα ) / (cos2α+sin2α)/sinαcosα

(cos square x + sin square x = 1 )

(1/cosα ) /(1/sinαcosα)

= sinα

Hence , By solving the given expression we get sinα as a final result.

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Answer:

x=1

Step-by-step explanation:

---------- -----------

x =1

Isolate the variable by dividing each side by factors that don't contain the variable.

2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.

Given that,

ABC Corp spent $31,250 on a production machine on January 1, 2019. The corporation is depreciating the equipment using the MACRS accelerated depreciation tables for 5-year property, half-year convention, and has chosen not to exercise Section 179 expensing or to claim bonus depreciation in 2019.

We have to find what is the machine's Year 3 depreciation deduction for 2021.

We know that,

Computation of 2018 depreciation (year 3) deduction for the machine using MACRS accelerated depreciation table for 5 year property.

Name of the asset is production machine

Basis of machine is $31,250

MACRS Percentage from MACRS Percentage Table A-1 by IRS Publication 946 for 5 year property using half year convention for 3rd year is 19.20%

2018 depreciation (year 3) deduction for the machine  is

$31,250×19.20%=$6,000

Therefore, 2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.

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The amount of paycheck of Salesperson 1 and Salesperson 2 is $770 and $905 respectively.

What is Percentage?

The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is%. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.

Solution:

Given: Paycheck of Salesperson 1 = 85% of Salesperson 2

Let, Paycheck of Salesperson 2 = x

So, paycheck of Salesperson 1 = 85/100 x

According to the question,

85/100 x + x = 1675

185/100x = 1675

x = 167500 / 185

x = 905.4$ = 905$

Salesperson 1 = 770$

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Answer:

25 + 9^3

Step-by-step explanation:

Answer:

130 more dollars.

Answer:

130

Step-by-step explanation:

Parallel lines have the same slope.

If one line has a slope of 6/7, then the other line also has a slope of 6/7.

If Robert had 362 in his bank account. If he first spent 54 and then 82 then the amount left in Robert bank account is $226.

Two or more expressions with an Equal sign is called as Equation.

Given that the amount in Roberts bank account is $362.

He first spent 54 and then 82

We need to find the amount left in Robert account.

This we can find by finding the total amount he spent and removing total amount spent from the total amount he has in his account.

The total amount he spend=54+82

Fifty four plus eighty two

136

One hundred thirty six.

The amount left we calculate by subtracting 136 from 362.

362-136

We get 226.

Hence, the amount left in Robert bank account is $226.

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The possible Kids' lunches are 32.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Using permutations:

you have

- 2 possible choices for the size (small and large),

- 2 possible choices for the cheese (with and without),

- 2 possible choices for the side order (fries and onion rings)

- 4 possible choices for the fruit drink (orange, grape, cherry and lemonade)

The total Kids' lunches possible, are the total combinations you can get, therefore:

2 × 2 × 2 × 4 = 32

There are 32 possible Kids' lunches.

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