given a function,how can the domain be determined​

The amount of tape that Abigail will use to cover the jewelry box is given as follows:

298 in².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

Hence the amount of tape, given by the surface area, is obtained as follows:

S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)

S = 298 in².

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421

#SPJ1

Answer:

To find how far above the water the lip balm will be after 3 seconds, we need to evaluate the polynomial -16t² + 220 when t = 3.

Substituting t = 3 into the polynomial, we get:

-16(3²) + 220 = -16(9) + 220 = -144 + 220 = 76

Therefore, after 3 seconds, the height of the lip balm above the water will be 76 feet.

Answer:

The answer is

13)CE

14)EG

15)BD

16)BF

Result:

The number of children having an age of 6 1/2 years more than 7 1/4 years = 3/4.

To do this, we would subtract the number of children who are 7 1/4 years old from the number of children who are 6 1/2 years old: x - y

Let x = number of children 6 1/2 years old

Let y = number of children 7 1/4 years old

x = 6 1/2 years or 13/2 years

y= 7 1/4 years or 29/4 years

= 13/2 - 29/4

= (26/4) - (29/4)

= -3/4

Coverting to the absolute value, we get:

|-3/4| = 3/4

Thus, 3/4 more children are 6 1/2 years old than 7 1/4 years old.

Learn more about absolute value at brainly.com/question/12928519

#SPJ1

The total number of people in attendance was 400 people in total.

Let:

x be the no of grandparents

y be the no of parents

z be the no of children

Since there are 400 people total, so we can write the equation:

x + y + z = 400

We also know that there were twice as many parents as grandparents, so we can write the equation:

y = 2x

We know that there were 50 more children than parents, so we can write the equation:

z = y + 50

Now we have a system of three equations with three variables:

x + y + z = 400

y = 2x

z = y + 50

We can solve this system using substitution method

First, we can use the second equation to express y in terms of x:

y = 2x

Next, we can use the third equation to express z in terms of x:

z = y + 50

z = 2x + 50

Now we can substitute these expressions for y and z into the first equation:

x + y + z = 400

x + (2x) + (2x + 50) = 400

5x + 50 = 400

5x = 350

x = 70

So there were 70 grandparents in attendance.

Using the second equation, we can find the number of parents:

y = 2x

y = 2(70)

y = 140

So there were 140 parents in attendance.

Using the third equation, we can find the number of children:

z = y + 50

z = 140 + 50

z = 190

So there were 190 children in attendance.

Therefore, the total number of people in attendance was:

70 grandparents + 140 parents + 190 children = 400 people in total.

Learn more about equation at https://brainly.com/question/18831322

#SPJ1

Answer:

The answer for Area is 189.29in²

Step-by-step explanation:

Area of compound =Area of semi circle +Area of rectangle

r=d/2=10/2=5in

A=1/2pir² + L×B

A=1/2×5² + 10×15

A=25pi/2+150

A=39.29+150

A=189.29in²

The value of the expression is 28 2/3

To determine the value of addition, we need to know that fractions are described as part of a whole number or variables.

From the information given, we have that;

1/9 times 3 to the 3rd power

This is represented as;

(1/9 × 3)³

Divide the values, we get

(3)³

Find the cube

27

Then, we have;

27 + 2(1/6+2/3)

Solve the bracket

27 + 2( 1+ 4 /6)

27 + 2(5/6)

Divide the values

27 + 5/3

81 + 5/3

86/3

Divide the values

28 2/3

Learn more about fractions at: https://brainly.com/question/11562149

#SPJ1

Step-by-step explanation:

Similar triangle ratio:

15  is to 10    as  AB is to 6

15/10 = AB / 6

6 * 15/10 =   AB  =  9   units

The angle between the slant height and the base of the cone is 30.2°.

Recall the formula of the volume of a cone:

V = (1/3)πr²h

where

V = volume,

r = radius,

h = height.

To get the h, we use the volume formula and substitute:

264 = (1/3)π(6²)h

Make h the subject of the formula and simplify:

h = (3/π)(264/36) = 8.8

Therefore, h = 8.8 m.

Now, we find the slant height using the Pythagorean theorem:

s² = r² + h²

Plugging in the values, we get:

s² = 6² + 8.8² = 102.64

s = √(6² + 8.8²)

s = 10.13

To find the angle between the slant height and the base, we use trigonometry:

tan θ = r / s

r = radius of the base

s = slant height

Plugging in the values, we get:

tan θ = 6 / 10.13

tan θ = 0.5925

Find the arctan of θ

θ = tan⁻¹(0.5925)

θ = 30.2°

Learn more about cone here:

https://brainly.com/question/29051184

#SPJ1

Answer:

the answer

Step-by-step explanation:

plein-air painting

Answer:

B' = (-8, -1)

C' (-1, 1)

Step-by-step explanation:

In your question, we are given A which is translated -3 units on the X axis, and translated -5 units on the Y axis.

Using this translation on points B and C we get B' = (-8, -1) and C' (-1, 1).

B = (-5, 4)

      -3, -5

B' = (-8, -1)

C = (2, 6)

     -3, -5

C' = (-1, 1)

Answer:

a₈₁ = - 482

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 2 and d = a₂ - a₁ = - 8 - (- 2) = - 8 + 2 = - 6 , then

a₈₁ = - 2 + (80 × - 6) = - 2 + (- 480) = - 2 - 480 = - 482

The length of DF in the triangle DEF is 10.8 units

The given triangle is DEF

We have to find the length of side DF

We know that the tan function is a ratio of opposite side and adjacent side

tan 42 = DF/12

0.9 =DF/12

DF=12×0.9

DF=10.8

Hence, the length of DF in the triangle DEF is 10.8 units

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

The equation (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

Given that:

(x - 3)²+(y - 7)² = 36

Expanding the square in the given equation, we get:

(x - 3)² + (y - 7)² = 36

(x - 3)(x - 3) + (y - 7)(y - 7) = 36

x² - 6x + 9 + y² - 14y + 49 = 36

x² + y² - 6x - 14y + 22 = 0

Therefore, the equation of the circle (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

More about the equation of the circle link is given below.

https://brainly.com/question/10618691

#SPJ1

The Area of Maria's canvas is 30 ft.

Area of Maria's canvas, we need to know the length of the other side of the rectangle. We can use the Pythagorean theorem to find this length. Let's call it SA.

According to the problem statement, the base edge ST measures 4 ft, and the diagonal AT measures 8.5 ft. Using the Pythagorean theorem, we have:

[tex]AT^2 = ST^2 + SA^2\\8.5^2 = 4^2 + SA^2\\72.25 = 16 + SA^2\\56.25 = SA^2\\SA = \sqrt{56.25}\\SA = 7.5\ ft[/tex]

Now we know that the length of the canvas is 7.5 ft, and the width is 4 ft. Therefore, the area of Maria's canvas is:

Area = length x width

Area = 7.5 ft x 4 ft

Area = 30 square feet

Therefore, the area of Maria's canvas is 30 square feet.

Learn more about Area here:

https://brainly.com/question/27683633

#SPJ1

Answer:

Step-by-step explanation:

tax

Answer:

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

Find the composition of the functions f(x) and g(x), which is written as f(g(x)).

Given functions:

Find f(g(x)):

Evaluate f(g(2)):

So, (f·g)(2) = 14.

The surface area of the figure in this problem is given as follows:

S = 48m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The figure in this problem is composed as follows:

Hence the surface area of the figure is given as follows:

S = 2 x (2 x 2 + 2 x 4 + 2 x 4) + 4 x 1/2 x 2 x 2

S = 48m².

More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421

#SPJ1

The length of the shortest side is 0.28ft

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor = dimension of new shape / dimension of old shape

Perimeter of new rectangle = 12 inches = 1 feet

perimeter of the old = 2(28+32)

= 100feet

scale factor = 1/100

therefore the dimension of the shortest length is

1/100 = x/28

100x = 28

x = 28/100

x = 0.28ft

The shortest length of scale drawing is 0.28feet.

learn more about scale factor from

https://brainly.com/question/25722260

#SPJ1

The required, difference between the perimeters of the two rectangles is 46.03 in. None of the options is correct.

Since rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k. Then:

k = XY / LM = 2.22 / 19

To find the value of k, we can divide 2.22 by 19:

k ≈ 0.117

The area of rectangle LMNP is given as 140.6 in^2. We can use this to find the length of NP:

LM * NP = area of LMNP

19 * NP = 140.6

NP ≈ 7.4 in

Since the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:

XY / YZ = LM / NP

2.22 / YZ = 19 / 7.4

YZ ≈ 1.167 in

Now we can calculate the perimeters of both rectangles:

Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in

Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in

The difference between the perimeters is:

52.8 - 6.77 = 46.03 in

Learn more about the perimeter here:

https://brainly.com/question/6465134

#SPJ1

Answer:5.6

Step-by-step explanation:

28 divided by 5 is 5.6

Answer: $33.6

Step-by-step explanation: 28(.20) will give us our $5.6 discount. now add that on top of 28.

Answer:

Only Carla's

Step-by-step explanation:

I believe the answer is only Carla's because even though the left side is factored, there is still an 8 on the right side. To apply the zero product property rule, the equation needs to equal 0

Meanwhile Carla's works because then the equation would be x²=9 which we can easily take the square root of

Answer:  Only Carla

Step-by-step explanation:

Only Carla

Carla said:

(x+1)(x-1)=8          FOIL

x²-1=8

x²=9

x=±3

Jordan said:

He will use 0 property rule but the factored portion must =0   It equals 8, so you can't use that property.

If the market requires a return of 15% on assets of this risk, the stock should be selling for $3.92.

We can calculate the stock price using the dividend discount model with the following formula: "Stock Price = Dividend / (Required Rate of Return - Dividend Growth Rate)".

Data:

Dividend =  $0.50

Increase its dividend by 2% per year.

The next dividend (D1) can be calculated as:

D1 = D0 x (1 + Dividend Growth Rate)

D1 = $0.50 x (1 + 0.02)

D1 = $0.51

Using these values, we can calculate the stock price as follows:

= $0.51 / (0.15 - 0.02)

= $0.51 / 0.13

= $3.92.

Read more about stock price

brainly.com/question/29362234

#SPJ1

The sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

Using Vieta's formulas, the sum of the roots of the polynomials is 1, so the sum of the two non-positive roots is -1. Let's call these roots r and s. Then we have:

Let r and s be the non-positive roots of the polynomial P(x) = x³ - x² - 18x + k. Then we have:

r + s = -1

rs + k = 18

The sum of the squares of these roots:

r² + s² = (r + s)² - 2rs = 1 - 2(18 - k) = -35 + 2k

For the non-positive roots to be real, the discriminant of the polynomial must be non-negative, i.e.,

D = 18² - 4(1)(-k) = 72 + 4k ≥ 0

Solving for k, we get:

4k ≥ -72

k ≥ -18

So, the smallest value of k that makes the non-positive roots real is -18, and the sum of their squares is:

r² + s² = -35 + 2(-18) = -71

Finally, the sum of the roots of P(x) = 1 (by Vieta's formulas).

Therefore, the sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70

Learn more about polynomials at brainly.com/question/1496352

#SPJ1

Answer:x = midpoint_x - (midpoint_x - (-3)) * (sqrt(5)/6) = 19.5 - (22.5 * sqrt(5))/6 = 19.5 - 3.75sqrt(5)

Step-by-step explanation:To find the x-coordinate of the point that is 2/3 of the distance from (-3, 2) to (42, 32), we first need to find the coordinates of that point.

The distance between the two endpoints of the line segment is:

d = sqrt((42 - (-3))^2 + (32 - 2)^2) = sqrt(45^2 + 30^2) = 15sqrt(45)

The distance from (-3, 2) to the desired point is:

(2/3)d = (2/3)sqrt(45^2 + 30^2)

Let's call the desired point (x, y). We can use the midpoint formula to find the coordinates of the midpoint of the line segment:

midpoint = ((-3 + 42)/2, (2 + 32)/2) = (19.5, 17)

The midpoint is halfway between the two endpoints, so the distance from (-3, 2) to the midpoint is:

sqrt((19.5 - (-3))^2 + (17 - 2)^2) = sqrt(22.5^2 + 15^2) = 15sqrt(5)

To find the coordinates of the desired point, we can use similar triangles. The ratio of the distance from (-3, 2) to the midpoint to the distance from (-3, 2) to the desired point is:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = 15sqrt(5) / 30sqrt(45) = sqrt(5)/6

The ratio of the distance from (42, 32) to the midpoint to the distance from (42, 32) to the desired point is the same:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = sqrt(5)/6

The value of x as shown in the triangular prism is 14 unit.

Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base.

To calculate the value of x of the rectangular pyramid, we use the formula below

Formula:

Where:

From the diagram and the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 14 unit.

Learn more about triangular pyramid here: https://brainly.com/question/30517561

#SPJ1