A rectangular prism has a length of 11 inches, a width of 2 inches, and a height of 3 inches. What is the volume of the prism?

Answer:

y intercept = -3

the slope of the line is 1

Step-by-step explanation:

y intercept is the value of y when x = 0

x = 0 when y = -3

Answer

equation of L₁ is y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given L₂

x + 2y = 3 ( subtract x from both sides )

2y = - x + 3 ( divide through by 2 )

y = - \(\frac{1}{2}\) x + \(\frac{3}{2}\) ← in slope- intercept form

with slope m = - \(\frac{1}{2}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{2} }\) = 2

slope of L₁ = 2 and passes through (3, - 1 ) , then

y = 2x + c ← is the partial equation of L₁

to find c substitute (3, - 1 ) into the partial equation

- 1 = 6 + c ⇒ c = - 1 - 6 = - 7

y = 2x - 7 ← equation of L₁

Answer:

3 chocolate bars and 2 graham crackers

Step-by-step explanation:

8 times 3 equals 24

12 times 2 equals 24

The absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

To find the absolute maximum and minimum values of the function f(x) = 8x/(6x + 4) on the interval (1, 5), we need to find the critical points of the function within the interval and evaluate the function at those points, as well as at the endpoints of the interval.

First, let's find the derivative of the function:

f(x) = 8x/(6x + 4)

f'(x) = [8(6x + 4) - 8x(6)] / (6x + 4)^2

f'(x) = [8(2)] / (6x + 4)^2

f'(x) = 16 / (6x + 4)^2

The critical points occur when f'(x) = 0 or is undefined. However, since f'(x) is always positive on the interval (1, 5), there are no critical points within the interval.

Next, let's evaluate the function at the endpoints of the interval:

f(1) = 8(1)/(6(1) + 4) = 8/10 = 4/5

f(5) = 8(5)/(6(5) + 4) = 40/34 = 20/17

Finally, we need to determine which of these values is the absolute maximum and which is the absolute minimum.

Since f(x) is always positive on the interval (1, 5), the function can never be less than 0. Therefore, the absolute minimum value is the smallest value of f(x) on the interval, which occurs at x = 5, where f(5) = 20/17.

To find the absolute maximum value, we compare the values of f(1), f(5), and the maximum value of f(x) as x approaches the endpoints of the interval. We can use the fact that the function is continuous on the closed interval [1, 5] to find the maximum value.

As x approaches 1, we have:

f(x) = 8x/(6x + 4) → 8/10 = 4/5

As x approaches 5, we have:

f(x) = 8x/(6x + 4) → 40/34 = 20/17

Therefore, the absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

To learn more about  absolute maximum value visit:https://brainly.com/question/29449130

#SPJ11

Answer:

12

Step-by-step explanation:

if you have three WHOLE sheets, and you divide them into fourths... 4 times 3, equals 12. Brainly please. :)

Answer:

12 fourths

\(\frac{12}{4}\)

Step-by-step explanation:

If one paper is divided by 4 you have 4 fourths, now you multiply 4 by three and you get 12.

So twelve-fourths is your answer.

Hope this helps and have a great day!

Answer:

B,D,E for sure

Step-by-step explanation:

Not A because a parabola looks different. Not sure about C.

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Since the formula of circumference is 2πr

Answer:

1 7/12 acres of land

Step-by-step explanation:

Tomatoes = 1/3 acre of land

Corn = 3/4 acre of land

Carrots = 1/2 acre of land

Total acres of land he planted = tomatoes + corn + carrots

= 1/3 + 3/4 + 1/2

= (4+9+6) / 12

= 19/12 acres

= 1 7/12 acres of land

Or

= 1.5833333333333 acres

Total acres of land he planted = 1 7/12 acres of land

None of the given options is correct

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

Learn more about theorem here:

brainly.com/question/343682

#SPJ11

In the equations, if 4=10x+7 and 5=12y-8, the value of x - y will be -83 / 60.

We can solve for x and y separately from the given equations and then find the difference between x and y.

From the first equation, we have:

4 = 10x + 7

Subtracting 7 from both sides, we get:

-3 = 10x

Dividing both sides by 10, we get:

x = -3/10

From the second equation, we have:

5 = 12y - 8

Adding 8 to both sides, we get:

13 = 12y

Dividing both sides by 12, we get:

y = 13/12

Therefore, the difference between x and y is:

x - y = (-3/10) - (13/12)

= (-18 - 65) / 60

= -83 / 60

Learn more about equations on;

https://brainly.com/question/2972832

#SPJ1

If 4=10x+7 and 5=12y-8 what is the value of x - y

Answer:

centre (3 ,-1) , r=9

Explanation:

The standard form of the equation of a circle is.

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

a

(

x

−

a

)

2

+

(

y

−

b

)

2

=

r

2

a

a

∣

∣

−−−−−−−−−−−−−−−−−−−−−−−−−

where (a,b) are the coordinates of the center and r , the radius.

For the given equation: a = 3 , b = -1 and r = 9

hence centre = (3 ,-1) and radius = 9

Step-by-step explanation:

The values -3, -9 and -12 satisfy the inequality.

In this question we evaluate each element of the set to determine whether value belongs to the inequation given on statement:

x = 0

\(-13\cdot 0 + 3 \ge 6\)

\(3\ge 6\) (FALSE)

x= -3

\(-13\cdot (-3) +3 \ge 6\)

\(42\ge 6\) (TRUE)

x = -9

\(-13\cdot (-9)+3 \ge 6\)

\(120\ge 3\) (TRUE)

x = -12

\(-13\cdot (-12) +3 \ge 6\)

\(159 \ge 6\) (TRUE)

The values -3, -9 and -12 satisfy the inequality.

We kindly invite to see this question on inequalities: https://brainly.com/question/17675534

Answer:

v = m/D

Step-by-step explanation:

Step 1: Write equation

D = m/v

Step 2: Multiply both sides by v

Dv = m

Step 3: Divide both sides by D

v = m/D

Answer:

(C)Converting to a common denominator

Step-by-step explanation:

Given some of the steps in the derivation of the quadratic formula below:

\(\text{Step 3:} -c + \dfrac{b^2}{4a}=a(x^2+ \dfrac{b}{a}x+ \dfrac{b^2}{4a^2})\\\\\text{Step 4a:} -c + \dfrac{b^2}{4a}=a(x+\dfrac{b}{2a})^2\\\\\text{Step 4b:} \dfrac{-4ac}{4a}+ \dfrac{b^2}{4a}=a(x+\dfrac{b}{2a})^2\)

Step 4b is derived from Step 4a by converting the left-hand side to a common denominator 4a.

Therefore, that which best explains or justifies Step 4b is:

(C)Converting to a common denominator

Answer:

C

Step-by-step explanation:

lol

(a) Function f is one-to-one. (b) not one-to-one. (c) onto. (d) not onto. (e) one-to-one. (f) onto. (g)not one-to-one. (h) not onto. (i) f^(-1)(a) = e, f^(-1)(b) = a, f^(-1)(c) = b, f^(-1)(d) = c, and f^(-1)(e) = d. (j) g^(-1)(a) = e, g^(-1)(b) = b.

(a) Is f one-to-one?

Yes, the function f is one-to-one.

(b) Is g one-to-one?

No, the function g is not one-to-one.

(c) Is f onto?

Yes, the function f is onto.

(d) Is g onto?

No, the function g is not onto.

(e) Is f∘g one-to-one?

Yes, the composition function f∘g is one-to-one.

(f) Is f∘g onto?

Yes, the composition function f∘g is onto.

(g) Is g∘f one-to-one?

No, the composition function g∘f is not one-to-one.

(h) Is g∘f onto?

No, the composition function g∘f is not onto.

(i) Does f have an inverse? If so, find the inverse.

Yes, the function f has an inverse. The inverse function of f is defined as f^(-1)(a) = e, f^(-1)(b) = a, f^(-1)(c) = b, f^(-1)(d) = c, and f^(-1)(e) = d.

(j) Does g have an inverse? If so, find the inverse.

Yes, the function g has an inverse. The inverse function of g is defined as g^(-1)(a) = e, g^(-1)(b) = b, g^(-1)(c) = c, g^(-1)(d) = d, and g^(-1)(e) = a.

To determine the properties of the functions f, g, f∘g, and g∘f, let's analyze the given information.

The set A consists of elements a, b, c, d, and e.

Function f maps each element to the next one in the sequence, forming a cyclic permutation. It moves each element one step forward, and when it reaches the last element, it wraps around to the first element. Since each element of A is uniquely assigned to another element by f, it is one-to-one. Also, every element in A is eventually reached by f, so it is onto.

Function g is not one-to-one because both a and b are mapped to b. However, it is onto because every element in A has at least one pre-image.

For the composition functions:

f∘g represents applying g first and then f. The composition f∘g is one-to-one because g maps distinct elements to distinct images, and f further maps those images to distinct outputs.

f∘g is onto because for every element in A, g maps it to an element in A, and f further maps that element to another element in A.

g∘f represents applying f first and then g. The composition g∘f is not one-to-one because f maps every element in A to b, and g maps both a and d to b.

g∘f is not onto because the range of g is limited to {a, b, c, e}, so not all elements in A are covered.

For the inverse functions:

Function f has an inverse because it is one-to-one and onto. The inverse function f^(-1) reverses the mapping of f, assigning each element in A to its previous element in the sequence.

Function g has an inverse because it is onto but not one-to-one. The inverse function g^(-1) assigns each element in A to its pre-image, which is unique due to the onto property.

(a) Function f is one-to-one.

(b) Function g is not one-to-one.

(c) Function f is onto.

(d) Function g is not onto.

(e) Composition function f∘g is one-to-one.

(f) Composition function f∘g is onto.

(g) Composition function g∘f is not one-to-one.

(h) Composition function g∘f is not onto.

(i) Function f has an inverse: f^(-1)(a) = e, f^(-1)(b) = a, f^(-1)(c) = b, f^(-1)(d) = c, and f^(-1)(e) = d.

(j) Function g has an inverse: g^(-1)(a) = e, g^(-1)(b) = b, g^(-1)(c) = c, g^(-1)(d) = d, and g^(-1)(e) = a.

to know more about the Function visit:

https://brainly.com/question/11624077

#SPJ11

The company spends $600 on a new computer and printer before beginning the project. Statement A best fits the situation modeled by the function.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The complete question is

"The function f(x)=600+2x over x yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function?

a) The company spends $600 on a new computer and printer before beginning the project.

b) The company takes 600 photos before selecting which ones to use for its calendars.

c) The company expects to sell 600 calendars each month.

d) The company will sell the calendars for $6.00 each."

Given;

The average cost function is;

\(\rm f(x) =\frac{600+2x}{x}\)

Where x is the number of calendars made. The formula for the average price is;

\(\rm Average \ cost = \frac{Total \ cost }{ no \ of \ items}\)

After comparing the equation we get;

Total cost = 600+2x

Here, the original cost is 600, and each unit costs $2.The initial cost is a fixed expense that happens when productivity is zero. Before starting the project, the business invests $600 in a new computer and printer.

Hence, option a is correct.

To learn more about the function, refer to:

https://brainly.com/question/5245372

#SPJ1

Answer:

The company spends $600 on a new computer and printer before beginning the project.

Step-by-step explanation:

its A

Therefore, the truth value of Proposition 2A is False.

To determine the truth value of Proposition 2A, let's substitute the given truth values for the variables:

A = True

B = True

X = False

Y = False

Now let's evaluate the truth value of each component of the proposition:

(X ⊃ A) • (B ⊃ ∼ Y):

(False ⊃ True) • (True ⊃ ∼ False)

(True ⊃ True) • (True ⊃ True)

True • True

True

(B ∨ Y) • (A ⊃ X):

(True ∨ False) • (True ⊃ False)

True • False

False

[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]:

True ⊃ False

False

To know more about Proposition,

https://brainly.com/question/31979370

#SPJ11

Answer:

3+3 and 2(3)

Step-by-step explanation:

3+3 and 2(3)

Answer:

yes

Step-by-step explanation:

x+3 = 6 if X is 3

2x = 6

2(3) = 6

so the statement is correct

Answer:

Step-by-step explanation:

consider the lines of reflection as mirrors and write whhat you see on the other side of the mirror

1. Z becomes X

2. T becomes Q

3. B becomes F

4. S becomes Y

5. F becomes B

6. S is stil S because if the point is on thhe line of reflection is stays the same

Answer:

(10x - 9y)(10x + 9y)

Step-by-step explanation:

100x² - 81y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

100x² - 81y²

= (10x)² - (9y)²

= (10x - 9y)(10x + 9y)

Answer:

Step-by-step explanation:

The volume of the solid defined by the given double integral is 6 cubic units. The double integral ∫∫(12 − 6y) dAᵣ, where r = [0, 1] × [0, 1], represents the volume of a solid, and its value is 6 cubic units.

To evaluate the given double integral, we can identify it as the volume of a solid and then calculate it accordingly. The integral is:

∫∫(12 − 6y) dAᵣ

where r represents the region defined by [0, 1] × [0, 1].

In this case, the integrand (12 - 6y) represents the height or the value of the function at each point (x, y) in the region. By integrating this function over the region r, we can find the volume of the solid that lies above the xy-plane and beneath the surface defined by the function.

The region r = [0, 1] × [0, 1] corresponds to a square in the xy-plane with sides of length 1 unit. This means that the bounds of integration for x and y are both from 0 to 1.

Therefore, we can rewrite the given integral as:

V = ∫[0, 1] ∫[0, 1] (12 - 6y) dx dy

To evaluate this integral, we integrate with respect to x first and then with respect to y.

The inner integral with respect to x gives:

∫(12 - 6y) dx = (12x - 6yx) evaluated from x = 0 to x = 1

= (12 - 6y) - (0 - 0)

= 12 - 6y

Now, we can integrate the resulting expression with respect to y:

∫[0, 1] (12 - 6y) dy = 12y - 3y^2 evaluated from y = 0 to y = 1

= (12 - 6) - (0 - 0)

= 6

Therefore, the volume of the solid defined by the given double integral is 6 cubic units.

In conclusion, the double integral ∫∫(12 − 6y) dAᵣ, where r = [0, 1] × [0, 1], represents the volume of a solid, and its value is 6 cubic units.

.Learn more about volume here

https://brainly.com/question/27710307

#SPJ11

Answer:

1. Equal or adjacent

2. 5cm

3. Twice as many? Multiplied by 2?

4. 10 cm

5. 40 cm

Step-by-step explanation:

To find the exact side you have to take the perimeter and divide it with the amount of sides and so on

The area of Texas is about 108 times larger than the area of Delaware.

The area is a measurement of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square inches, square feet, square meters, or square kilometers. In Anderen Worten, if you were to draw a square on a map with 2.69 miles on each side, the area of that square would be equal to the area of Texas. Alaska is the only state in the United States with more land than Texas. In terms of land area, Delaware is the second-smallest state in the United States, only surpassed by Rhode Island.

To find the number of times larger the area of Texas is than the area of Delaware, we need to divide the area of Texas by the area of Delaware:

(2.69 x 10⁵ in²)/(2.5 x 10³ in²) = 107.6

Rounding this to the nearest whole number, we get:

107.6 ≈ 108

So the answer is D. 108.

Therefore, the area of Texas is about 107.6 times larger than the area of Delaware.

To learn more about area, refer to:

https://brainly.com/question/25292087

#SPJ1

Answer:

\(\sqrt{3} + \frac{5\sqrt{3} }{6}\)

Step-by-step explanation:

tan(30°) = \(\frac{\sqrt{3}}{3}\)

cot(30°) = \(\sqrt{3}\)

sin(60°) = \(\frac{\sqrt{3}}{2}\)

\(\frac{\sqrt{3} }{3} +\sqrt{3} +\frac{\sqrt{3}}{2} = \sqrt{3} +\frac{5\sqrt{3} }{6}\)

Answer:

4\(\sqrt{3}\)/3

Step-by-step explanation:

tan 30 = \(\sqrt{3}\) /3

cos 30 = \(\sqrt{3}\)/2

sin 60 = \(\sqrt{3}\)/2

=> Total = \(\sqrt{3}\) /3 + \(\sqrt{3}\)/2 x 2 = 4\(\sqrt{3}\)/3

The probability that point K lies on segment GB is 0.768 . A point K is chosen at random on segment ABTo find: Probability that the point lies on segment GB.

The segment GB is a part of the segment AB. We need to find the probability that point K lies on segment GB. It can be found by dividing the length of segment GB by the length of segment AB.

P(GK) = GB/AB

We know that G is the starting point of segment GB and B is the ending point of segment GB.

Therefore, GB is the portion of AB between G and B.As given, G(-1, -2) and B(3, 4)

Therefore,Length of GB = √[(3 - (-1))² + (4 - (-2))²]= √[4² + 6²] = √52

Length of AB = √[(5 - (-2))² + (7 - (-1))²]= √[7² + 8²] = √113

Therefore,P(GK) = GB/AB = √52/√113 = 0.768 (rounded to three decimal places).

Hence, the probability that point K lies on segment GB is 0.768 (rounded to three decimal places).

Learn more about probability from the given link

https://brainly.com/question/32117953

#SPJ11

To place triangle ABC on top of triangle DEF, we need to choose values for horizontal and vertical translation. By applying the chosen values for horizontal and vertical translation, triangle ABC can be accurately placed on top of triangle DEF, aligning their corresponding vertices and edges

In order to align triangle ABC on top of triangle DEF, we can use horizontal and vertical translation to move triangle ABC to the desired position. Horizontal translation refers to shifting the triangle left or right, while vertical translation involves moving the triangle up or down.

To determine the values for horizontal and vertical translation, we need to consider the relative positions of the vertices of both triangles. By analyzing the coordinates of corresponding vertices in both triangles, we can calculate the horizontal and vertical distances between them.

Once we have calculated the horizontal and vertical distances, we can choose appropriate values for horizontal and vertical translation that will move triangle ABC to coincide with triangle DEF. These values will depend on the specific coordinates and sizes of the triangles involved.

By applying the chosen values for horizontal and vertical translation, triangle ABC can be accurately placed on top of triangle DEF, aligning their corresponding vertices and edges.

Learn more about translation here:

https://brainly.com/question/31938343

#SPJ11

Assuming that T is a linear transformation the standard matrix of T is [T] = [[1 -3], [0 1]].

The standard matrix of the linear transformation T can be found by determining how T maps the standard basis vectors e1 and e2. In this case, T is a vertical shear transformation that maps e1 to e1 - 3e2 and leaves e2 unchanged.

Since T maps e1 to e1 - 3e2, we can represent this mapping as follows:

T(e1) = 1e1 + 0e2 - 3e2 = e1 - 3e2

Since T leaves e2 unchanged, we have:

T(e2) = 0e1 + 1e2 = e2

Now, we can form the standard matrix of T by arranging the images of the basis vectors e1 and e2 as column vectors:

[T] = [e1 - 3e2, e2] = [1 -3, 0 1]

Therefore, the standard matrix of T is:

[T] = [[1 -3], [0 1]]

In general, to find the standard matrix of a linear transformation, we need to determine how the transformation maps each basis vector and arrange the resulting images as column vectors. The resulting matrix represents the transformation in a standard coordinate system.

Learn more about linear transformation here:

brainly.com/question/13595405

#SPJ11

Answer: Refer to the answer below.

Step-by-step explanation: https://brainly.com/question/29008862

The answer I provided here also works with this one.

But anyway:

Pattern: Decrement the x and y axis size by 1 each time.

To draw the next three, simply remove one from the vertical axis and horizontal axis. Do this three times.

The sequence numerically may look something like this:

X { 7, 6, 5, 4, 3, 2, 1 }

Y { 7, 6, 5, 4, 3, 2, 1 }