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The volume of the triangular prism is 4.5ft³

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

The volume of a triangular prism = area of the triangular base × height

area of base = 1/2 b× h

12in = 1foot

1 in = 1/12 foot

18 in = 1/12 × 18

= 1.5 feet

= 1/2 × 1.5× 2

= 1.5 ft²

Height of the prism = 3ft

Volume of the triangular prism = 1.5 × 3

= 4.5ft³

Therefore the volume of the triangular prism is 4.5 ft³

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Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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To find out the unit vector in the same direction of other vector, we can calculate the magnitude of its vector and then divide all coordinates by the magnitude, remember that the definition of a unit vector is that its magnitude is 1.

We can calculate the magnitude of a 2D vector as

                                              \(\Large\displaystyle\text{$\begin{gathered}v = \left(x, y\right)\\ \\\|v\| = \sqrt{x^2 + y^2}\end{gathered}$}\)

I'll call the vector (-4, 7) as v, so the magnitude of v is

                                       \(\Large\displaystyle\text{$\begin{gathered}v = \left(-4, 7\right)\\ \\\|v\| = \sqrt{\left(-4\right)^2 + \left(7\right)^2}\\ \\\|v\| = \sqrt{65}\\ \\\end{gathered}$}\)

So the unit vector that i'll call as v with an hat is

                                                   \(\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\end{gathered}$}\)

The vector divided by its magnitude, when we divide a vector by a scalar it's the same as divide all the coordinates, so

                                      \(\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\\ \\\hat{v} = \frac{v}{\sqrt{65}}\\ \\\hat{v} = \frac{\left(-4, 7\right)}{\sqrt{65}}\\ \\ \boxed{\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)}\end{gathered}$}\)

We can also remove the square root from the denominator, then

                            \(\Large\displaystyle\text{$\begin{gathered}\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}, \frac{7}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4\sqrt{65}}{65}, \frac{7\sqrt{65}}{65}\right)\\ \\\end{gathered}$}\)

Use what you prefer!

Hope you liked it

Questions? Ask me in the comments

Answer:

-4/5

Step-by-step explanation:

Answer:

$111.52

Step-by-step explanation:

You have to divide your total amount by 1.15 and that will give you your answer. To check your work you can add your answer and 15% of your answer together. {111.52+(111.52x0.15)=128.25}

The result correct of this expression is 38

-

In a numeric expression, we first resolve the numbers that are in symbol, such as:

The signs calculated in order are:

\( \\ \)

- ( - ) = +

+ ( + ) = +

- ( + ) = -

+ ( - ) = -

\( \\ \)

\( \large \sf = - 32 - ( - 52) - (15 - 33)\)

\( \large \sf = - 32 + 52 - (15 - 33)\)

\( \large \sf = - 32 + 52 - ( - 18)\)

\( \large \sf = - 32 + 52 + 18\)

\( \large \sf = - 32 + 70\)

\( \pink{ \boxed{ \large \sf = 38}}\)

So, the answer correct is 38

The  length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

For this case, consider the figure attached below.

Then, we are given the facts that:

Using the Pythagoras theorem, we get:

\(|AC|^2 = |AB|^2 + |BC|^2\\\\h^2 = (5\sqrt{2})^2 + (5\sqrt{2})^2 \\\\h^2 = 2(5\sqrt{2}))^2\)

Taking root, we get:

\(h = \sqrt{2 (5\sqrt{2})^2}\) (only positive root since h is denoting length, which is a non-negative quantity).

Thus, we get:

\(h = \sqrt{2 (5\sqrt{2})^2} = \sqrt{(5\sqrt{2})^2} \times \sqrt{2} = (5\sqrt{2}) \times \sqrt{2} = 5 \times (\sqrt{2})^2 = 5 \times 2 \\\\h= 10 \: \rm units\)

(square cancelled the square root).

Thus, the  length of the hypotenuse of the triangle whose other two sides are of the length 5√2 units is given by: Option B: 10 units.

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Answer:

10 units.

Step-by-step explanation:

just took the quiz

Answer:

8^8/3

Step-by-step

Part I

Part II

Part III

This a term that represents the amount of how hot or cold a substance is the unit used to measure temperature as regards the question is degrees Celsius.

The range of the graph is temperature while the domain is the time

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Answers:  

Magnitude of force P = 163.041494

Magnitude of resultant force = 184.320997

Values are approximate. Units are in newtons.

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

Explanation:

Let for P be pulled directly to the east. The vector for this force is <x, 0> where x is positive.

The 200 newton force has the vector <200*cos(120), 200*sin(120)>

The resultant vector is <x+200*cos(120),200*sin(120)>. Each component is the sum of the corresponding components of <x,0> and <200*cos(120), 200*sin(120)>

The resultant vector is also <r*cos(70),r*sin(70)>. Note how 70+50 = 120. The 50 degree angle is known, so we effectively do 120-50 = 70 to find the angle of the resultant vector with the positive x axis.

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

The resultant vector expressions we found were

Equate the y components of each resultant vector expression. Solve for r

r*sin(70) = 200*sin(120)

r = 200*sin(120)/sin(70)

r = 184.320997021376

Make sure your calculator is in degree mode.

Let's round this r value to 6 decimal places to simplify things a bit

r = 184.320997

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

Now equate the x components of each resultant vector expression, plug in the r value we found, and solve for x

x+200*cos(120) = r*cos(70)

x+200*cos(120) = 184.320997*cos(70)

x = 184.320997*cos(70) - 200*cos(120)

x = 163.041494

this value is approximate just like r is as well

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

The magnitude of force P is

magnitude = sqrt(x^2+y^2)

magnitude = sqrt(x^2+0^2)

magnitude = sqrt((163.041494)^2+0^2)

magnitude = 163.041494

Which is equal to the x value. This applies because y = 0.

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

The magnitude of the resultant is r = 184.320997 which we found earlier

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Step-by-step explanation:

For the what value of C is the function f(x) = when?

c. x= -2

3. x= 1

x^2 -4 /(x+2)(x-3) otherwise

continuous at x= -2 ?

Answer:

D:60

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x^2 - 5x + 3 + 2x - 7

4x^2 - 3x - 4

The function f(x) = 2x² - 7x + 10 is an odd function.

f(-x) = 2(-x)² - 7(-x) + 10

      = 2x² + 7x + 10

-f(x) = -[2x²- 7x + 10]

      = -2x² + 7x - 10

To determine whether the function f(x) = 2x² - 7x + 10 is even, odd, or neither, we compare f(-x) and -f(x).

1. f(-x) = 2x² + 7x + 10

2. -f(x) = -2x² + 7x - 10

To determine if f(-x) = -f(x) (even function), we substitute -x for x in f(x) and check if the equation holds.

1. f(-x) = 2x² + 7x + 10

         = f(x) (not equal to -f(x))

Since f(-x) is not equal to -f(x), the function is not even.

Next, to determine if f(-x) = -f(x) (odd function), we substitute -x for x in f(x) and check if the equation holds.

2. -f(x) = -2x² + 7x - 10

        = -(2x² - 7x + 10)

        = -(f(x))

Since -f(x) is equal to -(f(x)), the function is odd.

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Answer:

598.16

Step-by-step explanation:

Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²

Answer:

261.3 in.

Step-by-step explanation:

All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

Answer: I think the answer is c

Step-by-step explanation:

tell me if im wrong :(

Answer:150?

Step-by-step explanation:

The correct pairs of the functions and their inverses are given by the image at the end of the answer.

To find the inverse function, we exchange x and y in the original function, then isolate y.

The first function that we want to find the inverse is:

f(x) = (2x - 1)/(x + 2).

Hence:

x = (2y - 1)/(y + 2)

(y + 2)x = 2y - 1

xy + 2x = 2y - 1

xy - 2y = -1 - 2x

y(x - 2) = -1 - 2x

y = (-1 - 2x)/(x - 2) (which is the inverse function).

The second function which we want to find the inverse is:

y = (x + 2)/(-2x + 1)

Then:

x = (y + 2)/(-2y + 1)

x(-2y + 1) = y + 2

-2yx + x = y + 2

-2yx - y = 2 - x

-y(2x + 1) = 2 - x

y = (x - 2)/(2x + 1)  (which is the inverse function).

The third function which we want to find the inverse is:

y = (x - 1)/(2x + 1)

Then:

x = (y - 1)/(2y + 1)

2yx + x = y - 1

2yx - y = -1 - x

y(2x - 1) = -1 - x

y = (-x - 1)/(2x - 1) (which is the inverse function).

The fourth function which we want to find the inverse is:

y = (2x + 1)/(2x - 1)

Then:

x = (2y + 1)(2y - 1)

2yx - x = 2y + 1

2yx - 2y = 1 + x

2y(x - 1) = (1 + x)

y = (x + 1)/(2(x - 1)) (which is the inverse function).

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Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Answer:

B 27.73

Step-by-step explanation:

Use the Pythagorean theorem. It easiest to think of the distance between the two friends as a triangle in the rectangle. One side is 12ft and the other is 25ft.

12^2+25ft^2=769

The square root of 769 is 27.73

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

u  16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Le the numbers be x and y

Then we have equations:

As per the first equation:

Substitute in the second equation

Then finding the value of y

The principal if the bank manager also wants to advertise that one can earn $10 the first month is $4000.

From the information, the simple interest is $10 and the rate is illustrated as 3%.

The formula for the simple interest in a month is illustrated as:

S = (p × r × t/12 / 100)

r = rate

t = time

S = interest

Place the values in the formula:

10 = p × 3 × 1 / 100 × 12

10 = 3p/1200

Cross multiply

3p = 12000

Divide

p = 12000/3

p = 4000

The principal is $4000.

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The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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Answer:

MOP = 62

NOP = 62

Step-by-step explanation:

sorry the answer is tilted