The volume of the prism is 72 cubic feet. Find the missing height of the triangular prism, and the surface area.

The equation required is 9/ 4 (or 2 1/4).

An equation is a mathematical expression which require the application of some mathematical principles so as to simplify it, or determine the value of the unknown.

In the given equation, it can be simplified as;

1/2 + 5/8 + 9/8

find the LCM of the equation,

1/2 + 5/8 + 9/8 = (4 + 5 + 9)/ 8

                        = 18/ 8

divide the numerator and denominator by 2, to have

18/ 8 = 9/ 4

        = 2 1/4

The equation expected is 9/ 4 (2 1/4).

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The principal amount of $2,287.26 from compound interest at a rate of 4.5% per year owed after six years on a loan of $1300

Since n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, sothe final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

Given that certain loan program offers an interest rate of 4.5%, compounded continuously.

Assuming no payments are made so;

First, convert R as a percent to R as a decimal

r = R/100

r = 4.5/100

r = 0.045 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 1300/ (1 + 0.045 /365)(365)^(15)

P = 1300/ (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer:

16896

Step-by-step explanation:

3×1×11×512

=16896

Step-by-step explanation:

3×1×11×5×1×2=330

Answer:

5 km / 15 km/h = 0.3333 hours

Step-by-step explanation:

This is calculated by dividing the distance he has to travel (5 km) by his average speed (15 km/h) and then converting the result to minutes.

0.3333 hours x 60 minutes/hour = 20 minutes

Answer:

If you ever need help on a question and you don’t know the answer just remember this quote “ purple is always the answer”.

Step-by-step explanation: Hope this helps u!

0.00205 can be written in scientific notation as 2.05 x 10^-3.

Answer:

The answer is 2.05×10‐³

Step-by-step explanation:

0.00205 to scientifi notation or standard form

=2.05×10‐³

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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Answer:

y=−128(x+6)2+12

Step-by-step explanation:

From the information that the question gives us, we have that models:

EZ weights 10 pounds, Box = 10 cubic-foot, represented by letter E

Mini weights 20 pounds, Box = 8 cubic-foot, represented by letter M

Hefty weights 60 pounds, Box = 28 cubic-foot, represented by letter H

The van can hold on a maximum of 440 pounds and has 296 cubic-feet. We have the following equations, to get the optimal solution:

For the weight:

For the volume:

We subtract the two equations to get:

Divide the above equation by 4, to simplify the equation:

Now we express M in terms of H:

Now we start looking for integer solutions for the above equation, given that we want to maximize H, we can look for integer solutions starting with the largest possible, which is 4. But H=4 does not give an integer solution for M. We can try with H = 3

Great, now that we have the number of M (Mini models), we can find the number of Hefty models and EZ models,

For H (Hefty models) we replace M in 3M+8H=36, and solve for H:

To find E, we can take the first equation 10E+20M+60H=440, to express E in terms of H and M, replace and solve:

M = 4

H = 3

E = 18

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

tan= 4

Step-by-step explanation:

This is actually very easy, basically u have 5 - 9.

So you have positive nine and a negative sign, which is used for subtraction, so in the integers rule, positive- negative= negative

so its 4.

I HOPE ITS RIGHT, IM 11

If tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle. The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

It discusses how triangle side lengths and angles relate to one another. Using trigonometric formulas and functions, it is mostly used to determine the unknown side lengths and angles of a right-angled triangle. Six different functions are frequently employed in trigonometry.

It is given that tan(A)=5 and tan(B)=9

As we know,

\(\rm tan(A -B) = \frac{tan A - tan B}{1- tan A tan B}\)

Substitute the given values we get,

tan(A -B) = (tan A - tan B)/(1 + tan A tan B)

tan(A -B)  = (5-9) / (1 + 5 × 9)

tan(A -B) = (-4) / (1 + 45)

tan(A -B) = -4 / 46

tan(A -B) = -2/23

tan(A -B) = - 0.086

Thus ,if tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.

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Answer:

Step-by-step explanation:

If both lines are open the rate of filling is:

Since tank is 1/3 full we need to fill the remaining 2/3 of it.

Time required:

The important variables are the two types of test questions which can be represented as :

Variables are used to represent unknown values which could be worked out in a mathematical expression or problem.

The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer

Therefore, the correct option is C. m for multiple choice, s for short answer

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Step-by-step explanation:

The right trangular prism has 5 surface areas. 2 of them are triangles and 3 of them are rectangles.

Area of triangle

= 0.5(3/2)(2) = 3/2 square units.

Area of 1st rectangle

= (5/2)(5) = 25/2 square units.

Area of 2nd rectangle

= (3/2)(5) = 15/2 square units.

Area of 3rd rectangle

= (2)(5) = 10 square units.

Total Surface Area

= 2 * (3/2) + (25/2) + (15/2) + 10

= 33 square units. (A)

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

The quadratic expression in its standard form is;

ax² + bx + c

Given the expression in the question;

x² - 2x + ------

Compared with the standard for a quadratic expression

Let the missing value be represented by "c"

x² - 2x + c

Now, to find the value of c, we divide the coefficient of x by 2 and then square the result.

Note that, coefficient of x is b

c = ( b/2 )²

We substitute

c = ( -2/2 )²

c = ( -1 )²

c = 1

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

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Answer:

80 books = $400

Step-by-step explanation:

The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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Answer:

1. Choclate Drink

2. Coffee

3. 19 % difference

4.  1 % difference

5. 42% difference

Step-by-step explanation:

Answer:

This should be it

lmk if you have questions

y = x + 3.50.

Answer:

y = x + 3.50

Step-by-step explanation:

I did this lesson good luck!

Answer:

400 points for you

Step-by-step explanation:

To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.

New height = 67ft - 52ft = 15ft

Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.

Therefore, the area of the parallelogram is 900 square feet.

~~~Harsha~~~

Answer:

B. Find the area of the base and multiply it by the height of the cylinder.

Step-by-step explanation:

πr^2h is the formula for finding the volume of a cylinder.

You find the area of the base by squaring the radius, then do pi times base area times height to get the volume.

Answer:

39  shelves needed to build

Step-by-step explanation:

To find the number of shelves needed we need to divide the number of mystery books by 34

We know that. Each shelf can hold 34.

It is given that, There are 1,326 mystery books

So, 1,326/34

39  shelves needed to build

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer:

\(g^-^1(x)=-8\)

\(h^-^1(x)=\frac{x-4}{3}\)

\((h^-^1 \ o\ h)(-3)=-3\)

Step-by-step explanation:

When given the following functions,

\(g=[(-2,-7),(4,6),(6,-8),(7,4)]\)

\(h(x)=3x+4\)

One is asked to find the following,

1. Question 1

\(g^-^1(4)\)

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

\(g^-^1(4)\)

\(g(4)=6\\g(6)=-8\\g^-^1(4)=-8\)

2. Question 2

\(h^-^1(x)\)

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

\(h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)\)

\(h^-^1(x)=\frac{x-4}{3}\)

3. Question 3

\((h^-^1 \ o\ h)(-3)\)

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function (\(h^-^1\)) and simplify. Then substitute (-3) into the result.

\(h^-^1\ o\ h\)

\(\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x\)

Now substitute (-3) in place of (x),

\(=-3\)

Answer:

25

Step-by-step explanation:

The first number in the range 1 - 50 that is divisible by 2 is 2 itself.  Then 4, 6, 8, ....

Here's one way to think and count:

\(2 \rightarrow 1\\4 \rightarrow 2\\6 \rightarrow 3\\8 \rightarrow 4\\\vdots\\50\rightarrow 25\)

In the table, the number on the right is half the number on the left.  The numbers on the right are just counting numbers (natural numbers), so there are 25 even numbers between 1 and 50.

The value of x is -3 and y is 7 for equilateral triangle having x+1, 2x+4 and 3x+y sides.

We can use the fact that an equilateral triangle has equal lengths on each of its three sides to determine the values of x and y.

Given:

First side=x+y

second side= 2x+4

third side=3x+y

An equilateral triangle has three equal sides, hence the following equations can be constructed:

x + 1 = 2x + 4

2x + 4 = 3x + y

Let's tackle each of these equations separately:

x + 1 = 2x + 4

We will subtract x from both sides and subtract 4 from both sides in order to solve this equation:

x + 1 - x = 2x + 4 - x

1 = x + 4

By taking 4 away from both sides, we arrive at:

1 - 4 = x + 4 - 4 , -3 = x

Therefore, x has been determined to be -3.

Now, substitute the value of x in the second equation:

2x + 4 = 3x + y

2(-3) + 4 = 3(-3) + y

-6 + 4 = -9 + y

-2 = -9 + y

y = -2 + 9

y = 7

So, we determined that y has a value of 7.

As a result, the values of x and y are, respectively, x=-3 and y=7

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Answer:

Step-by-step explanation:

In an equilateral triangle all sides are equal.

So each of these sides (and their equations are equal to each other.)

To find x - set the first two (as they only involve x) equal to each other and solve.

x + 1 = 2x + 4

x -x + 1 = 2x - x + 4

1 = x + 4

1- 4 = x + 4 - 4

-3 = x

Then substitute -3 for x in the last equation to find y, also setting it equal to one of the other equations.

3(x) + y = x + 1

3(-3) + y = -3 + 1

-9 + y = -2

-9 + 9 + y = -2 + 9

y = 7

so x = -3 and y equal 7