whats the surface area of the rectangular prism

Answers

Answer 1

The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

What is the area of a rectangle?

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

How to calculate the area of the rectangular prism?

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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Related Questions

There are 8 blue socks in Sean’s drawer. After he removes 3 blue socks and 4 non-blue socks, the probability to pick a blue sock at random becomes 1/7. How many non-bluesocks were in Sean’s drawer originally?

Answers

Answer:

34

Step-by-step explanation:

you first write the equation:

(8-3) / (8+x-7) = 1/7, where x is the number of non blue socks

so, 5/(1+x) = 1/7

1+x = 35, so x=34

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Last one

Because if we simplify

(4x³y-6xy³)/2xy(2xy(2x²-3y²))/2xy2x²-3y²

Verified

Answer:

D is the correct Answer.

Step-by-step explanation:

4x^3+-6xy^3

      2xy

When dividing exponents you will subtract. Leaving you with 2x^3-3y^2.

Therefore your answer is D.

A. Undefined b. Zero c.negative b. Positive

Answers

I believe the slope is negative. If it was positive then it would have been " / "

Answer:

C

Step-by-step explanation:

• A vertical line has an undefined slope

• A horizontal line has a slope of zero

• A line sloping downwards from left to right has a negative slope

• A line sloping upwards from left to right has a positive slope

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

the line here slopes downwards from left to right and has a negative slope

A salesperson has 7 customers in denver and 13 customers in reno. in how many different ways could she telephone?

Answers

If a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.

Given that the salesperson has 7 customers in denver and 13 customers in reno.

We are required to find the number of ways in which he can make use of telephone.

Number of customers in denver=7

Number of customers in reno=13

Total customers=20

Since he can talk to one customer at one time and he can either choose customer from denver or reno, the number of ways by using combinations will be [tex]7C_{1}[/tex]+[tex]13C_{1}[/tex]

=7+13

=20 ways.

Hence if a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.

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You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying equal monthly payments of \$1,200 until the balance is paid off. If you're being charged 6\% per year, compounded monthly, how long will it take you to pay off the loan?

Answers

Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.

For this problem, the parameters are given as follows:

A(0) = 95000, r = 0.06, n = 12.

Hence the value of the loan after t years is:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]

[tex]A(t) = 95000(1.005)^{12t}[/tex]

You have monthly payments of $1,200, hence the amount paid after t years is:

P(t) = 12 x 1,200t = 14400t

Then we have to solve for:

A(t) = P(t)

[tex]14400t = 95000(1.005)^{12t}[/tex]

Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.

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A rectangular prism with a square base is cut from the center of a triangular prism. each side of the square base measures 1.7 units.what is the volume of the shaded solid? round to the nearest tenth of a cubic unit.11.6 units345.4 units357.0 units368.6 units3

Answers

Rounding to the closest tenth of a cubic unit, the shaded solid's volume is 45.4 cubic units.

What is rectangular prism?

The 3D shape of a rectangular prism has six rectangular faces. Multiply a rectangular prism's three dimensions—length, width, and height—to determine its volume. Cubic units are used to measure volume.

According to the given information:

The following formula can be used to determine a rectangular prism's volume:

Vr = Height * Width * Length

Triangular prism volume Vt is determined by its base area and height.

concerning the rectangular prism;

Vr = 1.7 × 1.7 × 4

Vr = 11.56 units in 3

Regarding the triangular prism

Vt = 0.5 × 5.7 × 5 × 4

Vt = 57 unit3

Volume of the solid shaded by Vt - Vr

The solid's shaded volume is equal to 57 - 11.56.

The colored solid's volume is 45.44 cubic units.

Due to this, the shaded solid's volume, when rounded to the nearest tenth of a cubic unit, is 45.4 cubic units.

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List the sides in order from the smallest to the largest 83 56 41

Answers

the order from smallest to largest is:

41, 56, 83.

How to list from smallest to largest?

Here we have 3 values, that are:

{83, 56, 41}

To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.

Then the middle number. Which is 56, that is larger than 41 and smaller than 83.

Finally, the largest number, which is 83.

Then the order is:

41, 56, 83.

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Find the value of each variable.

Answers

one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°

So in this case to get x we= 180°-105°=285°

therefore x is 285°

How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week

Answers

Answer: It will be A Day

Step-by-step explanation:

From the figure below, identify all pairs of alternate interior and alternate exterior angles

Answers

A.

alternate exterior

exterior means outside

like a front entrance to a home

1. o & t

2. n & u

B.

alternate interior

interior means inside

like as if its inside a house

1. p & s

2. q & r

( p & s ) AND ( q & r ) both look like the letter Z

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divide.
6 divided by 2 2/7

Answers

Answer:

2.625

Step-by-step explanation:

2 2/7 in decimal form is 2.2857

6 / 2.2857 = 2.625

Answer: 2.625 or 2 and 5/8

Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.

Answers

The volume of the figure is 1, 005. 4 mi³

Volume of a cylinder

Note that the figure is a cylinder

The formula for volume of a cylinder is given as;

Volume = πr²h

Where

h = height = 5 mi

r = radius = 8mi

Substitute into the volume

Volume = 3. 142 × 8 × 8 × 5

Volume = 1,005. 4 mi³

Thus, the volume of the figure is 1, 005. 4 mi³

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Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.​

Answers

Answer:

When the eqn cuts the x-axis , y=0

3x=12

x=12/3

x=4

So,at x=4 is the point at which the linear equation cuts the x-axis

Answer:

collect like terms

12xy=12

xy=1

A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade

Answers

The area of the plastic used to form the lampshade is 2021.25 square centimeters

How to determine the area of the plastic used to form the lampshade?

The given parameters in the question are:

Outer radius, R = 28 cm

Inner radius, r = 7 cm

Angle, ∅ = 315

The area of the plastic used to form the lampshade is calculated using the following area  of sector formula

A = ∅/360 * π(R² - r²)

Substitute the known values in the above equation

A = 315/360 * 22/7 * (28² - 7²)

Evaluate the exponents

A = 315/360 * 22/7 * (784 - 49)

Evaluate the difference

A = 315/360 * 22/7 * 735

Evaluate the product

A = 2021.25

Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters

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Find the indicated maximum or minimum value of f subject to the given constraint. maximum: f(x,y,z)=x2y2z2; x2 y2 z2=4

Answers

The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.

An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.

A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development.  Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.

Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.

From &22 = x²y 2

2

Given 2²+7+2=5

= <**,4),2=>

By Logange's multijet

(2643805 = 12'aresta

Mithaling by by and

and y

x²²* = P ←

: +(1,2,2) = $

= 125

279

The maximum value is 12r

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A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?

Answers

The approximate area of the hexagon  = 672 cm²

What is hexagon ?

In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.

apothem of the hexagon = 14 cm

perimeter of the hexagon = 96 cm

Area of the hexagon = [(3√3) / 2] a²     ; where a is the measure of the side

hexagon has 6 sides.

Perimeter = 6a

96 cm = 6a

96 cm / 6 = a

16 = a

There are 6 triangles in the hexagon .

Area of a triangle = (height * base) / 2

A = (14 cm * 16 cm) / 2

A = 224 / 2

A = 112 cm²

The approximate area of the hexagon = 112 cm²  * 6 triangles = 672 cm²

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Answer: D). 672 cm2

Step-by-step explanation:

H=(,),()

F=(),()

Help please asap

Thanks so much

Answers

From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

According to the statement

we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.

So, to find the points of the rectangle

firstly the given points are:

E(2,3) And G(-2,-2) and we have to find the point H and F.

So, The point H :

For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.

So, the point H become H(-3,3)

And for point F:

For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.

So, the Point F become F(2,-2).

So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

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Using the online tool, find two different combinations of radius and height that produce two cylinders with nearly the same volume. Record the
dimensions and volumes of the two cylinders below.

Answers

The radii and the heights of the two cylinders are

Cylinder 1: Height = 6 and Radius = 5Cylinder 2: Height = 10 and Radius = 3.87

How to determine the combinations of radius and height?

The volume of a cylinder is

V = πr²h

When the volumes of two cylinders are almost equal, then it means that:

V1 ≈ V2

This gives

πr²h ≈ πR²H

Divide both sides by π

r²h ≈ R²H

Assume that r = 5 and h = 6

So, we have:

5² * 6 ≈ R²H

Evaluate the product

150 ≈ R²H

Assume H = 10

So, we have:

150 ≈ R² * 10

Divide by 10

R² ≈ 15

Take the square root of both sides

R ≈ 3.87

Hence, the radii and the heights of the two cylinders are

Cylinder 1

Height = 6 and Radius = 5

Cylinder 2

Height = 10 and Radius = 3.87

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Answer:

These radius and height values will produce the same volume:

radius = 6 units and height = 18 units

radius = 9 units and height = 8 units

The angle between the generator and the central axis of a double-napped cone is 60°. a plane intersecting the cone makes an angle of 50° with the central axis. which conic section is formed?

Answers

The right option is (c).

As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.

What is Hyperbola?

A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.

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I understand that the question you are looking for is:

"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"

(a)circle

(b)ellipse

(c)hyperbola

(d)parabola

Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.

Answers

The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].

Then the plane we want has equation

[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]

Find the measure of the third angle of a triangle if the measures of the other two angles are given. 35.5 and 82.6

Answers

Answer:

61.9°

Step-by-step explanation:

The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.

Set up an Equation

Let the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...

[tex]35.5+82.6+x=180[/tex]

Solve the Equation

Start by adding the like terms on the left side of the equation:

[tex]118.1+x=180[/tex]

Then, subtract both sides by 118.1:

[tex]x=61.9[/tex]

Therefore the measure of the third angle of the triangle is 61.9°.

5x(3x-10) + (2x-6)(3x+8)

Answers

Answer: 21[tex]x^{2}[/tex] - 52x - 48

Step-by-step explanation:

Using the expanding rule we get

5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)

15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48

21[tex]x^{2}[/tex] - 52x - 48

Answer:

21x^2-52x-48

Step-by-step explanation:

5x(3x-10) + (2x-6)(3x+8)

Distribute

5x^2 -50x+6x^2-2x-48

Combine like terms

21x^2-50x-2x-48

21x^2-52x-48

What is the X
3x +15 and 2x + 20

Answers

Answer:

x = 5

Step-by-step explanation:

What is the X

3x +15 and 2x + 20

assuming that the question is an equation

3x + 15 = 2x + 20

3x - 2x = 20 - 15

x = 5

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

check

3 * 5 + 15 = 2 * 5 + 20

30 = 30

the answer is good

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.

The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.

12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?

Answers

The cost of each jersey is $8 dollar and that of shorts is $5

System of equation

This are expression that contain unknown equation and two or more equation.

According to the question, a soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.

The system of equation that represent the expression is given as;

12x + 12y = 156

4x + 6y = 62

____________
6x + 6y = 78

4x + 6y = 62


Subtract

6x-4x = 78 - 62

2x = 16

x = 8

since 4x + 6y = 62

2x+3y = 31

2(8) + 3y = 31

3y = 31-16

3y = 15

y = 5

Therefore the cost of each jersey is $8 dollar and that of shorts is $5

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HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.

Answers

Answer:

1/10

Step-by-step explanation:

Probability= number of brown pencil/number of pencil in the box

3/30

=1/10

Answer: 1/5

Step-by-step explanation:

30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.

30-10=20. There are 20 tan pencils.

6/30 is the probability of a brown pencil being pulled out.

This simplifies to 1/5.

2(x+2y)^2 + 3(x+2y) +1​

Answers

Answer:

[tex]3x+2y^2+2(x+y)+2y+1[/tex]

Step-by-step explanation:

1) Split the second term in [tex]2{(x+2y)}^{2}+3(x+2y)+1[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]2\times1=2[/tex]

2 - Ask: Which two numbers add up to 3 and multiply to 2?

2 and 1.

3 - Split  [tex]3x+2y[/tex] as the sum of [tex]2(x+y)[/tex]  and [tex]x+2y[/tex].

[tex]2x+2y^2+2(x+y)+x+2y+1[/tex]

2) Collect like terms.

[tex](2x+x)+2y^2+2(x+y)+2y+1[/tex]

3) Simplify.

[tex]3x+2y^2+2(x+y)+2y+1[/tex]

Thank you,

Eddie

I need to know how to solve this

Answers

Answer:

To find angle y you subtract the two angles form 180 degrees because it is a straight line. Then you subtract angle y and 72 from 180 because a triangle adds up to 180 degrees and you get angle x.

Hope this helps, ask if you have any more questions!

Brett needs to put this equation x − 2y = 16 into function notation so that he can identify the rate of change and the y-intercept. How should he display it?

Answers

Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

What is the Slope Intercept Equation?

The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.

Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:

x − 2y = 16

-2y = - x + 16

Divide both sides by -2

-2y/-2 = -x/-2 + 16/-2

y = 1/2x - 8

As a function it would be written as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

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The surface areas of two similar cylinders are 6cm² and 54cm².
i. Find the scale factor for the enlargement.
ii. If the larger cylinder has height 12cm, how high is the smaller one?
iii. What is the ratio of their volumes?

Answers

Answer:

3, 4, 27

Step-by-step explanation:

1) Area scale factor = 9

Length scale factor = 3 because √9

2) 12/3 = 4

3) 3³ = 27

Simplify the expression. h4(h3)–6

Answers

Answer:

[tex]h^7-6[/tex]

Step-by-step explanation:

1) Regroup terms.

[tex]h^4h^3-6[/tex]

2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]h^{4+3}-6[/tex]

3) Simplify 4 + 3 to 7.

[tex]h^7-6[/tex]

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