The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm.

A.108 cm³
B.54 cm³
C.486 cm³
D.324 cm³

Answers

Answer 1

Since only one side of the prism is given in the question, it is assumed that the prism has a square base. Since its height is different from its sides, it can also be called rectangular. The formula to find the volume of the prism is V = s² x h, where s = 6 cm and h = 9 cm So V = 6 x 6 x 9 cm V = 324 cm³

Related Questions

y=x^2+8x+6 16x-2y=-44

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What? Is that two problems? I'll change my answer, give me my answer.

A couch and coffee table cost a total of $1017. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
cost of couch:
cost of coffee:

Answers

Answer:

Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.

Step-by-step explanation:

Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,

x + y = 1017

Also, the cost of couch is two times that of coffee. So,

x = 2y

Substitute the value of x in first equation

2y + y = 1017

3y = 1017

y = 339

And, x + y = 1017

x + 339 = 1017

x = 678

Using the two equations, we find that y = $339 and x = $678.

So, the cost of couch is $678 and that of coffee is $339.

For more explanation, refer the following link:

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The perimeter of a triangle is 29 feet where one side of the triangle is twice the length of the shortest side. the largest side is 13 feet more than the shortest side. how long is the shortest side

Answers

x + 2x + (13 + x) = 29
3x + x + 13 = 29
4x = 29 - 13
4x = 16
x = 16/4
x = 4

The length of the shortest side is 4 ft

Answer:

The shortest side is 4 feet.

Step-by-step explanation:

The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.

So the perimeter in the case of a triangle is the sum of its three sides:

L₁ + L₂ + L₃ =Perimeter

In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:

L₁= shortest sideL₂=twice the length of the shortest side → L₂=2*L₁L₃=largest side (13 feet more than the shortest side) → L₃=L₁ + 13Perimeter= 29 feet

Replacing:

L₁ + 2*L₁ + L₁ + 13= 29

Solving:

(1+2+1)*L₁ + 13= 29

4*L₁ + 13=29

4*L₁ = 29-13

4*L₁ =16

L₁= 16÷4

L₁=4

The shortest side is 4 feet.

Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?

Answers

y=-3x+14 I hope this helps!

Answer:

[tex]y=-3x+14[/tex], slope intercept form

[tex]3x+y =14[/tex], standard form

Step-by-step explanation:

[tex]y + 1 = -3(x - 5)[/tex]

We need to write the given equation in slope intercept form or standard form

slope intercept form is [tex]y=mx+b[/tex]

To get slope intercept form , we need to get y alone

[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )

[tex]y+1=-3x+15[/tex] , subtract 1 on both sides

[tex]y=-3x+14[/tex]

Standard form is [tex]Ax + By = C[/tex]

To get standard form we keep x term and y term on the left hand side

[tex]y=-3x+14[/tex]

Add 3x on both sides

[tex]3x+y =14[/tex]

limit as x approaches 0 of csc3x/cotx

Answers

Hello Meggieh821, to find the lim as x approaches 0 we can check this by inserting a number that is close to 0 that is coming from the left and from the right.

For instance, we can find the lim by using the number -.00001 for x and solve
csc(3x) / cot(x)
csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3

We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3

So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3

[tex]\lim_{x\to 0} \frac{csc(3x)}{cot(x)} = \frac{1}{3}[/tex]

Final answer:

The limit of csc(3x)/cot(x) as x approaches 0 is 1, after applying trigonometric identities and the properties of limits.

Explanation:

The student is asking for the limit of the function csc(3x)/cot(x) as x approaches 0. This is a limit problem in calculus, which is a part of mathematical analysis that deals with the behavior of functions near certain points. To find the limit as x approaches 0 for the function csc(3x)/cot(x), we need to apply trigonometric identities and the properties of limits. The function csc(3x) can be rewritten as 1/sin(3x) and cot(x) as cos(x)/sin(x). So the original limit becomes:

lim(x → 0) [csc(3x)/cot(x)] = lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))].

Using the trigonometric limit lim(x → 0) (sin(x)/x) = 1 and lim(x → 0) (cos(x)) = 1, we can simplify the expression by substituting 3x for x in the limit sin(x)/x. We get:

lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))] = lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x).

As x approaches 0, cos(x) approaches 1 and 3x/x approaches 3, hence:

lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x) = lim(x → 0) (sin(x)/x) × lim(x → 0) 1/cos(x) × lim(x → 0) (3x/3sin(3x)) = 1 × 1 × (3/3) = 1.

The final limit of csc(3x)/cot(x) as x approaches 0 is 1.

Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?

Answers

multiply 17 by 6%

17 * 0.06 = 1.02 increase

17 +1.02 = 18.02 new hourly wage

14 minus the product of three and the number has 26

Answers

Assuming “has” means “equals”

14 - 3 (x) = 26
Subtract 14 from both sides
-3x = 12
Divide both sides by -3
X= -4

b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year? Show your work.

Answers

$1,263.75 is how much would be taxed
Take 8425 multiply it by 0.15 to get your answer

Answer:

The tax would be $ 1,263.75

Step-by-step explanation:

Given,

Total earning in one year = $ 8,425,

Income tax percentage per year on earning = 15%

Hence, the amount of tax at the end of one year

= 15% of the total earnings

= 15% of 8425

[tex]=\frac{15\times 8425}{100}[/tex]

[tex]=\frac{126375}{100}[/tex]

= $ 1,263.75

A clydesdale drinks about 120 gallons of water every 4 days.At this rate,about how many gallons of water does a clydesdale drink in 28 days

Answers

A clydes dale can drink up to 840 gallons of water in 28 days

Solve the inequality -×/7+4>3×.

Answers

The expression is no very clear.

It seems to be - x / 7 + 4 < 3x

If so, this is the solution.

1) 3x + x / 7 > 4

2) 21x + x > 28

3) 22x > 28

4) x > 28/22

5) x > 14/11

Answer: x > 14 / 11

find the value of x

Answers

180 - 44 = 136
136 / 2 = 68

x = 68 + 44 = 112

Line segment AB is the perpendicular bisector of line segment XZ. Which statement is true? A) XZ = AB B) XB = XZ C) ∠ABZ = ∠ABX D) ∠BAZ = ∠ABX

Answers

A perpendicular bisector is a special type of bisector because it intersects a segment at a 90 degree angle, and it passes through the segments midpoint.

Therefore based from this, we can create two true statements:

XB = BZ

and

∠ABZ = ∠ABX

Therefore the answer is:

Answer:

The answer is C. <ABZ = <BAX hop this hope this help

Liz wants to buy a shirt for $25. How much will Liz's shirt cost in Springfield(4.1%) Round up to the nearest cent? Show your work

Answers

In order to find the total amount of the shirt including tax, first convert the tax into a decimal:
4.1/100 = 0.041 %
Next multiply the cost of the shirt before tax by the tax in decimal form:
25 * 0.041 = 1.025
After that you will add the tax cost and the shirt cost:
25 + 1.025 = 26.025
Finally round to the nearest cent:
26.03
Hope this helps and let me know if you have more questions!

I think it would be $102.6

Segments and angles practice with special angles find the measures of the lettered angles

Answers

IM A BEGINNER SO DONT REALLY BUT I THINKS IT 532181

For a car rental, the rental agency charges $21.00$⁢21.00 per day, plus $0.23$⁢0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.

Answers

21d+.23x (d being per day) (x being every mile above 125)

Describe how to graph the solution of y ≤ −x² + 2x.

Answers

that's how you describe the answer of y ≤ −x² + 2x.

Graph the parabola opening down,
with the vertex at (1, 1),factor the quadratic as y < (less than or equal to) –1(x)(x – 2),find the roots of the parabola to be 0 and 2,graph the parabola with a solid boundary line,test a point that is not on the boundary,and shade inside the parabola.

Please help me with this

Answers

for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse

so for this:

the legs would be 2sqrt(10)

Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the x-axis
D) reflection across the y-axis

Answers

C) reflection across the x-axis

Answer: C is the answer

Step-by-step explanation:

The function shown is reflected across the y-axis to create a new function.

Which is true about the domain and range of each function?

A.Both the domain and range change.
B.Both the range and domain stay the same.
C.The domain stays the same, but the range changes.
D.The range stays the same, but the domain changes

Answers

Final answer:

Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.

Explanation:

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.

Learn more about Reflecting Functions Across Y-Axis here:

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The correct option is A. Both the domain and range change.

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The correct option is A. Both the domain and range change.

the slope of the line below is 2/5 and the y-intercept is (0,4) what is the slope intercept equation of the line?

Answers

Your equation would be y = 2/5x + 4 because 2/5 is your constant and 4 is what you get when x=0

Hope this helps!

Anna has 5 muffins but 8 friends coming over. How much will each friend get

Answers

Hello! To solve this question, all we have to do is 5/8. You can basically leave it like it is, because that’s your answer. Each friend will get 5/8 of a muffin.

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < 3/2x + 2

The origin is not included in the shaded region and the shaded area is above the line.

The origin is not included in the shaded region and the shaded area is below the line.

The origin is included in the shaded region and the shaded area is above the line.

The origin is included in the shaded region and the shaded area is below the line.

Answers

I'll do a similar problem, and I challenge you to do this on your own using similar strategies!

Take y > 7x+2
Plugging in the origin, we have (0,0) as our points, and 0 > 0*7+2=2, so 0>2. As 0 is not greater than 2 (less than is the way that it's pointing), this is false. In addition, as it is y greater than 7x+2, the shaded area is above the line due to that y is greater than, and since y is up and down, greater than means higher than.

Good luck, and feel free to ask any questions that come up!

Answer

third option

Step-by-step explanation:

A market sells bananas for $0.69 per pound. Which expression represents the cost, in dollars, of p pounds of bananas? 1 p/69 2 0.69p 3 p/0.69 4 69p

Answers

Assuming p is the pounds of bananas;

$0.69p would be the correct answer (2) because each pound costs $0.69

Hope I helped :)

Answer:

Option 2. 0.69p

Step-by-step explanation:

A market sells bananas for = $0.69 per pound

The cost, in dollars of p pounds of bananas = 0.69 × p

So the expression represents the cost, in dollars of p pounds of bananas

= 0.69p

Option 2. 0.69p is the right answer.

6 shirts 4 different pairs of pants, how many different combinations could she wear?

Answers

The shirts can be called A, B, C, D, E, F.
the pants can be called 1, 2, 3, 4.
if you combine these together you get
A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, D4, E1, E2, E3, E4, F1, F2, F3, F4 OR 24
You get 24 outfits.

Help?

Simplify. 9√56x^7y^12 Assume x and y are nonnegative.

Answers

Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.

Apply the product property of square roots:

9 * √(56) * √(x^7) * √(y^12)

Evaluate the square root:

9 * 2 * √(2 * 7) * √(x^7) * √(y^12)

Multiply the numbers:

9 * 2 * √(14) * √(x^7) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * |x^3| * √(x) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * √(x) * |x^3| * y^6

Apply the product property of square roots to the product of square roots is equal to the square root of the product:

9 * 2 * y^6 * |x^3| * √(14x)

Multiply the numbers:

18 * y^6 * √(14x) * |x^3|

Use laws of sine to answer

Answers

By sine rule:
[tex] \frac{18}{ \sin(32) } = \frac{bc}{ \sin(118) } [/tex]
so:
[tex]bc = \frac{18 \times \sin(118) }{ \sin(32) } \\ bc = 29.991... \\ bc = 30.0 \: (to \: 3 \: sig.figs)[/tex]

Some of the cds produced by a manufacturer are defective. from the production line, 5 cds are selected and inspected. how many sample points exist in this experiment?

Answers

Final answer:

There are 32 sample points in this experiment.

Explanation:

In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times to find the total number of sample points. Therefore, there are 32 sample points in this experiment.

Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.

State the vertex as an ordered pair.

y = -|3x +5|+7

Answers

in plain and short, what value of "x" makes the expression |3x + 5| to 0?

well, we can check by simply setting it to 0 and solving for x.

[tex]\bf 3x+5=0\implies 3x=-5\implies \boxed{x=-\cfrac{5}{3}}\\\\ -------------------------------\\\\ \textit{therefore, the vertex of }y = -|3x+5|\boxed{+7}\textit{ is at }\left(-\frac{5}{3}~,~7 \right)[/tex]

notice, all you do is, get the x-value that makes the expression to 0, and then append the constant outside it as the y-value, and that's the vertex.

Yori has 14.25 cups of cupcake batter if each cupcake used 0.75 cup of batter how many cups cakes can yori make?

Answers

14.25 / 0.75 = 19 <=== Yori can make 19 cupcakes

First, compare the statements
0.75=1 cupcake
14.25=Y cupcakes
I represented the unknown with Y.
Next, cross and multiply. 14.25 will multiply 1 to give 14.25 and 0.75 will multiply Y to give 0.75Y. That will be;
0.75Y=14.25
Divide both sides by 0.75
Y=14.25/0.75
Y=19
She can make 19 cupcakes. Hope that helped. Have a nice day

Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm

Answers

Answer:

Step-by-step explanation:

The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are:

A. 6cm by 1.5cm because

D. 18cm by 4.5cm because

E. 80cm by 20cm because

Given that

[tex]Length = 12cm[/tex]

[tex]Width = 3cm[/tex]

Divide the length and the width of the rectangle

[tex]k = Length \div Width[/tex]

[tex]k = 12cm \div 3cm[/tex]

[tex]k = 4[/tex]

This means that a scaled copy of rectangle A must have a value of 4 when the dimensions are divided.

Possible rectangles are:

A. 6cm by 1.5cm because [tex]6cm \div 1.5cm = 4[/tex]

D. 18cm by 4.5cm because [tex]18cm \div 4.5cm = 4[/tex]

E. 80cm by 20cm because [tex]80cm \div 20cm = 4[/tex]

The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm. A.108 cm³ B.54 cm³ C.486 cm³ D.324 cm³

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The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm.

A.108 cm³
B.54 cm³
C.486 cm³
D.324 cm³