A cylinder has a base radius of 10cm and a height of 19cm. What is its volume in cubic cm, to the nearest tenths place?

Answers

Answer 1

Cylinder Volume = PI * radius^2 * height
Cylinder Volume = 3.14159 * 100 * 19
Cylinder Volume = 5,969 cubic centimeters

Related Questions

please help im confused....

which ordered pair is a solution of the inequality?
2y+6<8
a. (4,13)
b. (-5,2)
c.(0,6)
d.(4,8)

Answers

Hello,

Here is your answer:

The proper answer to this question is option D "(4,8)".

Your answer is D.

If you need anymore help feel free to ask me!

Hope this helps!

Orlando bought a new couch for 2,736 , using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?

Answers

y = the money Orlando still owes
x = the number of months (from x = 0 to x = 24)
y = 2,736 - 114x

You can substitute any number between 1 and 24, and it will show how much Orlando continues to owe throughout the payment process.

Rosalie wants to get the entire outside of a cabinet laminated. The cabinet is 3 feet long, 2 feet wide and 5 feet high. The cost of lamination is $2 per square foot. How much will it cost Rosalie to get the cabinet laminated?

Answers

The first thing you should do in this case is find the surface area of the cabinet.
We have then that the surface area is:
A = 2 * ((l) * (w)) + 2 * ((l) * (h)) + 2 * ((h) * (w))
Where,
l: long
w: width
h: high
Substituting the values:
A = 2 * ((3) * (2)) + 2 * ((3) * (5)) + 2 * ((5) * (2))
A = 62 feet ^ 2
The cost of lamination is $ 2 per square foot:
So:
(62) * (2) = $ 124
Answer:
it will cost $ 124 Rosalie to get the cabinet laminated

To laminate the cabinet, the total surface area is calculated and multiplied by the cost per square foot. The cabinet has a surface area of 62 square feet, and with a lamination cost of $2 per square foot, it will cost Rosalie $124.

To calculate the cost for laminating the outside of a cabinet, we first need to find the total surface area to be laminated. Since the cabinet is a rectangular prism, we can use the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. In this case, l = 3 ft, w = 2 ft, and h = 5 ft.

Surface Area = 2(3 ft)(2 ft) + 2(3 ft)(5 ft) + 2(2 ft)(5 ft)
Surface Area = 2(6) + 2(15) + 2(10)
Surface Area = 12 + 30 + 20
Surface Area = 62 square feet

Now to find the total cost, we multiply the surface area by the cost per square foot: Total cost = Surface Area times Cost per square foot.
Total cost = 62 sq ft times $2/sq ft
Total cost = $124

Therefore, it will cost Rosalie $124 to get the cabinet laminated.

PLEASE HELP
7.06

1. Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1

A) -7, -28, -112, -448, -1792, -7168
B) -28, -112, -448, -1792, -7168, -28,672
C) -7, -28, -24, -20, -16, -12
D) 0, 4, -28, -24, -20, -16

2. Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...

an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)

3. Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5

A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)

4. Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...

A) Diverges
B) Converges; 231
C) Converges; 3751
D) Converges; 935

5. Find an equation for the nth term of the sequence.
-4, -16, -64, -256, ...

A) an = 4 • -4n
B) an = 4 • -4n + 1
C) an = -4 • 4n
D) an = -4 • 4n - 1

6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

A) an = 1 • (-2)n - 1
B) an = 1 • 2n
C) an = 1 • (-2)n + 1
D) an = 1 • 2n - 1

7. Write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 + ...

A) summation of four times six to the power of n from n equals zero to infinity
B) summation of four times negative six to the power of n from n equals zero to infinity
C) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
D) summation of four times six to the power of the quantity n plus one from n equals zero to infinity

8. Write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + ... + 132

A) summation of negative 27 times n from n equals 0 to infinity
B) summation of negative 27 times n from n equals 0 to 15
C) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
D) summation of the quantity negative 3 plus 9 n from n equals 0 to 15

9. Write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + ... + n3

A) summation of the quantity n minus 1 cubed from n equals 7 to infinity
B) summation of n cubed from n equals 7 to infinity
C) summation of n cubed from n equals 8 to infinity
D) summation of the quantity n plus 1 cubed from n equals 7 to infinity

10. Find the sum of the arithmetic sequence.
3, 5, 7, 9, ..., 21

A) 39
B) 120
C) 20
D) 23

11. Find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

A) 1363 divided by 3
B) 1364 divided by 15
C) 1364 divided by 3
D) 1363 divided by 15

12. An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

A) 390
B) 580
C) 620
D) 400

13. Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)

14. A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.

Answers

1. A. According to the expression a_n=4*a_n-1, each term after a1 is four times the previous term. The first term is -7 as given, 2nd term should be -7*4=-28, 3rd term is -28*4=-112, ... A is the correct answer.

2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.

3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).

4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.

5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).

6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).

7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.

8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.

9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).

10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.

11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.

12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.

13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.

14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.

Hello,
Please, see the detailed solution in the attached files.
Thanks

Find the value of x. The diagram is not drawn to scale.

Answers

Answer:

C. [tex]x=99^{\circ}[/tex]

Step-by-step explanation:

We have been given a image. We are asked to find the value of x.

We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

We can see that y and 116 degrees angles are linear angles, so we can set an equation as:

[tex]y^{\circ}+116^{\circ}=180^{\circ}[/tex]

[tex]y^{\circ}+116^{\circ}-116^{\circ}=180^{\circ}-116^{\circ}[/tex]

[tex]y=64^{\circ}[/tex]

Substitute [tex]y=64^{\circ}[/tex] in the equation:

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+64^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}-261^{\circ}=360^{\circ}-261^{\circ}[/tex]

[tex]x^{\circ}=99^{\circ}[/tex]

[tex]x=99[/tex]

Therefore, the value of x is 99.

a business analyst makes 20$ an hour for the first 42 hours he works during a week and 28$ an hour for each worked over 42 hours. which piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week

Answers

y=(20 × 42) + [28 × (x-42)]

Answer:

[tex]y=28(x-42)+840[/tex]

Step-by-step explanation:

Let he works for x hours in total.

We are given that he makes 20$ an hour for the first 42 hours

So, he earns in 1 hour = 20

He earns in 42 hours = [tex]20 \times42[/tex]

= [tex]840[/tex]

Now we are given that he earns $28 an hour for each hour worked over 42 hours.

Since he worked for 42 hours out of x hours .

So, remaining hours = x-42 hours

So,he earns for x-42 hours = [tex]28\times(x-42)[/tex]

y denotes his total earning of weekly

So, total earning [tex]y=28(x-42)+840[/tex]

Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is [tex]y=28(x-42)+840[/tex]

Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
A.260 cm³
B.520 cm³
C.1040 cm³
D.16,640 cm³
Will give brainliest answer!

Answers

there are two possibilities if no further information is given.
for two similar prisms, if the ratio of sides is a, the ratio of volume is a³
2080/260=8=2³
16640/2080=8=2³
2080/520=4, not a cubic number
2080/1040, not a cubic number
It is either A or D depending on which prism is bigger.

Final answer:

Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.

Explanation:

The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.

Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

Answers

To find the area of the cylinder we need to find its volume first. Remember that the formula for the volume of a cylinder is [tex]V= \pi r^{2} h[/tex]
where:
[tex]V[/tex] is the volume
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
From the question we know that [tex]A=175[/tex] and [tex]h=7[/tex]. Lets replace those values in our volume formula:
[tex]175= \pi r^{2} 7[/tex]
Now we can solve for [tex]r[/tex] to find our radius:
[tex]r^{2} = \frac{175}{7 \pi } [/tex]
[tex]r^{2} = \frac{25}{ \pi } [/tex]
[tex]r= \sqrt{ \frac{25}{ \pi } } [/tex]
[tex]r= \frac{5}{ \sqrt{ \pi } } [/tex]

Now that we know the radius, we can use the formula for the area of a cylinder [tex]A=2 \pi rh+2 \pi r^{2} [/tex]
where:
[tex]A[/tex] is the area
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
We know now that [tex]r= \frac{5}{ \sqrt{ \pi } } [/tex] and [tex]h=7[/tex], so lets replace those values in our area formula:
[tex]A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2} [/tex]
[tex]A= \frac{70 \pi }{ \sqrt{ \pi } } +50[/tex]
[tex]A=174.07[/tex]

We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.

An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.

A rectangle has a length of 6 inches and a width of 3 inches.

What is the effect on the perimeter when the dimensions are multiplied by 8?

The perimeter is increased by a factor of 8.
The perimeter is increased by a factor of 24.
The perimeter is increased by a factor of 64.
The perimeter is increased by a factor of 256.

This figure is made up of a triangle and a semicircle.

What is the area of this figure?

Use 3.14 for pi. Round only your final answer to the nearest tenth.

Enter your answer, as a decimal, in the box.

Answers

Q1.the given scale factor is 1:16
the area is 7 square feet
when calculating the area the scale factor is squared as well.
since the scale factor is 16, to find out area the scale should be squared that is,
16*16 = 256

then the new area is 7 square feet * 256
actual area = 256 * 7 = 1792 square feet
Q2. the rectangle with length 6 inches and width 3 inches.
the perimeter of the rectangle before changing dimensions are;
=(6*2) + (3*2)
= 12 + 6 = 18 inches
after multiplying the dimensions by 8,
new length = 6*8 = 48 inches
new width = 3*8 = 24 inches
new perimeter = (48*2) + (24*2)
= 96 + 48
= 144 inches
the perimeter ratio from new to old = 144:18
the perimeter has increased by (144/18) times
= 144/18 = 8
answer is perimeter increased by a factor of 8

q3)
area of the triangle
= 1/2 * height * base
= 1/2 * (5-2) *(4-(-3))
= 1/2 * 3 * 7
= 10.5 units²
area of semicircle
=pi*r2
r = 2-(-1.5)
= 3.5
area = 3.14 * (3.5)²
= 38.465 units²
total area = area of triangle + area of semicircle
= 10.5 + 38.465
= 48.965
round it off to the closest tenth
area = 49 units²

Which table represents a quadratic relationship?

A .x -2 -1 0 1 2 3
f(x) 4 2 1 0.5 0.25 0.125

B. x -7 -6 -5 -4 -3 -2
f(x) 135 128 105 72 35 0

C. x -2 -1 0 1 2 3
f(x) -23.4 -23.2 -23 -22.8 -22.6 -22.4

D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40

Answers

In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.

A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)

B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)

C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)

D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.

The appropriate choice is ...

... D. x -1 0 1 2 3 4

... f(x) 90 56 26 0 -22 -40

Answer: D. x -1 0 1 2 3 4

f(x) 90 56 26 0 -22 -40

Step-by-step explanation:

Answer for number 5?

Answers

5+3+5+3=16
192/16=(a)
(A)*5=length
(A)*3=width

We have
P = 2L + 2W
Where,
L: side
W: width
On the other hand we have that the ratio is:
L / W = 5/3
Clearing L we have:
L = (5/3) * (W)
Substituting in the expression of the perimeter:
P = 2 ((5/3) * (W)) + 2W
Rewriting:
P = (16/3) W
The perimeter is 192:
192 = (16/3) W
We cleared W:
W = (3/16) * (192)
W = 36
Finally we substitute W in the expression for L:
L = (5/3) * (W)
L = (5/3) * (36)
L = 60
Answer:
The width and length are:
W = 36 yards
L = 60 yards

Which is the formula for the volume of a sphere with diameter d?

A. S= 4πd²
B. S= πd²
C. S= [tex] \frac{4}{3} [/tex]πd³
D. S= [tex] \frac{1}{6} [/tex]πd³

Answers

The answer for this problem is D because the diameter for the sphere is d, so the radius is 1/2d. Substituting that into the formula of finding a circle with radius x is [tex]/frac4/3 pi * x^3. We get 1/3* pi*1/2d^3, which equals 1/6*pi*d^3, or D.

Which of the following would be a factor of the equation above.

Answers

A graph shows x-3 to be a factor, selection B.

The factorization would be (7x +3)(x -3).

b. (x-3) would be a factor, as would (7x+3) but that is not an answer choice

Could use some help!

Answers

answer is C.
0<= x < ∞

need help thank thank you

Answers

im pretty sure number 10 is B

Is the square root of eight a rational or irrational number

Answers

[tex]\bf \sqrt{8}\implies \sqrt{2\cdot 2\cdot 2}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}[/tex]

it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.

factoid: Ancient Greeks were scared of irrational numbers, and they steered clear from √2.

$7.80/hour = ____ cents/minute?

Answers

$7.80/60 seconds in a minute = $0.13 per minute

I believe it is $7.80 divided by 60 minute or seconds and you get $0.13. Or just take 7.80 divided by 60 = 0.13

Your Welocme

which rule describes the translation PQR --> P'Q'R'?

Answers

The "Pre Image" is the image that we started with, so the pink triangle.
The "Image" is the image that we ended with, so the blue triangle.

To determine how far we went from the pre image to the image, we can focus on one point, let's say point "P".

The pre image coordinates for point "P" are 2, 3.
The image coordinates for point "P'" are -1, 0.

To get from x value 2 to x value -3, we subtracted 3.
To get from y value 3 to y value 0, we subtracted 3.

So, our rule for this translation would be A, (x, y) ----> (x-3, y-3).

If the polygon shown below is a regular nonagon what is the value of x?

Answers

The sum of the measures of the angles of a polygon is given by (n - 2)(180), where n is the number of sides. In this case we would have (9-2)(180)=7(180)=1260. This is the sum of the angles. Since it is a regular nonagon, that means that all sides are congruent and all angles are congruent. Therefore we find the measure of each individual angle by dividing the sum, 1260, by the number of sides, 9. 1260/9=140. x forms a linear pair with one of the interior angles; that means that the interior angle, 140, added to x would give us 180. Therefore we find x by subtracting 180-140. x = 40.

The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.

Given :

A regular nonagon.

The sum of interior angles of a polygon is given by the equation:

= (n - 2)180 --- (1)

where 'n' is the total number of sides of the polygon.

Given that the polygon is the regular nonagon that means the total number of sides is 9.

Now, substitute the value of 'n' in the equation (1).

= (9 - 2)180

= [tex]1260^\circ[/tex]

Now, divide the above expression by 9 in order to get the value of one interior angle.

[tex]= \dfrac{1260}{9}[/tex]

= [tex]140^\circ[/tex]

Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:

140 + x = 180

x = [tex]40^\circ[/tex]

For more information, refer to the link given below:

https://brainly.com/question/19237987

Find the value of x.

Answers

The small triangle containing both the 6 and the ten should have its third side calculated.
Use a^2 + b^2 = c^2
a = 6
c = 10
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 100 - 36
b^2 = 64
b = 8
Note: - 8 has not meaning.

Now by similar triangles using the small triangle and the middle sized triangle on your right

6/8 = 8/(x - 6) Reduce 6/8. You don't have to but it makes things easier.
3/4 = 8/(x - 6) Cross multiply
3(x - 6) = 4*8 Remove the brackets.
3x - 18 = 32 Add 18 to both sides
3x = 50 Divide by 3
x = 50/3 = 16.667 <<<=== answer

The formula for volume of this rectangular prism is:

V = 2x 3 + 17x 2 + 46x + 40

Find an expression for the missing side length. Show all of your work for full credit.

Answers

By definition, the volume of a rectangular prism is given by:
[tex]V = (w) * (h) * (l) [/tex]
Where,
l: length
h: height
w: width
Substituting values we have:
[tex]2x ^ 3 + 17x ^ 2 + 46x + 40 = (w) * (x + 2) * (x + 4) [/tex]
From here, we clear the value of w.
[tex]w = (2x ^ 3 + 17x ^ 2 + 46x + 40) / ((x + 2) * (x + 4)) [/tex]
Factoring the numerator we have:
[tex]w = ((x + 2) * (x + 4) * (2x + 5)) / ((x + 2) * (x + 4)) [/tex]
Canceling similar terms we have:
[tex]w = 2x + 5 [/tex]
Answer:
The missing side is of length:
w = 2x + 5

The volume of a rectangular prism is the product of its dimension.

The missing side length is 2x + 5.

The volume is given as:

[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]

Let the missing side be y.

So, we have:

[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]

So, we have:

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]

Factorize

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]

Cancel out common factors

[tex]\mathbf{y = (2x +5)}[/tex]

Remove brackets

[tex]\mathbf{y = 2x +5}[/tex]

Hence, the missing side length is 2x + 5.

Answers

Answer:

Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

In other words, we can write this in terms of the composition of f and g as g(f(x))=x.

For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.

Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.

In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.

Given,the expression y=4x+12 for y as a function of x and solve for x.

Subtract 12 from both sides we get;

y-12 = 4x+12-12

Simplify:

y-12 = 4x

Divide by 4 to both sides we get;

[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]

Simplify:

[tex]x=\frac{1}{4}y - 3[/tex]

therefore, [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]

since, g(x) is the inverse of f(x)

⇒[tex] g(x)=\frac{1}{4}x-3[/tex]

Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.

[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]

Simplify:

g(f(x)) = x for all x

⇒ g(x) is the inverse of f(x)

Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]

Using inverse functions, it is found that that:

[tex]g(x) = \frac{x - 12}{4}[/tex]

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

The function f(x) is given by:

[tex]f(x) = 4x + 12[/tex]

Function g(x) is the inverse of f(x), then:

[tex]y = 4x + 12[/tex]

[tex]x = 4y + 12[/tex]

[tex]4y = x - 12[/tex]

[tex]y = \frac{x - 12}{4}[/tex]

[tex]g(x) = \frac{x - 12}{4}[/tex]

To learn more about inverse functions, you can take a look at https://brainly.com/question/16485117

The values √8 and √14 are plotted on the number line.

What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4

Answers

Firstly, you have to count the number of spaces between the two points on the line, which gives you 9. Now, remember that you are counting between tenths on a number line, so you divide 9 by 10 to give you your answer, 0.9.

Answer:

The correct option is 2.

Step-by-step explanation:

The values √8 and √14 are plotted on the number line.

From the given number line it is clear that

[tex]\sqrt{8}\approx 2.8[/tex]

[tex]\sqrt{14}\approx 3.7[/tex]

We have to find the approximate difference in tenths between the two values √8 and √14.

[tex]\sqrt{14}-\sqrt{8}\approx 3.7-2.8[/tex]

[tex]\sqrt{14}-\sqrt{8}\approx 0.9[/tex]

The approximate difference in tenths between the two values is 0.9.

Therefore the correct option is 2.

Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is

Answers

Final answer:

Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.

Explanation:

The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.

Learn more about Boyle's Law here:

https://brainly.com/question/21184611

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A sandwich shop uses the box size shown to pack boxed lunches. They have determined that they need to use bigger boxes. If the side lengths of the square faces are changed to 7 inches, by how much will this increase the volume of the box?

Answers

The original volume of the shape was 250. You come up with this by multiplying all sides together. So, 5x5x10=250.

We do the same for the new shape, which now has a 7 in place of the 5. So 7x7x10=490.

Lastly, we subtract the volume of the new shape from the volume of the old shape to see the difference. So, 490-250=240.

So the answer to this is 240.

Answer:

240 cubic cm

Step-by-step explanation:

Volume of the box before increament in sides = length*width*height

Length= 5 in.

Width=5 in.

Height = 10 in.

Putting these vales in formula

Volume of box = 5*5*10

=[tex]250cm^{3}[/tex]

Now If the side lengths of the square faces are changed to 7 inches,

So, Length will be 7 in.

Width will be 7 in.

So, new volume = 7*7*10

=[tex]490cm^{3}[/tex]

Thus increase in volume = 490-250 =240

Hence by 240 cubic cm will this increase the volume of the box

ASAP PLEASE:

Segment RS is congruent to segment DF. Which congruence statement is true?

- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD

Answers

Answer:

A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Step-by-step explanation:

We have been given a circle and we are told that segment RS is congruent to segment DF.

We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.

As both segments are congruent, therefore, both arcs will be congruent as well.

We can represent this information as:

[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Therefore, option A is the correct choice.

Use the rules of significant figures to answer the following question:

67.31 - 8.6 + 212.198

A. 270.9
B. 271
C. 270.908
D. 270

Answers

Answer:

A. 270.9

Step-by-step explanation:

We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'

So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908

Now, the resultant number is 270.908

Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )

Hence, 67.31 - 8.6 + 212.198 = 270.9

What form of a quadratic function would be graphed having the vertex at the same point as the y-intercept?

Answers

The answer is ax²+bx+c=y hope this helps

The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83

Answers

one may note that (1.6 , 6) is just another way to say x = 1.6 when y = 6.

and that (8 , y) is another way to say x = 8 and y is who knows.

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \textit{we know that } \begin{cases} x=1.6\\ y=6 \end{cases}\implies 6=\cfrac{k}{1.6}\implies 6(1.6)=k\implies 9.6=k \\\\\\ \qquad therefore\qquad \boxed{y=\cfrac{9.6}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{9.6}{8}[/tex]

Answer: 1.2

Step-by-step explanation:

The formula for inverse variation is given by :-

[tex]x_1y_1=x_2y_2[/tex]

The given points : (1.6, 6) and (8, y)

It means at x = 1.6 , y=6 .

To find the value of y at x=8 , we substitute [tex]x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y[/tex] in the above formula , we get

[tex]1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2[/tex]

Thus, the missing value = 1.2

Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?

Answers

The answer is $1,071.80.

General Idea:

We need to make use of the below formula to find the monthly payment..

[tex] Monthly \; Payment\; =\; \frac{P \times \frac{r}{12}}{(1-(1+\frac{r}{12})^{-m})} \\ \\ Where:\\ P\; is\; Principal\\ r\; is\; rate\; in\; decimal\; form\\ m\; is\; number\; of\; monthly\; payments [/tex]

Applying the concept:

Given:

[tex] P=\$224,500\\ r=4\%=0.04\\ m=30\; year \times 12 \; months/year=360\\ [/tex]

Substituting the given in the formula we will get the monthly payment.

[tex] Monthly\; Payment\; =\; \frac{224500 \times \frac{0.04}{12}}{(1-(1+\frac{0.04}{12})^{-360})} =\frac{\frac{8980}{12}}{(1-0.301796)} =\frac{748.3333}{0.698204} \\ \\ Monthly \; Payment= \$1071.7975 [/tex]

Conclusion:

The monthly payment during the initial period is $1072.

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