Surface area is the sum of the areas of all the surfaces of a three-dimensional object.
(True or false)

Answer:

T.S.A = 233.29 cm²

volume of the cone = 235.84 cm³

Step-by-step explanation:

Given;

diameter of the cone, d = 9 cm

radius of the cone, r = 4.5 cm

slant height of the cone, l = 12 cm

The total surface of the cone is calculated as;

T.S.A = πr²  +  πrl

T.S.A = πr(r + l)

T.S.A = 3.142 x 4.5(4.5 + 12)

T.S.A = 233.29 cm²

The volume of the cone is calculated as;

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where;

h is height of the cone

h² = 12² - 4.5²

h² = 123.75

h = √123.75

h = 11.12 cm

[tex]V = \frac{1}{3} \pi \times (4.5)^2 \times 11.12\\\\V = 235.84 \ cm^3[/tex]

The question is incomplete. The complete question is :

Fred drew the pentagon below how should Fred fold the pentagon to determine if ∠ C is congruent to ∠ D ?

Solution :

Given Fred drew a pentagon as shown below :

In mathematics, congruent angles are defined as the angles having the same measure or the same angle.

A angles of a regular pentagon always have the same measures and each angle is equal to 108 degrees.

In the context, Fred drew a pentagon and if he folds the pentagon along the vertical axis, the side BC aligns with the side DE and thus it makes the ∠ C congruent to ∠ D.

Step-by-step explanation:

if you draw an imaginary perpendicular line across the figure from the vertex which joins the line of 2 cm with the line that is making an angle of X then you can see that this figure is made up of two figures that is a triangle and a rectangle.

now from the angle given i.e X.

perpendicular= 5 cm

base = 14 -2= 12 cm

hypotenuse= ?

we know that,

h² = p²+b²

= 5²+12²=169

h= √169

h= 13

again,

cos X = b/h

= 12/13

Answer:

[tex] (x + 7)^2 + (y + 4)^2 = 4 [/tex]

Step-by-step explanation:

The equation of a circle with radius r and center (h, k) is:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

This circle has center (-7, -4) and radius 2.

The equation is:

[tex] (x + 7)^2 + (y + 4)^2 = 4 [/tex]

Answer:

B. 864π cu. in.

Step-by-step explanation:

Given the following data;

Diameter = 24 inches

Radius, r = diameter/2 = 24/2 = 12 inches

Height, h = radius/2 = 12/2 = 6 inches

To find the volume of the cylinder in cubic inches;

First of all, we would determine the area of its circular base.

Area of circle = πr²

Area = π * 12²

Area = 144π in² (in terms of pie, π)

Next, we would find the volume of the cylinder;

Mathematically, the volume of a cylinder is given by the formula;

V = πr²h

Where;

Substituting into the formula, we have;

Volume = 144π * 6

Volume = 864π cu. in

Answer:

B. 864π cu. in.

Step-by-step explanation:

The average weight of the soap bars is 4.007 ounces. Therefore, option 2 is the correct answer.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, the weight of 6 home made soaps are 4.003, 4.006, 4.012, 4.008, 4.004, and 4.009 ounces.

We know that, average = Sum of all the observations/Number of observations

Here, the average = (4.003+4.006+4.012+4.008+4.004+4.009)/6

= 24.042/6

= 4.007 ounces

Therefore, option 2 is the correct answer.

To learn more about an average visit:

https://brainly.com/question/11195029.

#SPJ3

Answer:

153

Step-by-step explanation:

[tex]other \: number = \frac{9 \times 459}{27} \\ \\ = \frac{459}{3} \\ \\ = 153[/tex]

Answer:

Other number is 153

Step-by-step explanation:

Usually, the product of the HCF and LCM will be the product of the 2 numbers in question.

The HCF and LCM are given as 9 and 459.

While one of the numbers used to find the HCF & LCM was 27.

Let the other number be y.

Thus;

27y = 459 × 9

y = 459 × 9/27

y = 153

Given:

The inequalities are:

[tex]-5x<-3[/tex] or [tex]2x<-8[/tex]

To find:

The solution for the given inequalities and graph the solution.

Solution:

We have,

[tex]-5x<-3[/tex] or [tex]2x<-8[/tex]

Solve the above inequalities separately.

[tex]-5x<-3[/tex]

Divide both sides by -5.

[tex]x>\dfrac{-3}{-5}[/tex]

[tex]x>\dfrac{3}{5}[/tex]             ...(i)

And,

[tex]2x<-8[/tex]

Divide both sides by 2.

[tex]x<\dfrac{-8}{2}[/tex]

[tex]x<-4[/tex]                       ...(ii)

From (i) and (ii). we get

[tex]x<-4[/tex] or [tex]x>\dfrac{3}{5}[/tex]

The interval notation of the solution is [tex](-\infty,-4)\cup \left(\dfrac{3}{5},\infty\right)[/tex].

The graph of the solution is shown below.

Answer:

6/10

Step-by-step explanation:

Look at is a whole. Half the plants are flowers, and just a few are bushes. That leaves other plants that are neither.

We can find a total amount of plants that are either flowers or bushes by combining the two.

Because 1/2 and 1/10 are not currently combinable, you must find a common denominator. This common denominator is 10. If you multiply 2 by 5, you'll get 10.

[tex]\frac{1}{2} +\frac{1}{10}[/tex]

[tex]\frac{5}{1} (\frac{1}{2} )+\frac{1}{10}[/tex]

[tex]\frac{5}{10} +\frac{1}{10}[/tex]

[tex]\frac{6}{10}[/tex]

This means that 6/10 of the whole number of plants are either flowers or bushes. You could also say it means that 4/10 of the plants are something other than flowers or bushes.

I hope this helped :)

Answer:

Step-by-step explanation:

5n⁵c⁻⁵ *  2n⁻⁵c³ = (5*2)*n⁵⁺⁽⁻⁵⁾ * c⁻⁶⁺³

                          =10*n° *c⁻³

                           = 10c⁻³               (n° = 1}

[tex]a^{m}*a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\frac{9r^{6}}{5r^{3}g^{2}}=\frac{9}{5g^{2}}*r^{6-3}\\\\=\frac{9r^{3}}{5g^{2}}\\\\\\\\\frac{9g^{-4}y^{4}}{3g^{6}y^{-2}}=\frac{9}{3}*g^{-4-6}*y^{4-(-2)}\\\\=3*g^{-10}*y^{4+2}\\\\=3g^{-10}*y^{6}\\\\=\frac{3y^{6}}{g^{10}}[/tex]

Answer:

Everything will be split in threes. You can do this by either multiplying the cost by 1/3 or dividing by 3.

Step-by-step explanation:

Answer:

3 because when x=2 the lines are at y 1 and 3, but the y 1 isn't shaded, so the answer is 3

Answer:

During a canoeing trip, it takes Raymond 4 hours to paddle 12 miles upstream. It takes him 3 hours to make the return trip paddling downstream. Find the speed of the canoe in still water

Step-by-step explanation:

sorry i dont know

Circumference of circle = 2πr

Putting values ::-

37.7 = 2 × 3.14 × r

r = 37.7 ÷ 6.28

r = 6.003 (approx)

therefore,

d = r × 2 = 6.003 × 2

d = 12.006

.·. Diameter of plate ≈ 12 cm.

Answer:

Associative property of addition

Answer:12264

Step-by-step explanation: (24)+2(24)+4(24)+8(24)+16(24)+32(24)+64(24)+128(24)+256(24)

Answer:

-12=4x-20

4x=12+20

4x=32

4 = 4

x=8

Answer:

[tex] - 12 = 4(x - 5) \\ - 12 = 4x - 4 \times 5(bracket \: multipiction) \\ - 12 = 4x - 20 \\ - 12 + 20 = 4x\\ 8 = 4x \\ x = \frac{8}{4} = 2 \\ x = 2 \\ thank \: you[/tex]

Answer:

if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps

Hope it helps

Answer:

10/3

Step-by-step explanation:

remember about right order

Answer:

JMK

Step-by-step explanation:

Answer:

[tex]-\frac{1}{5}[/tex] is the slope of the line.

Step-by-step explanation:

(7 , 1) = (x1 , y1)

(-3 , 3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=3 - 1/-3 - 7

=2/-10

=1/-5

=[tex]-\frac{1}{5}[/tex]

3x + 14 < 38

Subtract 14 from both sides:

3x < 24

Divide both sides by 3:

X < 8

Answer:

A. Diagonal line

Answer:

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Step-by-step explanation:

Given:

Length of the ladder = 20 ft

Distance between base of the ladder and wall = 4 ft

To find:

The angle measure of the ladder to the ground to the nearest degree.

Solution:

Ladder is the hypotenuse of a right triangle. Here, we have,

Hypotenuse = 20 ft

Base = 4 ft

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\cos \theta=\dfrac{4}{20}[/tex]

[tex]\cos \theta=\dfrac{1}{5}[/tex]

Taking cos inverse on both sides, we get

[tex] \theta=\cos^{-1}\dfrac{1}{5}[/tex]

[tex] \theta=78.46304^\circ[/tex]

[tex] \theta\approx 78^\circ[/tex]

Therefore, the correct option is A.

9514 1404 393

Answer:

  -14.5

Step-by-step explanation:

Let the number be represented by x.

  176.9/x . . . . the quotient of some number divided into 176.9

  4(176.9/x) . . . . the quotient multiplied by 4

  10.2 + 4(176.9/x) . . . . the product added to 10.2

And that totals -38.6:

  -38.6 = 10.2 +4(176.9/x)

Solution

  -48.8 = 4(176.9/x) . . . . subtract 10.2

  -12.2 = 176.9/x . . . . . . . divide by 4

  x = 176.9/(-12.2) . . . . . multiply by x/-12.2

  x = -14.5 . . . . . . . . . . . finish the division

The initial number is -14.5.

Answer:

-3 3/4

Step-by-step explanation:

So we have:

-1 1/4 + (-2 1/2)

Before solving this, lets just clean it up.

First off, since we know that a + and - sign equals a - sign, we can rewrite it as:

-1 1/4 - (2 1/2)

We need to also get a common denominator, which would be 4. The first fraction already has a denominator of 4, so it doesnt change. However, the second fraction is 1/2, and we need to multiply both sides by 2 to change the denominator from 2 to 4:

-1 1/4 - (2 2/4)

Now lets solve:

I will do the fraction seperate from the whole number to make it simpler:

-1 - 2

A negative subtracted makes it a larger negative so:

-3

-1/4 - 2/4

Again, a negative subtracted makes it a larger negative:

-3/4

Now recombine the numbers:

-3 3/4

So this is your answer.

Hope this helps!

Answer:

<I= 15degrees

Step-by-step explanation:

Using the cosine rule formulae;

j² = i²+k²-2i cos <J

j² = 37²+57² - 2(37)(57)cos <141

j² = 1369+ 3249- 4218cos <141

j² = 4618- 4218cos <141

j² = 4618-(-3,278)

j²= 7,896

j = √7,896

j = 88.86inches

Next is to get <I

i² = j²+k²-2jk cos <I

37² = 88.86²+57² - 2(88.86)(57)cos <I

1369 = 7,896.0996+ 3249- 10,130.04cos <I

1369 = 11,145.0996 - 10,130.04cos <I

1369 - 11,145.0996 = - 10,130.04cos <I

-9,776.0996=- 10,130.04cos <I

cos <I =9,776.0996 /10,130.04

cos<I = 0.96506

<I = 15.19

<I= 15degrees

Answer:

B. perpendicular Hope this helps!