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Answer:

250 cm²

Step-by-step explanation:

Lateral area of the prism is,

5×10×5

= 250 cm²

Lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].

" Lateral surface area is defined as the sum of  area of the all the surfaces except top and bottom of the given geometrical shape."

Formula used

Lateral surface area of pentagonal prism [tex]=5ah[/tex]

[tex]a=[/tex] edge length of the base

[tex]h=[/tex] height of the prism

According to the question,

For the given pentagonal prism,

Edge length of the base [tex]'a' = 5cm[/tex]

Height of the prism [tex]'h' = 10cm[/tex]

Substitute the value in the formula of lateral surface area we get,

Lateral surface area of pentagonal prism [tex]= 5 \times 5\times 10[/tex]

                                                                      [tex]= 250cm^{2}[/tex]

Hence, lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].

Learn more about  lateral surface area here

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I'm assuming your trying to find the weight of the math book so here it is:

Answer:

4 5/36

Step-by-step explanation:

You'd have to do 18 7/8 - 14 7/9 but you can't subtract them yet because they don't have common denominators. So, you have to multiply the 7/8 by 9 and the 7/9 by 8. Then you would get 63/72 and 56/72. Then you put that into the equation and get, 18 63/72 - 14 53/72. If you subtract those, you get the answer, 4 10/72. Which can be simplified as 4 5/36.

Answer:

Geometric mean of a and b: Square root of axb.

16x64 = 1024

Square root of 1024: 32.

So, the geometric mean is 32.

Hope this helps!

Step-by-step explanation:

The set of Natural numbers: {1, 2, 3, 4, 5, ...}

The set of Whole numbers: {0, 1, 2, 3, 4, 5, ...} ← it has the number 0

Answer:

1.5 per hour

Step-by-step explanation:

Answer:

[tex]{ \boxed{ \bf{c}}} \: \: \frac{3.8}{4} = s[/tex]

Step-by-step explanation:

[tex]{ \tt{4 \: pies \: = \: 3.8 \: ounces}} \\ { \tt{1 \: pie \: = \: ( \frac{1}{4} \times 3.8) \: ounces}} \\ { \tt{ = 0.95 \: ounces}}[/tex]

[tex]{ \underline{ \sf{ \blue{christ \: † \: alone}}}}[/tex]

Answer:

mate....where is red shaded region....

probably this will help ..... ;)

find the probability that a randomly selected point within the circle falls in the red shaded area

https://brainly.com/question/14113463?utm_source=android&utm_medium=share&utm_campaign=question

9514 1404 393

Answer:

  (a)  1/12

Step-by-step explanation:

The difference of adjacent terms is ...

  1/4 -1/6 = 3/12 -2/12 = 1/12

Answer:

the correct answer is b. Initially the car is 420 miles from its destination.

Step-by-step explanation:

Answer:

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Step-by-step explanation:

Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.

Therefore:

x + y = z                                  (1)

Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:

Cost of buying = Price it was sold for

The cost of the mango = 5z and the price it was sold for = 3x + 6y

3x + 6y = 5z                            (2)

Substituting z = x + y in equation 1

3x + 6y = 5(x + y)

3x + 6y = 5x + 5y

6y - 5y = 5x - 3x

y = 2x

x / y = 1/ 2 = 1 : 2

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

the answer is in the photo

Answer:

2/5

Step-by-step explanation:

[tex] - 2\frac{4}{5} \div ( - 7)[/tex]

[tex] = \frac{2 \times 5 + 4}{5} [/tex]

[tex] = \frac{10 + 4}{5} [/tex]

[tex] = \frac{14}{5} [/tex]

[tex] = - \frac{14}{5} \times 7[/tex]

[tex] = \frac{14}{5} \div 7[/tex]

[tex] = \frac{2}{5} [/tex]

Answer:

18

Step-by-step explanation:

HOPE I HELPED

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DESPERATELY TRYING TO LEVEL UP

         ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                        PEACE!

Answer:

A

Step-by-step explanation:

In this question, we are concerned with selecting which of the options best represents the difference of two squares.

Let’s have an exposition below as follows;

Consider two numbers, which are perfect squares and can be expressed as a square of their square roots;

a^2 and b^2

where a and b represents the square roots of the numbers respectively.

Inserting a difference between the two, we have;

a^2 - b^2

Now by applying the difference of two squares, these numbers will become;

a^2 - b^2 = (a + b)(a-b)

So our answer out of the options will be that option that could be expressed as above.

The correct answer to this is option A

Kindly note that;

x^2 -9 can be expressed as x^2 - 3^2 and consequently, this can be written as;

(x-3)(x + 3)

Answer:

Step-by-step explanation:

2√24 + 5√54

To combine the radicals first make sure the radicals have the same square root

That's

Since they have the same square root we can combine them

That's

We have the final answer as

Hope this helps you

Answer:

9108

Step-by-step explanation:

23^3+(-12)^3+(-11)^3                              remove parentheses

= 23^3-12^3-11^3                                  group difference of two cubes

= (23-12)(23^2+23*12+12^2) + 11^3      factor difference of two cubes

= 11 (23^2+23*12+12^2-11^2)                factor ou 11

= 11(23(23+12) + (12+11)(12-11))              apply difference of two squares

= 11 (23*35+23*1)                                  factor out 23

= 11(23*(35+1))                                       simplify

= 11*23*36                                             convert 11*23 into difference of 2 squares                                                                    

= (17^2-6^2)*6^2                                   expand parentheses

= 102^2-36^2                                       evaluate squares

= 10404 - 1296                                     subtraction

= 9108

(no calculator required)

Answer:

see below

Step-by-step explanation:

The phrase "at least" indicates that you use the symbol ≥, so that's where they got the ≥ from. The amount of water needed for each bushel is 1/3 * f or 1/3f because you need 1/3 gallons of water per one bushel. We know that the amount of water needed is at least 1/3 gallons per bushel. Since the amount of water is w, "at least" is ≥ and 1/3 gallons per bushel is 1/3f, the inequality is w ≥ 1/3f. I hope this makes sense.

Answer:

If Jorge goes up 25 (positive) and then goes 75 steps south (negative). Then you have to calculate 25-75. This equals -50. We know negative distance is south so he's final position will be 50 steps south.

Step-by-step explanation:

Answer:

well hlo again ( ˘ ³˘)♥ (◍•ᴗ•◍)❤

Answer:

2/13

Step-by-step explanation:

Cdgfsggdehfetgfrhfer

Answer:

I have explained the answer in detailed steps for you. If you do not understand any steps, please comment below, and I will help you out.

Answer:

None of the options are correct

Step-by-step explanation:

Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:

[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]

If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:

[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]

Therefore the distance cannot be gotten until the center of dilation is given

Answer:

6-2x

Step-by-step explanation:

six less than (subtraction) twice a number. 2 times a number x

Answer:

water in quarts is in the first jar after 10th pour = 12/11

Step-by-step explanation:

Let X represent first jar and Y represents second jar.

Lets give the initial value of 2 to the first jar which is filled with water. Lets say there are two liters of water in first jar.

Lets give the initial value of 0 to the second as it is empty.

So before any pour, the values are:

X: 2

Y: 0

After first pour the value of jar X becomes:

Previously it was 2.

Now half of water is taken i.e. half of 2

2 - 1 = 1

So X = 1

The value of jar Y becomes:

The half from jar X is added to second jar Y which was 0:

After first pour the value of jar Y becomes:

0 + 1 = 1

Y = 1

After second pour the value of jar X becomes:

Previously it was 1.

Now third of the water in second jar Y is added to jar X

1 + 1/3

=  (3 + 1)/3

= 4/3

X = 4/3

After second pour the value of jar Y becomes:

Previously it was 1.

Now third of the water in Y jar is taken and added to jar X so,

1 - 1/3

=  (3 - 1)/3

= 2/3

Y = 2/3

After third pour the value of jar X becomes:

Previously it was 4/3.

Now fourth of the water in the first jar X is taken and is added to jar Y

= 3/4 * (4/3)

= 1

X = 1

After third pour the value of jar Y becomes:

Previously it was 2/3

Now fourth of the water in the second jar X is added to jar Y

= 2/3 + 1/4*(4/3)

= 2/3 + 4/12

= 1

Y = 1

After fourth pour the value of jar X becomes:

Previously it was 1

Now fifth of the water in second jar Y is added to jar X

= 1 + 1/5*(1)

= 1 + 1/5

=  (5+1) / 5

= 6/5

X = 6/5

After fourth pour the value of jar Y becomes:

Previously it was 1.

Now fifth of the water in Y jar is taken and added to jar X so,

= 1 - 1/5

= (5 - 1)  / 5

= 4/5

Y = 4/5

After fifth pour the value of jar X becomes:

Previously it was 6/5

Now sixth of the water in the first jar X is taken and is added to jar Y

5/6 * (6/5)

= 1

X = 1

After fifth pour the value of jar Y becomes:

Previously it was 4/5

Now sixth of the water in the first jar X is taken and is added to jar Y

= 4/5 + 1/6 (6/5)

= 4/5 + 1/5

= (4+1) /5

= 5/5

= 1

Y = 1

After sixth pour the value of jar X becomes:

Previously it was 1

Now seventh of the water in second jar Y is added to jar X

= 1 + 1/7*(1)

= 1 + 1/7

=  (7+1) / 7

= 8/7

X = 8/7

After sixth pour the value of jar Y becomes:

Previously it was 1.

Now seventh of the water in Y jar is taken and added to jar X so,

= 1 - 1/7

=  (7-1) / 7

= 6/7

Y = 6/7

After seventh pour the value of jar X becomes:

Previously it was 8/7

Now eighth of the water in the first jar X is taken and is added to jar Y

7/8* (8/7)

= 1

X = 1

After seventh pour the value of jar Y becomes:

Previously it was 6/7

Now eighth of the water in the first jar X is taken and is added to jar Y

= 6/7 + 1/8 (8/7)

= 6/7 + 1/7

= 7/7

= 1

Y = 1

After eighth pour the value of jar X becomes:

Previously it was 1

Now ninth of the water in second jar Y is added to jar X

= 1 + 1/9*(1)

= 1 + 1/9

=  (9+1) / 9

= 10/9

X = 10/9

After eighth pour the value of jar Y becomes:

Previously it was 1.

Now ninth of the water in Y jar is taken and added to jar X so,

= 1 - 1/9

=  (9-1) / 9

= 8/9

Y = 8/9

After ninth pour the value of jar X becomes:

Previously it was 10/9

Now tenth of the water in the first jar X is taken and is added to jar Y

9/10* (10/9)

= 1

X = 1

After ninth pour the value of jar Y becomes:

Previously it was 8/9

Now tenth of the water in the first jar X is taken and is added to jar Y

= 8/9 + 1/10 (10/9)

= 8/9 + 1/9

= 9/9

= 1

Y = 1

After tenth pour the value of jar X becomes:

Previously it was 1

Now eleventh of the water in second jar Y is added to jar X

= 1 + 1/11*(1)

= 1 + 1/11

= (11 + 1) / 11

= 12/11

X = 12/11

After tenth pour the value of jar Y becomes:

Previously it was 1.

Now eleventh of the water in Y jar is taken and added to jar X so,

= 1 - 1/11

=  (11-1) / 11

= 10/11

Y = 10/11

Answer:

6/11

Step-by-step explanation:

1/2 + (1/2)(2/11) = 6/11

sus

Answer:

[tex]cos\alpha =\frac{7}{25}; \ tan\alpha =-\frac{7}{24}.[/tex]

Step-by-step explanation:

if π<α<2π and cotα<0, then 1.5π<α<2π. It means, that cosα>0 and tanα<0.

1) tanα=1/cotα; ⇒tanα= -7/24;

2) [tex]cos\alpha =\frac{1}{\sqrt{1+cot^2\alpha }}}; \ cos\alpha =\frac{7}{25}.[/tex]

25) First, find the amount of minutes in 2 hours. Note that there are 60 minutes in one hour:

2 x 60 = 120 minutes per 2 hours.

Next, the bacteria doubles every 20 minutes. 120/20 = 6, which means that the bacteria will double 6 times:

1 x 2 = 2

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 2 = 32

32 x 2 = 64

64 bacteria will be your answer.

~

26) The Area of a circle = πr²

Set the equation:

400π = π(r + 2)²

First, divide common factors from both sides, or π.

(400π)/π = (π(r + 2)²)/π

400 = (r + 2)²

√400 = √(r + 2)²

r + 2 = √400

r + 2 = √(20 x 20)

r + 2 = 20

r + 2 (-2) = 20 (-2)

r = 20 - 2

r = 18

18 is your final answer.

~

27)

The volume of a box can be found by multiplying length x width x height:

[tex]V (box) = l * w * h[/tex]

The volume given is 90, the height 3, and the width is 1 foot less then length:

First solve what you know:

[tex]V(box) = 90\\h = 3\\l = l\\w = l - 1[/tex]

Plug in the corresponding terms with the corresponding variable. Isolate the variable, l. Divide 3 from both sides of the equation:

[tex]90 = 3 * l (l - 1)\\\frac{90}{3} = \frac{3 * l(l -1)}{3}\\30 = l(l - 1)\\[/tex]

Distribute l to both terms in the parenthesis:

[tex]30 = l(l - 1)\\30 = l^2 - l[/tex]

Solve:

[tex]30 = (6)^{2} -6\\30 = 36 - 6\\30 = 30[/tex]

∴ [tex]l = 6[/tex]

Solve for width. Width is 1 less foot then length:

[tex]l - 1 = w\\l = 6\\[/tex]

∴ [tex]6 - 1 = w\\w = 5[/tex]

Equation: [tex]V (box) = l * w * h[/tex]

or

[tex]l = \frac{V(box)}{w * h}[/tex]

[tex]V(box) = 90\\h = 3\\l = 6\\w = 5[/tex]

( a ) Well we know that the limit for the range is 400 dollars, as ( 1 ) her greatest balance was 400 dollars, and ( 2 ) the balance is dependent on the days, and hence represents the range. Respectively the limit for the domain would be 3 weeks.

( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.

( c ) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be :

B(12) = 0

( d ) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.

Answer:

V = 60 m³

Step-by-step explanation:

Volume of Triangular Pyramid: V = 1/3bh

Area of Triangle: A = 1/2bh

b = area of bottom triangle (base)

h = height of triangular pyramid

Step 1: Find area of base triangle

A = 1/2(8)(5)

A = 4(5)

A = 20

Step 2: Plug in known variables into volume formula

V = 1/3(20)(9)

V = 1/3(180)

V = 60

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