Find the volume and total surface area of the composite figure below.​

Answer:

  A) L, N, O, P

Step-by-step explanation:

The even numbers on the number line are marked by the letters L, N, O, P.

_____

If a number gives an integer result when divided by 2, it is an even number. Zero is an even number, giving the integer zero when divided by 2.

Answer:

The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².

Step-by-step explanation:

An octagon is a polygon with eight sides. An octagon is regular (also called a regular octagon) is a polygon with all eight sides equal.

The apothem of a regular octagon is the shortest distance between the center and any of its sides, in other words, it is the distance that separates the center of the polygon from the central point of each side of the octagon.

The area is calculated using the following formula:

[tex]Area=\frac{n*L*Ap}{2}[/tex]

Where:

Being n = 8 being an octagon and the perimeter P the sum of the sides of the octagon (P = 8 * L), the area of ​​the regular octagon can be calculated by:

[tex]Area=\frac{P*Ap}{2}[/tex]

In this case:

Replacing:

[tex]Area=\frac{80ft*12.07ft}{2}[/tex]

Solving:

Area=482.8 ft²

The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².

Answer:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in  0 for x and solve for y.

x-intercept(s): ( 2,0 ), ( 1,0 ) (2,0), (1,0)

y-intercept(s): ( 0, − 10 )

Answer:

D

Step-by-step explanation:

The answer is 40km.

24 plus 10 equals to 34 and a few extra km would lead to 40km

Answer:

15a⁴b²-20a³b³+30a²b⁴

Step-by-step explanation:

3a²-4ab+6b²

so for 5a²b²

(5a²b²)(3a²-4ab+6b²)

=15a⁴b²-20a³b³+30a²b⁴

By applying the distributive property, 5a²b² × (3a²- 4ab + 6b²)​ = 15a⁴b² - 20a³b³ + 30a²b⁴

Given the expression: 5a²b² × (3a²- 4ab + 6b²)​

We would apply the distributive property by multiplying every term inside the parentheses by 5a²b².

This can be done as shown below:

5a²b² × (3a²- 4ab + 6b²)​ = 5a²b²(3a²) - 5a²b²(4ab) + 5a²b²(6b²)​

5a²b² × (3a²- 4ab + 6b²)​ = 15a⁴b² - 20a³b³ + 30a²b⁴

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Answer:

  f(-3) = -20

Step-by-step explanation:

We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...

  34, 10, -8, ?

The first differences of these numbers are ...

  10 -34 = -24

  -8 -10 = -18

And the second difference is ...

  -18 -(-24) = 6

For a quadratic function, second differences are constant. This means the next first-difference will be ...

  ? -(-8) = -18 +6

  ? = -12 -8 = -20

The value of the function at x=-3 is -20.

_____

The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)

Use a rigid transformation to prove that angle NPO is congruent to angle NLM

=====================================================

Explanation:

The AA stands for "angle angle". So we need two pairs of angles to prove the triangles to be similar. The first pair of angles is the vertical angles ONP and MNL, which are congruent. Any pair of vertical angles are always congruent.

The second pair of angles could either be

so we have a choice on which to pick. The pairing angle NOP = angle NML is not listed in the answer choices, but angle NPO = angle NLM is listed as choice B.

Saying angle NLM = angle LMN is not useful because those two angles are part of the same triangle. The two angles must be in separate triangles to be able to tie the triangles together.

We would use a rigid transformation to have angle NPO move to angle NLM, or vice versa through the use of a rotation and a translation.

Angle Angle AA similarity postulate states that two triangles are similar if

two angles in one of the triangles are congruent (equal) to two angles in the

other triangle

The correct option for the method and additional information that would

prove triangle ONP and triangle MNL similar by AA similarity postulate is

option B.

B. Use rigid transformation to prove that angle NPO is congruent to angle NLM

The reason for arriving at the above selection is as follows;

The known parameter in triangle ΔONP and ΔMNL are;

Lines MO and LP intersect at vertex point N.

The angles on opposite side of the point N (either side of the X shape

formed by the two lines) which are ∠ONP and ∠LNM are vertically opposite

angles or opposite angles.

According to vertically opposite angles theorem ∠ONP and ∠LNM, which

are vertically opposite angles are congruent, and we can write.

∠ONP ≅ ∠LNM

The required parameter;

To find the additional information that would prove ΔONP and ΔMNL by

AA (Angle-Angle) similarity postulate.

Strategy;

Given that from the drawing, one (vertex) angle in one triangle is congruent

to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is

required to prove that one other angle in triangle ΔONP is congruent to a

corresponding angle in triangle ΔMNL.

Solution;

Prove that either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or

∠NML respectively in ΔMNL by performing rigid transformations

(transformations that does not change shape) on either ΔONP or ΔMNL

including;

Therefore, the correct option is option B. Use rigid transformation to prove

that angle NPO is congruent to angle NLM.

Learn more about similarity, congruency postulates and rigid transformations here;

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Answer:

B = -5x + 30

Step-by-step explanation:

y= mx+b

m = slope = rise/run = -5

b = y-int = 30

Answer:

B = -5x + 30

Step-by-step explanation:

y= mx+b

m = slope = rise/run = -5

b = y-int = 30

Answer:

the lcm is 30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ..., 30

Multiples of 6: 6, 12, 18, 24, 30

Multiples of 10: 10, 20, 30

30 is the first number to appear on all three lists of multiples

=================================================

Work Shown:

Law of Cosines

c^2 = a^2 + b^2 - 2ab*cos(C)

22^2 = 20^2 + 18^2 - 2*20*18*cos(X)

484 = 724 - 720*cos(X)

484 + 720*cos(X) = 724

720*cos(X) = 724 - 484

720*cos(X) = 240

cos(X) = 240/720

cos(X) = 1/3

X = arccos(1/3)

X = 70.528779

X = 70.5

Make sure your calculator is in degree mode.

Answer:

C

[tex] \frac{4}{5} [/tex]

Co efficient means the number or value beside preventing the variable from standing alone

Answer:

c. 4/5

Step-by-step explanation:

4x/5 is the same as 4/5 * x

Answer:

47% is the statistic and 31% is the parameter.

Step-by-step explanation:

A parameter is a quantity of a variable representing certain characteristic of a population.

A statistic is a quantity of a variable representing certain characteristic of a sample.

The sample of parents of kindergartners selected is, n = 345.

The School records show that only 31% of parents of kindergartners sent their children to pre-kindergarten.

That is the population proportion is, p = 0.31.

This is the parameter value.

Of the 349 parents, 47% said they sent their children to pre-kindergarten.

That is the sample proportion is, [tex]\hat p[/tex] = 0.47.

This is the statistic value.

Thus, the correct option is:

47% is the statistic and 31% is the parameter.

Answer:

Postulate 5, The Parallel postulate: If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.

The parallel postulate is needed to derive the elements, but it seems too complex.

Answer:

a. 5/12

b. 7/18

Step-by-step explanation:

In this question, we are interested in computing the probabilities.

Firstly, we need to get the sample space of the results. This refer to all possible results that can emerge from the rolling of the two die.

This can be found in the attachment.

What is important to know however is that the total number of possible results is 36;

so let’s compute;

a. For a, let’s circle all sums which are greater than 7 ;

We can see a total of 16 circled sums;

So the probability is 15/36 = 5/12

b. Sum divisible by 4 or 6 or both

Let’s make a circle again ;

So we have a total of 14

So the probability will be 14/36 = 7/18

Answer:

VM = 15

Step-by-step explanation:

Given that line segment VM = 4x - 1

line segment MW = 3x + 3,

since M is the midpoint of VW, therefore:

VM = MW

Thus,

[tex] 4x - 1 = 3x + 3 [/tex]

Find the value of x

[tex] 4x - 3x = 1 + 3 [/tex]

[tex] x = 4 [/tex]

VM = 4x - 1

Plug in the value of x

[tex] VM = 4(4) - 1 = 16 - 1 = 15 [/tex]

VM = 15

Answer:

D. 4[tex]m^{2}[/tex]

Step-by-step explanation:

First find the area of 1 tile

= length * breadth

= 8 * 5

= 40[tex]cm^{2}[/tex]= 40/10000 = 0.004

no. of tiles= 1000

therefore, total area of 1000 tiles = area of room= 1000*0.004

=4[tex]m^{2}[/tex]

Answer:

(x+8)²

Step-by-step explanation:

x² + 16x + 64 = (x+8)²

(x+8)² = (x+8)(x+8) = x*x + x*8 + 8*x + 8*8 = x² + 8x + 8x + 64

         = x² + 16x + 64

Answer:

x = 15/2

Step-by-step explanation:

Solve for x:

x - 5 = 2 + 1/2

Hint: | Put the fractions in 2 + 1/2 over a common denominator.

Put 2 + 1/2 over the common denominator 2. 2 + 1/2 = (2×2)/2 + 1/2:

x - 5 = (2×2)/2 + 1/2

Hint: | Multiply 2 and 2 together.

2×2 = 4:

x - 5 = 4/2 + 1/2

Hint: | Add the fractions over a common denominator to a single fraction.

4/2 + 1/2 = (4 + 1)/2:

x - 5 = (4 + 1)/2

Hint: | Evaluate 4 + 1.

4 + 1 = 5:

x - 5 = 5/2

Hint: | Isolate terms with x to the left hand side.

Add 5 to both sides:

x + (5 - 5) = 5/2 + 5

Hint: | Look for the difference of two identical terms.

5 - 5 = 0:

x = 5/2 + 5

Hint: | Put the fractions in 5/2 + 5 over a common denominator.

Put 5/2 + 5 over the common denominator 2. 5/2 + 5 = 5/2 + (2×5)/2:

x = 5/2 + (2×5)/2

Hint: | Multiply 2 and 5 together.

2×5 = 10:

x = 5/2 + 10/2

Hint: | Add the fractions over a common denominator to a single fraction.

5/2 + 10/2 = (5 + 10)/2:

x = (5 + 10)/2

Hint: | Evaluate 5 + 10.

5 + 10 = 15:

Answer: x = 15/2

Answer:

7 1/2

Step-by-step explanation:

Hello!

To solve this we have to get x by itself

What we do to one side of the equation we have to do to the other

-5 + x = 2 1/2

To get -5 to the other side we have to add 5 to make it zero

What we do to the left side we have to do to the right

-5 + 5 + x = 2 1/2 + 5

Simplify

0 + x = 7 1/2

We can drop the 0

x = 7 1/2

The answer is 7 1/2

Hope this helps!

Answer:

720+810=1530

Step-by-step explanation:

Answer:

I think the answers are, rational and real.

Step-by-step explanation:

- 14 belongs to the sets of rational numbers and real numbers.

Rational Numbers: Any number that may be written as a ratio (or fraction) of integers is a rational quantity.

A Rational number is a number that is expressed because of the ratio of two integers, wherein the denominator ought to now not be the same as zero, whereas an irrational number cannot be expressed inside the form of fractions. Rational numbers are terminating decimals however irrational numbers are non-terminating and non-habitual.

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Answer:

No

Step-by-step explanation:

A parallelogram has opposite angels equal and opposite sides equal. in this case, only a single pair of angels are equal.

Answer:

From the pythagorean theorem:

AB²+BC²=AC²

x+35²=37²

x+1225=1369

x=1369-1225

x²=144 cm

x=radical 144=12

Answer:

[tex]\huge\boxed{b = 12 cm}[/tex]

Step-by-step explanation:

Using Pythagorean Theorem:

[tex]c^2 = a^2 + b^2[/tex]

Where c is hypotenuse(37 cm), and one of the side is 35 cm.

=> [tex]37^2 = 35^2 + b^2[/tex]

=> [tex]b^2 = 37^2-35^2\\[/tex]

=> [tex]b^2 = 1369 - 1225\\[/tex]

=> [tex]b^2 = 144[/tex]

Taking sqrt on both sides

=> b = 12 cm

Answer:

the one that doesn't belong is 5/3

Answer:

6.6 × 10^16

Step-by-step explanation:

Answer:

Step-by-step explanation:

i would believe that it would  so there is your answer

Answer:

1) a = 65

2) b = 61

3) c = 55

Step-by-step explanation:

1)

a + 115 = 180

a = 65

2)

b + 119 = 180

a = 61

3)

c + 75 + 50 = 180

c = 55

Answer:

Step-by-step explanation:

x = 52°

b = ¹/₂(2x) = x = 52°

y = 180° - 90° - x

y = 90° - 52° = 38°

a = 180° - 90° - y = 90° - 38° = 52°

p = 83°

q = ¹/₂p = 41.5°

(180° - c) + b + q = 180°

180° - c + 52° + 41.5° = 180°

    - c = - 93.5°

       c = 93.5°