In ΔDEF, d = 92 cm, e = 42 cm and ∠F=141°. Find the length of f, to the nearest centimeter.

The area of the regular hexagon is 585 square centimeters.

A regular hexagon is a polygon with six equal sides and six equal angles. To find the area of a regular hexagon, you can use the formula:

[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times \text{side length}^2 \][/tex]

However, in this case, the apothem (the distance from the center to the midpoint of a side) is given instead of the side length. The relationship between the apothem (\(a\)) and the side length (\(s\)) of a regular hexagon is given by:

[tex]\[ a = \frac{s}{2} \times \sqrt{3} \][/tex]

Rearranging this formula to solve for \(s\), we get:

[tex]\[ s = \frac{2 \times a}{\sqrt{3}} \][/tex]

Substituting this expression for \(s\) into the area formula, we get:

[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times \left(\frac{2 \times a}{\sqrt{3}}\right)^2 \][/tex]

Simplifying further:

[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times \frac{4 \times a^2}{3} \][/tex]

Canceling out common factors:

[tex]\[ \text{Area} = 2 \sqrt{3} \times a^2 \][/tex]

Now, substituting the given apothem ((a = 15) cm), we find:

[tex]\[ \text{Area} = 2 \times \sqrt{3} \times (15 \, \text{cm})^2 = 585 \, \text{cm}^2 \][/tex]

Therefore, the area of the regular hexagon is 585 square centimeters.

Answer:

Distributive property

commutative property

combine like terms or write a equivalent expression

Step-by-step explanation:

by definition it’s

Distributive property

commutative property

combine like terms or write a equivalent expression

Answer:

10 1/2 or 10.5

Step-by-step explanation:

V=l*w*h

Volume = length * width * height

length = 3 1/2 = 3.5

width = 1 1/5 = 1.5

height = 2

input the values V = 3.5 * 1.5 *2

multiply the first two numbers 3.5 * 1.5 = 5.25

multiply the first result by the third number 5.25 * 2 = 10.5

Volume = 3.5 * 1.5 *2= 5.25 * 2 = 10.5 = 10 1/2

3 1/2 * 1 1/5 * 2 = length * width * height = Volume = 10 1/2

Volume = 10 1/2

Answer:

Yes it is

Step-by-step explanation:

when you dived -14 by 4 you will get -3.5

The next three terms in the pattern following the rule 'add 9' are 36, 45, and 54.

Since the pattern follows the rule of adding 9 to get to the next term, we can simply continue this pattern from the last given term, which is twenty-seven triangles. Therefore:

Term four would have twenty-seven plus nine triangles, giving us 36 triangles.

Term five would be thirty-six plus nine, which results in 45 triangles.

Term six is forty-five plus nine, totaling 54 triangles.

The next three terms in the pattern following the rule 'add 9' are 36, 45, and 54.

Hope this will help u...

Answer: 317.39

Step-by-step explanation:

The price of the guitar decreased by15%

Original price is 275.99

To get the reduced amount

It will be 15% of the exact amount and add to the exact to get the original

15/100×275.99

=41.3985

To get exact,

reduced amount + sold price

=41.3985+275.99

=317.3885

=317.39

Answer:

11.9

Step-by-step explanation:

just took the test :D

Answer:

7.5 or 7 1/2 pounds of fruit.

Step-by-step explanation:

2.5 (2 1/2) + 1.25 (1 1/4) = 3 3/4 (3.75). 3 3/4 + 3 3/4 = 7 1/2 (7.5) pounds of fruit in total.

The value of c is 3 units and TR is 29 units. Therefore, option D is the correct answer.

Given that, △STR≅△XYZ, TR=14c−13, and YZ=10c−1.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

We know that, corresponding parts of congruent triangles are equal.

Here, TR=YZ

⇒ 14c-13=10c-1

⇒ 14c-10c=-1+13

⇒ 4c=12

⇒ c=3 units

So, TR=14c-13

= 29 units

The value of c is 3 units and TR is 29 units. Therefore, option D is the correct answer.

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123,000,000 as a multiple of a power of 10 is 1.23 x 10⁸.

The large values when shortened, they are written in the form of power of 10 by shifting decimals.

123,000,000 has eight zeroes to reduce and taken to the power of 10. Put decimal after counting eight digits from the right.

123,000,000 can be written as 1.23 x 10⁸.

Thus, 123,000,000 as a multiple of a power of 10 is  1.23 x 10⁸.

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To express 123,000,000 as a multiple of a power of 10, we identify it as 1.23 x 10^7.

The question asks to express 123,000,000 as a multiple of a power of 10. To do this, we need to understand how exponents of 10 work. The exponent tells us how many zeros are added to the right of 1 to create the number. For instance, 10^2 equals 100 because there are two zeros.

In the case of 123,000,000, we count the zeros following the initial digit(s). There are 7 zeros. Therefore, we can express 123,000,000 as 1.23 x 10^7. Here, 1.23 is the coefficient (a value greater than or equal to 1 but less than 10), and 10^7 indicates that the decimal point in 1.23 is moved 7 places to the right to get the original number, 123,000,000.

This method of notation is commonly used in scientific notation, which simplifies large numbers by expressing them as a multiple of a power of 10. It's a useful way to work with very large or very small numbers efficiently.

Answer:

(-6, -4)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

-5x + y = 26

2x - 7y = 16

Step 2: Rewrite Systems

-5x + y = 26

Step 3: Redefine Systems

y = 5x + 26

2x - 7y = 16

Step 4: Solve for x

Substitution

Step 5: Solve for y

Answer:

111.2 units³

Step-by-step explanation:

Base area = 2(a² + ½ab)

2(4)² + (4)(5.9)

= 55.6 units²

Volume = Base area × c

55.6 × 2

= 111.2 units³

Answer: 8

Step-by-step explanation:

As per the given volume and radius of the cylinder, the height of the cylinder in the diagram is approximately 8 cm.

In order to determine the height of the cylinder in the given diagram, we first need to understand the formula for calculating the volume of a cylinder. The formula for the volume of a cylinder is

=> V = π * r² * h,

where V represents the volume, π is a constant (approximately equal to 3.14159), r is the radius, and h is the height of the cylinder.

In the provided information, we are given that the radius of the cylinder is 6 cm (radius = 6 cm) and the volume of the cylinder is 904.78 cm³ (V = 904.78 cm³).

Now, we can rearrange the volume formula to solve for the height (h) of the cylinder. Divide both sides of the formula by (π * r²):

h = V / (π * r²)

Substitute the known values:

h = 904.78 cm³ / (3.14159 * 6²)

h = 904.78 cm³ / (3.14159 * 36)

h = 904.78 cm³ / 113.09724

h ≈ 7.99998 cm

Rounding the answer to the nearest whole number, the height of the cylinder is approximately 8 cm.

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Answer:

c.

Step-by-step explanation:

You could use a regression calculator to help you. You should try it its very helpful :)

Answer:

A. x - 3 + 7x - 9/x^2 - 2

did test on edge, got 100%

The height of the prism is x-3+ (7x-9)/([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+5x-3).

The formula for the volume of a rectangular prism is V = Ah, where A is the area of the base and h is the height. Since we are given the volume and the area of the base, we can solve for the height. We have V = ([tex]x^{2}[/tex]-2) * h and V = ([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+5x-3), so we can set these two equations equal to each other and solve for h.

([tex]x^{2}[/tex]-2) * h = ([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+5x-3)

Expanding both sides, we get:

[tex]x^{2}[/tex]h - 2h = [tex]x^{3}[/tex]h - 3[tex]x^{2}[/tex]h + 5xh - 3h

Combining like terms, we get:

([tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] + 5x - 3 - [tex]x^{2}[/tex] + 2 - 5x + 3) * h = 0

Simplifying, we get:

([tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2) * h = 0

Since [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2 cannot equal 0 (since it's a cubic polynomial), we can divide both sides by ([tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2) to solve for h:

h = 0 / ([tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2)

So the height of the prism is x-3+ (7x-9)/([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+5x-3).

Answer:

11y^2-26y

Step-by-step explanation:

8y(y - 4) + 3y(y+2)

8y^2-32y+3y^2+6y

11y^2-26y

Answer:

11y^2 -26y

Step-by-step explanation:

8y(y - 4) + 3y(y+2)

Distribute

8y^2 -32y +3y^2 +6y

Combine like terms

8y^2 +3y^2   -32y +6y

11y^2 -26y

Answer:

The domain is all real numbers, and the range is (y ≤ 0)

Step-by-step explanation:

It's best to start graphing piecewise functions by reading the "if" statements first, and you'll most likely shorten the chance of making an error by doing so.

Answer:

Yea its B

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Simple

The value of x is 15.

Here first we add P and Q together that equals x+13

After this, it  divide x+13 and 8 and make it equal to [tex]21\div x-9[/tex]

Now x should then equal 15

[tex]x+13\div 9 = 21\div x-9\\x^2+4x−117=168\\\\x^2 + 4x-285=0[/tex]

(x−15)(x+19)=0

x = 15

Therefore we can conclude that The value of x is 15.

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To find the value of x in a similar triangle question, you need to identify the corresponding sides and use their ratio to solve for x. In this case, PQR is similar to SQT, and the corresponding sides are PQ and SQ, PR and ST, and QR and QT. The ratio of the side lengths can be used to find the value of x.

If two triangles are similar, it means that their corresponding angles are equal, and the ratio of their corresponding side lengths is constant. In the given question, PQR is similar to SQT. To find the value of x, we need to identify the corresponding sides and find the ratio between them. Let's assume that the corresponding sides are PQ and SQ, PR and ST, and QR and QT. The ratio of the side lengths can be written as:

x / (p + q) = PQ / SQ. Using this ratio, we can solve for x by multiplying both sides of the equation by (p + q):

x = (PQ / SQ) * (p + q)

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Answer:

Step-by-step explanation:

Since it is a parallelogram so opposite sides are equal and parallel

4y = y + 18

4y - y = 18

3y = 18

y = 18 / 3

y = 6

Now

Length of AB = 4 * 6 = 24

hOPE IT HELPED :)

Answer:

y=6

AB= 24 units

Step-by-step explanation:

In a parallelogram the opposite or facing sides are equal therefore AB=CD

Answer:

angle = arc tangent(6/x)

for x=2 -> angle = 71.565°

Step-by-step explanation:

To find the relation of the distance x and the angle of elevation that you are seeing the airplane, we should use the tangent relation of the angle. The opposite side of the angle is the altitude of the airplane, and the adjacent side of the angle is the distance x.

So we have that:

tangent(angle) = 6/x

angle = arc tangent(6/x)

If we have the value of x = 2, the angle will be:

angle = arc tangent(6/2) = arc tangent(3)

angle = 71.565°

Answer:

15.49 inches

Step-by-step explanation:

Volume of a cylinder is given by

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

Making h the subject of the formula then

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

Where h is the height, V is volume and r is radius. Substituting 24.6 inches for r and 29468 cubic inches for V then

[tex]h=\frac {29468}{\pi 24.6^{2}}=15.493723673378\ in\approx 15.49\ in[/tex]

Therefore, the height is approximately 15.49 inches

The correct height of the cylinder that produces a volume of 29,468 in3 is 15 inches (Choice B).

To find the height of a cylinder with a volume of 29,468 cubic inches (in3) and a radius of 24.6 inches, we use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height.

Plugging in the known values, we get:
29,468 in3 = π(24.6 in)2h

Solving for h, the height of the cylinder, we perform the following steps:

Calculate the base area: Base Area = π(24.6 in)2

Divide the volume by the base area to find the height: h = Volume / Base Area

Calculate the height: h = 29,468 in3 / (π(24.6 in)2)

After performing the calculation, we conclude that the correct height of the cylinder that produces a volume of 29,468 in3 is 15 inches (Choice B).

Answer:

1. 4t^3, 9y, 1

2.11gh, 6t, 4

3.z, mn, 4v^2

Step-by-step explanation:

Each term is separated by + or -

Answer:

72 for q1 and q2 is 18

Step-by-step explanation:

Final answer:

To find the volume of a cuboid, multiply its length, width, and height. If made of 1 cm cubes, the volume is the number of these cubes. Halving the cuboid evenly would halve its volume.

Explanation:

To calculate the volume of a cuboid, you multiply the length, width, and height of the cuboid. The question doesn't provide specific dimensions, but assuming that you have them, the formula you would use is Volume (V) = length × width × height. If the cuboid consists of centimeter cubes, each with a side length of 1 cm, the volume in cubic centimeters will be equal to the number of these small cubes.

For example, let's say the dimensions of the cuboid are 5 cm × 3 cm × 4 cm. The volume would then be calculated as V = 5 cm × 3 cm × 4 cm = 60 cm³.

If the cuboid is split in half, the resulting two pieces would each have a volume that is half of the original total volume, assuming the split is made evenly.

Answer:

x = y + v/b

Step-by-step explanation:

You can solve for x by adding v/b to both sides since that is what will isolate x the quickest and that is what you want to do when you need to solve for something.

By adding v/b to both sides, you will end up with x=y+v/b and that’s your answer!

Hope this helps!

(Credit to math-way)

Given:

(a) To determine the inequality for x for the given line.

Inequality:

Since, from the figure, it is obvious that the number line contains an open circle at the point 3.

This means that the end value 3 is not included in the interval.

Hence, the inequality can be written as [tex]x<3[/tex]

Thus, the inequality for x is [tex]x<3[/tex]

(b) Given that [tex]2<y<6[/tex] where y is an integer.

We need to determine the possible values of y.

Values of y:

The values of y lie between 2 to 6. Since, the inequality is strictly lesser than, it does not contain the end value.

Therefore, the possible values of y are 3,4,5

(3) Given the inequality [tex]3 x+7>x+19[/tex]

We need to solve the inequality.

Solution:

[tex]3 x>x+12[/tex]

[tex]2 x>12[/tex]

 [tex]x>6[/tex]

Thus, the solution of the inequality is [tex]x>6[/tex]