Unless otherwise indicated, a line in geometry is understood to be _____. straight curved either

To find the area of a segment of a circle, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. By plugging in the values and following the steps, we can find that the area of the segment is 3840 - 16√3 square inches.

To find the area of a segment of a circle, we need to know the measure of the arc and the length of the chord. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. To find the area, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians.

First, we need to find the radius by using the length of the chord. The formula for the radius is r = 2c/sinθ, where c is the length of the chord and θ is the central angle in degrees. Plugging in the values, we get r = 8√3/(2sin60) = 4√3/sin60 = 4√3/(√3/2) = 8 inches. Now we can find the area using the formula A = (r^2/2)(θ - sinθ). Plugging in the values, we get A = (8^2/2)(120 - sin120) = 32(120 - √3/2) = 3840 - 16√3 square inches.

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Final answer:

The expression x⁴ + 8x² + 16 is a perfect square trinomial and it can be factored completely as (x² + 4)².

Explanation:

To factor completely the expression x⁴ + 8x² + 16, we should first recognize that this is a perfect square trinomial. A perfect square trinomial takes the form a² + 2ab + b², and can be factored into (a + b)².

Comparing our given expression to the perfect square trinomial, we see that x⁴ is the square of x² and 16 is the square of 4. Moreover, 8x² is twice the product of x² and 4, suggesting that the expression is indeed, a perfect square. Thus, we can factor it as:

(x² + 4)²

In conclusion, the expression x⁴ + 8x² + 16 can be factored completely as (x² + 4)².

Final answer:

To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial.

Explanation:

To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial of the form [tex]a^2 + 2ab + b^2[/tex]. The square root of the first term is [tex]x^2[/tex] the square root of the last term is 4, and twice the product of these square roots is [tex]8x^2[/tex], which matches the middle term of the given expression. Therefore, we can rewrite the expression as [tex](x^2 + 4)^2[/tex]. This is the completely factored form of the expression.[tex]a^2 + 2ab + b^2[/tex]

Answer:

A) CD

B)  AB

C) Plane ABCD is parallel to EFGH.

Plane BDFH is parallel to ACGE.

Plane ABFE is parallel to CDHG.

Step-by-step explanation:

We are given the following in the question:

A cuboid  ABCDEFGH is given.

A) line segment that is parallel to AB

A line segment that is parallel to AB is CD.

B) line segment that is skew to AB

Skew lines are the line that never lie in the same plane and never intersect each other.

Thus line segment FH is skew to line segment AB.

C) pair of parallel planes.

Plane ABCD is parallel to EFGH.

Plane BDFH is parallel to ACGE.

Plane ABFE is parallel to CDHG.

There are 432 total barns when multiplying 48 chicken farms by 9 barns per farm. For question number 27, without knowing the number of mice per barn, we cannot determine the exact number of cats needed to control the grain destruction.

To determine the number of total barns if there are 48 chicken farms near an Ohio town and each farm has 9 barns, we simply need to multiply the number of farms by the number of barns per farm. This can be represented by the equation: 48 farms times 9 barns/farm = 432 barns. Therefore, there are 432 total barns.Now, addressing the second question (Number 27): To calculate the number of cats required to control the destruction of stored grain by mice, we need to find out how many mice are in each barn, and then see how many cats are needed to kill that number of mice. A mouse eats 521 ikats of grain each year, and if we are to prevent the destruction of grain in each of the 24 barns, we need to find out how many mice a single cat can kill in a year, and then divide the number of mice by this figure.If one cat kills 96 mice a year, and assuming each barn has the same number of mice, then for one barn: Total mice killed in one barn/year = Number of cats times 96 mice/cat/year. Therefore, to find the number of cats needed: Number of cats = Total mice in one barn/year extdiv 96 mice/cat/year. Without the number of mice, we cannot complete the calculation. More information on the number of mice per barn is required to give a definitive answer.

Solution to y = 3x - 1: B. (2, 5)

Matching equation for "The sum of -4x and 2 is 9": A. -4x + 2 = 9

Solve x - 6 = -18: A. x = -12

Solve 4x + 3 = 47: A. x = 11

Let's solve each of the given equations one by one:

Solution to y = 3x - 1:

The equation y = 3x - 1 represents a linear relationship between x and y with a slope of 3 and a y-intercept of -1. To find the solution, we can substitute the given options for x and see which one satisfies the equation:

A. (4, 1): 1 = 3(4) - 1 => 1 = 12 - 1 => 1 = 11 (Not a solution)

B. (2, 5): 5 = 3(2) - 1 => 5 = 6 - 1 => 5 = 5 (This is a solution)

C. (4, 3): 3 = 3(4) - 1 => 3 = 12 - 1 => 3 = 11 (Not a solution)

D. (0, -3): -3 = 3(0) - 1 => -3 = 0 - 1 => -3 = -1 (Not a solution)

So, the solution is B. (2, 5).

Matching equation for "The sum of -4x and 2 is 9":

The statement can be translated into the equation: -4x + 2 = 9. So, the correct equation is A. -4x + 2 = 9.

Solving x - 6 = -18:

To solve for x, add 6 to both sides of the equation:

x - 6 + 6 = -18 + 6

x = -12

So, the solution is A. x = -12.

Solving 4x + 3 = 47:

To solve for x, subtract 3 from both sides of the equation:

4x + 3 - 3 = 47 - 3

4x = 44

Now, divide both sides by 4 to isolate x:

(4x)/4 = 44/4

x = 11

So, the solution is A. x = 11.

In summary, the solutions to the given equations are:

B. (2, 5)

A. -4x + 2 = 9

A. x = -12

A. x = 11

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The probability of picking a pair of red socks is 1/5.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, There are 5 red socks, 2 white socks and 3 blue socks in a basket.

So, The no. of sample space N(S) = 5 + 2 + 3 = 10.

Now pair of red socks means 2 red socks let it be N(A).

∴ The probability of picking a pair of red socks P(A) = N(A)/N(S).

P(A) = 2/10.

P(A) = 1/5.

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Answer:  the correct option is

(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.

Step-by-step explanation:  We are given to select the correct inverse of the conditional statement p → q if

p : x – 5 =10  and  q : 4x + 1 = 61.

We know that

the inverse of a conditional statement p → q is given by "not p → not q".

Therefore, the inverse of the given statement is

not p → not q

that is, if  x – 5 ≠ 10, then 4x + 1 ≠ 61.

Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."

Option (a) is CORRECT.

Answer:

The answer is -8

Hope this helps :)

The missing reason in the geometric proof for step 4 is that all sides of a square are congruent. This property is part of the definition of a square and justifies the statement AB ≅ BC ≅ CD ≅ DA.

The missing reason in the proof is: "all sides of a square are congruent" Option a.

This reason is necessary to establish statement 4: "AB ≅ BC ≅ CD ≅ DA". It's a critical property of a square that all its sides are congruent to each other. Once you establish this, you can proceed with statement 5 using SAS (Side-Angle-Side) congruence to prove △BAD ≅ △ABC, and then finally, using Corresponding Parts of Congruent Triangles are Congruent to conclude BD ≅ AC.

Here is the corrected step:

Nitrogen gas makes up approximately 78% of the atmosphere, not 50%, 1%, 99%, or 0.03%.

The correct answer is: d. 78%

Nitrogen gas (N2) makes up a significant portion of the Earth's atmosphere.

To determine the correct percentage, we need to consider the composition of the atmosphere:

The Earth's atmosphere is primarily composed of several gases, with the most abundant being nitrogen (N2) and oxygen (O2).

Other gases such as argon, carbon dioxide, neon, helium, and trace amounts of other gases are also present.

The correct answer is: d. 78%

Nitrogen gas (N2) constitutes approximately 78% of the Earth's atmosphere, making it the most abundant gas.

Oxygen (O2) is the second most abundant gas, accounting for about 21% of the atmosphere.

The remaining 1% consists of trace gases like argon, carbon dioxide, and others.

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Answer: it would be (D)

Step-by-step explanation:

The relationships between the sides and angles of the right triangles in

the question are given by trigonometric ratios.

1. The given triangle is ΔABC

The side opposite angle B is the side not bearing the letter B which is the side AC

2. The tangent of the angle, F, is given by the following formula;

[tex]\displaystyle tan(F) = \mathbf{\frac{Opposite \ side \ to \ angle \ F}{Adjacent \ side \ to \ angle \ F}}[/tex]

Therefore;

3. The sine of the angle Z is given by the following formula;

[tex]\displaystyle sin (Z) = \mathbf{ \frac{Opposite \ side \ to \ angle \ Z}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]

Therefore;

[tex]\displaystyle sin(Z) = \mathbf{\frac{XY}{40}}[/tex]

XY = √(40² - 32²) = 24

Which gives;

4. The trigonometric ratio for cos(D) is given as follows;

[tex]\displaystyle cos(D) = \mathbf{ \frac{Adjacent \ side \ to \ angle \ \angle D}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]

Therefore;

[tex]\displaystyle cos(D) = \frac{21}{75} = \frac{7}{25}[/tex]

5. The tangent of the angle 63° is expressed as follows;

[tex]\displaystyle tan(63^{\circ}) = \mathbf{\frac{8 \, m}{Distance \ AB \ (ground \ distance \ from \ wall)}}[/tex]

Therefore;

[tex]\displaystyle Distance \ AB = \frac{8 \, m}{tan(63^{\circ})} \approx \mathbf{4.076 \, m}[/tex]

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The final velocity of the sprinter is 7.23 meters per second.

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

Given that a sprinter starts from rest, and accelerates at 1.87 m/s² over a distance of 14.0 m.

The final velocity will be calculated by the equation of the motion formula as below,

V² = u² + 2as

V² = 2 x 1.87 x 14

V² = 52.36

V = √52.36

V = 7.23 meter per second

Hence, the final velocity is 7.23 meters per second.

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The answer is r(x) = (4x)^7

To calculate the discount amount on an item with a regular price during a sale of 40% off, use the function d(p) = 0.40 x p.

The question involves creating a mathematical function to calculate the amount of discount during a sale. The store is offering a 40% discount on items, so to find the discount amount d on an item with a regular price p, we can write the function as d(p) = 0.40 * p. Here, p represents the regular price of the item, and d represents the discount amount in dollars that will be subtracted from the regular price.

Answer:

It's 14 inches on Ed

Step-by-step explanation:

Final answer:

The volume of the sphere is given as 1372π/3 cubic inches. Using the volume formula for a sphere, V = (4/3)πr³, we calculate the radius and then double it to find the diameter, which is 14 inches.

Explanation:

The student asks for the diameter of the great circle of a sphere, given its volume is 1372π/3 cubic inches. To find this, we'll make use of the formula for the volume of a sphere, V = (4/3)πr³, where V represents the volume and r is the radius of the sphere.

Let's start by equating the given volume to the volume formula:

1372π/3 = (4/3)πr³

Cancelling out π and the fraction (4/3) on both sides, we get:

1372/4 = r³

This simplifies to:

343 = r³

Taking the cube root of both sides gives us the radius:

r = ∛343

r = 7 inches

The diameter of the sphere is twice the radius, so:

diameter = 2r = 2 × 7 = 14 inches

Therefore, the diameter of the great circle of the sphere is 14 inches.

Answer with Step-by-step explanation:

a. 0.34 × 6=2.04

b. 0.11 × 4=0.44

c. 17 × 0.07=1.19

d. 28 × 0.003= 0.084

e. 3.8 × 5=19

f. 5.931 × 7=41.517

g. 14.07 × 13=182.91

h. 3.005 × 32=96.16

i. 0.8 × 0.3=0.24

j. 0.45 × 0.05=0.0225

k. 0.09 × 0.02=0.0018

l. 0.074 × 0.08=0.00592

m. 2.3 × 0.9=2.07

n. 7.25 × 0.3=2.175

o. 4.53 × .003=0.01359

p. 53.67 × 0.056=3.00552

q. 1.1 × 3.7 =4.07

r. 3.76 × 18.9 =71.064

s. 4.57 × 6.1 =27.877

t. 24.13 × 1.48=35.7124

The equation representing this situation is expressed as [tex]\[ 10h + 8 = 48 \][/tex] and

Demi received 4 hours of tutoring services.

Let's denote the number of hours Demi received tutoring services as [tex]\( h \).[/tex]

The equation representing this situation can be expressed as:

[tex]\[ 10h + 8 = 48 \][/tex]

Now, let's solve for [tex]\( h \):[/tex]

[tex]\[ 10h = 48 - 8 \][/tex]

[tex]\[ 10h = 40 \][/tex]

[tex]\[ h = \frac{40}{10} \][/tex]

[tex]\[ h = 4 \][/tex]

So, Demi received 4 hours of tutoring services.

To find the equation representing the situation, we need to consider the total cost Demi paid. She paid $10 per hour for tutoring services, so the cost for the tutoring service itself is [tex]\( 10h \),[/tex] where [tex]\( h \)[/tex] represents the number of hours of tutoring. Additionally, she paid $8 for books and supplies, which is a fixed cost regardless of the number of hours. Therefore, we add $8 to the cost equation. This gives us [tex]\( 10h + 8 = 48 \).[/tex]

Next, we solve this equation to find the value of [tex]\( h \),[/tex] which represents the number of hours of tutoring. We subtract 8 from both sides to isolate the term [tex]\( 10h \),[/tex] giving us[tex]\( 10h = 40 \)[/tex]. Then, we divide both sides by 10 to solve for [tex]\( h \),[/tex] which gives us[tex]\( h = \frac{40}{10} = 4 \).[/tex]

So, Demi received 4 hours of tutoring services.

Complete question:

For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?