Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: ∠F ∠ F is supplementary to ∠G ∠ G and ∠G ∠ G is supplementary to ∠H ∠ H . Conjecture: ∠F ∠ F is supplementary to ∠H ∠ H .

Answer:

The length of the radius is 7.74 ft.

Step-by-step explanation:

It is given that the length of arc is s=8.1 and central angle of arc is [tex]\theta=\frac{3.14}{3}[/tex] in radian.

The formula for arc length is

[tex]s=r\theta[/tex]

Where, s is length of arc, θ is central angle of arc in radian and r is the radius of the circle.

Substitute s=8.1 and [tex]\theta=\frac{3.14}{3}[/tex] in the above formula.

[tex]8.1=r\times \frac{3.14}{3}[/tex]

[tex]8.1=r\times 1.0467[/tex]

Divide both sides by 1.0467.

[tex]\frac{8.1}{1.0467}=r[/tex]

[tex]7.73860705073=r[/tex]

[tex]r\approx 7.74[/tex]

Therefore the value of r is 7.74 ft.

Solution of equqation 15 - 3 7/8 is 11 1/8.

To solve 15 - 3 7/8, you need to follow these steps:

First, convert 3 7/8 to an improper fraction:

Next, convert 15 to a fraction with a common denominator of 8:

Now you subtract the improper fraction from the whole number fraction:

Convert the result back to a mixed number:

So, 15 minus 3 and 7/8 is 11 1/8.

Answer:

The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]

Step-by-step explanation:

Given : You accidentally dropped a coin from the top of 7 stairs.

To find : What is the probability that it will land below the sixth step and heads up?                                                        

Solution :

A coin has two sides - head and tail.

Probability of getting head is

[tex]P(H)=\frac{1}{2}[/tex]

Total stairs are 7.

Coin will land below the sixth step i.e. it land on 7th step.

So, Probability of landing coin on below the sixth step is

[tex]P(L)=\frac{1}{7}[/tex]

Now, The probability that it will land below the sixth step and heads up is

[tex]P=\frac{1}{2}\times \frac{1}{7}[/tex]

[tex]P=\frac{1}{14}[/tex]

Therefore, The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]

some people use 22/7, some use 3.14

 it is used in formulas for circles

A = (1,3)

C = (-4,-4)

-4-1 =-5, -5@ = 25

-4-3 = -7, -7^2 = 49

25+49 = 74

 sqrt(74) = 8.602

 round answer as needed.

To solve this problem, let us first assign the variables. Let us say that:

l = length of rectangle

w= width of rectangle

The given problem gives us the relation that:

l = 6 w – 2                            ---> 1

We know that the formula for area of rectangle is given as:

A = l w                                   ---> 2

Substituting equation 1 into 2:

A = (6 w – 2) w

A = 6 w^2 – 2 w

The area must not be greater 840 cm^2, therefore:

840 cm^2 = 6 w^2 – 2 w

w^2 – (1/3) w = 140

By completing the square:

w^2 – (1/3) w + (1/36) = 140 + (1/36)

(w – 1/6)^2 = 5041/36

w – 1/6 = ± 11.83

w = -11.66, 12

Therefore the maximum value that the width can take is 12 cm. Therefore the possibilities of width such that the area does not exceed 840 cm^2 is from 1 to 12 cm.

Answer:

1 cm to 12 cm

After performing the addition operation on both expressions, the resulting simplified expression is 7x^3+2x-4

Given Data

To add both Expression let us open brackets

= (4x3 − 3x − 7) + (3x3 + 5x + 3)

=  4x3 − 3x − 7 + 3x3 + 5x + 3

Collect like terms we have

= 4x^3+3x^3-3x+5x-7+3

= 7x^3+2x-4

Learn more about simplification here:

https://brainly.com/question/2548064

The Angelo family's car has a gas mileage of approximately 13.4 miles per gallon, calculated by dividing the total miles driven (254.6 miles) by the gasoline used (19 gallons).

A car's gas mileage is calculated by dividing the total number of miles driven by the amount of gasoline used. In this case, the Angelo family drove 254.6 miles and used 19 gallons of gasoline. So, to figure out their car's gas mileage, you would divide 254.6 miles by 19 gallons.

254.6 miles ÷ 19 gallons = 13.4 miles per gallon

Therefore, the gas mileage of the Angelo family's car is approximately 13.4 miles per gallon.

https://brainly.com/question/33812030

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Answer:

Step-by-step explanation:

100% = 1

202.98% is more than 100%, so is more than 1.

67.14% is less than 100%, so is less than 1.

Answer:

A) 5x^5 + 4x^4 + x^3

Step-by-step explanation:

The formula for a cone is given as:

V = π r^2 h / 3                    ---> 1

Where,

V = volume of the cone

r = radius of the circle base of the cone

h = is the perpendicular length from the center of the base of the cone to the tip at the top

It was given that:

h = d

but d = 2 r, therefore:

h = 2 r

Substituting this to equation 1:

V = π r^2 (2 r) / 3             

V = 2 π r^3 / 3

Since r = x, the answer from the choices is:

2πx3

The expression representing the volume of the cone is (2/3)πx^3, where x represents the cone's radius.

Step 1: Identify Key Information

We are given that the height (h) of the cone is equal to the diameter (d) of the base. The diameter is twice the radius (r).

Step 2: Apply Formula and Substitute

        Volume (V) = (1/3) * π * r^2 * h

        V = (1/3) * π * r^2 * (2r)

Step 3: Simplify the Expression

-8 + -7 +x

 add 7 to both sides

-1=x

so x = -1

Final answer:

To calculate the available farming land, 65% of the total 30 acres is determined, resulting in 19.5 acres available for farming.

Explanation:

To find out how many acres are available for farming, we need to calculate 65% of the total 30 acres of land the farmer owns.

The calculation is as follows:

Therefore, 19.5 acres of the farmer's land can be used for farming.

False,

 the equation should be

x+ (x+2) +(x+4) = 45

F(n+1)=-0.5f(n)  120 f (5)

A) #3 y = x+3, if you subtract x from y there is a difference of 3 in all of them.

B) #5 y = -x^2, the y value is the negative value of x raised to the 2nd power

C)#6 y = x^2+3, if you raise the value of x to the 2nd power and then add 3 you get the y value

D)#2 y=3x-1, if you multiply the value of x by 3 then subtract 1 you get the y value

opposite angles need to equal 180

 so angle 2 = 180-111 = 69 degrees