An artist is creating a sculpture using bendable metal rods of equal length. One rod is formed into the shape of a square and another rod into the shape of an equilateral triangle. If each side of the triangle is 2 inches longer than each side of the square, how long, in inches, is each rod?

The answer to the statement is:

                     TRUE

In order for a segment to form a triangle.

The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining third side of the given triangle.

Here we have three segments of length:

7 units, 9  units and 12 units.

Also, for any two pair:

7 and 9 we have:

7+9=16> 12

for 9 and 12 we have:

9+12=21>7

and for 7 and 12 we have:

7+12=19>9

Hence, the segments could form a triangle.

Answer:

x=7

Step-by-step explanation:

The Law of Detachment can be used to conclude that 7x - 2 = 47.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion must also be true. In this case, Statement 1 is a conditional statement: 'If x = 7, then 7x - 2 = 47.' Statement 2 tells us that x = 7. Since the hypothesis of Statement 1 is true (x = 7), we can apply the Law of Detachment to conclude that its conclusion must also be true. Therefore, we can validate Statement 1: '7x - 2 = 47.'

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Final answer:

To find vertical asymptotes of a function, factor the denominator, set each factor equal to zero, and solve for x.

Explanation:

To find vertical asymptotes of a function, we need to determine the values of x that make the function approach infinity or negative infinity. Vertical asymptotes occur when the function approaches these values but never reaches them.

To find the vertical asymptotes, follow these steps:

Factor the denominator of the function.

Set each factor equal to zero and solve for x.

The values of x obtained in step 2 are the vertical asymptotes.

For example, let's find the vertical asymptotes of the function f(x) = 1/x. The denominator is x, which is already factored. Setting x = 0, we find that x = 0 is the vertical asymptote.

Indication "12/10, n/30" (or "12/10 net 30") on an account represents a cash (sales) discount provided by the seller to the buyer for swift payment.

The term 12/10, n/30 is a classic credit term and means the following:

The discount date begins at August 9 and the last day would be August 19.

The '12/10, n/30' term means a 12% discount is given if payment is made within 10 days of the invoice date, and the entire invoice must be paid within 30 days. As such, the discount date is August 19.

The sale terms 12/10, and n/30 in the question denote a sale transaction where the seller is offering the buyer a 12% discount if they pay the invoice within 10 days of the invoice date. The 'n/30' part means that the rest of the invoice amount needs to be paid within 30 days. So, if the manager of the new business opts to take the cash discount, the discount date falls on August 19 (the invoice date - August 9 plus 10 days).

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To find how much the temperature fell, we created an equation using the given temperatures at 5 P.M. and 10 P.M. We subtracted the temperature at 10 P.M. from the one at 5 P.M. and found the temperature fell by 25 degrees.

The subject of this question is Mathematics and this question is for the Middle School grade level.

To solve this problem, we can create an equation using the given information about the temperature at two different times. At 5 P.M., the temperature (let's assume T1) is 20∘F. At 10 P.M., the temperature (let's assume T2) is -5∘F. Therefore, to find how much the temperature fell, we subtract the temperature at 10 P.M. from the temperature at 5 P.M., so the equation would be T1 - T2.

Substitute the temperatures into the equation: 20 - (-5) = 20 + 5 = 25.

Therefore, the temperature fell by 25 degrees.

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Answer:

A. 64π cubic centimeters

D. Gold (19300 kg per cubic meter)

The height of the cylinder is 3.04 unit

Step-by-step explanation:

A waffle cone for ice cream has a diameter of 8 centimeters and a height of 12 centimeters. What is the volume of the cone, in cubic centimeters?

A. 64π cubic centimeters

B. 32π cubic centimeters

c. 256π cubic centimeters

D. 192π cubic centimeters

EXPLANATION

Volume of a cone is given by the formula  V=[tex]\frac{\pi*r^{2}*h }{3}[/tex]

V = [tex]\frac{\pi *4^{2}*12 }{3}[/tex]   = 64π

The correction option is A

Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.

What kind of metal are the coins made of?

Bronze (8700 kg per cubic meter)

Silver (10500 kg per cubic meter)

Lead (11300 kg per cubic meter)

Gold (19300 kg per cubic meter)

the formula for Density is density = mass/volume

The density of the metal = 4825/0.25 = 19,300kg.

Therefor the coins are made of Gold

The correction option is D

A cylinder with radius 3 units is shown. Its volume is 86 cubic units.

Find the height of the cylinder.

Use 3.14 for π and round your final answer to the nearest hundredth.

The volume of a cylinder is given as V= πr^2h

86 =3.14 * 3^2*h

Make h the subject of the formula h =86/(3.14*9) =86/28.26 =3.04 unit

The height of the cylinder is 3.04 unit

Answer:

x - 2y = -1

this is correct

a) The radius of the navy pier wheel is 70 feet.

b) The radius of the first ferris wheel is 125 feet.

c) The speed of the wheel is 87.2 ft/sec

Given data:

The circumference of circle = 2πr

The area of the circle = πr²

a)

The circumference = 2πr

where π = 3.142

r = radius

Therefore, 2πr = 439.6

(2 * 3.142 * r) = 439.6

6.284r = 439.6

On simplifying the equation:

Radius = 439.6/6.284

Radius = 69.9

≈ 70 feet

b)

The Navy Pier Ferris Wheel in Chicago has a circumference that is ​56% of the circumference of the first Ferris wheel.

So, 56% of f = 439.6

0.56f = 439.6

f = 439.6/0.56

f = 785

The circumference of the first wheel is 785 feet.

Now, 2πr = 785

r = 785/2π

r = 785/(2×3.142)

r = 785/6.284

r = 124.9

≈ 125ft

c)

The first ferris wheel took nine minutes to make a complete revolution.

So, the speed of wheel is determined as:

s = 785/9

s = 87.2 ft/sec

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The complete question is attached below:

If the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.

a. What is the radius of the navy pier wheel?

b. what was the radius of the first ferris wheel?

c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?

C=439.6 ft.

Answer:

  a[1] = 2; a[n] = a[n-1] + 2

Step-by-step explanation:

The first term of the sequence is 2, so the first part of the definition is ...

  a[1] = 2

Each term is 2 more than the previous one, so the rest of the definition is ...

  a[n] = a[n-1] + 2

_____

Comment on recursive rules

A recursive rule has two parts. The first part tells what the initial value of the sequence is. The second part relates the next term to the previous term or terms.

For arithmetic and geometric sequences, each term is related to the previous term by a constant. For an arithmetic sequence, each term is the last term plus the common difference. For a geometric sequence, each term is the last term multiplied by the common ratio.

For the arithmetic sequence 2, 4, 6, 8,.., the recursive rule can be written as: the first term a_1 is 2, and for all subsequent terms (n > 1), a_n equals the previous term a_(n-1) plus 2.

The sequence given is an arithmetic sequence, where each term increases by 2. A recursive sequence is a sequence in which each term is defined based on its preceding terms. For the sequence 2, 4, 6, 8,... the recursive rule can be constructed as follows:

a_1 = 2

a_(n) = a_(n-1) + 2 for n > 1

In these rules, a_1 is the first term in the sequence, and a_(n) is the nth term of the sequence. a_(n-1) represents the term before the nth term in the sequence. This rule states that each term in the sequence is 2 more than the previous term.

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the first one,

 Scientific notation has to have a number to the left of the decimal point

The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].

Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:

ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]

The area of a trapezoid is given by:

Area = [tex]\frac{1}{2}[/tex] * base * height

For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:

Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]

We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:

Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]

Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]

Answer:

Step-by-step explanation:

First, let's formulate an equation. Let the independent variable be x to denote the number of hours. The dependent variable is y to denote the total cost. The equation should be:

y = 25x + 50

The table and graph is shown in the picture. Just use values of x as 1, 2, 3 and 4, find y and plot the points.

The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.

The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.

The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:

Circumference: C = 2π(4 inches) = 8π inches

Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches

Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.

The family has been members of the swimming pool for 8 months. This was calculated by setting up an equation with the formula for the total cost, C = 55m + 25, and solving for the number of months (m), with C set to the amount paid of $465.

To determine how many months a family has been members of a swimming pool with a membership cost of $55 per month plus a one-time registration fee of $25 and a total payment of $465, we need to set up an equation and solve for the number of months.

Let's denote the number of months as m. The total cost of the membership for m months is the monthly rate times the number of months plus the registration fee.

The equation representing the total cost (C) is:
C = 55m + 25

We know that the total cost is $465, so we substitute this value into the equation:

465 = 55m + 25

To solve for m, we first subtract 25 from both sides:

440 = 55m

Then, we divide both sides by 55 to find the number of months:

m = 440 / 55

m = 8

So, the family has been members for 8 months.

Answer: Congruent angles have the same measure

Step-by-step explanation: