Which of the following expression is equivalent to 6^-7?

To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)

The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)

The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)

Solving for\(\(x\),\) we divide both sides of the equation by 3:

\(\(x = \frac{71}{3}\).\)

Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.

The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:

\(\(x = 2\pi r\).\)

Substituting the value of x we found earlier, we have:

\(\(\frac{71}{3} = 2\pi r\).\)

Solving for r, we divide both sides of the equation by \(\(2\pi\):\)

\(\(r = \frac{71}{6\pi}\).\)

Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.

In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.

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Answer:

four times a number less 10 is equall to 16 ia not

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

From the question, we have the following parameters that can be used in our computation:

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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The perimeter of the triangle OQR is 68 cm

From the question, we have the following parameters that can be used in our computation:

Circles with the centers O, Q and R

When these centers are connected, the connection forms a triangle

The triangle OQR

Also from the question, we have the following values of radii

Radii = 8 cm, 11 cm and 15 cm

The perimeter of the triangle OQR is calculated as

Perimeter = Twice the sum of the radii

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 *(8 + 11 + 15)

Evaluate the sum

Perimeter = 2 * 34

Evaluate the products

Perimeter = 68

Hence, the perimeter is 68 cm

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Answer:

5040

your welcome

Answer:

A=35

hope this helps

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The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out

Distance travelled with 20 l of petrol in solution and final answer.

Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.

The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.

Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.

As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.

Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.

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Answer:

225 students

Step-by-step explanation:

Total number of students = 900 students

percent that bring lunch to school everyday = 25%

Number of student that bring lunch to school = 25% of 900

Number of student that bring lunch to school = 0.25 * 900

Number of student that bring lunch to school = 225

Hence 225 students bring lunch to school everyday

Answer: 1,000

Step-by-step explanation: if you multiply the 900 in 157,900 by a 1,000 you get the 900,000 in 901,532.

Answer:

quotient-206

remainder-1

Step-by-step explanation:

The third number so that the three numbers form a right triangle,

1)40

2)84

Therefore, we can form a right triangle with 9,41,40 and 13,85,84

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

1) By applying Pythagorean theorem,

a²+b²=c²

x²+9²=41²

x²=41²-9²

x²=1681-81

x²=1600

x=√1600

x=40

Therefore, the third number is 40

2) x²+13²=85²

x²=85²-13²

x²=7225-169

x²=7056

x=√7056

x=84

Therefore, the third number is 84

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The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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The relationship that represents a function with a greater rate of change than the function graphed is given as follows:

A. y = 4x - 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The slope represents the average rate of change of a linear function.

From the graph, when x increases by one, y decreases by two, hence the slope m is given as follows:

m = -2.

For function A, the function is defined as follows:

y = 4x + 3.

Hence the rate of change is given as follows:

m = 4, which is greater than -2.

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Answer:

y=8

Step-by-step explanation:

9y-7y=20-4

2y=16

y=16/2

y=8

Answer:

\((5xy + 7)(5xy-7) = 25x^2 y^2 - 49\)

Step-by-step explanation:

\((a - b)(a +b ) = a^2 - b^2 \\\\From \ given \ expression \ a = 5xy \ , \ b = 7\\\\Therefore , (5xy + 7 )(5xy - 7 ) = ( 5xy)^2 - ( 7)^2 \\\)

                                             \(= 25x^2 y^2 - 49\)

Answer:

25x²y² - 49

Step-by-step explanation:

We can do this by using the a+b formula:

(a+b)(a-b)= a² - b²

So,

(5xy+7)(5xy-7)

=(5xy)² - 7²

= 25x²y² - 49

Another way we can do this by expanding the algebraic expression:

(5xy+7)(5xy-7)

= 5xy(5xy-7) + 7(5xy-7)

= 25x²y² - 35xy + 35xy - 49

= 25x²y²- 49

Answer:

23/63x+1/4

Step-by-step explanation:

(1/7x + 3/8) + (2/9x - 1/8)=

1/7x + 3/8 + 2/9x - 1/8=

9/63x+14/63x+2/8=

23/63x+1/4

Answer:

what do you mean by land ?

The intensity of sound is proportional to the square of its amplitude.

Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:

I9/I8 = (10^(9/10))/(10^(8/10))

I9/I8 = 10^(0.1)

I9/I8 = 1.2589

Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.

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There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Using the unit circle to find sin 240 and cos 240, without using a calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

To find sin 240 and cos 240 without a calculator, we can use the unit circle, which is a circle with radius 1 centered at the origin in a two-dimensional coordinate system. The unit circle provides a convenient way to define the sine and cosine of an angle in terms of their coordinates on the circle.

The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle, and the cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.

For an angle of 240 degrees, we can find the corresponding point on the unit circle by constructing a line from the origin to the point on the circle.

we can see that the y-coordinate of the point is negative, so sin 240 = -sin (240 - 180) = -sin 60 = -1/2.

The x-coordinate of the point is also negative, so cos 240 = -cos (240 - 180) = -cos 60 = -√3/2.

We can use a calculator to check our answers by entering sin(240) and cos(240) with parentheses around the 240, as requested by the calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

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The volume of a cone will be 209.41 yard³.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

So the

V = (1/3)πr²h.

Given, data r = 5yards

h = 8 yards

Volume = 1/3 * π * r ²* h

= 1/3 * 3.141*25*8

=209.41 yard³

Hence, the volume of a cone will be 209.41 yard³.

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The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

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Answer:

16

Step-by-step explanation:

There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.

There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.

One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.

A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.

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Answer:

18n + 9

Step-by-step explanation:

Distribute 9 into the expression.

9*2n = 18n

9*1 = 9

18n + 9

Answer:

27- 1 = 26

Step-by-step explanation:

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)