A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, where a, b, c, d, e, and f are positive integers, a and e are relatively prime, and neither c nor f is divisible by the square of any prime. Find the remainder when the product abcdef is divided by 1000.

The solution of the set of equations: 6x - 2y = 8; 3x + 7y = 68  is (4,8)

The problem can be solved using elimination - substitution method.

Set of equations:

6x - 2y = 8   .... (equation 1)

3x + 7y = 68 ..... (equation 2)

Divide equation 1 by 2

3x - y = 4   ..... (equation 3)

Eliminate x by substracting equation 3 from equation 2:

3x + 7y = 68

3x   - y  = 4    _

      8y = 64

         y = 64/8

        y = 8

Substitute y = 8 into equation 3:

3x - 8 = 4

3x = 12

x = 12/3

x = 4

Hence, the solution is (4,8)

Your question is incomplete, but most probably your question was:

What is the solution for the following set of equations 6x - 2y = 8; 3x + 7y = 68 ?

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The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.

Lets look into some examples.

     x + y = 10  

      x - y = 2

By adding both equations,

     x + y + x - y = 10 + 2

 + y and - y are cancelled or y term is eliminated.

      2x = 12

       x  = 6

     2x + 3y = 10

   -3x + 3y  = 15

Here to eliminate y, we have to add the additive inverse of second equation.

  2x + 3y + 3x - 3y = 10-15

    5x = -5

      x = -1

   x + 4y = 5

   3x - y = 2

To equalize the y term we multiply the second equation by 4

   12x - 4y = 8

Adding both equations,

x + 4y + 12x - 4y = 5 + 8

13x = 13

x = 1

So elimination method is used for solving linear equations.

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Answer:

Step-by-step explanation:

divide them both by 2

which is 3/ 9

divide them both by 3

whic is 2/6

and finally divide them both by 6

which is 1/3

you can multiply them both by an number as well

take care

the value of x would be 22/3 after simplification.

The acts or process of simplifying something such that it is simpler to accomplish or understand, or the item that is the consequence of such simplifying: The group offers suggestions on how to make trade procedures simpler. In mathematics, we generally use the PEMDAS method to simplify the values.

Given, the equation in the form of x is  3/4(x−8)= −1/2

For the value of x

3/4(x−8)= −1/2

multiply by 4 on both sides

3(x - 8) = -2

divide by 3 into both the sides

x - 8 = -2/3

add 8 on both sides

x = -2/3 + 8

x =  22/3

therefore, the value of x for the given equation 3/4(x−8)= −1/2 is 22/3.

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The speed of Ana is in miles per hour 7.5mph

By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.

Speed = distance ÷ time

Distance =  3/4

Time =  1/10

Speed = 3/4  ÷  1/10

Speed =  3/4   x 10 = 15/2 miles per hour

or, 7.5mph

Divide the distance Ana covered by the time she ran to get her speed.

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The question is incomplete

Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour

Answer:

Step-by-step explanation:

A karate studio offers a 6 week session for

$175. How much would you expect to pay for

a 9 week session?

175 : 6 = 29.16

29.16 x 9 = 262.5

or

175 : 6 = x : 9

x = 175 x 9 : 6

x = 262.5

AAA triangles are impossible to solve further since there is nothing to show us the size.

The AAA triangle is a triangle in which all three angles are given, and the triangle is said to be similar to another triangle if any two of its three angles are equal to any two of its three angles.

Knowing only angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent.

There are four shortcuts that can be used to check whether two triangles are congruent.

You don't need to be familiar with all of the six corresponding parts, which include three angles and three sides.

When a triangle's three angles are known but not its sides, the answer is "AAA."

Since there is no information to indicate size, AAA triangles are impossible to solve further. We know their shape but not their size.

Hence, the AAA triangles are not solvable or difficult to find angles.

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The function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that $710 is invested in an account earning 3.7% interest (APR), compounded monthly.

We can write -

A = 710(1 + 0.37/12)¹²⁽¹⁾

A = 710(1 + 0.037/12)¹²

A = 710(1 + 0.031)¹²

A = 710(1.031)¹²

A = 710 x 1.45

A = 1029.5

Let the annual growth rate be R. Then, we can write the function for annual growth rate after {t} years as -

1029.5 = [tex]$ 710(1 + R/1)^{t}[/tex]

1029.5 = [tex]$710(1+R)^{t}[/tex]

1.45 = [tex]$(1 + R)^{t}[/tex]

1.45 = 1 + tR + .....                        {Binomial expansion}

Neglecting the binomial series from the third term as the value of the terms become negligible -

1.45 = 1 + tR

R = 0.45/t

Function for the amount after t years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]= A

Therefore, the function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

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Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : (X-5)-1

Thus,

after substituting the value of x with 9

We get,

=> (X-5) -1

=>(9-5)-1

=> 4 -1

=> 3

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

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The minimum number of pizzas must they sell in order to have at least $300 is 44.

What is the profit?

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.

The student council needs to raise $300 - $235 = $65 to reach their goal.

They make a profit of $1.50 for each pizza they sell.

so they need to sell $65 / $1.50 = 43.333 pizzas to reach their goal.

As you cannot sell a fractional number of pizzas, they need to sell at least 44 pizzas to raise enough money for the field trip.

Hence, the minimum number of pizzas must they sell in order to have at least $300 is 44.

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Scale factor required to map the first line segment onto second line segment is 3/9=0.33

The scale factor is the ratio of the length of the image to the length of the pre-image.

In this case, we're looking for the  that would map the first line segment (length 9cm) onto the second line segment (length 3cm).

To find the scale factor, we can divide the length of the image by the length of the pre-image:

scale factor = length of image / length of pre-image

In this case:

[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]

[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]

So the scale factor to map the first line segment onto the second line segment is 1/3.

It means the 1st line is 3 times longer than the second one.

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Answer:if the siblings are less and the child are more u should remove  the percent from the difference and put it to the another one the one from  down there so the difference is 70% so try the same from down  there is 18 so it got to be 20

Answer:20

According to unitary method, cat takes 12 steps to cover 9 feet.

Measure your stride length or assume that it is 2.2 feet for women and 2.5 feet for men to determine it. Add the stride length to the number of steps, for example, 2.2 feet multiplied by 1,000 feet equals 2,200 feet. The answer is 2,200 ft / 5,280 0.42 mi when expressed in miles.

Given, it takes a dog three steps to cover the same distance as a cat four steps.

4 steps of a cat = 3 steps of a dog

12 cat steps equal (3/4)*12 to 9 dog steps.

Additionally, a dog's step covers one foot.

The dog moves nine feet in nine steps.

So a cat takes 12 steps to cover 9 feet.

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Therefore , the solution of the given problem of algebra comes out to be

Product means to multiply and decreased means to subtract so option C only seems valid

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

Product means to multiply and decreased means to subtract so option C only seems valid

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x² + 4x + 4, this is a perfect square trinomial, which is expressed as

(x + 2)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 4x + 4

= (x)² + 2(2x) + 4

= (x)² + 2(x)(2) + 2²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 2)²

= (x + 2) (x + 2)

so, this is a perfect square trinomial.

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1. In a triangle line parallel to one side will divides other two sides in the same ratio

2. 8/x = 12/18

   x = 12

Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).

Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

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In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.

First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).

[tex]3/4 cups * 1 = 3/4 cups\\[/tex]

Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:

[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]

Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:

[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]

Mario can make 2.25 batches of cookies using all of his chocolate chips.

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The number of hours that the team trains per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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=========================================================

Work Shown:

x = number of years

y = population

y = 4000*1.02^x

4500 = 4000*1.02^x

4500/4000 = 1.02^x

1.125 = 1.02^x

log(1.125) = log(1.02^x)

log(1.125) = x*log(1.02)

x = log(1.125)/log(1.02)

x = 5.94784893412128

Rounding to the nearest year, it takes about 6 years for the population to reach 4500 people.

---------------

Check:

Plug in x = 5

y = 4000*1.02^x

y = 4000*1.02^5

y = 4416.3232128

y = 4416

We come up a bit short. Now try x = 6

y = 4000*1.02^x

y = 4000*1.02^6

y = 4504.649677056

y = 4505

We go a bit over the target, but it's better to go over rather than come up short.

This confirms the answer is approximately 6 years.

Answer:

Step-by-step explanation:

The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.

The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.

So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.

Answer:

n= 6

Step-by-step explanation:

7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3

Yes, you can make a triangle with three different length sides.

1. Draw three lines of different lengths on a piece of paper.

2. Connect the ends of the lines to form a triangle.

3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.

4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.

5. Measure each side of the triangle with a ruler and add them together.

6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.

7. Once the triangle is valid, it will be a triangle with three different length sides.

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The Light cream with 19.2% content will have 15.36g of milk.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here Light cream as 19.2% of 80g

∴ 0.192×80=15.36g

Hence, The Light cream with 19.2% content will have 15.36g of milk.

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This given figure carries onto themself at 360, 180, and 60 degrees respectively.

If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.

Given three figures those figures have rotational symmetry from their center point.  The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.

for figure 1

figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.

for figure 2

figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.

for figure 3

figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.

therefore, the given figures have 1, 2, and 6 rotational symmetry.

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Answer:

36

Step-by-step explanation:

let the number be 10x+y

x - y = 3 (eq 1)

given: y = 2x (eq 2)

putting 2 in 1

x - 2x = 3

-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)

y = 6

number is 36

Answer:

12

5

Step-by-step explanation:

if 8 chests = 4hrs

then X chests= 6hrs

cross multiply

48=4x

divide by 4

X= 12

repeat the same for the second using any and you'd get 5

Answer:25cm

Step-by-step explanation:area of triangle=1/2 × base× height

=1/2×10×5

= 25cm^2

Answer:

d ≈ 7.07 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )

d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]

  = [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]

  = [tex]\sqrt{7^2+1}[/tex]

  = [tex]\sqrt{49+1}[/tex]

  = [tex]\sqrt{50}[/tex]

  ≈ 7.07 units ( to 2 decimal places )

$1862  is Devi red from his biweekly paycheck for medical insurance

percentage, a relative value indicating hundredth parts of any quantity.

The annual cost of Randall coverage is 4900.

The college pays 62% of the cost.

We need to find How much is Devi red from his biweekly paycheck for medical insurance

Let us convert 62% to decimal value by dividing with 100

62/100=0.62

Now multiply 0.62 with 4900

0.62×4900

3038

Now subtract 3038 from 4900

4900-3038

1862

Hence, $1862  is Devi red from his biweekly paycheck for medical insurance

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