The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board? ( A=3.14r2)

Answer:

y-intercept is 1

Step-by-step explanation:

We need to find the equation of the line first.

The gradient is found using the formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

[tex]m=\frac{-1-2}{8--4}[/tex]

[tex]m=-\frac{1}{4}[/tex]

So the equation is y = [tex]-\frac{1}{4}[/tex]x + c

To find c we need to substitute the value of x and y into the equation:

-1 = [tex]-\frac{8}{4}[/tex] + c

-1 = -2 + c

1 = c

And c is the y-intercept so it is 1

Answer:

y- intercept = 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, - 1) and (x₂, y₂ ) = (- 4, 2)

m = [tex]\frac{2+1}{-4-8}[/tex] = [tex]\frac{3}{-12}[/tex] = - [tex]\frac{1}{4}[/tex], thus

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, - 1), then

- 1 = - 2 + c ⇒ - 1 + 2 = 1 ← y- intercept

Answer: 2.125 ft

Step-by-step explanation:

17/8=2.125

In order words each hole needs to be 2 ft and 1 and 1/2 inches apart.

Answer:

5 i think. im not good at math. sorry if wrong

Answer:

  4^-2

Step-by-step explanation:

The rules of exponents tell you ...

  (a^b)(a^c) = a^(b+c)

This means ...

  (4^6)(4^-8) = 4^(6-8) = 4^-2

To simplify the expression (4^6)(4^-8), add the exponents and rewrite the expression as 4^(-2). Then, use the rule that states any number raised to the power of -1 is the reciprocal of that number to rewrite 4^-2 as 1/(4^2) which equals 1/16.

To simplify the expression (4^6)(4^-8), we can use the rule that states when you multiply two powers with the same base, you add their exponents. In this case, 4^6 multiplied by 4^-8 will be equal to 4^(6 + (-8)). Simplifying the exponent, we have 4^(-2). Since any number raised to the power of -1 is the reciprocal of that number, we can rewrite 4^-2 as 1/(4^2) which is equal to 1/16.

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Answer:

3.28

Step-by-step explanation:

You want to find the discount price. Set a relation to where the well i cant really explain it but do 20/100 = x/16.40  because 100% of the price is 16.40 dollars. You want to find 20% of that so you find what you multiply to 100 to get 16.40 which is 6.0975. Then you do the same thing for the 20% to find 20% of the price which is 3.28. sorry im trash at explaining but i hope i helped.

Answer:

3.28

Step-by-step explanation:

im pretty darn sure this is right lol

Answer:29876

Step-by-step explanation:

Entire population is 100%

Male is 100%-45%

55%x54320=29876

Answer:

29,876 males

Step-by-step explanation:

If 45% of 54320 population is female. The population of male is calculated below.

The total population is 100% and female is 45%. Thus: 100% - 45% = 55%.

Percentage of male population is 55%. Hence, 55% of 54320 is calculated thus:

[tex] \frac{55}{100} \times 54320[/tex]

[tex] = 0.55 \times 54320[/tex]

[tex] = 29876[/tex]

Therefore, population of male if total population is 54320 is 29,876.

Check,

Female population percentage + male population percentage:

45% + 55% = 100%

24,444 + 29,876 = 54,320

Answer & Step-by-step explanation:

[tex]1)\\(3x+9)+(2x+4)\qquad\text{combine like terms}\\\\=(3x+2x)+(9+4)\\\\=\boxed{5x+13}\\\\===========================[/tex]

[tex]2)\\(2n+6)+(6n-2)\qquad\text{combine like terms}\\\\=(2n+6n)+(6-2)\\\\=\boxed{8n+4}\\\\===========================[/tex]

[tex]3)\\(-3x+9)+(6x-12)\qquad\text{combine like terms}\\\\=(-3x+6x)+(9-12)\\\\=\boxed{3x-3}\\\\===========================[/tex]

[tex]4)\\\left(\dfrac{1}{4}x+10\right)+\left(\dfrac{1}{2}x-7\right)\qquad\text{combine like terms}\\\\=\left(\dfrac{1}{4}x+\dfrac{1}{2}x\right)+(10-7)\\\\=\left(\dfrac{1}{4}x+\dfrac{1\cdot2}{2\cdot2}x\right)+3\\\\=\left(\dfrac{1}{4}x+\dfrac{2}{4}x\right)+3\\\\=\boxed{\dfrac{3}{4}x+3}\\\\===========================[/tex]

[tex]5)\\(3x+5)-(2x+2)\\\\=3x+5-2x-2\qquad\text{combine like terms}\\\\=(3x+2x)+(5-2)\\\\=\boxed{5x+3}\\\\===========================[/tex]

[tex]6)\\10-8=\boxed{2}\\\\===========================[/tex]

[tex]7)\\7.8x-2.5x=\boxed{6.3x}\\\\===========================[/tex]

[tex]8)\\(5.8x+10)-(3.4x+8)\\\\=5.8x+10-3.4x-8\qquad\text{combine like terms}\\\\=(5.8x-3.4x)+(10-8)\\\\=\boxed{2.4x+2}\\\\===========================[/tex]

[tex]9)\\(8x-2)-(2x+8)\\\\=8x-2-2x-8\qquad\text{combine like terms}\\\\=(8x-2x)+(-2-8)\\\\=\boxed{6x-10}\\\\===========================[/tex]

[tex]10)\\(-4x-3)-(-4x-3)\\\\=-4x-3-(-4x)-(-3)\\\\=-4x-3+4x+3\qquad\text{combine like terms}\\\\=(-4x+4x)+(-3+3)\\\\=0+0\\\\=\boxed{0}\\\\\text{You could do it shorter.}\\\text{The result will be 0 because we subtract}\\\text{ the same expressions from each other.}[/tex]

To add or subtract linear expressions, combine like terms. For example, to add 3x + 9 and 2x + 4, you combine the x terms and the constant terms separately to get 5x + 13. The same method is applied to the rest of the problems, resulting in simplified linear expressions.

Adding and Subtracting Linear Expressions:

To add or subtract linear expressions, you combine like terms, which are terms that have the same variables raised to the same power. Let's go through the problems one by one:

Sum of 3x + 9 and 2x + 4: (3x + 2x) + (9 + 4) = 5x + 13.

Add 2n + 6 and 6n - 2: (2n + 6n) + (6 - 2) = 8n + 4.

Add -3x + 9 and 6x - 12: (-3x + 6x) + (9 - 12) = 3x - 3.

Add 1/4x + 10 and 1/2x - 7: (1/4x + 1/2x) + (10 - 7) = 3/4x + 3.

Find the difference: (3x + 5) - (2x +2) = (3x - 2x) + (5 - 2) = x + 3.

Subtract 8 from 10: 10 - 8 = 2.

Subtract 2.5x from 7.8x: 7.8x - 2.5x = 5.3x.

Subtract (3.4x + 8) from (5.8x + 10): (5.8x - 3.4x) + (10 - 8) = 2.4x + 2.

Find the difference: (8x + 5) - (2x + 8) = (8x - 2x) + (5 - 8) = 6x - 3.

Evaluate (-4x -3) - (-4x -3): (-4x + 4x) - (-3 + 3) = 0x + 0 = 0.

These are the simplified forms of the linear expressions after combining like terms.

Answer:

A) The ratio of hypotenuse to base for the triangles is 0.75

Step-by-step explanation:

Here, the given  question is INCOMPLETE.

The following two triangles have the same angles, and are similar. What is the ratio of height to base for the triangles?

A) .75

B) 1.00

C) 1.25

D) 2.50

Here, given that the two triangles are similar.

In triangle one:

Height = 6 units , Base = 8 units

In triangle one:

Height = 3 units , Base = 4 units

Now,as the two given triangles are similar.

⇒Their corresponding sides are PROPORTIONAL.

[tex]\implies \frac{H}{h} = \frac{B}{b} = \frac{6}{8} = \frac{3}{4} = 0.75[/tex]

So, in both the triangles, the corresponding side ratio is 0.75.

Hence, the ratio of hypotenuse to base for the triangles is 0.75

The polygon is a heptagon whose interior measure is 900 degrees

Solution:

The formula for calculating the sum of the measures of the interior angles of a polygon is:

[tex]S = (n-2) \times 180[/tex]

Where,

S = Sum of all interior angles

n = number of sides

From the given data:

S = 900

Therefore,

[tex]900 = (n-2) \times 180\\\\Divide\ both\ sides\ by\ 180\\\\n - 2 = 5\\\\n = 5 + 2\\\\n = 7[/tex]

The number of sides is  7

Heptagon is a seven-sided polygon or 7-gon

Therefore, the polygon is a heptagon

Answer:

its d on e2020 if anyone wanted the simple answer

Step-by-step explanation:

Answer:

if $1 coin is for 4 presidents ,then

the number of years it will take to release the the 36 first presidents is given by[tex]\frac{36}{4}=9 years[/tex]

Step-by-step explanation:

step 1: you lay down preliminaries

step 2: you divide 36 presidents by 4 presidents per year, the result is the number of years it will take to publish the first 36 presidents.

Answer:

A. $3770

Step-by-step explanation:

The correct answer must be $3770 (not $3270), checking accounts and savings accounts are liquid assets. However, cars are not liquid assets because liquid assets are things that can be quickly turned into cash without losing much if any of their inherent value. In this case, the retirement account is not a liquid asset as it is designed to hold your money until retirement age, and given that Cesar is 35 years old so he has not reached retirement age.

Answer:

the answer is a 3770.

Step-by-step explanation:

The equation of the line is [tex]y=-\frac{3}{4}x+\frac{1}{4}[/tex]

Step-by-step explanation:

The equation of a line can be written using the following form

[tex]y-y_0 = m(x-x_0)[/tex]

where

m is the slope of the line

[tex](x_0,y_0)[/tex] are the coordinates of a point lying on the line

For the line in this problem, we know that:

[tex]m=-\frac{3}{4}[/tex] is the slope

[tex](x_0,y_0)=(-5,4)[/tex] are the coordinates of the point

Therefore, substituting into the equation,

[tex]y-4=-\frac{3}{4}(x-(-5))[/tex]

And re-arranging the equation we get:

[tex]y-4=-\frac{3}{4}(x+5)\\y-4=-\frac{3}{4}x-\frac{15}{4}\\y=-\frac{3}{4}x+(4-\frac{15}{4})\\y=-\frac{3}{4}x+\frac{1}{4}[/tex]

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Answer:

The diameter of the arena is 18.3 meters.

Step-by-step explanation:

        As,  14 laps = [tex]\frac{1}{2}[/tex] mile

        so, 1 lap = [tex]\frac{1}{28}[/tex] mile                               ( ∵14 × 2 = 28)

For the horse completing one lap it completes the perimeter of the circle.

            perimeter (P) =  [tex]\frac{1}{28}[/tex] mile

let diameter of that circle be represented as d,

                                  P=  [tex]\pi[/tex] × d

                            or,  [tex]\frac{1}{28}[/tex]  = [tex]\pi[/tex] × d

                            or, d= [tex]\frac{1}{28\pi }[/tex]

                              ∴ d= 18.3 meters.

The diameter of the arena is 18.3 meters.

Answer:

1hr = 60min

225min/ 60min = 3.75 hr

330 pgs. * 3.75hr = 1237.5 pages

He read 1237.5 pages in 225 minutes.

Jorge can speed read 1237.5 pages in 225 minutes.

If the speed of something is given per hour. We can convert it to per minute by dividing the speed by 60. This is because 1 hour = 60 minutes.

It is given that he can speed read around 330 words per hour.

We have to convert this into per minute.

This can be done as follows:

Speed = 330 pages per hour

= 330/60 pages per minute

= 5.5 pages per minute

We can multiply the number of pages per minute with the number of minutes to find how many pages he would have completed in that time:

5.5 * 225 = 1237.5 pages

Thus, we have found that Jorge can speed read 1237.5 pages in 225 minutes.

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The probability of rolling a 6 followed by either a 3 or a 4 on a six-sided die is calculated by multiplying the probability of rolling a 6 (1/6) by the probability of then rolling either a 3 or a 4 (1/3), resulting in a combined probability of 1/18.

The question posed is about the probability of rolling a 6 followed by either a 3 or a 4 on a standard six-sided die. To find this, we first consider that the probability of rolling a specific number, such as a 6, on a six-sided die is 1/6. This is because there are 6 outcomes and only one of those outcomes is the desired number.

When rolling for the second number, which could either be a 3 or a 4, we have two desired outcomes out of the six possible outcomes on the die. Therefore, the probability of rolling either a 3 or a 4 is 2/6, which simplifies to 1/3.

To find the overall probability of rolling a 6 followed by either a 3 or a 4, we multiply the two probabilities together: (1/6) * (1/3) = 1/18. Therefore, the probability of this event occurring is 1/18.

Answer:

Step-by-step explanation:

[tex]\frac{-1+6}{0-3}\\\\\frac{5}{-3}\\ m = -1.6667[/tex]

Answer:

1

Step-by-step explanation:

Answer:

The inequality to determine the number of rotations is given by

 r ≤ 5.25

Therefore the maximum number of rotations possible is 5.

Step-by-step explanation:

i.) The bottom of Ignacio's desktop is  74.5 cm from the floor.

ii.) The tops of his legs are 49.3 cm from the floor.

iii.) the difference between the bottom of Ignacio's desktop and the top of his legs = 74.5  - 49.3 = 25.2 cm.

iv.) Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8 cm.

v.) let the number of clockwise rotations be r.

vi.) therefore the inequality to determine the number of rotations is given by

  4.8r ≤ 25.2     therefore r ≤ 25.2/4.8    therefore r ≤ 5.25

Answer: 32767 pennies

Answer:

A. 7x + 6y

Step-by-step explanation:

49x² + 84xy + 36y²

Factoring the perfect square:

(7x + 6y)²

7x + 6y is a factor.

Final answer:

The correct binomial factor of the quadratic expression  [tex]49x^2 + 84xy + 36y^2 \ is \ 7x + 6y[/tex], which corresponds to option A.

Explanation:

To determine which binomial is a factor of the quadratic expression  [tex]49x^2 + 84xy + 36y^2,[/tex]we can try to factor the expression by grouping or using the factoring technique of a perfect square trinomial. On inspection, we see that 49, 84, and 36 are all multiples of 7, and also the expression resembles the square of a binomial.

The given expression can be written as:

[tex](7x)^2 + 2(7x)(6y) + (6y)^2[/tex]

This is the expanded form of the square of a binomial:

[tex](7x + 6y)^2 = 49x^2 + 84xy + 36y^2[/tex]

Hence, the factored form of the given expression is  [tex](7x + 6y)^2[/tex], which means that 7x + 6y is indeed a factor. So, the correct answer is option A.

Answer:

X/Y

Step-by-step explanation:

You cannot divide two variables so you just leave it as a fraction

The result of division, when, x divided by y is: x/y.

Here, we have,

given that,

What is x divided by y

i.e. now, we have to divide x by y

so, we get, x is the dividend, and y is the divisor,

so, x = numerator

and, y = denominator

we know that,

we cannot divide two variables so we just leave it as a fraction

i.e. we get,

x divided by y = x/y

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Answer:

x + 2y + 2

Step-by-step explanation:

1. Simplify 3 − 2 to 1

1 · x + 2y + 2

2. Simplify 1 · x to x

x + 2y + 2

Answer:

[tex]3x+13y=14\\\\6x+11y=-2[/tex]

Step-by-step explanation:

We have to check [tex](-4,2)[/tex] satisfies which system.

First System:

[tex]3x+13y=14\\\\6x+11y=-2\\\\Substitute\ (-4,2)\ in\ the\ equations\\\\3\times (-4)+13\times (2)=14\\\\-12+26=14\\\\14=14\\\\6\times (-4)+11\times (2)=-2\\\\-24+22=-2\\\\-2=-2\\\\(-4,2) \ satisfies\ this\ system\ of\ equation.\ Hence\ (-4,2)\ is\ the\ solution\ of\ this\ system.[/tex]

Second System:

[tex]4x+5y=12\\\\8x+3y=-4\\\\Substitute\ (-4,2)\\\\4\times (-4)+5\times (2)=-6\\\\-6\not=12\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Third System:

[tex]5x+4y=12\\\\7x+8y=12\\\\Substitute\ (-4,2)\\\\5\times (-4)+4\times (2)=-12\\\\-12\not =12\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Fourth System:

[tex]10x+3y=8\\\\17x+6y=10\\\\Substitute\ (-4,2)\\\\10\times (-4)+3\times (2)=-34\\\\-34\not =8\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Answer:

3x+13y=14\\\\6x+11y=-2

Step-by-step explanation:

Answer:trey wey ery day

Step-by-step explanation:

Answer:it’s 93 that’s all that matters

Step-by-step explanation:

Answer:

 The volume of a baseball is about 13.39 cubic inches.

Step-by-step explanation:

Answer:

Ricky had 1199 hits.

Pedro had 1482 hits.

Step-by-step explanation:

State your variables

let "p" be the number of Pedro's base hits

let "r" be the number of Ricky's base hits

Create equations using information from the problem

p + r = 2681         [1]

p = r + 283          [2]

Substitute equation [2] in equation [1] replacing 'p'

p + r = 2681

r + 283 + r = 2681

Combine like terms to simplify

2r + 283 = 2681

Isolate '"r" to solve for Ricky's base hits.

2r + 283 - 283 = 2681 - 283            Subtract 283 on both sides

2r = 2398        

2r/2 = 2398/2               Divide both sides by 2

r = 1199              Number of Ricky's hits

Substitute r = 1199 into any equation to find "p". I will use [2].

p = r + 283

p = 1199 + 283         Add

p = 1482              Number of Pedro's hits

Therefore Ricky had 1199 hits and Pedro had 1482 hits.

Ricky had 1199 hits and Pedro had 1482 hits.

To solve this problem, we can set up a system of equations. Let x represent the number of hits Ricky had. Pedro had 283 more hits, so Pedro's number of hits would be x + 283.

Together, their hits add up to 2681, so we can write the equation:

x + (x + 283) = 2681

Combining like terms:

2x + 283 = 2681

Subtracting 283 from both sides:

2x = 2398

Dividing both sides by 2:

x = 1199

Ricky had 1199 hits and Pedro had x + 283 = 1199 + 283 = 1482 hits.

Answer:

33,793.2 Kilometers per hour :3

Speed of rocket in kilometer in 13,049.4 miles

Given that;

Speed of rocket = 21,000 miles per hour

Miles in 1 kilometer = 0.6214 miles

Find:

Speed of rocket in kilometer

Computation:

Speed of rocket in kilometer = Speed of rocket × Miles in 1 kilometer

Speed of rocket in kilometer = 21,000 × 0.6214

Speed of rocket in kilometer = 13,049.4 miles

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Answer:

its increasing by 2,u can think of it as taking away the 2 in the ones place and skip counting by 2 like your in the ones place