Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation
4.5x+3y=2:
A(...,1/3)
B(2/3,...)

Answer:

  about 35.4 yards

Step-by-step explanation:

Make use of the formula for the area of a square and solve for the side length. The area (A) of a square of side length s is given by ...

  A = s²

You are given A and asked to find s. So you have

  1255 yd² = s²

To find s, you take the square root of both sides of the equation.

  √(1255 yd²) = √(s²)

  35.426 yd ≈ s . . . . . the square root of 1255 is irrational, so we have shown an approximation rounded to 3 decimal places.

Each side of the field is about 35.4 yards long.

_____

Any scientific or graphing calculator can compute the square root for you, as can any spreadsheet program or any of a number of on-line calculators. A Google or Bing search box will also compute the square root for you. (see attachment)

Answer:

Part 1) The commission is $35.6 and the total salary for week 1 is $285.6

Part 2) The commission is $45.04 and the total salary for week 2 is $295.04

Part 3) The commission is $39 and the total salary for week 3 is $289

Part 4) The commission is $32.96 and the total salary for week 4 is $282.96

Step-by-step explanation:

Let

x-----> the amount in sales

y----> Cindy Nelson’s salary

we know that

4%=4/100=0.04

so

The linear equation that represent this situation is

y=250+0.04x

case 1) week 1

Sales  $890

For x=890

substitute in the linear equation

y=250+0.04(890)

y=250+35.6=$285.6

therefore

The commission is $35.6

The total salary for week 1 is $285.6

case 2) week 2

Sales  $1,126

For x=1,126

substitute in the linear equation

y=250+0.04(1,126)

y=250+45.04=$295.04

therefore

The commission is $45.04

The total salary for week 1 is $295.04

case 3) week 3

Sales  $975

For x=975

substitute in the linear equation

y=250+0.04(975)

y=250+39=$289

therefore

The commission is $39

The total salary for week 1 is $289

case 4) week 4

Sales  $824

For x=824

substitute in the linear equation

y=250+0.04(824)

y=250+32.96=$282.96

therefore

The commission is $32.96

The total salary for week 1 is $282.96

The assumption of the inductive step is not correct. If [tex]\mathrm{max}(x,y)=2[/tex], for instance, it's entirely possible that [tex]x=1[/tex] and [tex]y=2[/tex].

Answer:

3m-3n

Step-by-step explanation:

We want to simplify the expression;

2m - [n - (m - 2n)].

We expand the parenthesis to obtain;

2m - (n - m + 2n)

2m - ( - m + 3n)

Expand further to get;

2m +m -3n

Combine the first two terms;

3m-3n

Answer:

A.  

x + y = 28

1.68x + 2.44y = 54.64

Step-by-step explanation:

Let x = paperback books and y = hardback books

x+y =28

We know that paperbacks cost 1.68 and hardback cost 2.44

1.68x + 2.44y = 54.64

We have 2 equations and 2 unknowns

x+y =28

1.68x + 2.44y = 54.64

Answer:

  x = 24

Step-by-step explanation:

The segments on either side of an angle bisector are proportional:

  (x +4)/44.8 = 35/56

  x +4 = 44.8·(35/56) = 28 . . . . multiply by 44.8

  x = 24 . . . . . subtract 4

Answer:

The value of x is 24.

Step-by-step explanation:

Given information: In ΔGHE, ED is angle bisector, EG=44.8 millimeters, GD=(x+4) millimeters, DH=35 millimeters, and EH=56 millimeters.

According to the angle bisector theorem, an angle bisector divide the opposite side into two segments that are proportional to the other two sides of the triangle.

In ΔGHE, ED is angle bisector, By using angle bisector theorem, we get

[tex]\frac{GD}{DH}=\frac{EG}{EH}[/tex]

[tex]\frac{x+4}{35}=\frac{44.8}{56}[/tex]

Multiply both the sides by 35.

[tex]x+4=\frac{44.8}{56}\times 35[/tex]

[tex]x+4=28[/tex]

Subtract 4 from both the sides.

[tex]x=28-4[/tex]

[tex]x=24[/tex]

Therefore the value of x is 24.

[tex]\displaystyle\\\frac{5}{\sqrt{11}-\sqrt{3}}=?\\\\\\\text{We rationalize the denominator.}\\\\\frac{5}{\sqrt{11}-\sqrt{3}}=\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}=\frac{5(\sqrt{11}+\sqrt{3})}{(11-3)}=\boxed{\bf\frac{5\sqrt{11}+5\sqrt{3})}{8}}[/tex]

Answer:

The correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Step-by-step explanation:

We need to find the quotient of [tex]\frac{5}{\sqrt{11}-\sqrt{3}}[/tex],

Rationalizing the above,

By multiply and divide by conjugate of its denominator,

[tex]\frac{5}{\sqrt{11}-\sqrt{3}} \times \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}[/tex]

[tex]\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}[/tex]

Since, [tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

[tex]\frac{5\sqrt{11}+5\sqrt{3}}{(11-3)}[/tex]

simplify,

[tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Therefore, the correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]

Answer:

See the attached photo for the calculations and answers

Step-by-step explanation:

The calculations and explanations are shown in the 3 attached photos below.

The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024

What is probability?

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

The probability of being dealt a flush:

For a suit there are 4 choices and 13C₅ choices for a card in that suit

Probability of flush = 4.( 13C₅)/52C₅

Probability of flush = 0.0019

The probability of being dealt one pair:

There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.

P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅

P(one pair) = 0.4225

The probability of being dealt two pairs:

There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.

P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475

The probability of being dealt three of a kind:

There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.

P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211

The probability of being dealt four of a kind:

There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.

P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024

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Step-by-step explanation:

Did they define mechanical pencils using the variable m?

Answer:

44%

Step-by-step explanation:

If p represents the number of portions and q represents the quantity in each portion, then the original amount needed was p·q.

After p is increased by 20%, its number is ...

p + 0.20·p = 1.20·p

After q is increased by 20%, its amount is ...

q + 0.20 ·q = 1.20·q

Then the new amount the parents must buy is ...

(1.20p)(1.20q) = 1.20²·pq = 1.44pq

This amount is ...

(1 + 44/100)·pq = pq + 44%·pq

It is 44% more than the original planned purchase.

Answer:

44 percent

Step-by-step explanation:

Answer:

$84.70

Step-by-step explanation:

Using the formula, B = 70(1+0.1)^2 = 70*1.21 = 84.7.

To find the dimensions of the rectangle, express its length in terms of its width as 'width + 6'. Substitute this in the formula for perimeter and solve to get width = 5 feet and length = 11 feet.

The problem stated relates to the geometric concept of perimeter and involves a bit of algebra. First, remember that the formula for the perimeter of a rectangle is 2(length + width). If the total perimeter is 32 feet, and the length is 6 feet longer than the width, we can describe the length as 'width + 6'.

Substitute these into the perimeter formula: 2((width + 6) + width) = 32. Simplify this to 2(width + width + 6) = 32, then simplify further to 2(2width + 6) = 32. Divide both sides by 2 to get 2width + 6 = 16. Solving for 'width', we get width = 5 feet. Therefore, the length (which is width + 6) would be 5 + 6 = 11 feet.

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6.

Intersecting chords:

RT x ST = PT x TQ

2 x 6 = 3 x TQ

12 = 3TQ

TQ = 12/3

TQ = 4

7.

AD = 90 -BE = 90-18 = 72

ADE = 180. DE = 180 - AD = 180-72 = 108

AE = 180.  AB = 180-18 = 162

DE = 108

BD = BE +DE = 18 + 108 = 126

DAB = 72 +   162 = 234

ADE = 90 degrees

8.

AB^2 = BC* (BC +x)

8^2 = 2 * (2 +x)

64 = 4 + 2x

60 = 2x

X = 60/2

X = 30

Answer:

Option A. (6,2)

Step-by-step explanation:

We have the following inequality:

[tex]y- x <-3[/tex]

Solving for y we have:

[tex]y<x-3[/tex]

The line that limits the region of inequality is

[tex]y = x-3[/tex]

Then the region of inequality are all values of y that are less than [tex]f (x) = x-3[/tex]

In other words, the points belonging to the inequality are all those that lie below the line.

To find out which point belongs to this region substitute inequality and observe if it is satisfied

A. (6,2)

[tex]2<6-3[/tex]

[tex]2<3[/tex]   is satisfied

B. (2, 6)

[tex]6<2-3[/tex]

[tex]6<-1[/tex]   it is not satisfied

C. (2, -1)

[tex]-1<2-3[/tex]

[tex]-1<-1[/tex] it is not satisfied

The answer is the option A

Answer:

X-intercept: (0,4)

Y-intercept: (-4,0)

Answer:

A.  The two triangles.

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In B, they kept the same shape, but not the same side.

In C, you can see the figure has been transformed,.

A bit if not A them it’s C (sorry I tried)

1. 7=k

2. 21+w=36

-21 -21

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

w=15

3. -5 =G+3

-3 -3

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

-8=G

4. 2b/2=12/2

b=6

5. 35/5=5R/5

7= R

6. Q/2 (2) = 6 (2)

Q=12

Answer:

Step-by-step explanation:

1) 14-7 = 7 = k

2) 21 + W = 36  →  W = 36 - 21  → W = 25

3) -5 = G + 3.  Add 5 to both sides, obtaining G = 8.

4) 2b = 12.  Div. both sides by 2:  b = 6

5) 35 = 5R.  Div. both sides by 5:  7 = R

6) Q/2 = 6; Mult both sides by 2: Q = 12

Answer:

120 floor seats, 80 stadium seats

Step-by-step explanation:

use extreme values

if all were floor seats, then cost would be 32*200, or 6400

6400-5440=960

32-20=12

960/12=80

200-80=120

120 floor seats and 80 stadium seats were sold.

Let's designate F as the number of floor seats and S as the number of stadium seats.

Given :

F + S = 200 (Equation for the total number of tickets)

32F + 20S = 5440 (Equation for the total sales amount)

We can use substitution or elimination to solve this system. If we multiply the first equation by 20 to get

20F + 20S = 4000

and subtract it from the second equation, we get:

12F = 1440

F = 120

We found the number of floor seats sold. We can then substitute F back into the first equation to find the number of stadium seats:

120 + S = 200

S = 80.

So, 120 floor seats and 80 stadium seats were sold.

Answer:

Yes , i thinks so because have letter and the result is perfect and have two statement.

Answer:

(8,0)

Step-by-step explanation:

The equation that models the path traced by the ball is

[tex]h(x)=-8x^2+64x[/tex]

To find the point at which the ball hit the ground, we must equate the function to zero.

[tex]-8x^2+64x=0[/tex]

Factor;

[tex]-8x(x-8)=0[/tex]

[tex]-8x=0,(x-8)=0[/tex]

This implies that;

x=0,x=8,

At x=0, the ball was not yet kicked.

So we take x=8, to be the time the ball hit the ground.

We substitute x=8 into the function to get;

[tex]h(8)=-8(8)^2+64(8)=0[/tex]

Hence the point at which the ball hit the ground is (8,0)

Answer:

6ft for 30°

8.5ft for 45°

10.4ft for 60°

Step-by-step explanation:

12(sin 30°)=x

x=6

12(sin 45°)=x

x=8.5

12(sin 60°)=x

x=10.4

By using right angle trigonometry and the cosine function (x = L cos θ), we find that a 12-ft ladder reaches 10.4 ft, 8.5 ft and 6 ft up a wall when it is leaned at 30°, 45° and 60° respectively.

The problem described here involves the use of right angle trigonometry, specifically the use of the cosine function. In order to determine how high up the wall the ladder reaches at an angle of 30°, 45° and 60°, we can use the formula: x = L cos θ.

Firstly, let's calculate the height at 30 degrees (θ = 30°). We know that cos 30° = √3/2, so we substitute into the formula: x = 12ft * √3/2 which approximately equals 10.4 ft.

Next, for 45 degrees (θ = 45°), cos 45° = √2/2. Substituting into the formula: x = 12ft * √2/2 = 8.5 ft.

Finally, for 60 degrees (θ = 60°), cos 60° = 1/2. Therefore, x = 12ft * 1/2 = 6ft). So, the ladder reaches 10.4 ft up the wall when the angle is 30°, 8.5 ft when the angle is 45°, and 6 ft when the angle is 60°.

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Answer:

531,441·g^6·h^8

Step-by-step explanation:

The operative rule of exponents is ...

(a^b)^c = a^(b·c)

Working from the inside out, according to the order of operations, we get ...

= (9^3·g^3·h^4)^2

= 729^2·g^(3·2)·h^(4·2)

= 531,441·g^6·h^8

Answer:

As we can see in the picture, we already knew 4 out of 6 sides of the figure so we need to find the other sides.

So the first missing side (the one near the 3 m one) should be:

7 - 4 = 3 (m)

The second missing side (the one near the 4m one) should be:

6 - 3 = 3 (m)

Now that we know all of the side lengths of the figure, the perimeter of the figure will be:

7 + 3 + 3 + 3 + 4 + 6 = 26 (m)

The answer would be 3/12 was used on the recipe. If 3/12 was used on the recipe and we know 2/12 was used to make a sandwich, 3/12 + 2/12 =5/12 used and that holds true being as there is 7/12 of the loaf left. 12/12 - 5/12 = 7/12

Hope I helped. Please mark me brainliest! :)

Answer:

1/10

Step-by-step explanation:

When Maggie gives a grape treat to her brother, there are 2 grape treats out of 5 total treats.

When Maggie selects another treat, there is 1 grape treat out of 4 treats left.

So the probability that both happen is:

2/5 × 1/4

1/10

Answer:

1. 37

2. 25

Step-by-step explanation:

In order to find a percentile of a given number set, you must first put the values in ascending order:

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

70% = 0.7

Since there are 10 numbers in the set, we'll multiply 10 by 0.7

10 × 0.7 = 7

So we are going to look at the seventh number in the set.

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

The seventh number in the set is 37.

We're going to do the same for finding the 40th percentile:

40% = 0.4

10 × 0.4 = 4

Finding the fourth number in the set...

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

... We get 25

And those are you answers, 37 and 25.

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$950\\ r=rate\to 1.5\%\to \frac{1.5}{100}\dotfill &0.015\\ t=years\dotfill &6 \end{cases} \\\\\\ A=950e^{0.015\cdot 6}\implies A=950e^{0.09}\implies A\approx 1039.5\implies \stackrel{\textit{rounded up}}{A=1040}[/tex]

Answer:

7.1 miles

Step-by-step explanation:

Consider right triangle HospitalSchoolSupermarket. In this triangle:

The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.

Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:

[tex]\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.[/tex]

Subtract from the second equation the first one:

[tex]x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi[/tex]

Thus,

[tex]x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.[/tex]

Answer:

8(2p − q)(4p² + 2pq + q²)

Step-by-step explanation:

You would use the difference of cubes to factor this polynomial.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

recursive: f(0) = 7; f(n) = f(n-1) -8

explicit: f(n) = 7 -8n

Step-by-step explanation:

The sequence is an arithmetic sequence with first term 7 and common difference -8. Since you're numbering the terms starting with n=0, the generic case will be ...

recursive: f(0) = first term; f(n) = f(n-1) + common difference

explicit: f(n) = first term + n·(common difference)

To get the answer above, fill in the first term and common difference values.