16 The perimeter of the pentagon is equal to the perimeter of the square.
Not to scale
5X tỉ 3
2x + 3
11
7x + 4
5x + 8
9x10
Find an expression for the length of one side of the square.
Give your answer in terms of x in its simplest form.

The probability that they do not use the swimming pool will be 0.2.

From the information given, there are 135 people in a sport centre and 31 people use the gym and the track while 4 people use all three facilities.

Based on the information given, the people who use the gym and the track only will be:

= 31 - 4

= 27

The probability that they do not use the swimming pool will be:

= 27/135

= 0.2

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The number of ways is 497420

The ways can the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled is [tex]22_{C_9}[/tex]

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

22C9 = 22! /(9!*13!) = 497420

Thus, In 497420 ways the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled.

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The value of nickels is $76.80.

The height of each nickel is 6.25 / 100 = 0.0625 inches.

Divide 8 feet by 0.0625 inches to find that there are

8×12 / 0.0625 = 1536 nickels in an 8 ft stack.

Their value is $76.80.

Nickel is a chemical detail with the symbol Ni and atomic range 28. It is silvery-white lustrous steel with a mild golden tinge. Nickel belongs to the transition metals and is hard and ductile.

Pure nickel, powdered to maximize the reactive surface vicinity, indicates a widespread chemical interest, but large pieces are slow to react with air underneath fashionable conditions because an oxide layer paperwork at the floor stops further corrosion (passivation).

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Answer:

c) 19

Step-by-step explanation:

To find the length of JH, subtract the length of HM from JM.

Length of JH = JM - HM

                      = 40 - 21

                      = 19

Answer:

JH = 19

Step-by-step explanation:

from the diagram

JH + HM = JM , that is

JH + 21 = 40 ( subtract 21 from both sides )

JH = 19

The substitution that should be used to rewrite the equation is u = x+5, the correct option is A.

The polynomials of the 2nd degree are called Quadratic Equations.

It has a general form as ax² +bx+c=0

To rewrite the expression as a quadratic equation  

6(x+5)² + 5(x+5)-4 = 0

=6(x+5)(x+5)+5(x+5)-4

=6(x² + 5x + 5x + 25)+5(x+5)-4

=6(x²+10x+25) + 5(x+5) - 4 = 0

=6x² + 60x + 5x + 150 + 25 - 4 = 0

=6x² + 65x + 171 = 0

This is the quadratic equation of the form ax² +bx+c=0

but if directly it has to be written in this ax² +bx+c=0 form , it can be written by substituting u = (x + 5)

6(x+5)² + 5(x+5)-4 = 0

6u²+5u-4 = 0

Therefore, the substitution that should be used to rewrite the equation is u = x+5, the correct option is A.

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[tex] \frac{?}{20} = \frac{6}{10} [/tex]

[tex] \frac{?}{2} = 6 \\ ? = 6\times 2 = 12[/tex]

Answer: 2   55   121

             22   5      11

Step-by-step explanation:

The slope intercept form is written as: y= mx+b

where m is slope and b is the y-intercept

Here m is 1/5 and -8 is b

So, 1/5 and -8

Hope it helps!

Answer: 3x + 23

it should be right!

Answer:

3x + 23

Step-by-step explanation:

To simplify this expression, the first thing we have to do is distribute the 4 outside the parentheses. This gives us 4x + 28 - 7 - x + 2. Now, we can combine like terms (those that have variables and those that don't) to get 3x + 23

We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.

Herein we have to prepare a solution with fertilizers by mixing two different solutions. The amount needed of the 51 % solution can be found by weighted averages:

(50/100) · (250 L) = (51/100) · x + (26/100) · (250 - x)

50 · 250 = 51 · x + 26 · 250 - 26 · x

24 · 250 = 25 · x

x = 240

We must mix 240 liters of the 51 % solution and 10 liters of the 26 % solutions to produce 250 liters of 50 % solution.

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The equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is having only one solution.

Given equation 0.75(x+40)=0.35(x+20)+0.35(x-20)

We have to find the number of solutions.

To find the number of solutions we have to solve the equation for the value of variable x. Equation is often solved to find the value of variables.

Equation : 0.75(x+40)=0.35(x+20)+0.35(x-20)

Opening the brackets and multiply the numbers outside by the numbers in the bracket.

0.75x+30=0.35x+7+0.35x-7

Take all the numbers having same variables at one end of equal to.

0.75x-0.35x-0.35x=7-7-30

0.75x-0.7x=-30

0.05x=-30

x=-30/0.05

x=-600

Which is the only value of x.

Hence the number of solutions of the equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is  one.

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Answer:

I believe the graph went 3 units up

Step-by-step explanation:

Answer:

2. 120

Step-by-step explanation:

3t2s

Replace variables t and s with 2 and 10

3 x 2 x 2 x 10

6 x 20

=120

So the answer is number 2. 120

By looking at the diagram, we can see that:

As you can see, the ray DE starts at point D and then passes through E, and then continues.

Then the only endpoint of that ray is D.

The ray GA starts at point G and goes through A (so it goes to the left of G).

The ray DF starts at point F and goes through F (So it goes to the right of D).

Then these two rays don't intersect, because D is at the right of G.

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Answer:

  (d)  intersection

Step-by-step explanation:

When given two inequalities, you must determine whether the solution set must satisfy both, or must satisfy either. The key is found in the conjunction associated with the inequalities.

Here, the conjunction is "and," which means the solution must satisfy both inequalities. It also means, the solution set will be the intersection of the solution sets of the different inequalities.

The attached number line shows the first solution set in red, the second solution set in blue, and the "and" (intersection) of those in purple.

The conjunction "or" will signify the solution set is the union of those of the separate inequalities.

Answer:

Please review my interpretation of the written expression.

Step-by-step explanation:

f(x) = 5*(4/5)^x    :  Is this correct?

If so, see attached graph.

One can calculate several points and then draw the graph, or use an online, and free, graphing app (DESMOS in this case).

Since the exponent is the variable, I'll pick a few vaules that are easy (for me) to calculate:

f(0) = 5*(4/5)^0

Anything raised to the 0th power is equal to 1, so we get 5*1 or 5 to make the point (1,5).

When x = 1, the fraction (4/5) remains (4/5) and when multiplied by 5, reduces to simply 4.  The second point is (1,4)

For the last point, I chose x to be 10.  5(4/5)^10 becomes 0.5.  The third point is (10,0.5)

We can see the line approaches 0 as x increases.

The 95% confidence interval for the mean is (1.535, 1.504).

It is given that a machine produces 1.50 pounds of cereal. The sample is 56 cereal boxes. The sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds.

Mean = 1.50 pounds

x = 1.52 pounds

Standard deviation = SD = 0.06 pounds

n = 56

We need to find the 95% confidence interval for the mean.

So, z = 1.96

So, the confidence interval would be

[tex]x[/tex]±[tex]z\frac{mean}{\sqrt{n} }[/tex]

[tex]1.52[/tex]±[tex]1.96*\frac{0.06}{\sqrt{56} }[/tex]

= [tex]1.52[/tex]±[tex]1.96*0.00801[/tex]

= [tex](1.52 + 0.0156996),(1.52 - 0.0156996)[/tex]

= [tex](1.535, 1.504)[/tex]

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Option B is the answer. The term for the geometric sequence that we have here is -3.

We have u1, u2, u3 = a, ar, ar², ar³

From here we have to find the common ratio that is used to divide the sets of numbers

6,561 divided by −2,187 = -3

Hence when we go further each of the value when divided by -3 gives the next value.

Hence the value for the geometric sequence is -3.

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Answer:

12

Step-by-step explanation:

just find the HCF, which will be

2² × 3 = 12

Step-by-step explanation:

Question 46.

[tex](2\sqrt{5}-\sqrt{2} )^2=(2\sqrt{5})^2-2*2\sqrt{5}*\sqrt{2} +(\sqrt{2})^2 } =4*5-4*\sqrt{2*5} +2=\\=20-4\sqrt{10}+2=22-4\sqrt{10}.[/tex]

Answer: E. None of these.

Question 47.

[tex]\frac{4\sqrt{5} }{\sqrt{3} } =\frac{4*\sqrt{5}*\sqrt{3} }{\sqrt{3} *\sqrt{3} } =\frac{4*\sqrt{5*3} }{3}=\frac{4\sqrt{15} }{3} .[/tex]

Answer: E. None of these.

Answer:

45) E 47) E

Step-by-step explanation:

45)

Remember the formula [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](2\sqrt5-\sqrt2)^2=(2\sqrt5)^2-2(2\sqrt5\times\sqrt2)+(\sqrt2)^2\\\\=20-2(2\sqrt{10})+4\\\\=24-4\sqrt{10}[/tex]

Hence E. None of these.

47)

[tex]\frac{4\sqrt{5}}{\sqrt3}=\frac{4\sqrt5\times\sqrt3}{\sqrt3\times\sqrt3}\\\\=\frac{4\sqrt15}{3}[/tex]

Hence E. None of these.

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Answer:

Circle B: 3

Both circle B + S: 6

Circle S: 1

Outside of box: 2

The orthocenter of the triangles ABC are (2, 0) and (3, 3)

Question 8

The coordinates are given as:

A(2,0); B(2, 4); C(6,0)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 4)/(6 - 2)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1)  + y1

Where:

(x1, y1) = (2,0)

So, we have:

y = 1(x - 2) + 0

y = x - 2

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 0)/(6 - 2)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (2,4)

So, we have:

x = 2

Substitute x = 2 in y = x - 2

y = 2 - 2

y = 0

So, we have:

(x, y) = (2, 0)

Hence, the orthocenter of ABC is (2, 0)

Question 9

The coordinates are given as:

A(1,1); B(3, 4); C(6,1)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 4)/(6 - 3)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1)  + y1

Where:

(x1, y1) = (1,1)

So, we have:

y = 1(x - 1) + 1

y = x

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 1)/(6 - 1)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (3,4)

So, we have:

x = 3

Substitute x = 3 in y = x

y = 3

So, we have:

(x, y) = (3, 3)

Hence, the orthocenter of ABC is (3, 3)

Question 18 - 20

Line 2x and x+ 3 are congruent lines

So, we have:

2x = x +3

Solve for x

x= 3

Line 3x and 2x + 5 are congruent lines

So, we have:

3x = 2x +5

Solve for x

x = 5

Line 2x - 3 and x + 2 are congruent lines

So, we have:

2x - 3 = x + 2

Solve for x

x = 5

Question 21 - 23

Line x + 5 and 3x + 7 are congruent lines

So, we have:

x + 5 = 3x + 7

Solve for x

x = -1

Line x + 6 and 5x - 4 are congruent lines

So, we have:

x + 6 = 5x - 4

Solve for x

x = 2.5

Line x + 8 and 5x + 7 are congruent lines

So, we have:

x + 8 = 5x + 7

Solve for x

x = 1/4

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Answer:

26.4

Step-by-step explanation:

Law Of Cosines:

    [tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]

    This should work for any side. This can generally be thought as:

   [tex]cos(\text{angle}) = \frac{\text{sum of squares of two other sides-opposite side squared}}{\text{2 times the product of the other two sides}}[/tex]

    If this is too confusing here's the formula for the other sides (which is essentially the same, just different variables)

   [tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}[/tex]

   [tex]cos(C) =\frac{a^2+b^2-c^2}{2ab}[/tex]

Anyways now just plug in the known values into the equation

[tex]cos(A)=\frac{4^2+6^2-3^2}{2(6)(4)}\\[/tex]

Square and multiply values

[tex]cos(A)=\frac{16+36-9}{48}[/tex]

Add the values in the numerator

[tex]cos(A)=\frac{43}{48}[/tex]

Take the inverse of cosine on both sides

[tex]A=cos^{-1}(\frac{43}{48})[/tex]

calculate arccosine (inverse cosine) using a calculator

[tex]A\approx 26.384[/tex]

Round to nearest tenth

[tex]A\approx26.4[/tex]

Answer:

Step-by-step explanation:

a women buys 3 dozen eggs. Later ,she discovers that x of them are broken. How many eggs are not broken​

3 * 12 - x =

36 - x

Answer:

$18

Step-by-step explanation:

Simply just multiply 30/100 with 60 = (30/100)*60 = (30*60)/100 = 18

The value of 30% off $60 is number 18.

To calculate a 30% discount off $60, you can follow these steps:

Convert the percentage to a decimal:

30% is equal to 0.30.

Multiply the original price by the decimal:

$60 × 0.30

= $18.

Therefore, a 30% discount off $60 would be $18.

The discounted price would be $60 - $18 = $42.

Hence, the value of 30% off $60 is 18.

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Answer: C. 3052,08 cm³.

Step-by-step explanation:

D=18 cm       V=?

[tex]R=\frac{D}{2} =\frac{18\ cm}{2} =9\ cm.\\\boxed {V=\frac{4}{3}*\pi *R^3 }\\V=\frac{4}{3}*\pi *9^3 \\V=4*\pi *3*9^2\\V=12*81*3,14 \\V=3052,08\ (cm^3).[/tex]

Answer:

1. Jamaal

2. 42 more dishes

Step-by-step explanation:

1. Jamaal: 25 dishes per hour and works for 3 hours

25(3) = 75 dishes

Daniel: Daniel can wash 22 dishes every two hours.

22 = 2x

11 = x

11(3) = 33 dishes

2. 75 - 33 = 42

Jamaal can wash 42 more dishes than Daniel.

Jamaal washes 25 dishes per hour and works for 3 hours. Daniel can wash 22 dishes every two hours. Jamaal washed 42 more dishes than Daniel in 3 hours.

Let's calculate the number of dishes washed by each person in 3 hours and then compare the results.

Jamaal:

Jamaal washes 25 dishes per hour and works for 3 hours.

Number of dishes washed by Jamaal in 3 hours = 25 dishes/hour * 3 hours = 75 dishes

Daniel:

Daniel washes 22 dishes every two hours.

To find the number of dishes washed by Daniel in 3 hours, we need to find how many times he washes dishes in 3 hours.

Number of times Daniel washes dishes in 3 hours = 3 hours / 2 hours (time for 1 cycle) = 1.5 cycles

Now, multiply the number of cycles by the number of dishes washed per cycle:

Number of dishes washed by Daniel in 3 hours = 1.5 cycles * 22 dishes/cycle = 33 dishes

Comparison:

Jamaal washed 75 dishes in 3 hours.

Daniel washed 33 dishes in 3 hours.

Now, let's find the difference in the number of dishes washed by each person:

Difference = Jamaal's dishes - Daniel's dishes

Difference = 75 dishes - 33 dishes = 42 dishes

Therefore, Jamaal washed 42 more dishes than Daniel in 3 hours.

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