Squares and square roots, a perfect square is a number whose square root is an even number

Based on the thickness of the rubber insulation and outside diameter, the diameter of the copper conductor is 0.376 inch.

The diameter of the copper wire can be found by the formula:

= Outer diameter - ( 2 x cotton insulation) - (2 x rubber insulation)

Solving gives:

= 500/ 1,000 - (2 x 12/ 1,000) - (2 x 50 / 1,000)

= 0.5 - (2 x 0.12) - (2 x 0.05)

= 0.376 inch

= 376 / 1,000 inch

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Answer:

3. 125

4. 115

5. m<1 = 70, m<2 = 55, m<3 = 55

6. m<2 = 50, m<3 = 50, m<4 = 80, m<6 = 130

The percentage reduction of the price of the video game from 60 to 45 was 25%.

The percentage reduction refers to the fractional reduction in the price of the video game.

This implies that a percentage is a fraction of a value.  Percentages are calculated over 100.

A percentage is, therefore, a number or ratio expressed as a fraction of 100, often denoted using the "%" sign.

The old price of the video game = 60

The new price of the video game = 45

Reduction in price = 15 (60 - 45)

Percentage reduction = 25% (15/60 x 100)

Thus, the percentage reduction of the price of the video game from 60 to 45 was 25%.

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Answer:

see explanation

Step-by-step explanation:

total parts = 3 + 18 + 6 + 3 = 30

3 grams of silver = [tex]\frac{3}{30}[/tex] = [tex]\frac{1}{10}[/tex]

18 grams of copper = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]

6 grams of aluminium = [tex]\frac{6}{30}[/tex] = [tex]\frac{1}{5}[/tex]

3 grams of zinc = [tex]\frac{3}{30}[/tex] = [tex]\frac{1}{10}[/tex]

Answer:

10 is the right answer...

Step-by-step explanation:

thanks

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[tex]\boldsymbol{\sf{3(x-4) > 5x +2 }}[/tex]

Use the distributive property to multiply 3 by x−4.

[tex]\boldsymbol{\sf{3x-12 > 5x+2 }}[/tex]

Subtract 5x on both sides.

[tex]\boldsymbol{\sf{3x-12-5x > 2 } }[/tex]

Combine 3x and −5x to get −2x.

[tex]\boldsymbol{\sf{-2x-12 > 2 }}[/tex]

Add 12 to both sides.

[tex]\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}[/tex]

[tex]\boldsymbol{\sf{-2x > 14}}[/tex]

Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.

[tex]\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}[/tex]

[tex]\boxed{\boldsymbol{\sf{x < -7 }}}[/tex]

So in the inequality 3(x-4)>5x +2, the value of x is -7.

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The car will be worth $20467 in 2017

The given parameters are:

Initial value, a = 38000

Depreciation rate, r = 6%

The value of the car after x years is represented by the following exponential equation

V(x)= a(1 - r)^x

Substitute the known values in the above equation

V(x) = 38000 * (1 - 6%)^x

2017 is 10 years from 2007

This means that x = 10

So, we have:

V(x) = 38000 * (1 - 6%)^10

Evaluate

V(x) = 20467

Hence, the car will be worth $20467 in 2017

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Answer:

6 children passes

Step-by-step explanation:

a = adult and c = children

25a + 15c = 440           and          a + c = 20

                                                     c = 20 - a

25a + 15(20-a) = 440

25a + 300 - 15a = 440

25a - 15a = 440 - 300

10a = 140

a = 140/10

a = 14 and this is 14 adult tickets

Now we plug the a value into the equation to find the c value

14 + c = 20

c = 20 - 14

c = 6

Verify answer:

25(14) = 15(6) = 440

350 + 90 = 440

440 = 440

Question 1

[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]

Question 2

By inspection, we know that [tex]x=2[/tex] is a root.

[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].

So, we can factor the equation as

[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]

m1 x m2 = - 1

Rearrange 4x + 2y = 8.

4x + 2y = 8

-4x, then ÷ 2

y = - 4x + 8 / 2

y = - 2x + 4

m1 = - 2, find reciprocal of - 2, by placing 1 over the 2

So, - 2 will become - 1/2, but multiplying this gives us a positive 1. Thus, m2 = 1/2

m1 x m2 = - 1

-2 x 1/2 = - 1

That means slope perpendicular to the line

4x + 2y = 8 is y = 1/2x, where a half is the gradient/slope.

Ans: 1/2

Hope this helps!

Answer:

[tex]a = 1, \ - 3[/tex]

Explanation:

[tex](a-6)(a+8) = -45[/tex]

distribute

[tex]a^2 + 8a - 6a - 48 = -45[/tex]

collect terms

[tex]a^2 + 8a - 6a - 48 + 45=0[/tex]

simplify

[tex]a^2 + 2a - 3=0[/tex]

factor

[tex](a - 1)(a + 3)= 0[/tex]

set to zero

[tex]a = 1, \ - 3[/tex]

Answer:

a = 1,  -3

Step-by-step explanation:

Given equation:

[tex](a-6)(a+8)=-45[/tex]

Expand the brackets:

[tex]\implies a^2+8a-6a-48=-45[/tex]

[tex]\implies a^2+2a-48=-45[/tex]

Add 45 to both sides:

[tex]\implies a^2+2a-48+45=-45+45[/tex]

[tex]\implies a^2+2a-3=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].  

Two numbers that multiply to -3 and sum to 2 are: 3 and -1.  

Rewrite the middle term as the sum of these two numbers:

[tex]\implies a^2+3a-a-3=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies a(a+3)-1(a+3)=0[/tex]

Factor out the common term (a + 3):

[tex]\implies (a-1)(a+3)=0[/tex]

Apply the zero product property:

[tex]\implies (a-1)=0 \implies a=1[/tex]

[tex]\implies (a+3)=0 \implies a=-3[/tex]

Verify the solutions by inputting the found values of a into the original equation:

[tex]a=1 \implies (1-6)(1+8) & =-5 \cdot 9 = -45[/tex]

[tex]a=-3 \implies (-3-6)(-3+8) & =-9 \cdot 5 = -45[/tex]

Hence both found values of a are solutions of the given equation.

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The answer is 2c.

Applying the Law of Exponents,

The radius of the orange circle is 1.5 unit and  the radius of the blue circle is 2.25 units

The figure that completes the question is added as an attachment

The orange circle

The radius of the green circle is given as:

r = 1

One and half green circle make up the radius of the orange circle.

So, the radius of the orange circle is

R = 1.5 * r

This gives

R = 1.5 * 1

R = 1.5

Hence, the radius of the orange circle is 1.5 unit

The blue circle

The radius of the orange circle is given as:

r = 1.5

One and half orange circle make up the radius of the blue circle.

So, the radius of the blue circle is

R = 1.5 * r

This gives

R = 1.5 * 1.5

R = 2.25

Hence, the radius of the blue circle is 2.25 units

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By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)

In geometry, the perimeter is the sum of the lengths of the sides of a figure.  Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.

Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:

OB = DE = 0.5 · √(24² + 10²)

OB = DE = 13

Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.  

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Answer:  C. 38 units

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!!  :)

Just did it and got it correct!

Answer:

[tex]m=-3[/tex]

Step-by-step explanation:

Given points:
[tex](5,3),(8,-6)[/tex]

1. Find the slope

The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).

The coordinates of point 1 are: [tex]x_1=5,y_1=3[/tex]

The coordinates of point 2 are: [tex]x_2=8,y_2=-6[/tex]

To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-6-3}{8-5}[/tex]

[tex]m=\frac{-9}{3}[/tex]

[tex]m=-3[/tex]

Answer:

31. (98,765 x 9) + 3 = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2

42.  1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

Conjecture -> solve these problems and see if they are equal on both ends

EX:  3 + 9 + 27 + 81 + 243 ->  363

       3 x 242 = 726 -> 726/2 = 363

Verified

The unit rate of the proportional relationship y = 3x is 3

The proportional relationship is given as:

y = 3x

Divide both sides by x

y/x = 3

For a proportional relationship y/x = k;

The unit rate is 3

This means that the unit rate of the proportional relationship y = 3x is 3

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Answer:309

Step-by-step explanation:

Answer:

91.5[tex]cm^{2}[/tex]

Step-by-step explanation:

The area of the rectangle:

a = lw

a =(21)(3) = 63

The area of the square:

a = lw

a = (5)(5) = 25

The area of a half circle:

a=[tex]\frac{\pi r^{2} }{2}[/tex]

a= [tex]\frac{3.14(1.5^{2}) }{2}[/tex]

a = [tex]\frac{3.14(2.25)}{2}[/tex]

a = [tex]\frac{7.065}{2}[/tex]

a = 3.5 rounded to the nearest tenth

63 + 25 + 3.5 =91.5

Answer: B

Step-by-step explanation: If it goes through a point, flip that point around and that is the point of the inverse. Do that for multiple points to get your answer, which is B

7 gallons are needed to cover 1241 square feet.

In this question,

Each gallon of porch and deck paint covers 200 square feet.

To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.

We use the unitary method to find out how many gallons of paint needs.

Using unitary method,

1241 / 200 = 6.205

However, we cannot buy a fraction of a gallon of paint.

So, the amount of gallons of paint needed is approximately equal to 7 gallons.

Therefore, 7 gallons are needed to cover 1241 square feet.

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According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

Herein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:

x = lim (n → ∞) |aₙ/aₙ₊₁|   (1)

The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:

|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]

|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]

Then, by applying the limit property for rational equations we find that limit of the expression within the series is:

L = 4 / 5

According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

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By the ratio test, the series diverges.

[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]

Answer:

Cosa/2-tana+sina

Step-by-step explanation:

Cosatana

The height is 2 units.

Find the area of the base of the square pyramid:

The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]

B is the area of the base, and H is the height of the pyramid

[tex]H= 6 units[/tex]

[tex]V=70 units^{3}[/tex]

Solve: B

[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]

To find the height of the square prism:

The volume of the square prism is equal: [tex]V=Bh[/tex]

B is the area of the base and h is the height of the prism

[tex]B=35 units^{2}[/tex]

[tex]V=70units^{3}[/tex]

Solve: h

[tex]70=\frac{35}{h}[/tex]

[tex]h=2units.[/tex]

The height is 2 units.

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The height of the square pyramid exists 2 units.

Volume of the square pyramid

[tex]$V = \frac{1}{3}BH[/tex]

where B exists in the area of the base  H lives at the height of the pyramid

we have H = 6 [tex]$$unit^3[/tex]

V = 70 [tex]$$unit^3[/tex]

substitute in the formula and solve for B, we get

[tex]$70 = \frac{1}{3}B(6)[/tex]

B = [tex]$\frac{70}{2}[/tex]

= 35 [tex]$$unit^3[/tex]

To estimate the height of the square prism

Volume of the square prism = Bh

Where B exists the area of the base

h exists the height of the prism

we have B = 35 and V = 70

substitute in the formula and solve for h

70 = (35)h

h = 2 units.

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Answer:

See below

Step-by-step explanation:

REMEMBER  sec = 1/cos ...so the left side is

[1/cos -1]   /  [1/cos  +1 ]    

  get common denominator for numerator and denominator

[ (1 -cos) /cos  ]  /  [ (1+cos) / cos ]    

 now flip the bottom fraction and multiply to get

[(1-cos/cos) ]  *  [ cos / (1+cos) ]    which simplifies to   ( the 'cos' term cancels)

(1-cos) / (1+cos)              done !

The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation ​(0, 0) ​is A'(0, 0), B'(1, 2) and C'(-1, 1)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.

Let us assume that the polygon has vertex at A(0, 0), B(3, 6) and C(-3, 3)

The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation ​(0, 0) ​is A'(0, 0), B'(1, 2) and C'(-1, 1)

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Answer:

2.72 / 16 x 28 = $4.76

Step-by-step explanation:

Since they give you $2.72 for 16 ounces you put in:

2.72 / 16 x 28 = $___

Then you just solve it to get $4.76:

2.72 / 16 = 0.17

0.17 x 28 = 4.76

Answer:

129 1/3 is the answer