half of 5/6. thanks​

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Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]

Allowing us to say,

[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]

The solution is 5

The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 )   be equation (1)

On simplifying the equation , we get

Taking the common factors on numerator , we get

A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )

A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )

Taking the common factor as ( x + 2 ) , we get

A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )

So , the equation is

A = lim x tends to 3 ( x + 2 )

Substitute the value of x = 3 , in the equation , we get

A = ( 3 + 2 )

A = 5

Therefore , the value of A is 5

Hence , the equation is A = 5

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Answer:

[tex]\bold{4r^3 (6-\pi)}[/tex]

Step-by-step explanation:

Let us try to visualize the given situation in the form of 2 Dimensional image as shown in the attached diagram.

Let the Diameter of spherical balls be D.

As the spherical balls are completely fit in the rectangular box, the sides of box become:

[tex]D \times D\times (3 \times D)[/tex] OR [tex]D\times D\times 3D[/tex]

We know that Diameter is twice of radius.

Therefore [tex]D = 2r[/tex]

So, the dimensions of rectangular box becomes:

[tex]2r \times 2r \times 6r[/tex]

Volume of a rectangular box is given as:

[tex]V = Length \times Width \times Height\\\Rightarrow V = 2r\times 2r\times 6r = \bold{24r^3}[/tex]

Now, let us find out the volume of each spherical ball.

Volume of a sphere with radius 'r' is given as:

[tex]V_{sphere} = \dfrac{4}{3}\pi r^3[/tex]

Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3 =4\pi r^3[/tex]

Now, the volume of space between the balls and rectangular box is = Volume of rectangular box - Volume of 3 balls

[tex]24r^3 - 4\pi r^3\\\Rightarrow \bold{4r^3 (6-\pi)}[/tex]

Answer:

23

Step-by-step explanation:

Answer:

Step-by-step explanation:

   starting          after        after         after

coordinates   reflection rotation   translation

      (x,y)              (x,-y)         (-y,-x)     (-y-2,-x-4)

A    (-2,1)             (-2,-1)         (-1,2)        (-3,-2)

B     (2,1)              (2,-1)         (-1,-2)        (-3,-6)

C    (2,-1)               (2,1)          (1,-2)         (-2,-6)

D    (-2,-1)              (-2,1)          (1,2)          (-2,-2)

Answer:

60

Step-by-step explanation:

1, Extand line y for which y intercepts CB at point K

2, line y is a straight line and thus KAB=180-110=70

3, AY parallel to CX thus angle CKA=130 which is a alternative angle of BCX (if you can't see then try to extend CX as well

4,BKA=180-130=50 as BC is a straight line

5, the sum of interior angle of a triangle is 180, and we have KAB and BKA, thus angle ABC = 180-KAB-BKA=180-70-50=60

Answer: 8

Step-by-step explanation: Think of the 32 in this problem as 32/1.

So rewriting, we have 1/4 × 32/1.

Now, the 4 and 32 cross-cancel to 1 and 8.

So we have 8/1 or just 8.

Answer:

  48/132

Step-by-step explanation:

The length of 1.5-inch screws is ...

  36 × 1.5 in = 54 in

The length of 2-inch screws is ...

  24 × 2 in = 48 in

The length of 2.5-inch screws is ...

  12 × 2.5 = 30 in

The total length of all screws is ...

  54 in + 48 in + 30 in = 132 in

Then the ratio of 2-in screw length to total screw length is ...

  2-in : total = 48 : 132

Answer:

Step-by-step explanation:

Hello, please consider the following.

We take y different from -5, as dividing by 0 is not allowed and we can compute as below.

[tex]\dfrac{y^2+3y-10}{3y+15}=\dfrac{(y+5)(y-2)}{3y+15}\\\\=\dfrac{(y+5)(y-2)}{3(y+5)}\\\\\large \boxed{\sf \bf \ \ =\dfrac{y-2}{3} \ \ }[/tex]

Thank you

Answer:

1035 cards

Step-by-step explanation:

the total number of baseball cards can be calculate by multiplying amount of pages and how many cards each page can hold.

115*9=1035 cards

Answer:

1035 cards

Step-by-step explanation:

Step 1: State what is known

The album contains 115 pages

Each page has 9 cards

Step 2: Assume the pages are full, calculate how much cards are in the album

115 pages x 9 cards per page = 1035 cards

Therefore there are 1035 cards in the album

Answer:

87

Step-by-step explanation:

[tex]\frac{96+85+90+92+x}{5} = 90\\[/tex]

[tex]\frac{353+x}{5} = 90[/tex]

[tex]353+x= 5(90)\\[/tex]

[tex]353+x=450[/tex]

[tex]x=87[/tex]

Answer:

Radius = 8.575 cm

Step-by-step explanation:

Formula for volume of a pyramid is;

V_p = ½Ah

Where A is area of base and h is height

Also, formula for volume of cone is given as;

V_c = ⅓πr²h

Now, we are told that V_p = V_c and that h is the same for both shapes.

Thus ;

½Ah = ⅓πr²h

h will cancel out to give;

½A = ⅓πr²

Cross multiply to give;

3A/2π = r²

Base area of pyramid is given as 154 cm². Thus;

(3 × 154)/2π = r²

r = √((3 × 154)/2π

r = 8.575 cm

Answer:

C.

Step-by-step explanation:

"Two more than three times a number is seven"

Add 2 to 3n and set it equal to 7.

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

The expression is defined as the relations of the numbers and the variables combined together to form the equation by the use of mathematical algebraic symbols like equal greater than or less than.

From the statement, two more than three times a number is seven.

Let n be the number. The three times a number is then written as,

⇒ 3n

And the expression that is 2 more than 3n is written as follows:

⇒ 2 + 3n

The expression equals 7. The equation is then given as,

3n + 2 = 7

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

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Answer:

-31

Step-by-step explanation:

-3 to the power of 2 means -3*-3 and since negative multiplied by negative is positive, that will give 9

9 + (2-6)(10)

9+-4(10)

9+ -40

9-40

-31

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

Answer:

k=17

Step-by-step explanation:

k+10=27

k=27-10

k=17

Hi there! Hopefully this helps!

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[tex]k + 10 = 27[/tex]

Subtract 10 from both sides.

[tex]k = 27 - 10[/tex]

Answer:

w=5000+0.7s

Step-by-step explanation:

if its possible give me 5 start I need it

Answer:

OK its that question

Answer:

-8x + 12

Step-by-step explanation:

We can use the distributive property of multiplication which states that a(b + c) = a * b + a * c. Therefore:

-4(2x - 3)

= -4 * 2x - 4 * (-3)

= -8x + 12

Answer: -8x -12

Step-by-step explanation:

Multiply -4 by 2x getting -8x

Then Multiply -4 by 3 getting 12

Since you can't subtract 12 from -8x this is the simplest way

Answer:

there are no zeros in f(x)

Step-by-step explanation:

[tex]f(x)=3x^2+9x+12\\\\f(x)=0\\\\0=3x^2+9x+12\\\\[/tex]

to know if the equation has real solutions we have to know if

[tex]b^2-4ac\geq 0[/tex]

a=3

b=9

c=12

[tex]9^2-4*3*12\\\\=81-144\\\\=-63[/tex]

so there aren't real solutions

hence there aren't any zeros in f(x)

Answer:

#1 Use Pythagorean theorem to solve DF

c²-b²=a²

5.83²-5²=a²

33.9889-25=a²

a²=8.9889

a=3.00 (rounded to nearest hundredth)

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# Use Trigonometry to find the angles

angle D:90

angle E: tan E=3/5

                    E=tan^-1 (3/5)

                    E=30.96 (rounded to nearest hundredth)

angle F: tan F=5/3

                    F=tan^-1 (5/3)

                    F=59.04 (rounded to nearest hundredth)

Answer:

36

Step-by-step explanation:

2 x 3 x 3 x 2 = 36

Answer:

might be four

not sure

good luck!

Answer:

f(g(x)) = 18x - 8

Step-by-step explanation:

f(x) = 3x + 7 and g(x) = 6x - 5

Substitute g(x) into f(x):

f(g(x)) = 3(6x - 5) + 7

Distribute the 3 from outside the parentheses:

f(g(x)) = (18x - 15) + 7

Combine like terms:

f(g(x)) = 18x - 8

Answer:

Step-by-step explanation:

16

Answer:

Yes, they vary directly

Step-by-step explanation:

y=kx; k is the constant (12 in this case) and as x increases y increases, so they vary directly

Answer:

Friday needs 11 bikes

Step-by-step explanation:

Mean = (summation of all the numbers)/the total number of the given data

(summation of all the numbers)

= 3.5+5.5+0+5+x

(summation of all the numbers)

= 14+x

the total number of the given data

=5

Mean= 5

Mean= (summation of all the numbers)/the total number of the given data

5= (14+x)/5

25= 14+x

25-14=x

11= x

Answer:

$ 5.5

Step-by-step explanation:

$33 for 6 sandwiches.

For 1 sandwiche = ?

Now,

= 33 ÷ 6

= $5.5

Thus, the unit rate is $5.5

Answer:

OPTION D

Step-by-step explanation:

The bracket is part of bodmas and the only thing it does is to divide equations to make it easier, so thereby I testify that the answer is 2.5/7

Answer:

A.P. : 10, 20, 30, 40, 50

G.P. : 5, 10, 20, 40, 80 .

Step-by-step explanation:

It is given that fourth term of a sequence is 40.

It is not given that whether the sequence is A.P. or G.P.

We need to write two different sequences that satisfy the given condition.

For A.P.,

Required sequence : 10, 20, 30, 40, 50

Here, first term is 10, common difference is 10.

For G.P.,

Required sequence : 5, 10, 20, 40, 80

Here, first term is 5, common ratio is 2.

Therefore, the two sequences are 10, 20, 30, 40, 50  and 5, 10, 20, 40, 80 .

Answer:

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

9x⁴ - 225y⁸

factor out a 9

9(x⁴ - 25y⁸)

factor (x⁴ - 25y⁸)

(x⁴ - 25y⁸)

x² • x² = x⁴

5y⁴ • -5y⁴ = -25y⁸

(x² + 5y⁴) (x² - 5y⁴)

↓

9(x² + 5y⁴) (x² - 5y⁴)