17. Ennis has a length of rope that measures 3 yards. He cuts all of the
rope into smaller pieces that measure yard each. How many cuts did ennis make

Answer:

1000m (option A)

Step-by-step explanation:

[tex]10^k^-^3 = m \\=>\frac{10^k}{10^3} = m \\=> 10^k = 1000 m[/tex]

Answer:

Yes . Divide by 10 for 10/20 to get 1/2.

10/10= 1

20/10= 2

10/20= 1/2

Answer:

Option B, 163 caps.

Step-by-step explanation:

The price of caps are = $6 per cap.

Shipping charge = $25

The total budget of the Laura = $1000

Since the $25 is shipping charge so subtract it from the budget = 1000 – 25 = $975

Here $975 will be used to buy the caps at the price of $6 per cap.

Thus, the number of caps = budget after subtracting the shipping fee / per cap price

Total caps = $975 / 6

Total caps = 162.5 or 163 caps.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]

Step-by-step explanation:

Given,

Length of the rectangle ( l ) = 3x + 5

Breadth of the rectangle ( b ) = 2x - 1

Perimeter of the rectangle ( P ) = 52

Finding the value of x

[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]

⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]

⇒[tex] \sf{52 = 2(5x + 4)}[/tex]

⇒[tex] \sf{52 = 10x + 8}[/tex]

⇒[tex] \sf{10x + 8 = 52}[/tex]

⇒[tex] \sf{10x = 52 - 8}[/tex]

⇒[tex] \sf{10x = 44}[/tex]

⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]

⇒[tex] \sf{x = 4.4 \: }[/tex]

Hope I helped!

Best regards!! :D

Answer:

The answer is

Step-by-step explanation:

f(x) = 6x² + 3

To find the inverse of the function above equate it to y

That's

f(x) = y

So we have

y = 6x² + 3

Next interchange the variables that's x becomes y and y becomes x.

x = 6y² + 3

Next make y the subject

Subtract 3 from both sides

That's

6y² + 3 - 3 = x - 3

6y² = x - 3

Divide both sides by 6

That's

Next find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

(5x-2)

Step-by-step explanation:

first factor the quadratic equation

10x²+26x-12 by factoring out the gcf of 2

2(5x²+13x-6)    to factor the quadratic, first multiply ac (5)(-6)

find factors of -30 that multiply to give you -30 and add to give you the middle term 13.

factors -2, 15

take your leading term 5x and put it over the 2 factors, then reduce when necessary.  it is not necessary to use the 5x² because the x in the denominator cancels one out)

5x/-2 and 5x/15 (this one can be reduced to x/3

(5x-2)(x+3) are the factors.

the shared factor is (5x-2)

Answer:

they share 5x-2 as common factor

Step-by-step explanation:

10x² + 26x – 12 and 2(5x – 2)(x – 3)

10x² + 26x – 12  take 2 as common factor

2(5x²+13x-6)     factorize

2(5x-2)(x+3)

they share 5x-2 as common factor

Answer:

64 poles

Step-by-step explanation:

Given the question :

Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?

Dimension of rectangular field = 100m by 60m

Length = 100m ; breadth = 60m

Since it is erected around the corners of the field, we need to calculate the entire perimeter of the rectangular field.

Perimeter of a rectangle : 2( length + breadth)

Perimeter = 2(100 +60) = 2(160) = 320m

Since the posts are erected 5m apart, the number of post needed will be :

Perimeter / 5

= 320 / 5

= 64 poles

Answer:

To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.

Answer:

77

Step-by-step explanation:

(6 + 3)² is same as (a +  b)²

Since (a +  b)² = a² + 2ab + b²

Therefore,

(6 + 3)² - 4

= (36 + 36 + 9) - 4

= 81 - 4

= 77  

Hi there! Hopefully this helps!

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

Since PEMDAS exists, we will do parentheses "(6+3)" first to get 9.

Then we do the exponent which is:

[tex]9^{2}[/tex] = 81.

Then we subtract.

81 - 4 = 77.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More broken down explanation:

[tex](6+3)^{2} -4[/tex]

Add 6 and 3 to get 9.

[tex]9^{2} - 4[/tex] ≈ [tex]77[/tex]

Calculate 9 to the power of 2 and get 81.

[tex]81-4[/tex] = [tex]77[/tex]

Answer:

Step-by-step explanation:

$2.50g + $5 = $15

$2.50g = 10

g = 4 games

The equation that is used to find the number of games that Max bowled is [tex]5+2.50x=15.[/tex]

Charge for shoe rental [tex]=[/tex] $[tex]5[/tex].

Charge per game [tex]=[/tex] $[tex]2.50[/tex].

Let [tex]g[/tex] represents the number of games.

The total charge is the sum of shoe rental charge and charge per game times the number of games.

Total money spent [tex]=[/tex] $[tex]15[/tex].

[tex]5+2.50x=15[/tex]

This is the equation that is used to find the number of games that Max bowled.

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Answer:

He gets less buying the two big bags

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

9+10 > 21

19 >21

This is not true so it cannot make a triangle

Answer:

4 7/24

Step-by-step explanation:

Answer:

103/24 or 4.29 or 4 7/24

Step-by-step explanation:

15 5/12 - 11 1/8

185/12 - 89/8

370/24 - 267/24 = 103/24

or

15 10/24 - 11 3/24 = 4 7/24

Answer: 14

Step-by-step explanation:

Given the sequence : 55 176 539 1628

Each number after the first is derived by multiplying by x and then adding y;

If x and y are > 0 and they are integers.

Taking 55 and 176:

176 = 55*x + y

539 = 176*x + y

55x + y = 176 - - - (1)

176x + y = 539 - - (2)

From (1) y = 176 - 55x

Substitute y = 176 - 55x into (2)

176x + 176 - 55x = 539

121x = 539 - 176

121x = 363

x = 363 / 121

x = 3

Put x = 3 in y = 176 - 55x

y = 176 - 55(3)

y = 176 - 165

y = 11

x = 3, y = 11

x + y = 3 + 11 = 14

Answer: (5 + 2x)(5 - 2x)

Step-by-step explanation:

It seems a bit backwards from the way these are usually set up, but still it is the difference of two perfect squares.

Answer:

the last one

Step-by-step explanation:

i took the test

If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.

Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.

Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.

Answer:

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball is approximately 4.66 inches

Step-by-step explanation:

The dimension of the ball with known radius = 16-inch

The surface area of the ball with 16-inch radius = 4×π×r² = π·D² = π×16² = 804.24772 in.²

Given that the ball uses one-half the rubber material coating used to cover the 16-inch ball, we have the surface area of the ball = 804.24772 in.²/2 = 402.12386 in.²

The radius, r₂ of the new ball is found as follows;

402.12386 in.² = 4×π×r₂²

r₂² = 402.12386 in.² /(4×π) ≈ 32

r₂ = √32 = 4·√2 ≈ 4.66 inches

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball ≈ 4.66 inches.

Answer:

Two equal sides = 14.4 inches each

Shortest side = 7.2 inches

Step-by-step explanation:

a + b + c = 36

a = b

a = 2c

then:

c = a/2

a + a + a/2 = 36

2a + a/2 = 36

4a/2 + a/2 = 36

5a/2 = 36

a = 2*36/5

a = 72/5

a = 14.4

a = 2c

14.4 = 2*c

c = 14.4/2

c = 7.2

a = b

b = 14.4

Check:

14.4 + 14.4 + 7.2 = 36

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

[tex]a^2-b^2=(a-b)(a+b)[/tex]

We have

[tex](\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14[/tex]

so that

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}[/tex]

Rewrite 16 and 32 as powers of 2, then simplify:

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7[/tex]

So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.

The rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

From the question, we are to rationalize the denominator of the given surd.

We are to write the answer in the form

[tex]\frac{A\sqrt{B}+C}{D}[/tex]

and find the minimum possible value of A + B + C + D

The given surd is

[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}[/tex]

To rationalize the surd, we will multiply the numerator and denominator by the conjugate of the denominator

The conjugate of the denominator is [tex]\sqrt{16}+\sqrt{2}[/tex]

Therefore,

[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \times \frac{\sqrt{16}+\sqrt{2}}{\sqrt{16}+\sqrt{2}}[/tex]

[tex]= \frac{\sqrt{32}(\sqrt{16}+\sqrt{2})}{(\sqrt{16}-\sqrt{2})(\sqrt{16}+\sqrt{2})}[/tex]

[tex]= \frac{\sqrt{512}+\sqrt{64})}{(\sqrt{16})^{2} -(\sqrt{2})^{2} }[/tex]

[tex]= \frac{16\sqrt{2}+8}{16-2}[/tex]

[tex]= \frac{16\sqrt{2}+8}{14}[/tex]

[tex]= \frac{2(8\sqrt{2}+4)}{2(7)}[/tex]

By comparing with, [tex]\frac{A\sqrt{B}+C}{D}[/tex]

A = 8, B = 2, C = 4, and D = 7

Then, the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

Hence, the rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

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Answer:

See below.

Step-by-step explanation:

So we have the parent function:

[tex]f(x)=x^2[/tex]

And it was transformed into:

[tex]g(x)=(3x)^2+6[/tex]

First, the +6 at the very end simply tells us that the graph was shifted upwards by 6 units.

For the (3x), this is essentially saying that:

[tex]f(x)=x^2[/tex]

If we use 3x for x:

[tex]f(3x)=(3x)^2[/tex]

Therefore, we essentially multiplied the x variable by 3.

In other words, this is a horizontal compression by a factor of 3.

So, our transformations are:

1) 6 units upwards

2) Horizontal compression by 3

Answer:

x=-1

Step-by-step explanation:

2x+6=3-x

Step 1: Simplify both sides of the equation.

2x+6=3−x

2x+6=3+(−x)

2x+6=−x+3

Step 2: Add x to both sides.

2x+6+x=−x+3+x

3x+6=3

Step 3: Subtract 6 from both sides.

3x+6−6=3−6

3x=−3

Step 4: Divide both sides by 3.

3x/3=−3/3

x=−1

Answer:

x=−1

Answer:

Step-by-step explanation:

We are going to assume that the cylinder is filled with water to the brim

Given that the data of the cylinder is

height h= 180 cm

radius r= 60 cm

The formula for the volume of a cylinder is

[tex]volume= \pi r^2h[/tex]

[tex]volume = 3.142*60^2*180\\\\volume= 3.142*3600*180\\\\volume= 20360.16 cm^3[/tex]

The volume of water in the cylinder is 20360.16 cm^3

Answer:

(-1,-9) PLEASE MARK BRAINLIEST!!!!!

Step-by-step explanation:

k(-4,-6) , m(-7,-3)

-7+4=-3

-3+6=3

-4+3=-1

-6-3=-9

(-1,-9)

The coordinate of L is  (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

if k is the midpoint of LM and k (-4,-6) and m(-7,-3).

It is required to find the coordinate of L:

Using the mid-point theorem:

Let the coordinate of L is (x, y)

(x - 7)/2 = -4

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

x - 7 = -8

x = -8 + 7

x = -1

(y - 3)/2 = -6

y - 3 = -12

y = -12 + 3

y = -9

The coordinate of L is  (-1,-9)

Thus, the coordinate of L is  (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).

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Answer:

24 : 84 = 2 : 7

Step-by-step explanation:

We can simplify the ratio 24 : 84 by dividing both terms by the greatest common factor (GCF).

The GCF of 24 and 84 is 12.

Divide both terms by 12.

24 ÷ 12 = 2

84 ÷ 12 = 7

Therefore:

24 : 84 = 2 : 7

Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= [tex]2^{2 + 3}[/tex]

= [tex]2^5[/tex]

Thus,

Yes, we add the exponents.

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Answer:134.7

Step-by-step explanation:

Answer:

The square root of 85

Step-by-step explanation:

The formula to find out the distance between the points is shown below:

The Distance is

[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

x_1 = -3

y_1 = -1

x_2 = 4

And, the y_2 = 5

Now place these values to the above formula

So, the distance is

[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]

= 9.22 units

Hence, the distance between points M and N is 9.22 units or the square root of 85

Hence, the second option is correct

Answer:

A

Step-by-step explanation:

The answer is A