Hot dogs come in packs of 10, while buns come in packs of eight. What are the least numbers of packs you should buy in order to have the same numbers of hot dogs and buns?.

The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

In this question,

we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]

We need to find the division of given rational expression.

We rewrite given rational expression as,

3x²-9 x / x-2 ÷ x² - 9 / 4 x-8

= 3x²-9 x / x-2 / x² - 9 / 4 x-8

= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )

= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]

= 12x / x + 3     .........(provided x ≠ -3)

Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

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The coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).

It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .

We have to find the coordinates of point L so that , ΔL K L is a scalene triangle.

What is a triangle ?

A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.

As per the question ;

The ΔL K L is a scalene triangle.

J has coordinates (0,0)

K has coordinates (2 a, 2 b) .

The possible coordinate of the point L will be (0,y) or (2a,y).

Let's check it.

Using the distance formula ;

JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]

JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]

JK = [tex]2\sqrt{a^2 + b^2}[/tex]

Similarly ;

JL = [tex]\sqrt{0^2 + y^2}[/tex]

JL = y

And

KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]

The sides are all of different lengths, so , we can conclude that this is a scalene triangle.

Thus , the coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).

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Each function's vertex, axis of symmetry, maximum or lowest value, domain, and range are all described as follows: Vertex: (125,125); range: (125,125); minimum: at y=125;  x=125; maximum: no., axis of symmetry is x=125.

The domain of a function is the set of values that we are allowed to enter into our function.

The set of values that a function can accept as input is known as its range.

            y=(x-125)²-125

we know that;

y=(x-h)²+k

Vertex: In this form, the vertex (or, in other words, the "pointy bit") is given to us in the (h ,k);here we have (125,125).

Axis of symmetry : Two equal segments of the parabola. It moves straight up and down via the vertex.

Thus, we may formulate an equation for the vertical line that passes through the vertex. It is x=125 in this query..

Maximum and lowest values: Here, we're concerned in examining the vertex to determine whether it is at the maximum or lowest of the parabola's range (i.e., when a negative sign is placed in front of the (x-h) = 0 term, respectively).

Range: The value of range is (125,∞ )

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Step-by-step explanation:

remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).

1.

domain : -infinity < x < +infinity

range : -1 <= y < +infinity

due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...

2.

domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.

the only forbidden value of x is therefore

3x + 5 = 0

3x = -5

x = -5/3

so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)

range : -infinity < y < +infinity

3.

domain : -infinity < x < +infinity

range : 0 <= y < +infinity

due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.

4.

this is 1/(2x) as I understand it.

similar to 2. we must avoid at 1/0 situation.

so, x must not be 0. everything else is possible

domain : (-infinity < x < 0) OR (0 < x < +infinity)

range : -infinity < y < +infinity

5.

everything is allowed and possible.

domain : -infinity < x < +infinity

range : -infinity < y < +infinity

Answer:

Step-by-step explanation:

The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.

Let 30minutes = 0.5 hours.

Let x represent the time for which the marshal has ran.

On this note, the robber must have galloped at; (x +0.5) hours.

Hence, it follows from the task content that if they are at the same distance from the bank; we have;

14(x+0.5) = 16(x)

14x + 7 = 16x

7 = 2x

x = 7/2 = 3.5 hours.

= 3.5 × 60minutes = 210minutes.

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Answer:

3500cm3

Step-by-step explanation: since A and B are equal, and B has a volume of 3500 cm3 then A will have the same.

Extra: The horizontal measure of A is 1500 and the verticle is 1500

Answer:

Step-by-step explanation:

change = dollar_amount - spent_amount

change = 50 - 36.85

change = 13.15

Answer:

3, 9% more people have green as their favorite color over yellow. 4. Picture is cut off so I can't see sorry 5. science and social studies 6. Mike spends 40% more time studying math then he does science

Step-by-step explanation:

Based on the fact that the right line is a reflection across the y-axis, the lines are the same, they are just in a different position.

What is a Reflection?

This refers to the rigid transformation type that is used to represent an image and does not change its size or length of it.

With this understanding, we can see that the pre-image and the image in a rigid transformation are congruent which makes the lines to be the same, even if they are in a different position.

Answer: The answer would be x = -3 + 0.5y.

Step-by-step explanation: pls give me brainliest. may help w/ my depression.

By Euclid's axioms we proved that AC=BD

Things which are equal to the same thing are also equal to one another.

If equals be added to equals, the wholes are equal.

If equals be subtracted from equals, the remainders are equal.

Things which coincide with one another are equal to one another.

The whole is greater than the part.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

    BD=BC+CD ........(2)

   subtract 1-2

we get, AC-BD=AB+BC-BC-CD

  AC-BD=AB-CD

we know AB=CD so we get

  AC-BD=0

 AC=BD

Hence, Proved

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Answer:

We established that AC=BD using Euclid's axioms.

Step-by-step explanation:

Things that are equivalent to one another are also equivalent to the same object.

The wholes are equal if equals are added to equals.

The remainders are equal when equals are subtracted from equals.

Things are equivalent to one another if they occur simultaneously.

A component cannot possibly equal the whole.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

   BD=BC+CD ........(2)

  subtract 1-2

we get, AC-BD=AB+BC-BC-CD

 AC-BD=AB-CD

we know AB=CD so we get

 AC-BD=0

 AC=BD

Hence, Proved

Answer:

[tex]\displaystyle 25 = GQ[/tex]

Step-by-step explanation:

If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:

[tex]\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}[/tex]

Plug the result into the expression for the length of GQ to get twenty-five units.

I am joyous to assist you at any time.

Answer:

26 miles

Step-by-step explanation:

add 9 miles to 17 miles= 26 miles

According to the question, to check whether the events are mutually exclusive or not mutually exclusive for the rolling pair of dice to get the total either as six or ten.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time .For instance, in any event nobody can run forward or backward together at the same time.

Rolling a pair of dice to get the sum as 6, then is not mutually exclusive.

The calculation is as shown below:

P(E) = 6+5-1/36

= 10/36

= 5/18

= 27.8 %

Now, rolling a pair of dice to get either the sum as 6 or 10.

P(6 or 10)

= P(6)+P(10)

= 5/36+ 3/36

= 8/36

= 2/9

= 22%

Hence, it is not mutually exclusive event because the calculated percentage is 22%.

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limx→0sinaxcosbxsincx=limx→0(cosbx⋅sinaxax⋅cxsincx⋅ac)=ac

We need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).

It is given that Δ MNO with right angle at point M has legs of lengths a and 2a .

We have to position the triangle on coordinate plane.

What is a right angled triangle ?

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

As per the question ;

The triangle is a right angle triangle, so it's two sides can be located

on axis.

Place the right angle of the triangle Δ MNO at M.

i.e., M will have coordinates (0,0)

The origin will allow the two legs to be along the x and y-axes , so position the triangle in the first quadrant.

As N is on the y-axis ;

Its x-coordinate will be 0 and the y-coordinate will be a , because the leg is a units long.

i.e., N will have coordinates (0,a)

As O is on the x-axis,

its y-coordinate will be 0 and the x-coordinate will be 2a , because the leg is 2a units long.

i.e.,

O will have coordinate (2a,0)

We can put these coordinates after placing the triangle in the first quadrant i.e., M (0,0) , N (0,a) & O (2a,0).

Thus , we need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).

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The joules are in 12.1 g of parsley is 24.806936 Joules of energy

10g has 4.9 cal

1g has 4.9/10 cal

Energy in 12.1 g = 4.9 x 12.1 / 10 = 5.929 Cal = 5.929 x 4.18400 = 24.806936 Joules of energy [1 calorie = 4.18400]

In the International System of Units (SI), a joule is a unit of work or energy equal to the work done by a force of one newton acting through one meter. It is named after the English scientist James Prescott Joule and equals 107 ergs, or about 0.7377 foot-pounds. The joule is equivalent to one watt-second in electrical terms, which is the amount of energy released in one second by a current of one ampere through a resistance of one ohm.

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The surface area of earth is 514.4million [tex]Km^{2}[/tex] and the volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].

Radius of Earth = 6400 (approximately).

Earth is a sphere. So by using the formula of Surface Area of sphere we can calculate the Surface area of earth as follows,

Surface Area of Earth = 4[tex]\pi r^{2}[/tex] = 4 × (3.14) × [tex](6400)^{2}[/tex]

                                    =  4 × 3.14 × 40960000

                                    = 514457600 [tex]Km^{2}[/tex]

                                    = 514.4million [tex]Km^{2}[/tex]

The surface area of earth is 514.4million [tex]Km^{2}[/tex] .

Similarly, by using the formula of volume of sphere we can calculate the volume area of earth as follows,

Volume of Earth = (4/3)[tex]\pi r^{3}[/tex]

                           = (4/3)×(3.14)×[tex](6400)^{3}[/tex]

                           =(1.3333)(3.14)(2.6214 × [tex]10^{11}[/tex])

                           = 1.0975 × [tex]10^{12}[/tex] [tex]Km^{3}[/tex]

                           = 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex]

The volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].

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Given the question, <11 and <14 are supplementary because they sum up to give 180 degrees. Detail below

These are angles that sum up to give 180 degrees. On the other hand, angles on a straight line sum up to give 180 degrees.

Considering the question given above, we can prove that <11 and <14 are supplementary as follow:

<11 + <12 = 180 (angle on straight line)

But

<12 = <14 (corresponding angles)

Thus,

<11 + <14 = 180

Recall

Angle that sum up to give 180 are called supplementary angles

Therefore,

<11 + <14 = 180 => supplementary

From the illustrations given above, we can see clearly that <11 and <14 are supplementary angles

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The missing term is 6.

Here the sequence is -1,__, 11...

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the sequence is in an arithmetic sequence, as there is a common difference between the two numbers.

To find the nth term of the sequence we have a formula:

[tex]a_{n}[/tex] = a + (n-1)d

From this we can find a common difference, as we know the 3rd term of the sequence.

[tex]a_{3}[/tex] = -1 + (3-1) d

11 = -1 + 2d

2d = 12

d = 6

Now we have to the 2nd term of the series we have

[tex]a_{2}[/tex] = -1 + (2-1) 6

   = -1 + 6

   = 5

Therefore the 2nd i.e., the missing term of the sequence is 5

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Based on the given task content, the number of members in the marching band if the band has fewer than 200 members is 195 members

When the band members are told to line up in rows of eight but five is left over. This means the overall number is an odd number.

When they are lined up in rows of six, but three are left over. So, eliminate numbers with 3, 5, 6 ,9, 0.

Finally they are lined up in rows of seven, but four are left over.

So, eliminate numbers with 7 also.

So, all eliminated numbers are : 2,3,4,5,6,7,8,9,10

Left numbers are 1.

Given is that the band has fewer than 100 members. So, it can be 71 ,81 ,91

199, 195, 193, 191

We can check with 81.

81/4 = 20 remainder 1

81/6 = 13 remainder 3

81/7 = 11 remainder 4

So, the answer is 81.

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Answer:

1) 15

Step-by-step explanation:

The smallest integer is 15 because,

There are 7 consecutive integers with n + 6 being the largest, therefore:

7n + 21 = 6(6 + n)

7n + 21 = 36 + 6n

7n - 6n + 21 = 36

n + 21 = 36 ⇒ n = 36 - 21 = 15

Hope this helps!

2) -3  

2/5 = .4

The coordinates of E in Quadrant lll is (3 - [tex]2\sqrt{3}[/tex], -4)

Given,

m < F = 90°

E (x, y) in quadrant lll

F(-3, 4), G(-3, 2)

FG = The longer leg.

FG = [tex]\sqrt{(-3-(-3)^{2} )+(2-(-4)^{2} }[/tex] = [tex]\sqrt{36}[/tex] = 6

FE = [tex]\frac{FG}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }[/tex] = 2[tex]\sqrt{3}[/tex]

GE = 2FE = 2 × 2√3 = 4√3

ΔEFG is a 30° - 60° - 90° triangle with the longest leg FG = 6.

We apply the 30° - 60° - 90° triangle theorem to determine the short side FE and the hypotenuse GE.

l = 4√3

h = 2√3

[tex]\sqrt{(x-(-3))^{2} +(y-(-4))^{2} }[/tex] = (2√3)²

[tex]\sqrt{(x-(-3))^{2} +(y-2)^{2} }[/tex] = (4√3)²

∴ (x + 3)² + ( y + 4)² = 12

   (x + 3)² + (y - 2)² = 48

Solving this, we get:

Coordinates of E as (3 - 2√3, -4)

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Answer:

[tex] \sf \large \: p = 8[/tex]

Step-by-step explanation:

Let's solve the equation step by step,

p – 6 = 2

Add +6 to both sides

p - 6 + 6 = + 6

p = 8

Answer:

8

Step-by-step explanation:

The approximate distance from Charlotte to El Paso is  1. 62 × 10 miles . Options A and C

From the information given, we have that;

To determine the distance from Charlotte to El Pasco, we have the expression

= 7 × distance from Charlotte to Knoxville

Substitute the value

= 7 × 2.31 × 10 miles

= 1. 62 × 10 miles

Thus, the approximate distance from Charlotte to El Paso is  1. 62 × 10 miles . Options A and C

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The measure of ∠B rounded to the nearest whole number is 71°

From the question, we are to calculate the measure of ∠B.

In the given diagram, we have a right triangle.

In the right triangle,

The hypotenuse is 21

Adjacent is 7

From SOH CAH TOA,

We have that

sin θ = Opposite / Hypotenuse

cos θ = Adjacent / Hypotenuse

tan θ = Opposite / Adjacent

Thus,

we can write that

cos B = 7/21

cos B = 1/3

B = cos⁻¹(1/3)

B = 70.528

B ≈ 71°

Hence, the measure of ∠B rounded to the nearest whole number is 71°

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Answer:

I believe the answer is 30.

Step-by-step explanation:

-

The conclusion based on this data is that C. The hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.

It should be noted that from the information, the change in plant height for each group over a two-week period was averaged and recorded.

It should be noted that as more fertilizer was added, the height of the plant reduced. This shouldn't be so.

Therefore, the conclusion based on this data is that the hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.

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Answer: C

Step-by-step explanation: Edge 2022

Answer:

x = 24

Step-by-step explanation:

[tex]\frac{x}{8}[/tex] = 3 ( multiply both sides by 8 to clear the fraction )

x = 8 × 3 = 24

Answer: 24

Step-by-step explanation:

x/8 = 3

x = 3x8

x = 24

Answer:

4

Step-by-step explanation:

The slope of the line with points p(x, y) and p′(x′, y′) is given by:

[tex] (\frac{x. \: - \: x}{y. \: \: - y } )[/tex]

[tex] (\frac{8 - ( - 4)}{5 - 2} )[/tex]

12/3

slope = 4