A shipping box in the shape of a cube has an edge length of 8 inches. It can hold 8 mugs with no extra space between them. If the dimensions of the shipping box are all doubled, what is the maximum number of mugs that the larger box can hold? 16 24 48 64

Answer:

The value of k =3

Step-by-step explanation:

[tex]x^2+y^2-6y-12=0[/tex] We need to solve this equation to become in standard form to find the value of k.

[tex]x^2+y^2-6y-12=0\\x^2+y^2-6y = 12\\(x)^2 +(y^2-2(y)(3)+(3)^2) = 12 +(3)^2\\(x)^2+(y-3)^2 = 12+9\\(x)^2 +(y-3)^2 = 21[/tex]

The given standard form is:

[tex]x^2+(y-k)^2=21[/tex]

Comparing it with [tex](x)^2 +(y-3)^2 = 21[/tex]

The value of k =3

Answer:

k = 3

Step-by-step explanation:

Equation of the given function has been given as x² + y² - 6y - 12 = 0.

We have to convert this equation in the standard form of x² + (y - k)² = 21 to get the value of k.

x² + y² - 6y - 12 = 0

x² + y² - 6y + 9 - 9 - 12 = 0

x² + [y²- 2(3y) + 3²] - 21 = 0

x² + (y - 3)²- 21 = 0

x² + (y - 3)² = 21

Now by comparing this equation with the standard form of the equation we get the value of k = 3

Answer:

1st option

Step-by-step explanation:

By observation, we can see that the graph crosses the y-axis at y = -2. Therefore the y-intercept is -2.

we can also see that the graph intersects the axes at  (0,-2) and (3,0)

the formula for a linear slope when given two points (x1, y1) and (x2,y2) is given by :

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

In our case, x1 = 0, y1 = -2, x2= 3 and y2 = 0

hence m = (0 - (-2)) / (3-0) = 2/3

Hence the slope is 2/3

Only option 1 satisfies the values for both y-intercept and slope that we calculated.

Answer:

A) The slope is 2/3 and the y intercept is -2

Step-by-step explanation:

This is the correct answer for edge

Check the picture below.

By using a right triangle rectangle, we will see that the distance is equal to 3 miles.

You can think of the distance as the hypotenuse of a right triangle with legs that measure 1.8 miles and 2.4 miles.

Then, using the Pythagorean theorem we can write:

H^2 = (1.8 mi)^2 + (2.4 mi)^2

H = √((1.8 mi)^2 + (2.4 mi)^2) = 3mi

So the distance between Callie's house and the grocery store is 3 miles.

If you want to learn more about right triangles, you can read:

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Answer:

First subtract 7 from each side of the equation

Step-by-step explanation:

2x+7 = 13

First subtract 7 from each side of the equation

2x+7 -7 = 13-7

2x = 6

Next divide each side by 2

2x/2 = 6/2

x=3

Answer:

X=3

The answer should have a positive sign.

Step-by-step explanation:

First, you subtract by 7 both sides of equation.

2x+7-7=13-7

Simplify.

13-7=6

2x=6

Then, divide by 2 both sides of equation.

2x/2=6/2

Simplify, to find the answer.

6/2=3

X=3 is the correct answer.

Answer:

b.

Step-by-step explanation:

Answer:

Answer is (c) knowing that it is going to rain tomorrow, and going to bed before 9

Step-by-step explanation:

Because they are not related in any way, going to bed early doesn't effect the weather.

Option C, knowing that it is going to rain tomorrow, and going to bed before 9 p.m, represents independent events as the outcome or occurrence of one does not affect the other probabilistically.

The question at hand is asking which of the provided options are examples of independent events. In probability theory, independent events are those whose occurrence or outcome does not affect the probability of the other occurring. Going through the options provided:

It's essential to differentiate between events that may logically seem connected and those that truly affect each other's outcomes in the context of probability theory.

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For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:

[tex]l ^ 2 + l ^ 2 = x ^ 2[/tex]

Where:

l: It's the side of the square.

[tex]2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}[/tex]

We know that the area of a square is given by:

[tex]A = l ^ 2[/tex]

So, the area is:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer:

[tex]A = \frac {x ^ 2} {2}[/tex]

Answer:

Option A: 1/2 x^2

Step-by-step explanation:

Answer:

x = 4.

Step-by-step explanation:

log(x) + log(x+5) = log(6x +12)

log x(x +5) = log(6x + 12)

Therefore x(x + 5)= 6x +12

x^2 + 5x - 6x - 12 = 0

x^2 - x - 12 = 0

(x - 4)(x + 3) = 0

x = -3, 4.

logs of negative values do not exists so the anser is x = 4.

©

The value of x  is -3 , 4 ; option C is the solution to the equation

What is an Equation ?

An equation is a mathematical statement between two algebraic expressions equated by an equal sign.

A logarithm equation is given in the question.

log(x)+ log(x+5) = log(6x +12)

The equation of Logarithm says

log (x .y) = log x + log y

From the equation

log(x)+ log(x+5) can be written as log (x(x+5))

log (x(x+5)) = log(6x +12)

We can relate this as

(x(x+5)) = 6x +12

x² + 5x = 6x +12

x² -x -12= 0

x² -4x +3x -12 = 0

x (x-4)+3(x-4) = 0

(x+3)(x-4) = 0

x = -3 , x=4

Therefore the option C is the solution to the equation

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To solve the equation, we can use algebraic techniques to find the value of 'x'.

To solve the equation, we can let the number be represented by 'x'. The equation can then be written as: (1/5)x + 5x = 7x - 18. Simplifying this equation gives us: (1/5)x + 5x - 7x = -18. Combining like terms, we get: (6/5)x = -18. Dividing both sides by 6/5 gives us the value of 'x'.

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Follow below steps:

The question involves solving a linear equation to find an unknown number. To solve "one fifth of a number plus five times that number is equal to seven times the number less 18", the first step is to let "x" represent the unknown number and then create an equation based on the given information.

We start by translating the words into an equation:

One fifth of a number can be written as "(1/5)x".

Five times that number is written as "5x".

Seven times the number less 18 is written as "7x - 18".

So our equation becomes "(1/5)x + 5x = 7x - 18". Simplifying, we get "(6/5)x = 7x - 18".

Combining like terms yields "(1/5)x = -18", and we solve for x to find the value of the unknown number: "x = -90".

Through this process, the student can identify the value of the number in question.

Answer:

B. Pythagorean triple

Step-by-step explanation:

To prove Pythagorean triple, we must prove that

ML² + LN² = MN²

or MN = √( ML² + LN²)

= √( 9² + 12²)

= √( 81 + 144)

= √( 225)

= 15 = value of MN given in diagram (proven)

Answer:

True

Step-by-step explanation:

This is a parabola.  The coefficient of the x^2 term is -3

Since it is negative, the parabola opens downward

Answer: False

Step-by-step explanation: A-Pexw

First note that f(x) means the same thing as y. To solve for f(x) or y you need to plug in -5 for x and solve using the rules of PEMDAS

5(-5) + 40

-25 + 40

15

When x is -5 then y is 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Part 1)

a.1) The central angle of pentagon is 72°

a.2) The central angle of hexagon is 60°

a.3) The central angle of decagon is 36°

a.4) The central angle of dodecagon is 30°

b.1) The measure of each interior angle of pentagon is 108°

b.2) The measure of each interior angle of hexagon is 120°

b.3) The measure of each interior angle of decagon is 144°

b.4) The measure of each interior angle of dodecagon is 150°

Part 2) The central angle and the interior angle are supplementary angles

Part 3) As the number of sides increases, the central angle decreases and the interior angle increases.

Step-by-step explanation:

Part 1. For each polygon, include the following information in the paragraph box below:

a) What was the central angle you used to locate the vertices? Show your calculation.

we know that

To find the central angle divide 360 degrees by the number of sides of the polygon

case a.1) Pentagon

The pentagon has 5 sides

so

The central angle is equal to

360°/5=72°

case a.2) Hexagon

The pentagon has 6 sides

so

The central angle is equal to

360°/6=60°

case a.3) Decagon

The pentagon has 10 sides

so

The central angle is equal to

360°/10=36°

case a.4) Dodecagon

The pentagon has 12 sides

so

The central angle is equal to

360°/12=30°

b) What is the measure of each interior angle of the polygon? Show your calculation

we know that

The sum of the interior angle of the polygon is equal to

S=(n-2)*180°

where

n is the number of sides

To find each the measure of each interior angle, divide the sum of the interior angles by the number of sides

case b.1) Pentagon

The pentagon has 5 sides

so

S=(n-2)*180°

S=(5-2)*180°=540°

Divide by the number of sides

The measure of each interior angle is equal to

540°/5=108°

case b.2) Hexagon

The hexagon has 6 sides

so

S=(n-2)*180°

S=(6-2)*180°=720°

Divide by the number of sides

The measure of each interior angle is equal to

720°/6=120°

case b.3) Decagon

The hexagon has 10 sides

so

S=(n-2)*180°

S=(10-2)*180°=1,440°

Divide by the number of sides

The measure of each interior angle is equal to

1,440°/10=144°

case b.4) Dodecagon

The hexagon has 12 sides

so

S=(n-2)*180°

S=(12-2)*180°=1,800°

Divide by the number of sides

The measure of each interior angle is equal to

1,800°/12=150°

Part 2. What is the relationship between the central angle and the interior angle?

we know that

The sum of the central angle plus the interior angle is equal to 180 degrees

therefore

The central angle and the interior angle are supplementary angles

Verify

Pentagon

72°+108°=180°

Hexagon

60°+120°=180°

Decagon

36°+144°=180°

Dodecagon

30°+150°=180°  

Part 3. As the number of sides increases, how do the angles change?

we know that

As the number of sides increases, the central angle decreases and the interior angle increases.

Answer:

1. 53 by 58 , 222 ft

2. 321000

3.1080

4.  3.5

Step-by-step explanation:

1. 23+15+15 = 53

28+15+15= 58

53+53+58+58= 222

[tex]3\div\dfrac{1}{2}=3\cdot2=6[/tex]

Answer:

6

Step-by-step explanation:

3 divided by 1/2

To solve this first put a 1 as the denominator for the 3 to make it a fraction

3/1 divided by 1/2

To divide fraction you need to change the division sign to a multiplication sign and the second fraction into its reciprocal

3/1*2/1

Now multiply across

6/1 which is also 6

Answer:

x.

Step-by-step explanation:

h(f(x) = x.

For example the inverse of  f(x) = 2x  is g(x) = x/2

f((gx)) 2 (x/2)

= 2x / 2

= x.

If h(x) is the inverse of f(x), then  the value of h(f(x)) is:

                                   x

Inverse of a function-

The inverse of  a given function is a function which reverses the action of the other function.

Also, the composition of a function and it's inverse no matter in which order they are applied always gives us the identity function.

( Identity function-- Identity function is a function which when applied to some other function always retains that function )

i.e.   If h(x) is the inverse of f(x) ; then we have:

                  [tex]h(f(x))=f(h(x))=x[/tex]

The statement that is true in every aspect regarding his claim is:

The series is given as:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9[/tex]

which could also be written by:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n(\dfrac{1}{3})^n\cdot 3^2[/tex]

i.e.

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{-n}\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{2-n}[/tex]

which is not equivalent to: [tex]\sum_{n=0}^{3} 3^{2-n}[/tex]

Since,  on expanding the actual series we get the sum as:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=(-\dfrac{1}{3})^0\cdot 9+(-\dfrac{1}{3})^1\cdot 9+(-\dfrac{1}{3})^2\cdot 9+(-\dfrac{1}{3})^3\cdot 9\\\\\\=9-\dfrac{1}{3}\times 9+\dfrac{1}{3^2}\times 9-\dfrac{1}{3^3}\times 9\\\\\\=9-3+1-\dfrac{1}{3}\\\\\\=\dfrac{22}{3}[/tex]

Now, the expansion of:

[tex]\sum_{n=0}^{3} 3^{2-n}[/tex] is:

[tex]\sum_{n=0}^{3} 3^{2-n}=3^2+3^1+3^0+3^{-1}\\\\\\=9+3+1+\dfrac{1}{3}=\dfrac{40}{3}[/tex]

Answer:

D in short

Step-by-step explanation:

Ed2021

Answer: x=8

Step-by-step explanation:

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

Set the first factor equal to 0 and solve.

x−8=0

x−8=0

Answer:

35 cubic inches

Step-by-step explanation:

V= lwh

1*5*7= 35

Answer:

The answer is 35 cubic inches.

Step-by-step explanation:

For volume problems (with prisms, such as cardboard boxes) all you have to do is multiply all the dimensions, height, width, and length.

Answer:

B. 11x^2 − x + 10

Step-by-step explanation:

(5x^2 + 2x + 1) + (6x^2 − 3x + 9)

I like to line them up vertically

  (5x^2 + 2x + 1)

+ (6x^2 − 3x + 9)

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

11 x^2  -  x   + 10

Answer:

0.65 > 3/5

Step-by-step explanation:

3/5 is 0.6 in fraction form

0.65 is greater than 0.6.

Therefore, 0.65 is greater than 3/5.

hope this helps!

Answer: grade 7

Step-by-step explanation:

Grade 7: 20/22 students in club

Grade 8: 20/28 students in club

Grade 7 has higher % of students in science club

Answer:

Grade 7

Step-by-step explanation:

The relative row frequency of members of the Science Club is: Member of Science Club / Total

in Grade 7: 20/22 = 0.91.

And in Grade 8 is: 20/28 = 0.71.

Then, students of Grade 7 are more likely to be members of the science club.

Answer:

g(x) = (x + 3)^2 + 5(x + 3) - 1

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  f(x) = x^2 + 5x - 1.

Shifting the graph of this function 3 units left results in

g(x) = (x + 3)^2 + 5(x + 3) - 1

Answer:

R = 134

Step-by-step explanation:

This is a 5 sided figure.  The interior angles add to  (n – 2)180  where n is the number of sides

(5-2) * 180 = 540

Add up all the angles and set it equal to 540

R+ 78+109+113+106 = 540

Combine like terms

R + 406 = 540

Subtract 406 from each side

R +406-406 = 540-406

R = 134

Answer:

Step-by-step explanation:

24 = 8 · 3

32p = 8 · 4p

24 + 32p = 8 · 3 + 8 · 4p = 8 · (3 + 4p)

Answer:

It’s a

Step-by-step explanation:

Answer:

It's A: 4.8 lb

Step-by-step explanation:

4/6 divided by 2/6 is 2.

you multiply the 4/6 by 6/2 to get 24/12. You then simplify it and get 2 as your answer.

Answer:

I mean if it's there dream then why stop it? Its there life and we can't really stop that cause regardless what you say or do they're gonna find a way to do it. So I would say yes.

I am going to assume this is a poll? For our opinions?

If so then yes, I think that kids should be allowed to play dangerous sports..Football fatalities remain rare, but the game can be dangerous. That doesn't mean kids shouldn't play, same with hockey and any other

Answer:

[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]

Step-by-step explanation:

[tex]2x^2-5x+1=3[/tex]

To solve for x, we make right hand side 0

Subtract 3 from both sides

Given equation becomes

[tex]2x^2-5x-2=0[/tex]

We apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=2, b=-5, c=-2

[tex]x=\frac{5+-\sqrt{5^2-4(2)(-2)}}{2(2)}[/tex]

[tex]x=\frac{5+-\sqrt{41}}{4}[/tex]

[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]