An open box with a volume of 128 cm3 can be made
by cutting a square of the same size from each corner
of a square piece of metal 12 cm on a side and folding
up the edges. What is the length of a side of the square
that is cut from each corner?

The average rate of change of the function is -59.4

The formula for calculating the rate of change of the function is expressed as:

[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]

Given the function

[tex]f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120\\[/tex]

Get the value of f(2)

[tex]f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2\\[/tex]

Substitute into the formula to have:

[tex]f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4[/tex]

Hence the average rate of change of the function is -59.4

Learn more on the rate of change here: https://brainly.com/question/11627203

Answer:

y+3=-6(x+8)

Step-by-step explanation:

Because we already know a point and the slope, we can put our equation in the form y-y1=m(x-x1);

y+3=-6(x+8)

Answer:

A = 2.42 sq. meters

Step-by-step explanation:

13 feet = 13 × 0.305 = 3.965 meter

2 feet = 2 × 0.305 = 0.61 meter

A = lw

A = (3.965) × (0.61)

A = 2.41865 sq. meters

A = 2.42 sq. meters

Answer:

Kim's age is twice of that of her sister. We'll let k2 = Kim and k = Kim's sister.

So, k2. When you add Kim's age to her sister age you get 36.

Because Kim is twice the age of her sister k2. And because it said 'add' then we put a + sign. k2 + s = 36. Now let's solve it.  

k2 + k = 36 < Given

3k = 36 < Combine like terms

k = 12 < Divide both sides by 3

We know Kim's sister is 12 y/o but what about Kim herself? Earlier we assigned Kim to k2. Substitute 12 for k and you get 12(2) = 24

Kim's sister is 12 y/o and Kim is 24 y/o

Step-by-step explanation:

Mark as brainliest please

Kim's age = x

Age of her sister = y

Acoording to conditions, [tex]x=2y[/tex]

The equation  is,

[tex]x+y = 30 \\\\\implies 2y + y = 30\\\\\implies 3y = 30 \\\\\implies y = 10\\\\x = 2y = 2(10) = 20\\\\\text{Hence, Kim is 20 years old and her sister is 10 years old.}[/tex]

Answer:

12

Step-by-step explanation:

The Pythagorean theorem shows that 400 or 20² - 256 or 16² = 144 or 12² which means that the other side is 12

x=12

Answer:

Step-by-step explanation:

The vertex is halfway between the focus and the directrix:

  ((-7, 7) +(-7, 3))/2 = (-14, 10)/2 = (-7, 5) . . . . vertex coordinates

The value of p is the distance from the focus to the vertex:

  7 -5 = 2 = p

In vertex form, the equation of the parabola is ...

  y = 1/(4p)(x -h)^2 +k . . . . . . vertex (h, k)

  y = 1/8(x +7)^2 +5

Answer:

12 laps

Step-by-step explanation:

15÷4=3.75

45÷12=3.75

not sure whether it's true or not but at least I got the answer-

Answer:

Step-by-step explanation:

Euler's polyhedron formula, V − E + F = 2

Bottom left as it's measurements and shape are the closest to the one Jan has

Answer:

No, it is not a prime factorization, this is the real prime factorization

Step-by-step explanation:

2⁵x 3 x 5⁴ x 11

The first one was not a prime factorization because 8 is not a prime number.

The leading term is the term with the highest degree (highest exponent number). Here, the leading term is =》B) - 5x²y³

³ is the highest degree in the given expression.

_____

Hope it helps ⚜

Answer: The base is going to be 6 inches.

Step-by-step explanation:

So to find the area of a triangle we need to know the formula which is A= 1/2bh (A= one half times base times height) So, all we need to do is multiply the area by 2

32*2=72 Then to find the missing length, we divided the area by 12 which is 6.

Answer:

138

Step-by-step explanation:

Answer:

I'm not going to give the answer yet to see if you can figure it out.

Step-by-step explanation:

1. Find the place that your are rounding to. Ex: 6085

2. Then, look "nextdoor"; the number to the right of the number underlined. Ex: 6085

3. If this number is 1-4, then keep it the same. If it is 5-9, then add one to the digit to the left. Ex: 6085 becomes 6185

4. All of the digits to the right stay the same. Ones to the left become zero. Ex: 6185 becomes 6100.

I hope this helps!

Answer:

The answer is reflection on the y-axis

Step-by-step explanation:

Reflection on the x-axis will change the y-intercept

Horizontal shrink will change the slope but not to the point of making the 3 negative

Horizontal stretch is the same concept

Thus Reflection on the y-axis on the y-axisis the answer

Hope this helps!

Answer:

13 AND 14

Step-by-step explanation:

THERE IS NO PICTURE OR ANY ANSWERS

To Prove:-

JK=IJ

JK= ½IK = IJ= ½IK

JK= IJ(Equal Distance)

GK//HI (Parallel)

Therefore, JK congruent IJ

Hope This Helps

Answer:A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour.

Step-by-step explanation:

had this question

Answer:

276 guests

Step-by-step explanation:

Let the number of guests be n.  We are to find the value of n.

Then (1/3)n + (5/12)n + 69 = n, or

                (9/12)n + 69 = n or (12/12)n

Solving for n, we get    (3/12)n = 69, or (1/12)n = 23, or n = 12(23) = 276

There were 276 guests at the wedding.

Check:  Does (1/3)(276) + (5/12)(276) + 69 work out to 276?  yes

Answer:

0.7, 7/10

Step-by-step explanation:

3.5% of 20 would be 3.5/100x20 = 3.5/5 = 0.7. Also, 0.7 = 7/10.

Answer:

1 cm

Step-by-step explanation:

Answer:

5 milimeters

Step-by-step explanation:

Answer:

If he pays with 2 Hundred Dollar Bills he will get $45.52 in change.

Explanation:

$70.96 + $83.52 = $154.48

2 Hundred Dollar Bills = $200.00

$200.00 - $154.48

A) This event is a union. If a card is of the suit of clubs or a face card or both, then it belongs to the set of "cards with clubs or a face".

For the probability in question, we use the inclusion/exclusion principle:

P(club or face) = P(club) + P(face) - P(club and face)

That is, we add the probabilities of drawing a club and of drawing a face card, and subtract the probability of both conditions being met because, in a certain sense, we've double-counted the event of the card being both of clubs and a face. The sets "club" and "face" are not disjoint; there is overlap between them.

Then we have

P(club) = 13/52

P(face) = 12/52

P(club and face) = 3/52

so that

P(club or face) = 13/52 + 12/52 - 3/52 = 22/52 = 11/26

B) This event is an intersection. If a card is of the suit of clubs and a face card, then it belongs to both the set of clubs and the set of face cards.

We already found the probability of the intersection above:

P(club and face) = 3/52

C) If a given card is not a club and not a face card, this is the same as saying the card is neither a club nor a face card. In other words,

P(not club and not face) = P(not(club or face))

and this probability is complementary to the probability that a card is either a club or face, which is to say

P(not(club or face)) = 1 - P(club or face)

Using the result from part (A), we have

P(not club and not face) = 1 - 11/26 = (26 - 11)/26 = 15/26

Answer:

Y-intercept: -3

Equation: y = -2/3x -3

Step-by-step explanation:

Slope intercept equation: y = mx + b, m is the slope and b is the y-intercept

Substitute m with -2/3, your equation should now be y = -2/3x + b

To find the y-intercept, plug in the point (-12,5) and solve for b.

1. 5 = -2/3(-12) + b

2. 5 = 8 + b

3. b = 8 - 5

4. b = 3

Applying the leg rule, the value of z in the right triangle given is: √30 units.

The leg rule states that, hypotenuse/leg = leg/part.

Given the following:

Plug in the values into the leg rule:

10/z = z/3

z² = (10)(3)

z² = 30

z = √30 units

Learn more about the leg rule on:

https://brainly.com/question/25016594

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Answer:

see below

Step-by-step explanation:

here we are using the distributive property and noting that i^2=-1 so the answer is -36i-(63i^2) or -36i+63