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3 years ago

You are building a birdhouse that will have a volume of 128 in^3. the birdhouse will have the dimensions shown

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

5 0

$a.\\V-the\ volume\\\\V(w)=4\cdot w\cdot (w+4)=4w^2+16w\ [in^3]\\\\b.\\V=128\ in^3\ \ \ \Rightarrow\ \ \ 4w^2+16w=128\ \ \ \Rightarrow\ \ \ 4w^2+16w-128=0\ /:4\\\\w^2+4w-32=0\\\\w^2+4w+4-36=0\ \ \ \Leftrightarrow\ \ \ (w+2)^2=36\\\\w+2=6\ \ \ \ \ or\ \ \ \ \ w+2=-6\\\\w=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ w=-8\ \ \ \ (and\ \ \ w>0)\\\\w=4\ \ \ \Rightarrow\ \ \ w+4=8\\\\Ans.\ the\ dimensions\ of\ the\ birdhouse:\ \ 4\ in,\ 4\ in,\ 8 \ in$

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Elk middle school has 264 students. There are 84 students in the eighth grade. There are 22 fewer seventh-grade students than si

Vinvika [58]

Answer:

There were 84 students in 6th grade, 68 in 7th grade, and 90 in 8th grade.

Step-by-step explanation:

Given that Elk middle school has 264 students, and there are 84 students in the eighth grade, and there are 22 fewer seventh-grade students than sixth-grade students, to determine how many students there are in each grade, the following calculation must be performed:

(264 - 84) / 2) - 22 = X

(180/2) - 22 = X

90 - 22 = X

68 = X

6th grade = 84

7th grade = 68

8th grade = 90

Therefore, there were 84 students in 6th grade, 68 in 7th grade, and 90 in 8th grade.

3 0

3 years ago

1. A student has several boxes of penils in his backpack. Each box contains 12 pencils. The student

romanna [79]

Answer:

I think it is A because 12 is the slope and 3 is just b... try y = mx + b

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the shape of the grap

kap26 [50]

1) y-intercept => x = 0, => y = f(0) = 0 - 0 + 0 - 36 = -36

2) x-intercept => y = 0 => factor the function (start by dividing by x -2)

f(x) = (x-2)(x-3)(x-6) =0 => x =2, x = 3, x = 6 (these are the x-intercepts)

3) critical points:

between x = 2 and x = 3, there is a local maximum

between x =3 and x = 6 there is a local minimum

3) Shape.

The function comes growing from - infinity.

In the third quadrant the function is negative (it does not pass throuhg the second quadrant)

It enters to the fourth quadrant intercepting the y-axis at y = -36. It continues growing and intercepts the x-axis at x = 2.

It continues increasing until a maximum local positive value, starts to decrease, intercepts the x-axis at x = 3, continues decreasing, becomes negative, gets a local minimum in the fourth quadrant, starts to increase, intercepts the x-axis at x = 6, becomes positive, and continues growing.

3 0

3 years ago

Belle's Cupcakes recently sold 6 pistachio cupcakes and 8 other cupcakes. Considering this data, how many of the next 56 cupcake

VikaD [51]

Answer: 24 pistachios cupcakes.

Step-by-step explanation:

We know that:

They recently sold 6 pistachio cupcakes and 8 other cupcakes.

Then we can model this with the ratio 6:8

This means that for each 6 pistachio cupcakes sold, they also sell 8 of another type of cupcakes.

Whit this info, if they sell 56 cupcakes, how many of them will be pistachio cupcakes?

Using the ratio above, we must find a number N such that:

N*6 + N*8 = 56.

N*(6 + 8) = 56

N*14 = 56

N = 56/14 = 4.

This means that:

out of the 56 cupcakes, 4*6 = 24 are pistachios cupcakes

4*8 = 32 are other cupcakes.

Then you should expect that 24 out of the 56 cupcakes are pistachios cupcakes.

6 0

3 years ago

I NEED ANSWER SUPER BAD PLEASE!!!!!!!!!!!What is the greatest integer less than 100 for which the greatest common divisor of tha

PtichkaEL [24]

Answer:

Step-by-step explanation:

We will list out the numbers which are factors of 12. They include:

1, 2, 3, 4, 6, 12.

We need to get the highest number that has its greatest factor to be 4. It means that 6 and 12 cannot divide it.

To do this, we will write out the multiples of 4. They include:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88,92,96.

We will have to choose the highest number which only 4 can divide and 6 and 12 cannot divide.

Since we are looking for the largest, We can try dividing all the numbers by 4, 6, and 12 starting from 96.

We will quickly see that 4 can divide 92 but 6 and 12 cannot.

This gives us 92 as the answer.

4 0

3 years ago