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2 years ago

Suppose you wanted to make an open-topped box out of a flat piece of cardboard that is 25 inches long

Mathematics

2 answers:

grigory [225]2 years ago

7 0

i dont know man

Step-by-step explanation:

...

Artemon [7]2 years ago

6 0

Answer:

5 inches

Step-by-step explanation:

The side of the square you cut has length x.

The total length of the cardboard is 25". Once you cut the two corners, the length of the base of the box is 25 - 2x.

The total width of the cardboard is 20". Once you cut the two corners, the width of the base of the box is 20 - 2x.

The height of the box is x.

The volume of the box is

V = LWH

V = (25 - 2x)(20 - 2x)x

V = (2x - 25)(2x - 20)x

The volume is 750 cu in.

(2x - 25)(2x - 20)x = 750

Now try each value in the choices for x, and see which one works.

Try x = 3

(2(3) - 25)(2(3) - 20)(3) = (-19)(-14)(3) = 798

798 is not equal to 750, so x = 3 does not work.

Try x = 4

(2(4) - 25)(2(4) - 20)(4) = (-17)(-12)(4) = 816

816 is not equal to 750, so x = 4 does not work.

Try x = 5

(2(5) - 25)(2(5) - 20)(5) = (-15)(-10)(5) = 750

750 is equal to 750, so x = 5 does not work.

Answer: 5

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Find all solutions to 6x^4+13x^3–71x^2+67x=15

yarga [219]

Answer:

x = 1 or x = 3 / 2 or x = −5 or x = 1 / 3

Refer the attachment for steps

Hope it helps

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3 0

3 years ago

Ivan has 15 yards of green felt and 12 yards of blue felt to make 3 quilts if Ivan uses the same total number of yards for each

mixas84 [53]

Answer:

9 yards

Step-by-step explanation:

Let the length of each quilt be 'l'.

Given:

Length of green felt (g) = 15 yards

Length of blue felt (b) = 12 yards

Total number of quilts = 3

Now, the length of 3 quilts is given as:

$Total\ length=l+l+l=3l$ ----- (1)

As per question:

Total length = Length of green felt + Length of blue felt

Total length = $g+b$

$Total\ length=15+12=27$ --------- (2)

Now, comparing equations (1) and (2), we get:

$3l=27\\\\l=\frac{27}{3}\\\\l=9\ yards$

Hence, each quilt measures 9 yards in length.

3 0

3 years ago

For a given function ƒ(x) = x2 – x + 1, the operation –ƒ(x) = –(x2 – x + 1) will result in a

Mekhanik [1.2K]

Given:

The function is:

$f(x)=x^2-x+1$

To find:

The result of the operation $-f(x)=-(x^2-x+1)$ .

Solution:

If $g(x)=-f(x)$ , then the graph of f(x) is reflected across the x-axis to get the graph of g(x).

We have,

$f(x)=x^2-x+1$

The given operation is:

$-f(x)=-(x^2-x+1)$

So, it will result in a reflection across the x-axis.

Therefore, the correct option is A.

4 0

2 years ago

Use the number line to answer the question. Each tick represents 1 unit.

Yanka [14]

Answer and Step-by-step explanation:

Essentially, you are describing the position of point K using the location of the other points on the graph.

Let's start listing some descriptions:

K is:

3 more than H

2 more than J

3 less than L

4 less than M

7 less than N

12 less than P

Now look at the answer choices and compare it to what we wrote.

We see that the answer choices A, B, and D are incorrect (based on what we wrote), and that answer choice C is correct.

[C. 7 less than N] is the correct answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

3 0

3 years ago

Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin

Sauron [17]

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

$f^{-1}(x) = \sqrt{\frac{x -4}{4}}$ ---- function inverse

Step-by-step explanation:

Given

$f(x) = 70 \cdot 64x$

Solving (a): The amount present after 1 day.

Here, $x =1$

So:

$f(1) = 70 \cdot 64*1= 4480$

Solving (b): The amount present after 2 days.

Here, $x =2$

So:

$f(2) = 70 \cdot 64*2= 8960$

Solving (c): The amount present after 3 days.

Here, $x = 3$

So:

$f(3) = 70 \cdot 64*2= 13440$

Solving (d): The inverse function of:

$f(x)= 4x^2 + 4$

Replace f(x) with y

$y= 4x^2 + 4$

Swap x and y

$x= 4y^2 + 4$

Rewrite as:

$4y^2 = x -4$

Divide by 4

$y^2 = \frac{x -4}{4}$

Take square roots

$y = \sqrt{\frac{x -4}{4}}$

Replace y with function inverse

$f^{-1}(x) = \sqrt{\frac{x -4}{4}}$

6 0

2 years ago