my Christmas present to you​

Answer:

[tex]\sqrt{49 - x^{2}}[/tex]

Step-by-step explanation:

Pythagorean theorem  [tex]c^{2} = a^{2} + b^{2}[/tex] Then:

[tex]7^{2} = x^{2} + y^{2}\\y^{2} = 7^{2} - x^{2}\\y^{2} = 49 - x^{2}\\y = \sqrt{49 - x^{2}}[/tex]

the lenght of the third side = [tex]\sqrt{49 - x^{2}}[/tex]

Ф = [tex]sin^{-1} (\frac{x}{7} )[/tex]

Ф = [tex]cos^{-1} (\frac{y}{7} )[/tex]

Ф = [tex]tan^{-1} (\frac{x}{y} )[/tex]

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

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[tex]\\ \sf\Rrightarrow (10101)_2[/tex]

[tex]\\ \sf\Rrightarrow 1\times 2^0+0\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4[/tex]

[tex]\\ \sf\Rrightarrow 1+4+16[/tex]

[tex]\\ \sf\Rrightarrow (21)_{10}[/tex]

Answer:

undefined

Step-by-step explanation:

Step-by-step explanation:

(7,9)and (5,8)

x1,y1 x,y

now

x=(x1 + x2)divide by 2

now putting the value

5 = (7+ x2) by 2

2 is in divide then get the 2 in right side with 5 in muntiply form

5×2=7+x2

10=7+x2

10 - 7=x2

x2=3

using the same process do it

y=(y1+y2) by 2

Answer: 7678687nx09

dad

Step-by-step explanation:

[tex]3 \times \frac{5}{11} [/tex]

turns into

[tex] \frac{3}{1} \times \frac{5}{11} = \frac{15}{11} = 1 \frac{4}{11} [/tex]

[tex]12 \times \frac{3}{4} = \frac{12}{1} \times \frac{3}{4} = \frac{36}{4} = 9[/tex]

Because 36 goes into 4 nine times.

Answer:

Approximately 9666 people

Step-by-step explanation:

We can describe this trend as the formula [tex]P=8914(1.0136)^{n}[/tex] where [tex]P[/tex] is the population of the town [tex]n[/tex] years after 2000.

Therefore, the population of the town in 2006 will be [tex]P=8914(1.0136)^{6}\approx9666[/tex]

Answer:

-4

Step-by-step explanation:

That's the answer above

Answer:  Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size.

Step-by-step explanation: pls give brainlist

Answer:

(y-7) +25

Step-by-step explanation:

( y-7 ) +25

25 is added after the difference. so that's only the answer.

Answer:

A.

(w.3)+5

=w. 3+5

=w . 8

B.

(w.30) +5

=w.30+5

=w . 35

C.

(w.30) + (w.5)

=w.30+w.5

=w+w.30.5

=2w . 35

D.

(w.5)+3

=w . 5+3

=w . 8

so, B is the expression which is equivalent

to w . 35

Answer:

Step-by-step explanation:

The number of books the library holds before it received the grant is 17,312 books

Let the original number of books in the library be x

If the collection  now is five times more than the original number of books, then;

x + 69,248 = 5x

5x - x = 69,248

4x = 69,248

x = 69,248 /4

x = 17,312

Hence the number of books the library holds before it received the grant is 17,312 books

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Answer:

2 hours; $130

Step-by-step explanation:

We can do this by setting up an equality since we are finding when they are the same. Say x is the number of horus:

65 * x = 60 + 35* x

30 * x = 60

x = 2 hours

The cost will be the same at two hours, and plugging it in, we can get 65*2=130.

Answer:

That is the answer

The answer is

Answer:

True; this [tex]x[/tex] would indeed be a factor of [tex]z[/tex].

Step-by-step explanation:

"[tex]x[/tex] is a factor of [tex]y[/tex]" means that there is a whole number [tex]p[/tex] such that [tex]x\, p = y[/tex].

Likewise, [tex]y[/tex] is a factor of [tex]z[/tex] if and only if there is a whole number [tex]q[/tex] such that [tex]y\, q = z[/tex].

This [tex]x[/tex] would be a factor of [tex]z[/tex] if there is some whole number [tex]r[/tex] such that [tex]x\, r = z[/tex].

The first equality [tex]x\, p = y[/tex] implies that [tex]y[/tex] may be substituted with [tex]x\, p[/tex].

Substitute the [tex]y[/tex] in the second equality [tex]y\, q = z[/tex] with [tex](x\, p)[/tex] to obtain:

[tex](x\, p)\, q = z[/tex].

Rearrange to obtain:

[tex]x\, (p\, q) = z[/tex].

The product of two whole numbers is still a whole number. Since [tex]p[/tex] and [tex]q[/tex] are both whole numbers, [tex]p\, q[/tex] would also be a whole number.

Thus, if [tex]r = p\, q[/tex], then [tex]x\, r = x\, (p\, q) = z[/tex], while [tex]r[/tex] would be a whole number.

Therefore, this [tex]x[/tex] would indeed be a factor of [tex]z[/tex].

Answer:

Here is what I think the answer is.

n+2n+8 = 5n-10

3n+8 = 5n-10

    -8         -8

3n = 5n-18

-5n  -5n

-2n = -18

----      -----

-2         -2

n = 9

Step-by-step explanation:

It would be 8 + 2 = 10 - 5n I think.

y = x is a positively sloped line, meaning that it points to the right. It also has a y-intercept of (0,0).

y = -1/2x + 3 is a negatively sloped line, meaning that it points to the left. It has a y-intercept of (0,-3).

The correct graph is Graph A.

Hope this helps! :)

Answer:

x = 19

Step-by-step explanation:

3x - 3 = 6(x - 10)

3x - 3 = 6x - 60 Use dist property

Subtract 3x from both sides

-3 = 3x - 60

Add 60 to both sides

57 = 3x

Divide both sides by 3

19 = x

Answer:

B and A

Step-by-step explanation:

What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).

The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…

I hope this helps :)!

Answer:

  1 in : 50 mi

Step-by-step explanation:

You can eliminate the choices that don't make any sense by comparing the given numbers to the offered choices:

  given:

  15 in : 750 mi

__

A. 1 in : 50 mi . . . . . . . . equivalent to dividing the given ratio numbers by 15

B. 15 in : 100 mi . . . . . . same inches, wrong miles

C. 1 in : 750 mi . . . . . . . wrong inches, same miles

D. 1 mi : 50 in . . . . . . . . both inches and miles are wrong (the ratio has the units swapped)

__

In the given ratio, the numerical number of miles (750) is 50 times the numerical number of inches (15). This is the ratio you're looking for among the answer choices. You need to pay attention to both the numerical values and their associated units.

Answer:

Point B is

Step-by-step explanation:

Answer:

B (-2,-4)

Step-by-step explanation:

Answer:

Slope:40 Y-intercept: 70 (AKA, B)

Step-by-step explanation:

y=mx + b

(mx is slope, the x can show u where the slope is usually located.)

let me know if im wrong

Answer:

2p + 3e = 14

Step-by-step explanation:

The required equation is [tex]0.50\ p+0.75\ e= 3.50\\[/tex]

Given, Alejandro bought $3.50 worth of pencils and erasers at the school store.

The cost of each pencil is $0. 50.

The cost of each eraser is  $0. 75.

Since He denotes no. of pencil by p and no. of eraser by e, so the required equation will be,

[tex]0.50\ p+0.75\ e= 3.50\\[/tex].

Hence the required equation is [tex]0.50\ p+0.75\ e= 3.50\\[/tex]

For more details on Equation solving follow the link:

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Answer:3,312.50

Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 2500 is 100%, so we can write it down as 2500=100%.

4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.

5. Now we have two simple equations:

1) 2500=100%

2) x=3.25%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

2500/x=100%/3.25%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

Answer:

5(3)^(n-1)

a*b^n

5 is the second value (n-1), so a=5

the amount triples (*3) every minute, so b=3

D, or an = 5(3)^n-1, is correct!

Let’s break this down...

5 is the number of files that we have in the first minute. The 3 triples the 5. Since there is an exponent, the growth is exponential and will always triple the product before it.

Hope this helps :)

Answer:The function is odd

Step-by-step explanation:

Answer:

x= 2 so it is even.

Step-by-step explanation:

Answer:

I think the answer is D please forgive me if I'm wrong

Answer: the answer is  -5

Step-by-step explanation:

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