Which are perfect square trinomials? Select two options.

x2 − 9
x2 −100
x2 − 4x + 4
x2 + 10x + 25
x2 + 15x + 36

The volume of the box is the amount of space in it.

The dimension of the postcard is:

[tex]\mathbf{Length = 10}[/tex]

[tex]\mathbf{Width = 18}[/tex]

Let x represents the length of the cut.

So, the dimension of the box is:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

(a) The function that represents the volume of the box

This is calculated as:

[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

(b) The dimension that maximizes the volume

We have:

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 7.3,2.1}[/tex]

The value x = 7.3 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 2.1}[/tex]

Recall that:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]

[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]

[tex]\mathbf{Height = 2.1}[/tex]

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]

[tex]\mathbf{Volume = 168.1}[/tex]

Hence, the maximum volume of the box is 168.1 cubic inches

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Answer:

I think the greater fraction is 27/5

Answer:

Step-by-step explanation:

what is greater: 19/5, 27/5, 10/3, 14/5​

fractions are divisions, we divide to see the greater

19/5= 3.8

27/5= 5.4

10/3= 3.33

14/5= 2.8

Answer:

x = -6

Step-by-step explanation:

Combine like terms.

5x + 6 = -24

Subtract 6 from both sides.

5x = -30

Divide by 5 on both sides.

x = -6

Follow Me:-

[tex]3x + 4 + 2x + 2 = - 24 \\ \\ = > 5x + 6 = - 24 \\ \\ = > 5x = - 24 - 6 \\ \\ = > 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{5} \\ \\ = > x = - 6[/tex]

Answer:

-1

Step-by-step explanation:

Using the formula to find gradient or slope:

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

Using any two points from the graph: (-2, 0) (0, -2)

Substitute this into the equation to get the answer of -1.

Answer:

24

Step-by-step explanation:

3x8=24

6x4=24

8x3=24

Answer:

15%

Step-by-step explanation:

24/160 = 0.15

0.15*100 = 15

Answer:

Step-by-step explanation:

Pythagorean theorem: base ² +altitude² = hypotenuse²

1) hypotenuse² = base² + altitude²

          x² = 6² + 3²

               = 36 + 9

               = 45

         x = √45

         x = 6.7 cm

4) base ² +altitude² = hypotenuse²

x ² + 3.7 ² =  4.2 ²

x ² + 13.69 = 17.64

             x ² = 17.64 - 13.69 = 3.95

             x = √3.95

            x = 1.99 cm

10)c ² = a ² + b ²

           = 3 ² +4 ²

         = 9 + 16

  c ² = 25

c = √25 = 5

11) a ² + b ² = c ²

9 ² +b² = 13 ²

81 + b² = 169

     b² = 169 - 81 = 88

b = 9.38

12) a² + b² = c²

12² + b² = 22²

  144 + b² = 484

           b² = 484 - 144 = 340

           b =√340 = 18.44

Answer:

x ÷ 4 ≤ 5

Step-by-step explanation:

Answer:

  ∠FGH = ∠HGI = 29°

  ∠FGI = 58°

Step-by-step explanation:

GH is marked as an angle bisector, so we have ...

  ∠FGH = ∠HGI

  2x -9 = 3x -28

  19 = x . . . . . . . . . . . . add 28-2x to both sides

Of course, the angle FGH is the sum of its parts. Then the angle measures are  ...

  (2x -9)° = (2·19 -9)° = 29°

  ∠FGH = ∠HGI = 29°

  ∠FGI = 58°

Answer:

it is called rectangularization

Step-by-step explanation:

Answer:

answer is D :

√24 = 4.89

which is the nearest to 5 and possible answer

Answer:

3z+13

Step-by-step explanation:

Perimeter is found by adding all the sides

z+2+z+2+z+9

3 z variables  2+2+9=13

Simplified equals

3z+13

Hope this helps!

Please mark this answer as brainiest :)

Answer:

1,23,098

Step-by-step explanation:

............

:)!!!!!!!!!!!!!!!!!!!

:)

<3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3

Step-by-step explanation:

50000÷10

=5000

Answer:

60% if this is an edge question

Answer:

-2, -1, 0, 1

Step-by-step explanation:

-2

-1

0

1

All the possible values of t in the inequality - 3 < t < 2 is,

t = - 2, - 1, 0, 1

Used the concept of inequality that states,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that;

The inequality is,

- 3 < t < 2

Here the given inequality means all the values of t are lies between - 3 and 2.

That is,

t = - 2, - 1, 0, 1

Therefore, the value of t are t = - 2, - 1, 0, 1

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Answer:

Hello!

After reading your question I have calculated the correct answer to be:

47.22

Step-by-step explanation:

The way I solved this equation was I first split the equation into two parts.

I took the two whole numbers, being "34" and "12", and made their own equation:

"34+12=?"

And then I took the two partial numbers "0.98" and "0.24" and made their own equation:

"0.98+0.24=?"

I then solved both equations:

"34+12= 46"

"0.98+0.24= 1.22"

And added those two solutions together to come up with the final solution:

"46+1.22= 47.22"

Hope this helped!

Answer:

47.22 is the answer

Step-by-step explanation:

hope it helps you

Answer:

You didn't ask a question.

Step-by-step explanation:

Answer:

Part 1. 325 - (135 + 89) = c

Part 2. ≤ 101

Step-by-step explanation:

No because for 5x10, you just add 10 5 times for 50. For 5x5x5, you multiply 5x5 and get 25 then multiply it again with the other 5 and get 125.

Answer:

No

Step-by-step explanation:

No, because 5 × 5 × 5 = 25 × 5 and that does not equal 10×5.

Answer:

b. 5

Step-by-step explanation:

f(x)=(x+a)/b

or bf(x)=x+a

let f(x)=y

by=x+a

flip x and y

bx=y+a

or y=bx-a

or f^{-1}(x)=bx-a

also g(x) is inverse of f(x)

bx-a=cx-d

so b=c,a=d

again let g(x)=y

y=cx-d

flip x and y

x=cy-d

cy=x+d

y=(x+d)/c

or g^{-1}(x)=(x+d)/c

also f(x) is inverse of g(x)

so (x+a)/b=(x+d)/c

so a=d,b=c

so in either case a=d,b=c

take b=c=1

a=d=2

f(x)=(x+2)/1=x+2

g(x)=1x-2=x-2

so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0

g(x) with y-intercept -2 and slope 0

if we take b=c=2,a=d=3

f(x)=(x+3)/2=x/2+3/2

g(x)=2x-3

here f(x) is of slope 1/2 and y-intercept 3/2

g(x) is of slope 2 and y intercept -3

part 3.

f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d

An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.

Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2: g(x) = 3x - 2, the inverse.

Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.

An inverse function in mathematics exists function which "reverses" the another function.

TASK 1

Part 1

Let y = f(x) = (x + a) / b

x = g(y) = by-a = cy-d,

so c = b and d = a.

Let d = a = 2 and c = b = 3

f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2

y = f(x) = (x+2) / 3

3y = x+2  

x = 3y-2 = g(y)

so g(x) = 3x - 2, the inverse.

Part 3

g(f(x)) = 3

f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,

so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.

x       -2  -1        0    1     2

f(x)    0    1/3   2/3   1    4/3

g(x)  -8   -5      -2    1      4

Part 4

The graph is given below.

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5

(b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by

[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]

[tex]$ x-36+30=-5 \sqrt{x }[/tex]

[tex]$ x-6=-5 \sqrt{x}$[/tex]

Square both sides:

[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].

Part 2

(a) So x=36 or 1 (apparently).

Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.

So x=36 is an extraneous solution.

substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.

(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.

Substitute x=1 in the original equation: -1+2+3=4 is true.

So x = 1 is the solution.

Part 3

(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].  

(b) the solution was simpler and there was no ambiguity.

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Answer:

B,D,E

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

im smart

Answer:

D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft