What is the absolute value of I -32 I?

Answer:

[tex]2\sqrt{2}[/tex] is irrational .

Step-by-step explanation:

The Natural numbers are {1,2,3,4,5,6,7,....}.

Natural numbers are also called counting numbers because they are numbers people use to count with.

Whole numbers are almost the same as natural numbers.  They include one extra number which is 0.

So the whole numbers are {0,1,2,3,4,5,6,7,...}.

Irrational numbers are real numbers that aren't rational numbers.

Rational numbers are number that can be written as fractions where the numerator and denominator are integers (bottom integer is not 0).

Terminating decimals, repeating decimals, and integers all can be written this way which makes them rational.

Integers are numbers in the set {...,-4,-3,-2,-1,0,1,2,3,4,...}.  So these are your counting numbers, 0, and the opposite of your counting numbers.

You want to figure out which set does [tex]2\sqrt{2}[/tex] belong to.

You cannot simplify this number anymore than it is. So this is definitely not a number you can count to. It is not the opposite of a counting number.  It is also not 0.  We have ruled out the following sets: Natural, whole, and integers.

So it is between rational and irrational.

[tex]\sqrt{a} \text{ is irrational if } a \text{ is not a perfect square}[/tex].

[tex]\sqrt{a} \text{ is rational if } a \text{ is a perfect square}[/tex].

2 is not a perfect square.

[tex]\sqrt{2} \text{ is irrational}[/tex]

So [tex]2\sqrt{2} \text{ is also irrational}[/tex]

Answer:

p->q.

~p.

[tex]\therefore[/tex] ~q.

Step-by-step explanation:

I'm going to assume you are looking for symbolic representation.

p=it's a weekend

q=I exercise

The arrangement is this:

If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.

If           p            ,     q          .              ~p              .  So,   ~q.

I try to space out my symbols to show you what I was replacing with what. (By the way I'm still not done.)

I replaced "it's a weekend" with p.

I replaced "it's not a weekend" with ~p  which means not p.

I replaced "I exercise" with q.

I replaced 'I won't exercise" with ~q which means not q.

If then, statements are symbolized with an arrow, ->.  Example, p->q means if p then q.

Back to the argument:

If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.

If           p            ,     q          .              ~p              .  So,   ~q.

This first sentence is an if then statement with hypothesis p and conclusion q so it can be rewritten as p->q.

I'm going to replace so with [tex]\therefore[/tex].  I'm just trying to show what the conclusion of the argument is with this symbol.

This is the argument in symbolic representation:

p->q.

~p.

[tex]\therefore[/tex] ~q.

This is translated into English as "If it's a weekend, I exercise" (p q), "It's not a weekend" (p), and "I won't exercise" (q).

A logic statement is a statement that uses logical symbols and operators to represent the relationships between propositions or statements.

It is a formal expression of symbolic logic that can be evaluated as true or false based on the truth values of its constituents.

Logic statements are used to reason about the truth of statements and the validity of arguments in mathematics, philosophy, computer science, and other fields.

"If p then q," "p and q," "p or q," "not p," and "p if and only if q" are all logical statements.

The logic statement that represents this argument is:

(p → q) ∧ ¬p → ¬q

Thus, when translated into English, this reads: "If it's a weekend, I exercise" (p → q), "It's not a weekend" (¬p), therefore "I won't exercise" (¬q).

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Your question seems incomplete, the probable complete question is:

Which logic statement represents this argument? If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise. Assume that p represents “It’s a weekend” and q represents “I exercise.” (p q) p [(p q) p] q [(p q) p] q [(p q) p] q

Answer:

Step-by-step explanation:

[tex]\text{Put}\ g=2\ \text{to the expression}\ g(g+1)^2:\\\\2(2+1)^2=2(3)^2=2(9)=18[/tex]

Answer:

B. 7,596,288 ft³

Step-by-step explanation:

volume of cylinder = π * r^2 * h

volume = 3.14 * (240 ft)^2 * 42 ft

volume = 7,596,288 ft³

Answer: B . [tex]7,596,288 ft^3[/tex]

Step-by-step explanation:

The volume of a cylinder is given by :_

[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.

Given : A new dolphin tank is being built outside of Houston. The tank will be a cylinder with a depth of 42 feet and a radius of 240 feet.

i.e. r=240 and h = 42

Now, the volume of tank will be :_

[tex]\text{Volume}=(3.14) (240)^2 (42)=7,596,288[/tex]

Hence, the tank will hold [tex]7,596,288 ft^3[/tex] water.

Answer:

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Step-by-step explanation:

Compare [tex]ax^2+bx+c[/tex] to [tex]3x^2+4x-2[/tex].

We have [tex]a=3,b=4,c=-2[/tex].

The quadratic formula is for solving equations of the form [tex]ax^2+bx+c=0[/tex] and is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So we are going to plug in our values in that formula to find our solutions,x.

If you want to notice it in parts you can.

Example I might break it into these parts and then put it in:

Part 1: Evaluate [tex]b^2-4ac[/tex]

Part 2: Evaluate [tex]-b[/tex]

Part 3: Evaluate [tex]2a[/tex]

------Let's do these parts.

Part 1: [tex]b^2-4ac=(4)^2-4(3)(-2)=16-12(-2)=16+24=40[/tex].

This part 1 is important in determining the kinds of solutions you have. It is called the discriminant.  If it is positive, you have two real solutions.  If it is negative, you have no real solutions (both of the solutions are complex).  If it is 0, you have one real solution.

Part 2: [tex]-b=-4[/tex] since [tex]b=4[/tex].

Part 3: [tex]2a=2(3)=6[/tex].

Let's plug this in:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

or in terms of our  parts:

[tex]x=\frac{\text{Part 2} \pm \sqrt{\text{Part 1}}}{\text{Part 3}}[/tex]

[tex]x=\frac{-4 \pm \sqrt{40}}{6}[/tex]

40 itself is not a perfect square but it does contain a factor that is.  That factor is 4.

So we are going to rewrite 40 as [tex]4 \cdot 10[/tex].

[tex]x=\frac{-4 \pm \sqrt{4 \cdot 10}}{6}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4} \cdot \sqrt{10}}{6}[/tex]

[tex]x=\frac{-4 \pm 2\cdot \sqrt{10}}{6}[/tex]

I'm going to go ahead and separate the fraction like so:

[tex]x=\frac{-4}{6} \pm \frac{2 \cdot \sqrt{10}}{6}[/tex]

Now I'm going to reduce both fractions:

[tex]x=\frac{-2}{3} \pm \frac{1 \cdot \sqrt{10}}{3}[/tex]

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Final answer:

Using the quadratic formula with a=3, b=4, and c=-2, the solution set for the quadratic equation 3x^2 + 4x - 2 = 0 is x = (-4 + 2√(10)) / 6 and x = (-4 - 2√(10)) / 6.

Explanation:

To find the solution set of the quadratic equation 3x2 + 4x - 2 = 0, we can use the quadratic formula:

x = (-b ± √(b2 - 4ac)) / (2a)

Here, comparing with the standard form ax2 + bx + c = 0, we identify a = 3, b = 4, and c = -2. Substituting these values into the quadratic formula gives us:

x = (-(4) ± √((4)2 - 4(3)(-2))) / (2(3))

x = (-4 ± √(16 + 24)) / 6

x = (-4 ± √(40)) / 6

x = (-4 ± 2√(10)) / 6

Which simplifies to two solutions:

x = (-4 + 2√(10)) / 6

x = (-4 - 2√(10)) / 6

These are the two solutions to the given quadratic equation.

Answer:

Option C is correct.

Step-by-step explanation:

The equation given is y = 0.5x +5

where x is the number of miles and y is the total cost.

We need to find total cost y if the car has traveled 30 miles

so, x=30

Putting value of x in the given equation:

y = 0.5x +5

y = 0.5(30) + 5

y = 15 + 5

y = 20

So, the total cost is $20

Option C is correct.

Answer:

the answer is $20 i just did that one :))

Step-by-step explanation:

good luck!

Answer:

-6/-5 is the slope

Step-by-step explanation:

Y2 - Y1 / X2 - X1 so

-1 - 11 / -5 - 5 = -12 / -10 simply it and get -6 / -5

Slope equals rise over run

Answer:

6/5

Step-by-step explanation:

Answer:

y = - 2x - 3

Step-by-step explanation:

Given

y - 5 = - 2(x + 4) ← in point- slope form

Distribute the right side

y - 5 = - 2x - 8 ( add 5 to both sides )

y = - 2x - 3 ← in slope- intercept form

Answer:

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Step-by-step explanation:

Given function is:

f(x) = x/1 + x

In order to find f(x+h) we have to put x+h in place of x

[tex]f(x)=\frac{x}{1+x} \\f(x+h)=\frac{x+h}{1+x+h}[/tex]

Therefore,

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Answer: B

Got it right lol

Answer:

16 cubic feet per hour

Step-by-step explanation:

This is simple conversion from inches to feet.

Step 1: Write the scale of conversion

---> quantity of water in 1 minute = 462 cubic inches

--->1 cubic feet = 1728 cubic inches

--->1 hour = 60 minutes,

Step 2: Calculate feet per hour

Quantity of water in 1 hour =  0.0347 x 462

---> quantity of water in 1 hour =  = 16.0314 cubic feet

---> Rounded off to--> 16 cubic feet

Therefore, 462 cubic inches per minute is 16 cubic feet of water per hour

Answer:

16 cubic feet of water

Step-by-step explanation:

Given,

Water leaves the spigot at a rate of 462 cubic inches per minute,

That is, the quantity of water in 1 minute = 462 cubic inches

1 cubic feet = 1728 cubic inches

⇒ 1 cubic inches = [tex]\frac{1}{1728}[/tex] cubic feet,

Thus, the quantity of water in 1 minute = [tex]\frac{462}{1728}[/tex] = [tex]\frac{77}{288}[/tex] cubic feet

Also, 1 hour = 60 minutes,

⇒ 1 minute = [tex]\frac{1}{60}[/tex] hours,

Hence, quantity of water in [tex]\frac{1}{60}[/tex] hour = [tex]\frac{77}{288}[/tex] cubic feet

⇒  quantity of water in 1 hour = [tex]\frac{60\times 77}{288}=\frac{4620}{288}[/tex] = 16.0416666667 cubic feet ≈ 16 cubic feet,

Hence, 16 cubic feet of water is this per hour.

Answer:

See explanation.

Step-by-step explanation:

The 'base' of a rectangular prism refers to only one side of the rectangular prism, which is a rectangle.

The formula for the area of a rectangle is as follows:

[tex]A=lw[/tex]

Where A = area, l = length, and w = width.

The 'base' of a cylinder refers to only one side of the cylinder, which is a circle.

The formula for the area of a circle is as follows:

[tex]A=\pi r^2[/tex]

Where A = area and r = radius.

Just in case you typed your question incorrectly and were asking for surface area, here is the formula for surface area for both as well:

Rectangular prism: [tex]A=2(wl+hl+hw)\\[/tex]

Cylinder: [tex]A=2\pi rh+2\pi r^{2}[/tex]

Answer:

w=5

Step-by-step explanation:

14-9=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{ w + 9 = 14}[/tex]

[tex]\huge\text{SUBTRACT by the \#9 on your sides! }[/tex]

[tex]\huge\text{Like: w + 9 - 9 = 14 - 9}[/tex]

[tex]\huge\text{Cancel out: 9 - 9 because it equals 0}[/tex]

[tex]\huge\text{Keep: 14 - 9 because it helps us solve for w}[/tex]

[tex]\huge\text{w = 14 - 9}[/tex]

[tex]\huge\text{14 - 9 = w}[/tex]

[tex]\huge\text{14 - 9 = 5}[/tex]

[tex]\huge\text{w = 5}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: w = 5}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

6

Step by step explanation:

2 + 2 * x = 10

2x+2=10

2x+2−2=10−2

Therefore, x = 6

Answer: false

Step-by-step explanation:

The statement that the shapes of the horizontal cross-sections of the cone below are all congruent except for the vertex is false

The horizontal cross-sections of a cone contains a circle, while the vertical cross-sections contains  a triangle

The triangle and the cone may or may not have the same area.

Hence, the statement is false

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Answer:

x = ± 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

12 - x² = 0 ( add x² to both sides )

12 = x² or

x² = 12 ( take the square root of both sides )

x = ±[tex]\sqrt{12}[/tex]

  = ± [tex]\sqrt{4(3)}[/tex] = ± 2[tex]\sqrt{3}[/tex]

Answer:

Not equivalent.

Step-by-step explanation:

Simplifying the first expression:

11p + 2(p + 3)    Distribute the + 2 over the parentheses:

= 11p + 2p + 6

= 13p + 6.  **

Now, the second:

1 + p(13) + 2

= 13p + 1 + 2

= 13p + 3.  **

So they are not  equivalent.

Answer:

Step-by-step explanation:

Given the function f(x), the  function g(x) = f(x) + k represents the function f(x) shifted k units downwards.

In this case, given that k=-3 (k<0). The graph is shifted 3 units down. Therefore,  we can conclude that the correct option is Option C.

Answer:

the answer is 'because'

Answer: [tex]T=8+ 1.50 x+0.75y[/tex] , where 'x' denotes the number of additional inch to the pizza and 'y' denotes the number of additional toppings.

Step-by-step explanation:

Let 'x' denotes the number of additional inch to the pizza and 'y' denotes the number of additional toppings.

Given : A 10-inch cheese pizza costs  $8.

i.e. Fixed cost = $8

Each additional inch costs $1.50, and each additional topping costs $0.75.

∴ Cost of additional inch = $1.50 x

∴ Cost of additional topping = $0.75y

Then The Total cost of any pizza would be :

Total cost = Fixed cost + Cost of additional inch + cost of additional topping

= $8+ $1.50 x+$0.75y

⇒ Equation  that represents the cost of a pizza :

[tex]T=8+ 1.50 x+0.75y[/tex]

An equation that represents the cost of a pizza will be C = 8 + 1.50x + 0.75y

Total cost (C) will then be:

= 8 + (1.50 × x) + (0.75 × y)

C = 8 + 1.50x + 0.75y

Therefore, the equation to represent the cost is C =  8 + 1.50x + 0.75y

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Answer:

-2/9 =x

Step-by-step explanation:

2/5 (x − 2) = 4x

Multiply each side by 5/2

I do this because we want to get rid of the fraction in the denominator.  I also know that the right side has a 4 in the numerator so, the 2 in the denominator that we are multiplying by will cancel.

5/2 *2/5 (x − 2) = 4x*5/2

x-2 = 20/2 x

x-2 = 10x

Subtract x from each side

x-2 -x = 10 -x

-2 = 9x

Divide each side by 9

-2/9 =9x/9

-2/9 =x

Answer:

x=-2/9

Step-by-step explanation:

First, divide both sides by 2/5

(2/5)*(x-2)/2/5=4x*5/2

x-2=10x, Subtract x from both sides.

-2=9x, Divide both sides by 9

x=-2/9, If you need you can check your answer by substituting the value of x into the original equation.

Answer:

Step-by-step explanation:

We have:

rectangle 4.8 m × 3.8 m

two triangles with base b = 4.8 m and height h = 2.6 m

two triangle with base b = 3.8 m and height h = 2.9 m.

The formula of an area of a rectangle l × w:

[tex]A = lw[/tex]

Substitute:

[tex]A_1 = (4.8)(3.8) = 18.24\ m^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_2=\dfrac{(4.8)(2.6)}{2}=6.24\ m^2\\\\A_3=\dfrac{(3.8)(2.9)}{2}=5.51\ m^2[/tex]

The Surface Area:

[tex]S.A.=A_1+2A_2+2A_3\\\\S.A.=18.24+2(6.24)+2(5.51)=41.74\ m^2[/tex]

Answer:

GIVE THE OTHER DUDE BRAINLISET

Step-by-step explanation:

The option "KM" does not represent a direct line segment in the drawing as there is no straight path connecting points K and M without passing through another point.

The figure contains various labeled points connected by lines representing different segments except for NK; hence option NK does not name an existing line segment in the drawing.

1) In this case, all options refer to line segments except for "KM." The points K and M are not connected by a straight line; instead, point N lies between them. Therefore, KM is not a direct line segment in this drawing.

It's essential to understand that a line segment is named after its end points and consists of these points and all the points on the line between them. Since there is no direct path from point K to M without passing through another point (N), KM cannot be considered as a single, uninterrupted line segment.

2)The image you provided contains a geometrical diagram with five labeled points: J, K, L, M, and N. Line segments are drawn connecting these points forming an X shape. The options given are JL, MN, JK, and NK.

Upon careful examination of the image, it is evident that line segments JL (from point J to L), MN (from point M to N), and JK (from point J to K) are present in the drawing. However, NK (from point N to K) is not a line segment depicted in this drawing.

Answer:

[tex]x^{2} -1[/tex]

Step-by-step explanation:

we know that

Every difference of squares problem can be factored as follows:

[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]

If the polynomial represent a difference of squares every number must be a perfect square (Remember that a number is a perfect square if its square root is an integer.)

Verify each case

case 1) we have

[tex]x^{2} -1[/tex]

In this case both numbers are perfect square

so

[tex]x^{2} -1=(x+1)(x-1)[/tex]

therefore

The polynomial represent a difference of squares

case 2) we have

[tex]x^{2} -8[/tex]

In this case 8 is not a perfect square

therefore

The polynomial not represent a difference of squares

case 3) we have

[tex]4x^{2} +16[/tex]

[tex]4x^{2}+16=4(x^{2}+4)[/tex]

In this case both numbers are perfect square

but is a sum of squares

therefore

The polynomial not represent a difference of squares

case 4) we have

[tex]9x^{2}-18[/tex]

[tex]9x^{2}-18=9(x^{2}-2)[/tex]

In this case 2 is not a perfect square

therefore

The polynomial not represent a difference of squares

Answer:

Step-by-step explanation:

(40*0.9)+(40*-x)

36-40X

Answer: 36-40X

   Answer:

[tex]\displaystyle =36-40x[/tex]

 Step-by-step explanation:

  Distributive property:

          ↓

[tex]\displaystyle A(B+C)=AB+AC[/tex]

A= 40, B=0.9, and C=x

[tex]\displaystyle 40*0.9-40x[/tex]

Then multiply numbers from left to right.

[tex]40*0.9=36[/tex]

[tex]\displaystyle 36-40x[/tex], which is our answer.

Answer:

x=-2  y=3

Step-by-step explanation:

7x-2y=-20

9x+4y=-6

Multiply the first equation by 2

2(7x-2y) = 2 * -20

14x - 4y = -20

Add this to the second equation

14x - 4y = -40

9x+4y=-6

--------------------------

23x = -46

Divide by 23

23x/23 = -46/23

x = -2

Now we solve for y

9x+4y=-6

9(-2) +4y = -6

-18 + 4y = -6

Add 18 to each side

-18+18 +4y = -6+18

4y = 12

Divide by 4

4y/4 = 12/4

y=3

Answer:

Step-by-step explanation:

it's even because f(-x)=f(x)

Answer:

even function

Step-by-step explanation:

recall that:

a function is EVEN if and only if f(-x) = f(x) for all x in the domain of f

a function is ODD if and only if f(-x) = -f(x) for all x in the domain of f

we observe that for the function

f(x) = 3x^4

because x has been raised to an even power, that f(x) will always be positive (or zero), regardless of whether x is negative or positive.

i.e

f(x) = f(x)   and   f(-x) = f(x)

This behavior is described by the definition of an EVEN function (given above)

Hence f(x) is an even function

Answer:

To simplify the following expression: 6 / (7+3i), we're going to multiply and divide the entire expression by (7+3i), as follows:

[tex]\frac{6 (7-3i)}{ (7+3i)(7-3i)} = \frac{42-18i}{58} = 0.72 - 0.31i[/tex]

Now, the denominator has NO imaginary numbers.

Answer:

21/29 - 9/29i

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ a=5\\ b=3 \end{cases}\implies \cfrac{(x-0)^2}{5^2}+\cfrac{(y-0)^2}{3^2}=1\implies \cfrac{x^2}{25}+\cfrac{y^2}{9}=1[/tex]

Answer:

The fourth one: [tex]\frac{\sqrt{2+\sqrt{2} } }{2}[/tex]

Step-by-step explanation:

The exact value of sin 112.5° can be found using the half-angle identity formula. Substituting values for sin 45° and cos 90°, we find that the exact value of sin 112.5° is ± √2/2.

We can find the exact value of sin 112.5 using half-angle identity. As we know, 112.5 degrees is equal to 45 degrees/2 + 90 degrees, these values are much simpler to work with. Let's start by understanding the half-angle formula, which is sin(x/2) = ± √[(1 - cos x) / 2] .

The exact value of sin 45 degrees is √2/2 and cos 90 degrees is 0.

Now, let's put these values in our half-angle formula

sin 112.5 = sin(45/2 + 90) = √[(1 - 0) / 2] = ± √[1/2] = ± √2/2

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