The quotient of three times a number and 4 is at least -16

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:

negative, with slope of -5 and the y-intercept is at 1.

Step-by-step explanation:

Answer:

- 1

Step-by-step explanation:

Using the rules of exponents

[tex]a^{0}[/tex] = 1

[tex](a^n)^{m}[/tex] = [tex]a^{nm}[/tex]

Given

27[tex]a^{0}[/tex][tex](-\frac{1}{3}) ^{3}[/tex]

Note [tex]a^{0}[/tex] = 1 for any value of a, thus

= 27 × 1 × - [tex]\frac{1}{3^{3} }[/tex]

= 27 × 1 × - [tex]\frac{1}{27}[/tex] ← cancel the 27 on numerator/ denominator

= 1 × - 1

= - 1

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:

−2x^2−x−8

Step-by-step explanation:

5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8

5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8

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:

[tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

If the probability of having a boy or a girl is the same, then

the probability of having a boy = a probability of having a girl = 1/2.

Let B denote boy and G denote the girl.

The sample space of having three children is:

BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.

The probabilities of each of those events is

[tex]Pr(BBB)=Pr(BBG)=Pr(BGB)=Pr(GBB)=\\ \\=Pr(BGG)=Pr(GBG)=Pr(GGB)=Pr(GGG)=\\ \\=\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{8}.[/tex]

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:

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:

-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:

Last one.

Step-by-step explanation:

Let's look at the fist one

x+1<-1 and x+1<1

Subtract one on both sides for both inequalities:

  x<-2 and x<0

Graph it!  

*********************************o                       x<0

 *************o                                                 x<-2

________(-2)_________(0)____________

So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.

Let's look at the second one

x+1<=1  and x+1>=1

Subtract one on both sides for both inequalities:

x<=0    and  x>=0

Graph it!

                           @*****************  x>=0

*********************@                         x<=0

-----------------------(0)-------------------

The only number included by both graphs is 0 so it still has a solution. The solution is 0.

Let's look at the third one:

x+1<1   and   x+1>1

Subtract one on both sides for both inequalities:

 x<0    and     x>0

Graph it!

************************O                                   x<0

                               O************************* x>0

---------------------------(0)------------------------------

These inequalities have no overlap.  They don't even both include zero because of the open circle (the lack of equal sign).  This is the compound inequality that has no solution.

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:

21

Step-by-step explanation:

[tex] \frac{v}{7} = 3[/tex]

Multiplying both sides by 7, we get

[tex] \frac{v}{7} \times 7 = 3 \times 7 [/tex]

The two 7s on the left cancel out to give 1, so

[tex]v = 21[/tex]

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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:

Last choice.

Step-by-step explanation:

8, 5, 2, -1, ...​

Make a table

n            |      1            2             3           4          5  

an          |      8           5             2           -1         -4

You really should just think of this as finding the equation of a line.

The slope can be used by using any two points.

How about

(1  ,  8)  and

(2 ,  5)?

------------I really like to find the slope by lining up my points and subtracting vertically and then putting second number on top of first.

That is the same as using the formula directly which is (y2-y1)/(x2-x1)

or (y1-y2)/(x1-x2) which gives you the same thing too.

Subtracting the pairs now:

(1  ,  8)

-(2 ,   5)

-----------

-1       3

So the slope is 3/-1 or -3/1 or -3.

So you can already rule out choice B.

So we have the equation is y=-3x+b

where y really represents an and x really represents n here.

You can use any point that you know is on the line to find b.

How about (1,8)?

Plug it into y=-3x+b.

y=-3x+b

8=-3(1)+b

8=-3+b

11=b

So the line is y=-3x+11

Want to confirm?

No problem:

At x=1 you have y=-3(1)+11=-3+11=8 which is first number in the list.

At x=2 you have y=-3(2)+11=-6+11=5 which is second number in the list.

At x=3 you have y=-3(3)+11=-9+11=2 which is the third number in the list.

At x=4 you have y=-3(4)+11=-12+11=-1 which is the fourth number in the list.

So we have confirmed our solution of y=-3x+11.

So the answer is an=-3n+11

Answer:

190

Step-by-step explanation:

40/100 x 198= 76

40/100 x 198= 114

114-76= 38

Answer:

190.

Step-by-step explanation:

Let x represent total number of votes.

We have been given that Joel got 60% of the votes, which was 38 votes more than Sean.

60% of total votes: [tex]\frac{60}{100}x=0.60x[/tex]  

Since Joel got 60% of total votes, so Sean got 40% of total votes that is [tex]\frac{40}{100}x=0.40x[/tex]  

Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:

[tex]0.60x=0.40x+38[/tex]

[tex]0.60x-0.40x=0.40x-0.40x+38[/tex]

[tex]0.20x=38[/tex]

[tex]\frac{0.20x}{.20}=\frac{38}{.20}[/tex]

[tex]x=190[/tex]

Therefore, the total number of votes cast is 190.

Answer:

Part 1) [tex]C=90\°[/tex]

Part 2) [tex]A=63\°[/tex]

Part 3) [tex]b=6.8\ units[/tex]

Part 4) [tex]a=13.4\ units[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The triangle ABC is a right triangle

so

Angle C is a right angle

therefore

[tex]C=90\°[/tex]

step 2

Fin the measure of angle A

we know that

In the right triangle ABC

∠B+∠A=90° -----> by complementary angles

we have

[tex]B=27\°[/tex]

substitute

[tex]27\°+A=90\°[/tex]

[tex]A=63\°[/tex]

step 3

Find the length side b

we know that

In the right triangle ABC

[tex]sin(B)=b/c[/tex]

[tex]b=(c)sin(B)[/tex]

substitute the given values

[tex]b=(15)sin(27\°)=6.8\ units[/tex]

step 4

Find the length side a

we know that

In the right triangle ABC

[tex]sin(A)=a/c[/tex]

[tex]a=(c)sin(A)[/tex]

substitute the given values

[tex]a=(15)sin(63\°)=13.4\ units[/tex]

Answer:

A = 63 , a = 13.4, b = 6.8

Step-by-step explanation:

Answer:

Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]-3x-y < 12[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line [tex]-3x-y=12[/tex]

[tex]2x+3y\geq 9[/tex] -----> inequality B

The solution of the inequality B is the shaded area above the solid line [tex]2x+3y=9[/tex]

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

A solution to the system of inequalities is any point in the shaded area.

therefore

Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)

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:

6

Step by step explanation:

2 + 2 * x = 10

2x+2=10

2x+2−2=10−2

Therefore, x = 6

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^{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:

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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Answer: A. 1/5 because it's the actual right answer.

Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].

The ratio of corresponding sides are equal, and this ratio is called the scale factor.

We know that

ΔABC and ΔXYZ are similar from the figure

[tex]\frac{XY}{AB}=\frac{YZ}{BC} =\frac{XZ}{AC}[/tex]

Substitute the values

[tex]\frac{9}{45} =\frac{12}{60}=\frac{7}{35} =\frac{1}{5}[/tex]

Therefore, Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].

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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:

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:

The volume of the prototype is [tex]V=250\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a hexagonal prism is equal to

[tex]V=BH[/tex]

where

B is the area of the hexagonal base

H is the length of the rectangular face

we have

[tex]B=25\ in^{2}[/tex]

[tex]H=10\ in[/tex]

substitute

[tex]V=(25)(10)[/tex]

[tex]V=250\ in^{3}[/tex]

Answer:

Volume of the prototype is 250 in.³

Step-by-step explanation:

Given:

Base area of the watch packaging case = 25 in.²

Length of the rectangle on the side = 10 in.

To find: Volume of the packaging prototype.

Prototype of the packaging of the watch is in shape of prism whose base is a hexagon and sides are in shape of rectangle.

So, Volume of the prism = Base Area × Height

Thus, Volume of the Prototype = 25 × 10

                                                   = 250 in.³

Therefore, Volume of the prototype is 250 in.³

Answer: D. -3x+9i)(x+3i) i hope this helped :)

Answer: D is the correct answer

Step-by-step explanation:

A P E X