After simplification, how many terms will be there in 4x3 + 9y2 - 3x + 2 - 1?
3
6
5
4.

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Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

Answer:

strength of the relationship between two variables.

Step-by-step explanation:

The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.

The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.

Answer:

(5x – 6y)^4

Step-by-step explanation:

Given

[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]

Required

The factored form

Solving (a): (5x – 6y)^4

Expand using pascal triangle;

Exponent 4 is represented as: 1 4 6 4 1. So, we have:

[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]

Expand:

[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]

Remove brackets

[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]

Hence, (a) is correct

Answer:

t≥-25

Step-by-step explanation:

this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.

Answer:

Step-by-step explanation:

(–3s + 2t)(4s – t)

= -3s (4s - t) + 2t(4s - t)

[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]

[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]

Answer: -12s^2 + 11st -2t^2

Step-by-step explanation:

= (-3s + 2t)(4s - t)

= -12s^2 + 3st + 8st -2t^2

= -12s^2 + 11st -2t^2

Answer Provided by GauthMath please heart and comment thanks if you like.

Answer:

B

Step-by-step explanation:

To solve this use a unit circle (see pic)

Go to the 300 degree

Then look at the y coordinate (y coordinate because it's cosine)

Which matches with answer choice B

Answer:

Kindly check explanation

Step-by-step explanation:

Since the triangle is right angled ; we can solve for x using Pythagoras :

x = hypotenus ; hence ;

x² = opposite² + adjacent²

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

Using Trigonometry :

Sin D = side opposite D / hypotenus = 8/17

Cos D = side Adjacent D / hypotenus = 15 / 17

Tan D = side opposite D / Adjacent side = 8/15

Sin F = side opposite F / hypotenus = 15/17

Cos F = side Adjacent F / hypotenus = 8 / 17

Tan F = side opposite F / Adjacent side = 15/8

Answer:

XW = 78

Step-by-step explanation:

Both triangles are similar, therefore based on triangle similarity theorem we have the following:

XW/XZ = VW/YZ

Substitute

XW/6 = 104/8

XW/6 = 13

Cross multiply

XW = 13*6

XW = 78

Answer: 4 hours

Step-by-step explanation:

The median number is always in the middle the other numbers have to be equal on both sides 5 is the middle number on the plot 6th graders have 4 dots and 8th graders have 0 dots which means the hourly difference is 4

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Answer:

  D.

Step-by-step explanation:

The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.

Answer:

Here we can only answer A and B.

For a given function f(x), the average rate of change in a given interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:

[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(14*5 + 6) - (14*0 + 6)}{5} = \frac{14*5}{5} = 14[/tex]

The average rate of change is 14.

B) We have g(x) = 3*(2x) - 6

we can rewrite this as:

g(x) = 3*2*x - 6 = 6x - 6

And we want to find the rate of change in the interval [0, 5]

is:

[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(6*5 - 6) - (6*0 - 6)}{5} = 6[/tex]

Answer:

<ADB = 61degrees

Step-by-step explanation:

From the diagram shown, triangle ADB is isosceles since they projected out from the chord AD. Hence;

<ABD + <ADB + <BAD = 180

Since <ADB = <BAD, then;

<ABD + <ADB + <ADB = 180

Given that:

<ABD = 58degrees

58 + 2<ADB = 180

2<ADB = 180 - 58

2<ADB = 122

<ADB = 122/2

<ADB = 61degrees

Answer90 degrees

Step-by-step explanation:

Step-by-step explanation:

1. 12/18/3 = 4/6....!!!

Answer:

6

Step-by-step explanation:

I would first simplify the fraction on the left:

12/18 = 2/3

Then:

2/3 = 4/x

2x/3 = 4

2x = 4*3

x = 4*3/2

x = 12/2

x = 6

Answer:

train A=38mph train B=44mph

Step-by-step explanation:

Setting up a table:

         s            t           d

A     x            190/x    190

B    x+6      220/x+6  220

Train A was 6mph slower as shown in the table, so to make it easier, train a is identified as x, train b would be x+6

Their distances are put in their respective column.

You find time from distance divided by speed.

So time would be written as such.

Since you know they take the same amount of time, for the equation, you connect them with an equal sign. Cross multiply to something like:

190(x+6)=220x

190x+1140=220x

1140=30x

x=38

You plug this in and get the speed for train A as 38, and train B as 44.

Hope this helps ^^

Answer: C. NO

Step-by-step explanation:

There are no outfiers

Answer:

36

Step-by-step explanation:

Total students un the contest = 84

Number of students who gave their speech yesterday:-

[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]

so 21 students gave their speech yesterday

= 63

Number of students who gave their speech today:-

[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]

Number of students who have given their speech:-

= 21 + 27

= 48

Number of students who still haven't given their speech :-

= total - 48

= 84 - 48

= 36

Answer: Choice A)

Take her phone and laptop with her to get something to eat

=======================================================

Explanation:

It's always a good idea to keep a close watch on your stuff in a public place like an airport. This is for 2 reasons:

So that's why choice A is the best answer here.

Choice B and C are bad ideas, because of the items mentioned above. Choice D could work but Marnie would have to trust that stranger, which may be a very bad idea. Ideally the stranger would be trustworthy, but there's no way of her knowing for sure. So it's better to go on the side of caution and rule out choice D.

Answer:

100 % or 1

Step-by-step explanation:

There are two dice

Each dice has a possible roll of 1,2,3,4,5,6

The possible sums are 2,3,4,5,6,7,8,9,10,11,12

The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1

Answer:

Step-by-step explanation:

I'm going to go through this as I would when teaching it to my students for the first time. This is a super simple one, so it shouldn't be too hard. Begin with what you know:

A snowball is a sphere. Since we are told that the surface area is changing (decreasing, to be exact), it would make sense to know the formula for the surface area of a sphere:

[tex]S=4\pi r^2[/tex] where r is the radius. Let's take the derivative of this using implicit differentiation to see what it is we need to solve this:

[tex]\frac{dS}{dt}=4\pi*2r\frac{dr}{dt}[/tex], where dr/dt is the rate at which the radius is changing. If we look at the problem, we are looking for the rate at which the DIAMETER is changing. So instead of using the radius in the original formula, we need to write it in terms of the diameter. We know that

d = 2r so

[tex]r=\frac{d}{2}[/tex] and we will put that into the formula for r to get:

[tex]S=4\pi(\frac{d}{2})^2[/tex] and simplify a bit:

[tex]S=4\pi(\frac{d^2}{4})[/tex] and the 4's cancel each other out, leaving us with simply:

[tex]S=\pi d^2[/tex] Now let's take the derivative:

[tex]\frac{dS}{dt} =\pi 2d\frac{dD}{dt}[/tex] where the rate of the surface area is -8 ("decreasing" rate makes this number a negative) when the diameter is 11. Filling in:

[tex]-8=\pi(2)(11)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:

[tex]\frac{dD}{dt}=-\frac{8}{22\pi}[/tex] , which rounds to

[tex]\frac{dD}{dt}=-1.142\frac{cm}{min}[/tex] and again, the negative means that the diameter is decreasing.

Answer:

n = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 30 = n / 2 sqrt(3)

2 sqrt(3) tan 30 = n

2 sqrt(3) * sqrt(3)/3 = n

2 = n

We have to find,

The required value of n.

Now we can,

Use the trigonometric functions.

→ tan(θ) = opp/adj

Let's find the required value of n,

→ tan (θ) = opp/adj

→ tan (30) = n/2√3

→ n = 2√3 × tan (30)

→ n = 2√3 × √3/3

→ n = 2√3 × 1/√3

→ [n = 2]

Thus, the value of n is 2.

Answer: 90° counterclockwise

Step-by-step explanation:

Answer:

35/45 or 7/9

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Given two points on the line, we can use the slope formula

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

    = ( 7 - -3)/(3 - -2)

    = (7+3)/(3+2)

    = 10/5

    =2

Answer:

I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.

Step-by-step explanation:

Answer:

Same I think it's B but I'm not entirely sure

Step-by-step explanation:

Answer:

-92

Step-by-step explanation:

4(-5)^2 - 6(-5)^2 + 7(-5)-7

4(25) --6(25) - 35 -  7

100-150 - 35 -7

= -92

The identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number. For example, 32x1=32.

Answer: I don’t know lol maybe 1460

Step-by-step explanation: