Point-Slope Form of a Line

The equation Q = 2 x M represents the relationship between question and time.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Zack takes a test, in which he answers at rate of 2 question per minute.

Also, Q represents questions

And M represents minutes.

According to given condition,

In 1 minute, Zack answers 2 question,

In M minutes, Zack answers 2 x M question,

Total questions presented by Q,

Q = 2 x M.

The required relationship for M and Q is Q = 2 x M.

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Question 1

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Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) =  -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:  

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

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Question 2

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Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

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Question 3

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Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]

The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)

[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]

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Question 4

[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

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Explanation:

[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]

Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

Let's see what happens if we tried plugging x = -1 into this composite function:

[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

Answer:

x=5[tex]\frac{16}{3}[/tex]/(4-[tex]\frac{16}{3}[/tex])

Step-by-step explanation:

Hi, these are not my strong point, Sorry if its incorrect.

6-[tex]\frac{2}{3}[/tex](x+5)=4x

I first did 6-[tex]\frac{2}{3}[/tex]

6/1 -2/3,  18/3-2/3 =16/3

[tex]\frac{16}{3}[/tex](x+5)=4x

I then expanded the bracket to get [tex]\frac{16}{3}[/tex]x+5[tex]\frac{16}{3}[/tex]

[tex]\frac{16}{3}[/tex]x+5[tex]\frac{16}{3}[/tex]=4x

Then I took away [tex]\frac{16}{3}[/tex]x from both sides to get.

5[tex]\frac{16}{3}[/tex]=4x-[tex]\frac{16}{3}[/tex]x

I then factorised x out

5[tex]\frac{16}{3}[/tex]=x(4-[tex]\frac{16}{3}[/tex])

I then divided by the bracket to get:

x=5[tex]\frac{16}{3}[/tex]/(4-[tex]\frac{16}{3}[/tex])

Answer:

4/7

Step-by-step explanation:

[tex]6 - \frac{2}{3} (x + 5) = 4x[/tex]

U take -2/3 into the brackets

[tex]6 - \frac{2}{3} x - \frac{10}{3} = 4x[/tex]

Put all values with x on one side

[tex]6 - \frac{10}{3} = 4x + \frac{2}{3} x[/tex]

Ensure that they all have the same denominator so that u can add and subtract

[tex] \frac{18}{3} - \frac{10}{3} = \frac{12}{3} x + \frac{2}{3} x[/tex]

[tex] \frac{8}{3} = \frac{14}{3} x[/tex]

Drop the denominator since they both have the same denominator

[tex]8 = 14x[/tex]

divide both sides by 14

[tex] \frac{8}{14} = \frac{14}{14} x[/tex]

[tex]x = \frac{4}{7} [/tex]

Given AP is 21 ,18,15,...

First term = 21

Common difference = 18-21 = -3

Let an = -81

We know that

an = a+(n-1)d

⇛21+(n-1)(-3) = -81

⇛ 21-3n+3 = -81

⇛24-3n = -81

⇛ 24+81 = 3n

⇛ 105= 3n

⇛ n = 105/3

⇛ n = 35

35th term of the AP is -81.

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Which term of the AP:3, 8, 13, 18,...,is 78?

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Answer:

Observational study

Step-by-step explanation:

Answer:

xy-11=5

ANSWER:

=16

Step-by-step explanation:

hope it helps to you

mark me as a brainlest please

Applying the given probabilities, it is found that there is a 0.42 = 42% probability of watching a movie today.

These following probabilities involve a movie being watched today:

Hence, adding them:

[tex]p = 0.5(0.6) + 0.3(0.4) = 0.3 + 0.12 = 0.42[/tex]

0.42 = 42% probability of watching a movie today.

A similar problem is given at https://brainly.com/question/14398287

Answer:

1.25

Step-by-step explanation:

The answer in decimal is 1.25

35/28= 1.25

= 35 ÷ 28

by 1

=35 - 28 = 7

Introducing decimals

= 70 to 28

by 2

= 70 - 56 = 14

adding zero to 14

= 140 to 28

by 5

= 140 - 140 =0

the answer is 1.25

I did it this way through division hope you'll understand. All the best.

Answer:

The answer is B

Step-by-step explanation:

Answer:

I’m not sure what that means but I think it’s the one with the blue

Step-by-step explanation:

Answer:

80° because 50° 60° 70° and 80°

Answer:

There must he a circulation. May not be causation.

Answer:

G

Step-by-step explanation:

Therefore, the option [tex]G(-1,1)[/tex] is correct.

What is the inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Here given inequality equation

[tex]3x- 2y \geq -1[/tex]

When the points [tex](-1,1)[/tex] so it would be

[tex]3(-1)-2(1)\geq -1\\\\-3-2\geq -1\\\\-5\geq -1[/tex]

Hence, the option [tex]G(-1,1)[/tex] is correct.

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Answer:

I believe it would be 9/2 !

Step-by-step explanation:

Answer:W= B-3 or 3=B-W

Step-by-step explanation:

Answer:

54 X 68=3672

Step-by-step explanation:

Answer:

9 and 21

Step-by-step explanation:

setting up the equation

let x and y represent the two numbers

this means that x + y = 30

x - y = 12

using substitution to solve

if x - y = 12, that can be rearranged to x = y + 12.

substitute x = y + 12 into x + y = 30

you get (y + 12) + y = 30

simplify

2y + 12 = 30

2y = 18

y = 9

plug this into the original equation x + y = 30. this would be

x + 9 = 30

x = 21

the numbers are 21 and 9.

Answer:

128 degrees

Step-by-step explanation:

Opposite interior angles

Answer:

The package label stated that the net weight is 381.8g If every package has ... brand of candies have a mean weight of 0.8616g and a standard deviation of ...

Answer:

I’m pretty sure it’s 588

Step-by-step explanation:

14.70 * 40 = 588

Answer:

B

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Prime numbers after 167, 118, 82, 57, 41, are:

37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2

Prime numbers are numbers that only have two factors, 1, and themselves.

Apart from these factors, no number can divide them without a remainder.

By observation, the numbers 167, 118, 83, 57, 41, are written in descending order.

This means that the prime number to be chosen will be lesser than 41

Prime numbers lesser than 41 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Learn more on prime numbers here: https://brainly.com/question/145452

Answer:

perimeter=114

AREA= 308

Step-by-step explanation:

A^2 + B^2=C^2

then A+B=+C= P for triangle

52= triangle perimeter

rectangle:

(l+w)*2=p for rectangle=62

then add 52+62= 114

AREA- Triangle

b*h/2

22*10=220

220/2

= 110

AREA- Rectangle

l*w=A

22*9=198

ADD BOTH AREAS

198+110=308

HOPE IT HELPS

Answer:

[tex]\huge\boxed{2\times10^3}[/tex]

Step-by-step explanation:

[tex](8\times10^{-3})\div(4\times10^{-6})=\dfrac{8\times10^{-3}}{4\times10^{-6}}=\dfrac{8}{4}\times10^{-3-(-6)}=2\times10^{-3+6}=2\times10^3[/tex]

Used:

[tex]\dfrac{a^n}{a^m}=a^{n-m}\ \text{for}\ a\neq0[/tex]