4. Explain what the solution to the equation f(x) = g(x) means, both graphically and algebraically.

Answer:

3/36

Step-by-step explanation:

Answer:

2(3x) or 3x+3x could work

Answer:

f^(-1)(x) = 1/5x

Step-by-step explanation:

[tex] \large{f(x) = mx + b \longrightarrow f^{ - 1} (x) = \frac{x - b}{m} }[/tex]

Inverse Function is when we swap the x-term and y-term. Here is an explanation to the inverse of linear function above.

[tex] \large{f(x) = mx + b}[/tex]

Here we define f(x) = y. It is better to use y instead of f(x)

[tex] \large{y = mx + b}[/tex]

Swap x-term and y-term.

[tex] \large{x = my + b}[/tex]

Arrange/Simplify in the y-isolated equation.

[tex] \large{x - b = my} \\ \large {\frac{x - b}{ m} = y} \\ \large{ y = \frac{x - b}{m} }[/tex]

Since the function is in inverse form. It's recommended to use f^(-1) to point out that the function is an inverse of the original function.

[tex] \large \boxed{ {f}^{ - 1} (x) = \frac{x - b}{m} }[/tex]

Hence, y = (x-b)/m is an inverse of y = mx+b. A one-to-one function can have an inverse form. Back to the question!

We are given the linear function:

[tex] \large{f(x) = 5x}[/tex]

We will be using substitution method by substituting the original function in inverse form.

Since we know that the slope is 5 and doesn't have y-intercept which is b-value. Hence

[tex] \large{ {f}^{ - 1} (x) = \frac{x - 0}{5} } \\ \large{ {f}^{ - 1} (x) = \frac{x }{5} } \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]

Or we swap x-term and y-term.

[tex] \large{f(x) = 5x} \\ \large{y = 5x} \\ \large{x = 5y} \\ \large{ \frac{x}{5} = y} \\ \large{y = \frac{x}{5} = \frac{1}{5} x} \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]

Answer:

x < -4

I have attached the graph of the equation below and it looks exactly the same to the graph given!

Hope this helps!

Here is the graph of the equation above:

Answer:

D

Step-by-step explanation:

Answer:

1800

Step-by-step explanation:

Just find the area of all the triangles and add

Answer:

18 metres squared

Step-by-step explanation:

it looks like you want to find the area of the kite as a whole, and lucky for you, the kite is conveniently cut into right triangles.

to find the area of a right triangle, you use the equation

A = (b × h)/2

where A is the area, b is the base, and h is the height.

now we plug in the numbers for each individual area and solve for the total area.

let's start with the 1st triangle, where it's base is 30cm and the height is 25 cm.

A = (30 × 25)/2

A = 375 cm squared

now the next one whose base is 30 and it's height is also 25 (We just did this last time so the area is the same)

A = 375 cm squared

now we'll do the next one whose base is 30 and height is 35.

A = (30 × 35)/2

A = 525 cm squared

and the last one is the same as the one we just did so I'll just copy the other answer.

A = 525 cm squared

alright now we'll add up all of the areas we just found to get the total area of the kite.

Total A = 375 + 375 + 525 + 525

Total A = 1800 cm squared

now we will divide our total by 100 because it takes 100 centimetres to get 1 metre and what we have right now is centimetres.

1800/100 = 18 metres squared.

Answer:

179

Step-by-step explanation:

Step 1: Subtract the lesser amount from the larger amount

[tex]625 - 446 = 179[/tex]

Therefore, Mia has 179 more stamps than Paul

Answer:

13+8=21 in 8 years

13+y=blank years for now

hope this helps

have a good day  :)

Step-by-step explanation:

Answer:

24.

Step-by-step explanation:

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Then the greatest common factor is 24.

Answer:

65 cm

Step-by-step explanation:

16^2 x 63^2 = 65^2

We'll be using the Pythagoras property to solve this question.

According to the Pythagoras property,

H denotes hypotenuse

B denotes base

P denotes perpendicular

Here,

→ (x)² = (35 cm)² + (12 cm)²

→ x² = 1225 cm² + 144 cm²

→ x² = 1369 cm²

→ x = √(1369 cm²)

→ x = 37 cm

Therefore, value of x is 37 cm.

Answer: Choice B

y=1.0x+10

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

Explanation:

Without the actual (x,y) coordinates for each point, it's nearly impossible to get the answer. However, we can note that the blue regression line is intersecting the y axis at y = 10 (or around there). So its very likely that the answer is y=1.0x+10 which is choice B

The equation y=1.0x+10 is in the form y = mx+b with,

The next best answer is y = -0.8x+12, since 12 is fairly close to 10. The y intercept portion isn't fully shown but again it appears the blue line is crossing at y = 10.  

Answer:

There was a mistake in line D

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

Explanation:

Note in the previous line C that Noah multiplied both sides by 5. This is to clear out the fractions, since each have a denominator of 5.

In line D, Noah only multiplied those outer '5's by the first term in each parenthesis group. He didn't use the distributive property correctly.

The distributive property is a*(b+c) = a*b+a*c.

The 'a' is multiplied to everything inside, which are the terms b and c.

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

Here are what the steps should look like from line D and onward. Take note of the 30 and 100. This is from 5*6 = 30 and 5*20 = 100.

We end up with the same thing on both sides. So this confirms that x = 14/5 is the solution to the original equation.

Answer:

[tex]a _{n} = a( {r}^{n - 1} ) \\ a _{n} = 80(2 {}^{n - 1} ) \\ a _{n} = \frac{80. {2}^{n} }{ {2}^{ 1} } \\a _{n} = 40( {2}^{n} ) \\ a _{n} = ( {2}^{3} \times 5)( {2}^{n} ) \\ a _{n} = 5( {2}^{n + 3} )[/tex]

Answer:

24km²

Step-by-step explanation:

12-4 is 8 and if you visualize the triangle being put on top of the other triangle it makes a complete rectangle in which you multiple 8 time 3 to get 24 km²

Answer:

24 km²

Step-by-step explanation:

12 - 4 = 8

8 ÷ 2 = 4

4 · 3 = 12

12 ÷ 2 = 6

4 · 3 = 12

6 km² + 12 km² + 6 km²

24 km²

Answer:

When you multiply a number by a fraction, the number always decreases. When you multiply a number by 1/2, it's always half of the original number

Step-by-step explanation:

For example, take 4 x 1/2. It can be written as four halves. What do we get when we add four halves together?

1/2 + 1/2 + 1/2 + 1/2 = 2!

2 is less than 4. It is also half of the number four

Answer:

v = - 2

Step-by-step explanation:

Given

- 12 = 2 + 5v + 2v ( subtract 2 from both sides )

- 14 = 7v ( divide both sides by 7 )

- 2 = v

Answer:

[tex](a)\ x < 150[/tex]

[tex](b)\ x = 149; x = 148[/tex]

Step-by-step explanation:

Given

[tex]Amount = 150[/tex] --- not more than

[tex]x \to[/tex] spending

Solving (a): Represent as an inequality

Not more than means <

So, the inequality is:

[tex]Spending < Amount[/tex]

[tex]x < 150[/tex]

Solving (b): The first two possible solutions

These are the numbers closest to 150 i.e. 149 and 148

Hence, [tex]x = 149; x = 148[/tex]

This is equivalent to y = 3x+4 (slope intercept form)

By "standard form", I mean the form Ax+By+C = 0.

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

Explanation:

Let's solve the first equation for y

x+3y-4 = 0

x+3y = 4

3y = 4-x

3y = -x+4

y = (-x+4)/3

y = (-x/3) + (4/3)

y = (-1/3)x + (4/3)

The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.

Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.

So this mystery perpendicular line we're after has a slope of 3.

It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.

2x+5y-20 = 0

2(0)+5y-20 = 0

5y-20 = 0

5y = 20

y = 50/5

y = 4

The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.

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

We found that:

So we know that,

y = mx+b

y = 3x+4

is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well

y = 3x+4

y-3x = 4

-3x+y = 4 .... one way to express standard form

-3x+y-4 = 0 .... another standard form

Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.

Answer:

16+3x=22.75

22.75-16=6.75

6.75÷3=2.25=x

Answer:

y = x-4

Step-by-step explanation:

y = x +4

This has a slope of 1 since it is in the form y = mx+b where m is the slope and b is the y intercept

Parallel lines have the same slope

The line we are interested in passes through the point (0,-4) which means it has a y intercept of -5

y = mx+b

y = 1x-4

y = x-4

Given :

A cuboid shaped tank with sides 3.2 cm , 2.8 cm and 1.6 cm.

To Find :

The volume of the tank.

Solution :

We know, volume of a cuboid is given by product of its sides or :

[tex]V = l\times b \times h\\\\V = 3.2 \times 2.8 \times 1.6 \ cm^3\\\\V = 14.336 \ cm^3[/tex]

Therefore, the volume of the tank is 14.336 cm³ .

Answer:

The first is A and the second Is A

Answer:

8

Step-by-step explanation:

y=kx

-12=-4k

k=3

24=3x

x=8

y=kx

-12=-4

k=3

24=3x

X=8

Answer:

19

Step-by-step explanation:

The boots are the value of 10, since 3 equal 30. The man is the value of 5 since there are two men (10) and one boot (also 10) which made 20. The ribbon is the value of 4 since there is one man (5) and 2 ribbons (8 ) which made 13. add 10, 5 and 4 and you get 19.

Answer:

16

Step-by-step explanation:

From the first equation, I can infer that one pair of boots equals 10 because 10+10+10=30. Also, I can infer that just one boot equals 5 because there are 6 boots in total and 5+5+5+5+5+5=30

From the second equation, I can infer that one boy equals 5 because 2 boys which equal 10 plus one pair of boots which equals 10 is 20.

From the third equation, I can infer that one pair of ribbons is 4 because the boy equals 5 and 13-5=8. There are two pairs of ribbons so 8/2=4. I can also infer that just one ribbon is 2 because 8 divided by 4 individual ribbons is 2.

So, for the last equation, it would be 5+9+2 which the answer would equal 16. The one boot that would equal 5 plus the boy and 2 individual ribbons he's holding in his hands would equal 9 plus one ribbons which would equal 2 would all equal 16.

Hope this is helpful.

Answer:

The perimeter would be  6x + 12

Step-by-step explanation:

The perimeter of a triangle is the sum of all its sides.

The measures of the sides of the given triangle are:-

3x + 2, x + 6 and 2x + 4

So, to find perimeter add these values together:-

3x + 2 + x + 6 + 2x + 4

Bring all the 'x' terms together first and then the other numbers so we can add them:-

3x + 2x + x + 2 +  6  + 4

6x + 12

AB = [tex]x[/tex] + 6

BC = 2 [tex]x[/tex] + 4

AC = 3 [tex]x[/tex] + 2

The perimeter of the triangle.

[tex]{\boxed{\mathcal{\red{The\: perimeter \:of\:the\:triangle\:is\: 6x\:+\:12.\:✅}}}}[/tex]

We know that,

[tex]\sf\pink{Perimeter\:of\:a\:triangle\:=\:Sum\: of\: all \:three\: sides}[/tex]

[tex] = AB + BC + AC \\ = x + 6 + 2x + 4 + 3x + 2 \\ = 6x + 12[/tex]

[tex]\sf\red{Therefore, \:the\: perimeter\:of \:the\:triangle\: is \:6x\:+\:12.}[/tex]

[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]

Answer:

[tex]y = {(0.7634)}^{4} \\ log(y) = 4 log(0.7634) \\ log(y) = - 0.46899 \\ y = {10}^{ - 0.46899} \\ y = 0.3396[/tex]