Select the correct answer. Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27

To solve this, we need to turn this word problem into a system of linear equations. To do this, let's use x to stand for Mr. Fontana's age, and y to stand for his son's age.

The first sentence states that eight years ago, Mr. Fontana was six times as old as his son.

eight years ago = x - 8

Fontana was six times as old as his son = 6(y - 8). Remember, we need subtract 8 from his son's age, which is why I wrote it as 6(y - 8), and his father was 6 times his son's age 8 years ago, which is why I multiplied 6 by y - 8.

Now, putting this all together gives us our first equation:

x - 8 = 6(y - 8)

We can now rewrite this equation in standard form:

x - 8 = 6y - 48 ----->

x - 6y = -48 + 8 ----->

x - 6y = -40 <----- this is our first linear equation

To find our second, we need to turn the second sentence into an equation. It says that in 12 years, Mr. Fontana will be twice as old as his son:

x + 12 = 2(y + 12)

Now, we need to rewrite this equation in standard form:

x + 12 = 2y + 24 ----->

x - 2y = 24 - 12 ----->

x - 2y = 12 <----- this is our second linear equation. We now have our system of equations:

x - 6y = -40

x - 2y = 12

Now we can find the father's age (x) and his son's age (y). First, multiply the second equation by -1, giving us:

x - 6y = -40

-x + 2y = -12

Now we can add both equations together:

x - x - 6y + 2y = -40 + -12 ----->

-4y = -52

Solve for y, by dividing both sides of the equation by -4, giving us:

y = 13

So, now we know the son's age: 13

To find the father's age, replace y in either the first equation or the second equation, with 13. Let's use the first equation:

x - 6(13) = -40 ----->

x - 78 = -40 ----->

x = 78 - 40 ----->

x = 38

Therefore, Mr. Fontana is 38 years old and his son is 13 years old.

Answer:

B

Step-by-step explanation:

[tex] \frac{3}{8} \div \frac{2}{7 } \\ = \frac{3}{8} \times \frac{7}{2 } \\= \frac{21}{16} \\ = 1 \frac{5}{16} [/tex]

Answer:

The man traveled 20km by train.

Step-by-step explanation:

If x is the distance he traveled by train, you can write this equation to represent the situation:

[tex]10+x+2x=70[/tex]

Then, you can simply solve for x:

[tex]10+3x=70\\3x=60\\x=20[/tex]

The man traveled 20km by train.

[tex]10+(20)+2(20)=70\\10+20+40=70\\70=70[/tex]

it's took 10 hour maybe what subject is this

Answer:

$1155

Step-by-step explanation:

10% of the first $900 is $90.

The rest of her sales is 8000 - 900 = 7100. 7100 * .15 = 1065.

Add them together to get $1155.

Answer:674.475

Step-by-step explanation:

(690)(0.15)= 103.5

690-103.5= 586.5 (after first markdown)

(586.5)(0.15)= 87.975

586.5+87.975 (Final price after markup)

Answer:

23°

Step-by-step explanation:

Opposite angles so:

60° = 2x + 14

Therefore:

x = 23°

Answer:

x is 23°

Step-by-step explanation:

those opposite angles and are always equal to each other...so to get x take 60-14 then answer divide by two

Answer:

x=120

Step-by-step explanation:

this is obtained by finding 22% of x, and equating it to the answer as shown below

x *22/100 = 26.4

22x/100 = 26.4

22x = 2640

x =120

Answer:

1/4

Step-by-step explanation:

1/4 because it is one piece out of the four cuts. if it were yellow, than it would be 2/4, or 1/2

Answer:

I don't have any idea of that question

Step-by-step explanation:

I'm sorry

Answer:

(w+3)(w+1)

Step-by-step explanation:

In w^2 + 3w+w + 3,

we group it so that it looks like (w^2+w) + (3w+3)

Then we factor so that is w(w+1) + 3(w+1).

Distributive property(converse) allows us to simplify to (w+3)(w+1)

Answer:

1280

Step-by-step explanation:

look at the 6 in the number

is it 4 or less

or is it 5 or more

as the number is 6 ( more than 5)

then you are going to add 1 to the tens

so the final answer is 1280

I really hope this helps and have a great day

Check the picture below.

Answer:

1

Step-by-step explanation:

Look at the LHS: you have the square of x, then you have 2 times x, times -1. to complete a square you just need to add the square of -1, that is 1. That becomes

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

Answer:

Y intercept is (0,3)

Step-by-step explanation:

Check out the image

Answer:

6x - 20 = 4x + 50

2x = 70

x = 35

Answer:

1/12

Step-by-step explanation:

rolling 4 on a cube= 1outcome/6 total=1/6

pulling red marble= 3 possible red marble/6 total marbles=1/2

1/6*1/2=1/12

Answer:

x=-1/2

Step-by-step explanation:

2x+2=4x+3

-1=2x

x=-1/2

Answer:

y = -2/5 x +1

Step-by-step explanation:

We know two points on the line (-5,3) and ( 5,-1)

We  can find the slope using the slope formula

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

m = ( -1 -3)/( 5- -5)

   = (-1-3)/ (-5+5)

  -4/10

 =-2/5

Using the slope intercept form of the the lint

y = mx+b  where m is the slope and b is the y intercept

y = -2/5 x+b

Using one of the point and substitute in for x and y

3 = -2/5 (-5) +b

3 = 2 +b

1 = b

y = -2/5 x +1

The equation of the line passes through the points (0, 1) and (5, -1) will be;

[tex]y = - \dfrac{2}{5}x + 1[/tex]

The equation of a line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 1) and (5, -1).

Now,

Since, The equation of line passes through the points (0, 1) and (5, -1).

So, We need to find the slope of the line.

Hence, the Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 1) / (5 - 0)

m = - 2 / 5

Thus, The equation of the line with slope - 2/5 is,

[tex]y - 1 = - \dfrac{2}{5} (x - 0)[/tex]

[tex]y - 1 = - \dfrac{2}{5}x[/tex]

[tex]y = - \dfrac{2}{5}x + 1[/tex]

Therefore, The equation of a line is [tex]y = - \dfrac{2}{5}x + 1[/tex].

To learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ3

[tex]\rule{2000pt}{1000000pt}[/tex]

The equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]  

The graph is an exponential function, and it passes through the points:

[tex](x,y) = (1,1)\ (0,2)[/tex]

An exponential function is represented with:

[tex]y = ab^x[/tex]

At (0,2), we have:

[tex]ab^0 = 2[/tex]

This gives

[tex]a(1) = 2[/tex]

[tex]a = 2[/tex]

At (1,1), we have:

[tex]ab^1 = 1[/tex]

[tex]ab = 1[/tex]

Substitute 2 for (a)

[tex]2b = 1[/tex]

Divide both sides by 2

[tex]b = \frac 12[/tex]

Substitute values for a and b in [tex]y = ab^x[/tex]

[tex]y = 2(\frac 12)^x[/tex]

Hence, the equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]

Read more about exponential functions at:

https://brainly.com/question/19704059

Step-by-step explanation:

hope it will help you and please mark the answer as brillant please.

BA=(3),(3),(-1) is the answer

Answer:

All the mentioned can be constructed with the help of piling method. But, for construction of B and D we need a point as well.  

Please give brainliest only need 3 more brainliest before next rank!

Step-by-step explanation:

a) Yes, a cube can be formed by stacking polygons. If we stack squares one upon another, then the resulting 3-D figure would be a cube.

b) Yes, a cone that does not include the point can be made by stacking disc. If we stack discs such that the discs are arranges in descending order then the resultant 3-D figure would be a cone that does not include a point.

c) Yes, a pyramid can be formed by stacking polygons.

If we stack squares such that they are arranged in descending order of their side length and stacked by a point on the top. Then the resultant figure would be a  pyramid that includes a vertex.

f) There are many types of prism. Fro example a rectangular prism can be constructed by simply stacking rectangle polygon on one another.

e) Yes, a cone can be formed by stacking disc.

We need to stack disks arranged in descending order of their radius stacked with a point on the top. The resulting figure would be a cone that includes a point.

f) Yes, a cylinder can be formed by stacking. We need to stack discs of same radius to get a cylinder.

Answer:

B and D

Step-by-step explanation:

Answer:

The domain corresponds to the values of the x and the range to the values of the y. So:

D: {-3, 0, 3}

R: {-6, 0, 6}

Answer:

[tex]\huge\boxed{A.}[/tex]

Step-by-step explanation:

Domain:

"Set of values on x-axis"

Domain = {-3,0,3}

Range:

"Set of values on y-axis"

Range = {-6,0,6}

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

68

Step-by-step explanation:

because 180-44=136

136:2=68 (since TRS=TSR, there is formula)

Answer:it's a for sure I think