What is the solution to the system of equations graphed below?
- 3x+2
y = 5x + 28

Answer:

23.09 meters.

Step-by-step explanation:

Sin(60) = opposite / hypotenuse =  pole / steel wire

pole = 20 m

angle = 60 degrees.

sin(60) = 20/ hypotenuse       multiply both sides by the hypotenuse

hypotenuse * sin(60) = 20      divide by sin(60)

hypotenuse = 20 / 0.866        do the division    

hypotenuse = 23.09

The steel wire = 23.09 meters.

Answer:

(3,4)

Step-by-step explanation:

The system of equations is:

x+6y=27

7x-3y=9.

I looked up "metodo de igualacion". It is basically American for doing substitution.

However, the only difference is you are asked to solve both equations for a variable.

The first equation looks easy to solve for x. So I'm going to solve both equations for x.

x+6y=27

Subtract 6y on both sides:

x     =-6y+27

7x-3y=9

Add 3y on both sides:

7x    =3y+9

Divide both sides by 7:

x     =3/7 y +9/7

So both equations are solved for x.  You want to find when the x's are the same because you are looking for a common amongst the lines given.

So we have

-6y+27=3/7 y  +9/7

I hate the fractions honestly so I'm going to multiply both sides by 7 so they will no longer be for now:

-42y+189=3y + 9

Now add 42y on both sides:

         189=45y+9

Subtract 9 on both sides:

        180=45y

Divide both sides by 45:

            4=y

If 4=y, then y=4.

So now once we have obtain 4 for y, we will use one of the equations given along with it to find x. Just choose one. Choose the easier looking one to you.

I like the x=-6y+27 with y=4.

So replace y with giving you:

x=-6(4)+27

x=-24+27

x=3

So the solution is (x,y)=(3,4).

x=3 and y=4.

By using the method of substitution, we isolate one variable, substitute it in the other equation, and solve for the remaining variable. Applying these steps to the provided system of equations gives us the solution x=3, y=4.

The provided system of equations can be solved using the method of substitution. For this method, we first need to isolate one variable in one of the two equations. In this case, let's isolate 'x' from the first equation, which gives us:
x = 27 - 6y.
Now, we substitute this 'x' value into the second equation to get:
7(27 - 6y) - 3y = 9.
This simplifies to:
189 - 42y - 3y = 9
Combining like terms gives us:
-45y = -180
We can solve for 'y' by dividing each side by -45:
y = 4.
Substituting this value of 'y' back into the first equation gives us:
x = 27 - 6(4) = 3.
Therefore, the solutions for the system are x=3 and y=4.

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Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]

Step-by-step explanation:

First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1)  by the denominator (which is 2) of the fraction:

[tex]\frac{1}{2}=0.5[/tex]

Now you must add 0.5 to the whole number part. Then:

[tex]1+0.5=1.5[/tex]

In order to find the ratio of cleaner to water, you must divide 1.5  cups of cleaner by 12 cups of water.

Therefore, the ratio is:

[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]

Answer:

B.the set of all first elements of the function

Step-by-step explanation:

the domain is all the x variables in a function

Answer:

B. The set of all first elements of the function.

Step-by-step explanation:

We have been given a incomplete sentence. We are asked to complete our given sentence.

We know that the domain of a function is all real values of independent variable for which a function is defined and gives exactly one output.

We know that independent variable is x, which is first element of a point, therefore, the domain of a function is the set of all first elements of the function.

Answer:

D. More Than 1 Solution

Step-by-step explanation:

Let the system of equations be:

[tex]a_1x+b_1y=c_1...(1)[/tex]

[tex]a_2x+b_2y=c_2...(2)[/tex]

If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.

What that means is that; the two graphs intersects at infinitely many points.

Therefore the system must have infinitely many solutions.

In other words the system has more than one solution.

NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.

Answer:

r ≤ 29, r-5

The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

Amount to spend = $24

Regular price = r

Sale = $5

Sale Price = r-5

The regular price will be $5, at the max, more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price:

r-5 ≤ 24

r ≤ 29

So, the product Roopesh can afford is $29 or less than that.

What is the unknown? r ≤ 29

Following expression can represent the sale price:

Sale price = r-5  

The sale price can be compared with the regular price with the following:

Inequality representing the situation: r-5 ≤ 24

Answer:

Step-by-step explanation:

What is unknown?

We are missing the regular price of an item

Which expression can represent the sale price?

$24 - x = the sales price

and the x equals the original price since we don't know the actual price.

Which comparison could  be used?

$24 spend on a birthday gift to a the shopping sale offering $5 off the regular price.

And the rest I don't know son or girl

Answer:

(L + 10)/(L + 16) = 0.8

Step-by-step explanation:

She needs to answer L more questions to get a grade of 80%.

When she answers L more questions correctly, she will have answered L + 10 questions correctly.

The total number of questions will be L + 16.

L + 10 must be 80% of L + 16

(L + 10)/(L + 16) = 0.8

Cheryl must use the equation 0.80 = (10 + I) / (16 + I) to determine how many consecutive questions she needs to answer correctly to reach her goal of 80% accuracy on her test.

Cheryl has answered 16 questions on her online test with 10 correct responses. To achieve her goal of 80% accuracy, she must determine how many additional questions she must answer correctly in a row.

To find the necessary total number of correct answers (T) for 80% accuracy, we use the equation:

0.80 = (10 + I) / (16 + I)

where I represents the number of consecutive questions Cheryl answered correctly after the initial 16 questions.

Answer:

Its C. XD sorry i just answered this.

Step-by-step explanation:

Hope this helped again! :3

Answer:

Each path in the diagram is a possible outcome with a probability of 1/4. The sum of all paths should equal 1.

 The answer is C.

Answer:

1 triangle is possible

Step-by-step explanation:

If there are two sides and a non included angle is given then there could be 0,1 or 2 triangles depend on the measure of the given angle and the lengths of the given sides.

We will discuss some conditions which will clarify that how many triangles are there in the given condition.

CASE 1: If A is obtuse and a>b then there is 1 triangle.

CASE 2: If A is obtuse and a<b then there is 0 triangle.

CASE 3:  If A is acute and a>b then there is 1 triangle.

CASE 4:  If A is acute  and h<a<b then there are 2  triangles possible.

CASE 5: If A is acute  and a=h then there is 1 right angle triangle.

CASE 6: If A is acute and a<h then there are 0 triangles possible.

Therefore according to the given condition A= 6° which is acute and a>b, So this condition matches the CASE 3:

According to this there is 1 triangle possible....

Answer:

Area of the triangle is 25.9 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°

∵ b = 2.92 feet

- b is the side opposite to angle B

∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°

- Lets find c the side opposite to angle C by sing the sine rule

∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]

∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]

- By using cross multiplication

∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]

- The area of the triangle = 1/2 (b)(c)sin∠A

∵ The sum of the interior angles of a triangle is 180°

∴ m∠ A + m∠ B + m∠ C = 180°

∵ m∠ B = (28/3)°

∵ m∠ C = (242/3)°

∴ m∠ A + 28/3 + 242/3 = 180

∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides

∴ m∠ A = 90°

∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)

∵ sin(90) = 1

∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²

* Area of the triangle is 25.9 feet²

The height of the triangle is approximately [tex]4.35\text{ mm}[/tex]

Step-by-step explanation:

The area of a triangle can be calculated by using the Heron's formula.

Heron's formula:  

Suppose a triangle has sides [tex]a'[/tex], [tex]b'[/tex] and [tex]c'[/tex], then the semi-perimeter [tex]S[/tex] of the triangle is represented by the expression,

[tex]S=\frac{a'+b'+c'}{2}[/tex]

The area [tex]A[/tex] of the traingle is formulated below.

[tex]\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}[/tex]

To calculate the area of the triangle with sides [tex]9 \text{ mm}[/tex] , [tex]6 \text{ mm}[/tex] and [tex]12 \text{ mm}[/tex], first find the semi-perimeter.

[tex]S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}[/tex]

Now, the area of the triangle is calculated below.

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122[/tex]

Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,

[tex]\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}[/tex]

Now, the area of the same triangle can also be calculated as,

[tex]A=\frac{1}{2}(12)(x)\\A=6x[/tex]

In the above calculations, area of the triangle is calculated in two ways.

Therefore, both the areas can be equated to obtain the altitude [tex]x[/tex].

[tex]6x=26.122\\x=\frac{26.122}{6}\\x=4.35[/tex]

Thus, the height of the triangle is evaluated as [tex]\fbox{4.35 \text{ mm}}[/tex].

Learn more:

1. Prove that AB2+BC2=AC2https://brainly.com/question/1591768

2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? https://brainly.com/question/9880052

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Area of triangle

Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle

Answer:

4.3 mm

Step-by-step explanation:

I got it correct on founders edtell

Answer:

1

Step-by-step explanation:

To solve, combine like terms.

Subtract 6x from both sides.

[tex]2=3x-1[/tex]

Add 1 to both sides.

[tex]3=3x[/tex]

Divide both sides by 3.

[tex]1=x[/tex]

Answer: $212.5

Step-by-step explanation:

250% = 2.5

So we multiply 85.00 by 2.5

85*2.5=212.5

So it is $212.5

Answer:

your answer is  $212.5

Step-by-step explanation:

Answer:

(2, 22 )

Step-by-step explanation:

Given the 2 equations

y = 7x + 8 → (1)

y = x + 20 → (2)

Substitute y = 7x + 8 into (2)

7x + 8 = x + 20 ( subtract x from both sides )

6x + 8 = 20 ( subtract 8 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Substitute x = 2 in (2) for corresponding value of y

y = x + 20 = 2 + 20 = 22

Solution is (2, 22 )

Answer:

(2,22)

Step-by-step explanation:

A-P-E-X :)

Answer:

[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]

Step-by-step explanation:

1st boat:

Parabola equation:

[tex]y=ax^2 +bx+c[/tex]

The x-coordinate of the vertex:

[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a[/tex]

Equation:

[tex]y=ax^2 -2ax+c[/tex]

The y-coordinate of the vertex:

[tex]y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10[/tex]

Parabola passes through the point (-8,1), so

[tex]1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1[/tex]

Solve:

[tex]c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}[/tex]

Parabola equation:

[tex]y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}[/tex]

2nd boat:

Parabola equation:

[tex]y=ax^2 +bx+c[/tex]

The x-coordinate of the vertex:

[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0[/tex]

Equation:

[tex]y=ax^2+c[/tex]

The y-coordinate of the vertex:

[tex]y_v=a\cdot 0^2+c\Rightarrow c=-7[/tex]

Parabola passes through the point (-8,1), so

[tex]1=a\cdot (-8)^2-7\\ \\64a-7=1[/tex]

Solve:

[tex]a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7[/tex]

Parabola equation:

[tex]y=\dfrac{1}{8}x^2 -7[/tex]

System of two equations:

[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]

Let P = Patrick's age

P + 8 = 18

The equation is P + 8 = 18

Let P = Patrick's age

An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.

A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.

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Answer:

Id say 35

Sorry of im wrong :{

Answer:

Option C.   2508 cubic inches is the correct answer

Step-by-step explanation:

From the figure we can see that, a sink

Points to remember

Volume of hemisphere = (2/3)πr³

Where 'r' is the radius

To find the volume of large hemisphere

Here radius = 13 in

Volume V₁ =  (2/3)πr³

 = (2/3) * 3.14 * 13³

 = 4599.33 cubic inches

To find the volume of small hemisphere

Here radius = 13 - 3 = 10 in

Volume V₂ =  (2/3)πr³

 = (2/3) * 3.14 * 10³

 =2093.33 cubic inches

To find the volume of sink

Volume = V₂ - V₁

  = 4599.05 - 2093.33

 =2505.72 ≈ 2508 cubic inches

Option C.   2508 cubic inches is the correct answer

Answer:

Option B 125°

Step-by-step explanation:

In this problem we need to calculate the measure of angle ∠6

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

see the attached figure to better understand the problem

∠6=(1/2)[arc AB+arc CD]

(arc AB+arc CD)=360°-(60°+50°)=250°

substitute

∠6=(1/2)[250°]=125°

Answer:

3x+8 I think

Step-by-step explanation:

add 5, -1 and 4

Answer:

The CORRECT answer is C,  7x+4

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]

Step-by-step explanation:

[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]

Answer: [tex]x^{16}\ y^{22}[/tex]

Step-by-step explanation:

The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]

Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have

[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]

Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]

( its also an equivalent expression to given expression.)

Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have

[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]

Hence, the expression is equivalent to given expression :

[tex]x^{16}\ y^{22}[/tex]

Answer:

(gof) (1) = 0

Step-by-step explanation:

f(x) = -4x + 7

g(x) = 2x - 6

(gof) (1)

First find f(1)

f(1) = -4(1) + 7

f(1) = -4+7=3

Then put 3 in for x in g(x)

g(f(1) = 2(f(1))-6

        = 2 (3) -6

        = 6 -6

        = 0

[tex](g\circ f)(x)=2(-4x+7)-6=-8x+14-6=-8x+8\\\\(g\circ f)(1)=-8\cdot1+8=0[/tex]

Answer:

[tex]x\leq10[/tex]

Step-by-step explanation:

we know that

The algebraic expression of the phrase "It is at most ten" is equal to

[tex]x\leq10[/tex]

All real numbers less than or equal to 10 (the number 10 is included)

The solution of this inequality is the interval -----> (-∞,10]

Answer:

B

Step-by-step explanation:

Answer:

1/3x+4 ≤ 2x+12

Step-by-step explanation:

x ≤ -24/5

Answer:

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Step-by-step explanation:

Given  : The sum of one third a number and 4 is at the most the sum of twice that number and 12.

To find : Write expression .

Solution : We have given statement

According to question :

Let the number = x

One third of a number = [tex]\frac{1x}{3}[/tex].

Sum of one third of number and 4 =  4 +  [tex]\frac{1x}{3}[/tex].

Twice a number  =  2x

Sum of twice that number and 12 =  2x +  12

So,  sum of one third a number and 4 is at the most the sum of twice that number and 12.

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

greater than equal to sign for at most.

Therefore, 4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Answer:

-3

Step-by-step explanation:

If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3

Answer:

4x^2(5x^4 / 2x^2)= 10 x^4

Step-by-step explanation:

We want factorize the expression 4x^2(5x^4 / 2x^2)

And to do this, we need to remember key properties of exponents.

Those are:

[tex]x^{m} / x^{n} = x^{m-n}[/tex]

[tex]x^{m} * x^{n} = x^{m+n}[/tex]

So

4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4

Answer:

Explicit form:    [tex]a_n=8+4n[/tex]

Seventh term:  [tex]a_7=36[/tex]

You gave the recursive form:

[tex]a_n=a_{n-1}+4 \text{ with } a_1=12[/tex]

Step-by-step explanation:

You already have the recursive formula which is:

[tex]a_n=a_{n-1}+4[/tex] where [tex]a_1=12[/tex].

Maybe you looking for the explicit form and also the 7th term?

You were just looking for the 7th term.  Sometimes you can read the recursive formula pretty easily and understand the pattern that is happening.

[tex]a_{n-1}[/tex] is the term right before [tex]a(n)[/tex].  Just like [tex]a_5[/tex] would be the term right before [tex]a_6[/tex].

Anyways becak to our recursive for a sequence that was given:

[tex]a_{n}=a_{n-1}+4[/tex] says term=previous term+4.

So you adding 4 over and over to generate the terms of a sequence.  This is arithmetic sequence because it is going up by same number (or could go down by same number).  The common difference is 4.

[tex]a_1=12[/tex]

[tex]a_2=12+4=16[/tex]

[tex]a_3=16+4=20[/tex]

[tex]a_4=20+4=24[/tex]

[tex]a_5=24+4=28[/tex]

[tex]a_6=28+4=32[/tex]

[tex]a_7=32+4=36[/tex]

Now if you don't like that. You could just blindly without trying to understand the meaning of it just plug numbers in:

[tex]a_1=12[/tex]

For if we wanted to know the 2nd term; we would plug in 2 for n:

[tex]a_2=a_{2-1}+4[/tex]

[tex]a_2=a_1+4[/tex]

[tex]a_2=12+4[/tex]

[tex]a_2=16[/tex]

Plug in 3 for the 3rd term:

[tex]a_3=a_{3-1}+4[/tex]

[tex]a_3=a_2+4[/tex]

[tex]a_3=16+4[/tex]

[tex]a_3=20[/tex]

Plug in 4 for the 4th term:

[tex]a_4=a_{4-1}+4[/tex]

[tex]a_4=a_3+4[/tex]

[tex]a_4=20+4[/tex]

[tex]a_4=24[/tex]

Plug in 5 for the 5th term:

[tex]a_5=a_{5-1}+4[/tex]

[tex]a_5=a_4+4[/tex]

[tex]a_5=24+4[/tex]

[tex]a_5=28[/tex]

Plug in 6 for the 6th term:

[tex]a_6=a_{6-1}+4[/tex]

[tex]a_6=a_5+4[/tex]

[tex]a_6=28+4[/tex]

[tex]a_6=32[/tex]

Plug in 7 for the 7th term:

[tex]a_7=a_{6-1}+4[/tex]

[tex]a_7=a_5+4[/tex]

[tex]a_7=32+4[/tex]

[tex]a_7=36[/tex]

Now if you look at the points we just got (I will just go up to 4 terms):

n  (treat as x)  |  1           2                3                 4

a(n) (treat as y|  12        16               20                24

The explicit form in not in terms of other terms of the sequence.  You are looking here for an equation that relates n (x) to a(n) (y).

I'm just going to use x and y until the end where I will replace them back in terms of n and a(n).

This is a line because the's rise/run (the slope) is the same per choosing of points.

That is the following is true:

[tex]\frac{16-12}{2-1}=\frac{20-16}{3-2}=\frac{24-20}{4-3}[/tex] son on....

These all the the value 4, the same number that the arithmetic sequence is going up by.  

So in an arithmetic sequence, the common difference is the slope of the line.

I'm going to use point-slope formula which is [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

So we have m=4 and [tex](x_1,y_1)[/tex] could be any of the 7 we found, but I will choose (1,12) for it:

[tex]y-12=4(x-1)[/tex]

Add 12 on both sides:

[tex]y=12+4(x-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

This is actually in the form of most books formulas for an explicit form which is [tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term and d is the common difference.

So another way to do the problem:

You would have to know the following are equivalent:

[tex]a_n=a_{n-1}+d[/tex] with [tex]a_1 \text{ is given}[/tex]

and

[tex]a_n=a_1+d(n-1)[/tex].

If you know these are equivalent then you could compare [tex]a_n=a_{n-1}+d[/tex] to [tex]a_n=a_{n-1}+4[/tex] and determine d is 4.

You could also see that [tex]a_1[/tex] is give as 12.

Then you just plug into:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

You could also simplify this equation just a bit.

You could distribute and then combine a pair of like terms.

Like so,

[tex]a_n=12+4(n-1)[/tex]

[tex]a_n=12+4n-4[/tex]

[tex]a_n=8+4n[/tex]

Step-by-step explanation:

200 calories come from fat, out of 5000 calories total.  We can find the percentage with a proportion:

200 / 5000 = x / 100

x = 4

4% of the total calories come from fat.