Rewrite the following equation in slope-intercept form. 17x − 4y = 20

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:

its 3 OR C

Step-by-step explanation:

Answer:

a. about 8.3%

b. 2.172 m

Step-by-step explanation:

a. 1.81 * x = 1.96

x = 1.083

Percent increase is approximately 8.3%

b. 1.81 * 1.2 = x

x = 2.172 m

Answer:

If you're moving the vehicle to the right, shoulder check by moving your head 90° to the right. Turn your head 90° degrees in the direction you're moving the vehicle. And, if you're moving the vehicle to the left, you shoulder check to the left by turning your head 90° to the left.

[tex]\begin{cases} x=-7\implies &x+7=0\\ x=0\implies &x=0\\ x=1\implies &x-1=0\\ x=6\implies &x-6=0 \end{cases}\qquad \implies (x+7)(x)(x-1)(x-6)=\stackrel{y}{0} \\\\\\ (x+7)(x)\stackrel{using~\mathbb{FOIL}}{(x^2-7x+6)}=0\implies (x^2+7x)(x^2-7x+6)=0[/tex]

[tex]\begin{array}{llll} x^2-7x+6\\ \qquad \times ~x^2\\\cline{1-1} x^4-7x^3+6x^2 \end{array}\qquad +\qquad \begin{array}{llll} x^2-7x+6\\ \qquad \times ~7x\\\cline{1-1} 7x^3-49x^2+42x \end{array} \\\\\\ (x^4-7x^3+6x^2)+(7x^3-49x^2+42x)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x^4-43x^2+42x=y~\hfill[/tex]

[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]

now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.

let's recall something else, that same/same = 1, so

[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]

therefore

[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]

[tex] \rm \frac{19}{12} - \frac{3}{4} = \frac{9}{12} - \frac{9}{12} = \frac{9 - 9}{12} = \frac{0}{12} = \bf0 \: \: (done.)[/tex]

Answer:

[tex]\frac{19}{12} - \frac{3}{4}=\frac{5}{6}[/tex]

Step-by-step explanation:

[tex] \frac{19}{12} - \frac{3}{4} [/tex]

[tex] = \frac{19 \times 4}{12 \times 4} - \frac{3 \times 12}{4 \times 12}[/tex]

[tex] = \frac{76}{48} - \frac{36}{48} [/tex]

[tex] = \frac{76 - 36}{48}[/tex]

[tex]= \frac{40}{48} [/tex]

[tex] = \frac{40 \div 8}{48 \div 8} [/tex]

[tex] = \frac{5}{6}[/tex]

Answer:

The bisector of a given angle

Step-by-step explanation:

Because, the given picture shows an acute angle and the markings on it are of which you can see when a bisector is being searched for.

Answer:

Slope = 4

Step-by-step explanation:

Change in Y = 4

Change in X = 1

Slope = Δy/Δx = 4/1 = 4

Answer: 1600m^2

Its a square so all sides are equal. So...

400m * 400m

= 1600m^2

The maximum number of bags is an illustration of the greatest common factor

The maximum number of bags John can make is 8

The given parameters are:

[tex]Chocolate=48[/tex]

[tex]Peanut=56[/tex]

Start by expressing 48 and 56 as a product of their factors.

[tex]Chocolate = 1 \times 2 \times 2 \times 2 \times 2 \times 3[/tex]

[tex]Peanut = 1 \times 2 \times 2 \times 2 \times 7[/tex]

The product of the common factors between the above products is:

[tex]Factors = 1 \times 2 \times 2 \times 2[/tex]

Multiply

[tex]Factors = 8[/tex]

The above represents the greatest common factor of 48 and 56.

Hence, the maximum number of bags John can make is 8

Read more about greatest common factor at:

https://brainly.com/question/219464

Step-by-step explanation:

To determine the maximum number of bags John can make, we need to find the greatest common divisor (GCD) of the two quantities: 48 chocolate chip cookies and 56 peanut butter cookies.

The GCD is the largest number that divides both quantities without leaving a remainder. It represents the maximum number of bags that can be made, with each bag containing an equal number of cookies of each type.

Let's find the GCD of 48 and 56:

Step 1: List the divisors of each number:

Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Step 2: Identify the common divisors in both lists:

Common divisors of 48 and 56: 1, 2, 4, 8

Step 3: Determine the greatest common divisor (GCD):

The greatest common divisor of 48 and 56 is 8.

So, John can make a maximum of 8 bags, with each bag containing an equal number of chocolate chip and peanut butter cookies.

PLEASE MARK AS BRAINLIEST IF SATISFIED WITH THIS ANSWER PLEASE

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:

again, a line cutting through 2 parallel lines must have the exact same angles with both of them. otherwise they would not be parallel.

therefore, both angles must be identical

3x + 2 = 2x + 6

x = 4

Answer:

D. -1 the amount of water decreases by 1 gallon every minute.

Step-by-step explanation:

15, 0 -> 12, 3  

3 - 0 = 3  

-------

12 - 15 = -3

3/ -3 = -1

Answer:

50 cm

Step-by-step explanation:

let x be the heigth we are looking for.

Each rectangle that covers the cuboid is the product of two dimensions [tex](60\cdot40;\ 60x;\ 40x)[/tex]

Since it's a cuboid, we assume opposite sides are equal.

So each rectangle is counted twice:

[tex]Area=2(60\cdot40+60x+40x)=14800[/tex]

Now, we just isolate x:

[tex]60\cdot40+60x+40x=7400\\2400+100x=7400\\100x=5000[/tex]

Answer:50 cm

Answer:

the y intercept is 5/3

the y intercept is 3/5

Answer:

The given perimeter is \[44cm\]. Hence, the area of the given square is \[121c{m^2}\].

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

3/4mile takes 1/12 hours

so a whole hour is 3/4 / 1/12 = 3/4*12 = 9miles/hour

Answer:

3/2 miles per hour

Step-by-step explanation:

To find his average speed, divide 3/4 mile by 1/2 hour:

 3        2

----- *  ------ = 3/2 miles per hour

 4         1

Answer:

x + (4x-20) = 180

by linear pair

therefore x= 70

Applying the definition of linear pair, the value of x is: D. 40.

Therefore:

x + (4x - 20°) = 180°

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 40

Therefore, applying the definition of linear pair, the value of x is: D. 40.

Learn more about linear pair on:

https://brainly.com/question/13218054

Answer:

f(2) = 2.5×2-10.5

=5-10.5

=-5.5

g(2) = 64(0.5×2)

= 64×1

=64

f(3)=2.5×3-10.5

=7.5-10.5

=-3

g(3)=64(0.5×3)

=64×1.5

=96

f(4)=2.5×4-10.5

=10-10.5

=-500

g(4)=64(0.5×4)

=64×2

=128

f(5)=2.5×5-10.5

=12.5-10.5

=2

g(5)=64(0.5×5)

=64×2.5

=150

I think it is the processs It will help you

Answer:

i think the perimeter is 60

Step-by-step explanation:

9²+12² = x²

15 = x

perimeter = 15×4 = 60

Answer:

try this answer x2 + 2xy + y2 - 16

Answer:  1170 miles

Work Shown:

(18 miles)/(1 gallon) = (x miles)/(65 gallons)

18/1 = x/65

x/65 = 18

x = 65*18

x = 1170

Answer: 1170 miles

1 gallon of gas --> 18 miles

65 gallon of gas --> 18 * 65 (which is 1170 miles)

[tex]\huge \rm༆ Answer ༄[/tex]

Measure of each side of a triangle can't be greater than the sum of the other two sides and can't be smaller than the difference between the two other sides. therefore the most appropriate choice is ~

I hope it helps ~

We have:

1) 3 + 5 = 8 ⇒ wrong

2) 4 + 7 > 9 ⇒ right

3) 2 + 11 < 15 ⇒ wrong

ANSWER: 4 cm, 7 cm, 9 cm

Ok done. Thank to me :>

Answer: The blue dot's value on the number line is 1.

Step-by-step explanation: Each two-skip interval from -7 to -3 is a skip of 4. Therefore, -3 skipped two times is -3 + 4, which equals 1, therefore the blue dot's value on the number line is 1.

Answer:

B,C,D,F, those are yhe right answer