Why is the function below called a rational function?

f(x) =x+3
——
x-2

Answer:

Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2) After 10 seconds.

Step-by-step explanation:

We have the function:

[tex]f(x)=-5x^2+40x+100[/tex]

Where f(x) represents the height x seconds after it is released into the air.

Part 1)

First, let's distribute a -5 out of the function:

[tex]f(x)=-5(x^2-8x-20)[/tex]

Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.

We can use -10 and 2. So:

[tex]f(x)=-5(x^2+2x-10x-20)[/tex]

Factor:

[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]

Hence, our factored form is:

[tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2)

We want to find after how many seconds does it take for the projectile to reach the ground.

If it reaches the ground, the height above the ground, f(x), will be 0.

So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:

[tex]0=-5(x-10)(x+2)[/tex]

Zero Product Property:

[tex]x-10=0\text{ or } x+2=0[/tex]

Solve for x:

[tex]x=10 \text{ or } x=-2[/tex]

Since x measures time, -2 does not make sense in this context.

Therefore, our solution is x=10.

So, after 10 seconds, the projectile will hit the ground.

Answer:

y = x/2 -1/2

Step-by-step explanation:

let’s write this equation as

y = 2x + 1

to find the inverse let’s switch x and y

x = 2y + 1

and solve for y

x -1 = 2y

y = x/2 -1/2

so the inverse is

y = x/2 -1/2

Answer:

i need more details

Step-by-step explanation:

Answer:

27 liters

Step-by-step explanation:

18-4=14

14-2=12

12+12=24

24+3=27

Answer:

18miles per day

Step-by-step explanation:

Just do 108/6

Answer:

I believe it would be 3 reflection followed by translation.

Step-by-step explanation:

Answer:

129.3 pounds

Step-by-step explanation:

A restaurant bought 36.5 pound of meat from a store

The following month they also bought 71.3 pounds of meat and 21.5 pounds of chicken

Therefore the total pounds of meat bought by the restaurant can be calculated as follows

= 36.5 + 71.3 + 21.5

= 129.3 pounds

Answer:

3

Step-by-step explanation:

We can recognize this equation as a linear equation, which is given by the following formula:

[tex]y=mx-b[/tex], where m is the slope and b is the y-intercept.

Thus, we see that 3 is the slope, and 9 is the y-intercept.

Answer:

I think it is -1

Step-by-step explanation:

Simplify the problem first.

Let's start with the numerator.

FYI, this, ^, means raised to the power of.

4^3 = 64

-12 + 2^2 = -12 +4 which equals -8

64/-8 = -8

Now simplify the denominator.

(2*3)^2 = 6^2 which equals 36.

-5*2*3 = -10*3 which equals -30

Then add the 2 to the end.

36 + (-30) + 2 = 6 + 2 which equals 8. This is the denominator.

Your fraction now is:

-8/8

Simplify this and you will get -1 as the simplest form.

Please forgive me if this is incorrect.

9514 1404 393

Answer:

  -1

Step-by-step explanation:

A suitable calculator can find the value for you.

  [tex]\dfrac{4^3/(-12+2^2)}{(2\times3)^2+(-5\times2\times3)+2}=\dfrac{64/(-12+4)}{6^2+(-5\times2\times3)+2}=\dfrac{64/(-12+4)}{36+(-5\times2\times3)+2}\\\\=\dfrac{64/(-8)}{36+(-30)+2}=\dfrac{-8}{6+2}=\boxed{-1}[/tex]

Answer:

y = - [tex]\frac{3}{5}[/tex] x + 1

Step-by-step explanation:

Parallel lines have equal slopes

Calculate m of CD using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = C(- 3, 4) and (x₂, y₂ ) = D(7, - 2)

m = [tex]\frac{-2-4}{7+3}[/tex] = [tex]\frac{-6}{10}[/tex] = - [tex]\frac{3}{5}[/tex] , thus

y = - [tex]\frac{3}{5}[/tex] x + 1 ← is parallel to CD

Answer:

37-9=28

Step-by-step explanation:

it was 28 F then rose 9 which is 37 so 37-9 =28

The  equation is  37 - 9= x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

After the temperature rose 9°F, the thermometer read 37°F.

let  x be the temperature before the 9º increase.

So, 37 - 9= x

x= 28°F.

Hence, the equation is  37 - 9= x.

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Step-by-step explanation:

h= 55/12 if thats what u askin for

5h – 15 + 7h = 40

value of h

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex] :\implies \bold{5h + 7h = 40 + 15}[/tex]

[tex] :\implies \bold{12h= 55}[/tex]

[tex]:\implies \bold{h = \dfrac{55}{12} }[/tex]

[tex]:\implies\underline{\boxed{ \bold{h = 4.583}}}[/tex]

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex]:\implies \bold{(5 \times 4.583) – 15 +( 7 \times 4.583)= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies\underline{\boxed{ \bold{ 40= 40}}}[/tex]

Answer:

9 would be removed i believe

Step-by-step explanation:

Answer:

hehehe

Step-by-step explanation:

hehehe

Answer:

Step-by-step explanation:

The last step should be: using distributive property by taking out of parentheses the common factor √5

4√5 + 9√5 = √5(4 + 9) = 13√5

The error is made at the last step

it should be 13√5 instead of 13√10.

Answer:

The Watermelon candies cost 13 more cents then the chocolate.

Step-by-step explanation:

$3.48 divided by 12 is 29 cents

$1.28 divided by 8 is 16 cents

Subtract 16 from 29 and get 13

If Lickety Sweet's Candy Store sells candy by the ounce. Maura paid $3.48 for a 12-ounce bag of hard watermelon candies and $1.28 for an 8-ounce bag of chewy chocolate candies, then she paid 13 more cents for watermelon candies cost per ounce than the chocolate candies

Two or more expressions with an Equal sign is called as Equation.

Given,

Lickety Sweet's Candy Store sells candy by the ounce.

For 12-ounce bag of hard watermelon candies Maura paid $3.48

For 8-ounce bag of chewy chocolate candies Maura paid $1.28

Let us find cost of each watermelon candie

$3.48 divided by 12

3.48/12=29 cents

$1.28 divided by 8

1.28/8=16 cents

Subtract 16 from 29 and get 13

29-16=13

Hence 13 cents more do the watermelon candies cost per ounce than the chocolate candies

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Answer:54.29%

Step-by-step explanation:

Answer: 73.33A

Step-by-step explanation:

Resistance (R)= 3.0 kN

Voltage (V)= 220 volts

Current (I)= Unknown

The formula to calculate the current will be:

Current = Voltage / Resistance

Current = 220 / 3.0

Current = 73.33 A

Therefore, the current needed to operate the electric fan is 73.33.

Answer:

x=12

Step-by-step explanation:

3x+7=5x-17

2x=24

x=12

Step-by-step explanation:

(x_42)(x+42)...

....

Answer:

Step-by-step explanation:

So,

$140 Dollars per 18 feet

Divide by 18 on both sides

140/18=18/18

140/18 is equal to 7 and 2/9

The answer is 7.77777778

Answer:

4

Step-by-step explanation:

Move numbers to right hand side

Answer:

34

Step-by-step explanation:

8/2 = 4

6 times 5 = 30

4 + 30 = 34

Answer: A: 3 square feet per minute

Step-by-step explanation:

The square feet more that Paula can shovel in 1 minute more than Melinda is 3 square feet per minute.

30x + + 30y = 450 equation 1

20x + 25y = 345 equation 2

Where:

x = square feet shovelled by Melinda

y = square feet shovelled by Paula

The first step is to multiply equation 1 by 20 and equation 2 by 30

600x + 600y = 9000 equation 3

600x + 750 y = 10,350 equation 4

Subtract equation 3 from equation 4

150y = 1350

Divide both sides by 150

y = 9 square meters

Substitute for y in equation 1

30x + 30(9) = 450

30x + 270 = 450

30x = 450 - 270

30x = 180

x = 6 square meters

9 - 6 = 3 square meters

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Answer:

-2(5x+6y-18) = -10x-12y+36

Answer:

small pizza-sp

additionl topping=atp

If sp=6.00

and atp=0.75 for every topping how ,uch would it cost for three toppings

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

Answer:

(3-7)x or -4x depends on what your teacher is looking for