Function g can be thought of as a scaled version of f(x)=x^2


Write the equation for g(x)

So, Vanessa's score = v. Let's work from there.

We know that 59 is decreased by Vanessa's score, which is subtraction, and thus: 59 - v

Then, we're told that that quantity is 7. "Is" can be used in place of an equals sign: = 7

Therefore, our equation is as follows: 59 - v = 7

Hope this helps!! :)

Hi there! Assume that this is your question.

[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx}[/tex]

Before we get to Integral, you have to know Differentiation first. If you know how to differentiate a polynomial function then we are good to go in Integral!

We call the function that we are going to integrate as Integrand. Integrand is a function that's differentiated. In Integral, Integrating requires you to turn the function from differentiated to an original function.

For Ex. If the Integrand is x² then the original function is (1/3)x³ because when we differentiate (1/3)x³, we get x²

[tex] \large{f(x) = \frac{1}{3} {x}^{3} \longrightarrow f'(x) = {x}^{2} } \\ \large{f'(x) = 3( \frac{1}{3} ) {x}^{3 - 1} } \\ \large{f'(x) = {x}^{2} }[/tex]

So when we Integrate, make sure to convert Integrand as in original function. From the question, our Integrand is x²+2x. The function is in differentiated form. We know that x² is from (1/3)x³ and 2x comes from x²

[tex] \large{ f(x) = {x}^{2} \longrightarrow f'(x) = 2x} \\ \large{f'(x) = 2 {x}^{2 - 1} } \\ \large{f'(x) = 2x}[/tex]

Thus,

[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx} \\ \large{\int \limits^a_b ( \frac{1}{3} {x}^{3} + {x}^{2}) }[/tex]

Normally, if it's an indefinite Integral then we'd just put + C after (1/3)x³+x² but since we have a and b, it's a definite Integral.

[tex] \large{ \int \limits^b_a f(x)dx = F(b) - F(a)}[/tex]

Define F(x) as our anti-diff

From our problem, substitute x = a in then subtract with the one that substitute x = b

[tex] \large{ (\frac{1}{3}{a}^{3} + {a}^{2} ) - ( \frac{1}{3} {b}^{3} + {b}^{2}) }[/tex]

Simplify as we get:

[tex] \large \boxed{ \frac{1}{3}{a}^{3} + {a}^{2} - \frac{1}{3} {b}^{3} - {b}^{2}}[/tex]

Answer:

4x-6=30

4x=36

x=9

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

x = 9

Explanation:

Move all terms that do not contain x to the right side and solve.

Answer:

D)

Step-by-step explanation:

-5x + 4 - 3x² + 7x - 4

-3x² + 2x

Answer:

(–5x + 4) – (3X²–7x + 4) = ( – 3x² + 2x )

Answer:

[tex](a)\ -16t^2 + 7t + 63=0[/tex]

[tex](b)\ t = 2.215[/tex]

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 7t + 63[/tex]

Solving (a): Equation when it hits the ground.

This means that [tex]h(t) = 0[/tex]

So, we have:

[tex]h(t) = -16t^2 + 7t + 63[/tex]

[tex]-16t^2 + 7t + 63=0[/tex]

Solving (b): The value of t in (a)

[tex]-16t^2 + 7t + 63=0[/tex]

Using quadratic formula, we have:

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

This gives:

[tex]t = \frac{-7 \± \sqrt{7^2 - 4*-16*63}}{2*-16}[/tex]

[tex]t = \frac{-7 \± \sqrt{49+ 4032}}{2*-16}[/tex]

[tex]t = \frac{-7 \± \sqrt{4081}}{-32}[/tex]

[tex]t = \frac{-7 \± 63.88}{-32}[/tex]

Split

[tex]t = \frac{-7 + 63.88}{-32}; or\ t = \frac{-7 - 63.88}{-32}[/tex]

[tex]t = \frac{56.88}{-32}; or\ t = \frac{-70.88}{-32}[/tex]

[tex]t = -1.7775; or\ t = 2.215[/tex]

Time can't be negative; So:

[tex]t = 2.215[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]b(t) = 3000 * 2^t[/tex]

The question is incomplete;

A possible question could be to calculate the initial amount of beetle

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

Where

[tex]a \to Initial\ amount[/tex]

By comparison:

[tex]a = 3000[/tex] --- The initial number of beetles

Another question could be to solve for f(t), after a certain number of weeks (say 3)

Substitute 3 for t in: [tex]b(t) = 3000 * 2^t[/tex]

[tex]b(3) = 3000 * 2^3[/tex]

[tex]b(3) = 3000 * 8[/tex]

[tex]b(3) = 24000[/tex]

Answer:

15 days

Step-by-step explanation:

Don't you mean 1/3?  If so,

 5 cans

-------------------- = 15 days

1/3 can/daily

Answer:

(0,-5)

Step-by-step explanation:

move the x point to the right three times im pretty sure

Answer:

[tex]-4[/tex]

Step-by-step explanation:

Step 1: Apply the rule

[tex]\left(-64\right)=-64\\\\=\sqrt[3]{-64}[/tex]

Step 2: Apply the radical rule

[tex]\sqrt[3]{-64}=-\sqrt[3]{64}\\\\=-\sqrt[3]{64}[/tex]

Step 3: Factor the number

[tex]\:64=4^3\\\\=-\sqrt[3]{4^3}[/tex]

Step 4: Apply the radical rule

[tex]\sqrt[3]{4^3}=4\\\\=-4[/tex]

Therefore, [tex]\:\sqrt[3]{\left(\:-\:64\right)}\:=\:-4[/tex]

Answer:

-4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Unit rate is the number of circuit boards a minute:

Correct choice is B

Answer:

6ft

Step-by-step explanation:

The answer is 6 feet

Have a good day:)

Answer:

x=5.657 or because rouded 5.7

Step-by-step explanation:

ill give explaniation if want

Answer:

(I don't understand 36 sorry, but I can help you with 35)

C. 5.7 feet

Step-by-step explanation:

35. This question is asking you to use the pythagorean theorem, this is the formula:

a² + b² = c²

--------

So we know the lengths of a and b,

a² = 16

b² = 16

We add those together:

16 + 16 = 32

-------

The next step is to calculate [tex]\sqrt{32}[/tex]

[tex]\sqrt{32}[/tex] ≈ 5.7

------

Have a good day :)

-3 -12 -5 in that order

Answer:

-3

-12

-33

Step-by-step explanation:

sorry if i m wrong.

Answer: x = 2

Step-by-step explanation:

4x + 4 = 2x + 8

2x = 4

x = 2

Answer: x = 2.

Step-by-step explanation: 4x+4=2x+8 subtract 4 from both sides.

4x = 2x+4 subtract 2x on both sides

2x = 4        divide both sides by two

x = 2

I hope this helps, have a nice day.

Answer:

36 feet

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 48t[/tex]

Required

Determine the maximum height attained

First, calculate the time to reach maximum height;

In a quadratic equation;

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

The maximum is:

[tex]x = -\frac{b}{2a}[/tex]

So, we have:

[tex]t = -\frac{b}{2a}[/tex]

Where

[tex]a = -16; b = 48[/tex]

So:

[tex]t = -\frac{b}{2a}[/tex]

[tex]t = -\frac{48}{2 * -16}[/tex]

[tex]t = -\frac{48}{-32}[/tex]

[tex]t = \frac{48}{32}[/tex]

[tex]t = 1.5[/tex]

The maximum height is at: [tex]t = 1.5[/tex]

So, we have:

[tex]h(t) = -16t^2 + 48t[/tex]

[tex]h_{max}=-16 * 1.5^2 + 48 * 1.5[/tex]

[tex]h_{max}=36[/tex]

Graph the linear equation. 3x-4y= 24

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

Let x = 0, then y = -6

Let y = 0, then x = 8

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

Plot (0,-6) and (8,0) and draw a line thru them to get:

Respuesta:

03:40 pm;

15: 40;

20 minutos antes de las 4 pm;

40 minutos después de las 3 pm

Explicación paso a paso:

20 minutos antes de las 4 de la tarde se pueden expresar de las siguientes formas:

Basado en un tiempo de 12 horas, podría escribirse tiene: 3: 40 pm

Usando el formato de reloj de 24 horas; donde 3 pm es equivalente a 15; por lo tanto, podría escribirse como: 15:40

Además, el tiempo se puede informar en palabras de la siguiente manera:

20 minutos antes de las 4 pm

También ;

40 minutos después de las 3 pm

Answer:

86.70 cm^2

Step-by-step explanation:

circumference = 11 x 3 = 33

circumference of a circle =  nD

33 = 3.14 X D

D = 10.51

r = 10.51 / 2 = 5.25

Area = nr^2

3.14 x 5.25^2 = 86.70 cm^2

Answer:

Increase in her mass = 3.472 kg

Her new mass = 46.872 kg

Step-by-step explanation:

Her original mass = 43.4 kg

Percentage increase in her mass = 8%

Increase in her mass = 8% of 43.4 kg

= 8/100 * 43.4 kg

= 0.08 * 43.4 kg

= 3.472 kg

Increase in her mass = 3.472 kg

b) Work out her new mass

Her new mass = Her original mass + Increase in her mass

= 43.4 kg + 3.472 kg

= 46.872 kg

Her new mass = 46.872 kg

Answer:

b² - 12b + 36

Step-by-step explanation:

use the FOIL method:

b² - 6b - 6b + 36

combine the 'like' terms in the middle:

b² - 12b + 36

Answer:

See below

Step-by-step explanation:

Given the expression

x(x-3) = 0

This can be written as x = 0 and x - 3 = 0

x = 0 and x = 0+3

x = 0 and x = 3

Hence the equation has 2 solutions since it is a quadratic equation

B) Given x^2 = -81

Take the square root of both sides

√x² = ±√-81

x =±√-81

Note that √-1 = i

x = ±9i

x = 9i and -9i

Hence this equation has 2 solutions because of its quadratic nature

C) (x−1)(x−1)=0

x - 1 = 0 and x = 1 = 0

x = 1 twice

Hence this equation has 1 solution because of its repitition of root

Answer:

0 ≤ x ≤ 30

Step-by-step explanation:

In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

f(x) = 250(1.25)ˣ

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 250

0 ≤ x ≤ 30

All positive integers greater than 100

All real numbers

Solution:

Given that f(x) = 250(1.25)ˣ, where x is the number of days and f(x) is the population of the birds after x days. This means that at the beginning of the month of September (i.e. at x = 0), the population of the birds was 250. And as each day goes by, the population of the bird increases by a factor of 1.25.

The domain of a function is the set of all possible independent variables. In this case the number of days (x) is the independent variable. Since in the month of September there are 30 days, therefore the domain is:

0 ≤ x ≤ 30

Answer:

hmm very diffecult.

Step-by-step explanation:

if f (x) = StartRoot

Answer:

See Explanation

Step-by-step explanation:

Required

Function(s) with the same slope as function 1

The question is incomplete as function 1 and the three additional functions are not given.

However, I will provide a general explanation.

A slope is represented as:

[tex]y = mx + b[/tex]

Where

[tex]m \to[/tex] slope

So, considering the following equations

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

[tex]y = \frac{3x}{2} + 9[/tex]

[tex]y = 2x - 5[/tex]

[tex]y = -2x + 3[/tex]

The following equations have the same slope

[tex]y = 2x + 3[/tex] and [tex]y = 2x - 5[/tex]

Because: [tex]y = mx + b[/tex] implies that:

[tex]m = 2[/tex] for [tex]y = 2x + 3[/tex] and [tex]y = 2x - 5[/tex]

Answer:

996

Step-by-step explanation:

largest 3 digit number is 999

then just reduce slowly to find ans

Answer:

The largest 3-digit number divisible by 6 is 996.

consider the numbers are x,2x,3x,4x,5x

Given;

(x+2x+3x+4x+5x)/5 = 11

15x = 55

x= 55/15 = 11/3

The numbers are

11/3, 22/3, 11, 44/3, 55/3

Answer:

20000/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2000%=2000/100=20/1