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3 years ago

What is the range of f(x)=10-x^2

Mathematics

1 answer:

natka813 [3]3 years ago

5 0

Answer:

https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.536412.html

Step-by-step explanation:

Look at this link, I promise it will help you out!

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Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

solniwko [45]

$Rewrite the expression 6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$$

The ratio of $\frac{q}{p}$ = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form $ax^{2} + bx + c$ to the vertex form

$a(x - h)^{2} + k$ . The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: $a(x + m)^{2} + n$ , such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

= $6(j^2 - \frac{2}{3} j )+12$

= $$6(j^2 - \frac{2}{3} j + \frac{1}{9} )+\frac{102}{9}$ (Completing Square method)

= $6( j- \frac{1}{3} )^{2} + \frac{34}{3}$

On comparing with the given equation we get

p = - $\frac{1}{3}$ and q = $\frac{34}{3}$

∴ $\frac{q}{p}$ = $\frac{\frac{34}{3} }{\frac{-1}{3} }$

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

7 0

2 years ago

The diameter of a wheel of a car is 30cm. If the car travels at an average speed of 13.2m/s, find the number of revolutions made

Marysya12 [62]

Answer:

Approximately $50420$ revolutions (rounded to the nearest whole number.)

Step-by-step explanation:

Convert the diameter of this wheel to meters: $d = 30\; \rm cm = 0.30\; \rm m$ .

Circumference of this wheel:

$\pi \, d = \pi \times 0.30\; \rm m \approx 0.942\; \rm m$ .

Distance travelled in one hour:

$\begin{aligned}v \cdot t &= 13.2 \; \rm m \cdot s^{-1} \times 3600\; \rm s \\ &= 47520\; \rm m\end{aligned}$ .

Number of revolutions required for covering that distance:

$\displaystyle \frac{47520\; \rm m}{(\pi \times 0.30\; \rm m)} \approx 50420$ .

3 0

3 years ago

Felicia invested $25,000 into an account earning 3% interest compounded annually. She makes no other deposits into the account a

madam [21]

The formula is
A=p (1+r)^t
A future value?
P present value 25000
R interest rate 0.03
T time 9 years

A=25,000×(1+0.03)^(9)
A=32,619.33

7 0

3 years ago

Paul wanted to bring his family to the Children’s Museum. There was an exhibit with carnival rides. The tickets for each ride we

Nostrana [21]

We want to define and solve a linear equation to model the given case.

The answers are:

a) x = number of tickets, y = total cost.

b) y = $1.35*x + $6.35

We know that:

The tickets for each ride were $1.35 per ticket.

Paul purchased 30 tickets

He spent a total of $46.85 (on tickets and admission)

The cost for the 30 tickets is:

30*$1.35 = $40.50

a) Now we can define two variables:

y = total cost

x = number of tickets

b) the linear equation would be:

y = $1.35*x + P

Where P is the price of admission.

And we know that the total cost for 30 tickets is $46.85, then we have:

$46.85 = $40.50 + P

$46.85 - $40.50 = P = $6.35

So the admission price is $6.35

This means that the linear equation is:

y = $1.35*x + $6.35

c) Brief explanation, we have the variable y that represents the total cost, it is equal to the admission price (which we found) plus $1.35 times the number of tickets bought (x).

If you want to learn more, you can read:

brainly.com/question/13738061

3 0

3 years ago

Pls help me I’m failing math

maw [93]

Answer:

0.95p and 1 *0.95p

Step-by-step explanation:

6 0

3 years ago