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3 years ago

12

Solve the following quadratic by completing the square.

1 answer:

Salsk061 [2.6K]3 years ago

5 0

Answer:

(x-3)squared -7

Step-by-step explanation:

always half the middle and then write x and whatever symbol is after x

You might be interested in

If f(x) = 4 – x^2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

inna [77]

Answer:

23

Step-by-step explanation:

f(x)=4-x²

g(x)=6x

g(x)-f(x)=6x-(4-x²)

g(x)-f(x)=6x-4+x²

so, when (g-f)(3), it means that x=3

.:(g-f)(3)=6(3)-4+(3)²

= 18 - 4 +9

=14+9

=23

7 0

3 years ago

Which is the inverse of the function f(x) = x2 − 4?

Rudiy27

The function is not one-to-one function, hence the inverse doesn't exist for the whole domain of the function. But if we restrict the domain to $x\in(-\infty,0]$ or $x\in[0,\infty)$ , then we can give the inverse.

$f(x)=x^2-4\\\\y=x^2-4\\\\x^2=y+4\\\\x=\sqrt{y+4} \vee x=-\sqrt{y+4}\\\\f^{-1}(x)=\sqrt{x+4}\vee f^{-1}(x)=-\sqrt{x+4}$

So, when $D_{f(x)}:x\in(-\infty,0]$ , the inverse is $f^{-1}(x)=-\sqrt{x+4}$ and when $D_{f(x)}:x\in[0,\infty)$ , the inverse is $f^{-1}(x)=\sqrt{x+4}$ .

7 0

3 years ago

Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 22 of the 45 boxes on the

kherson [118]

Answer:

0.2333 = 23.33% probability that both of them have the secret decoder ring

Step-by-step explanation:

The cereals are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

45 boxes, which means that $N = 45$

22 have the secret decoder ring, which means that $k = 22$

Two boxes, which means that $n = 2$

What is the probability that both of them have the secret decoder ring?

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,45,2,22) = \frac{C_{22,2}*C_{23,0}}{C_{45,2}} = 0.2333$

0.2333 = 23.33% probability that both of them have the secret decoder ring

8 0

3 years ago

What is the solution to the system of equations 8x-10y=-23 and 9x+10y=-16

sammy [17]

8x-10y=-23
9x+10y=-16
(8x+9x)+(10y-10y)=(-23+(-16))
17x+0y=-39
x=-39/17
8(-39/17)-10y=-23
-312/17-10y=-23
-10y=-23+312/17
-10y=-79/17
y=79/170

3 0

4 years ago

What is the correct expansion of (2x+3) (2x^2-5)

Dmitry_Shevchenko [17]

Answer:

4x^3 + 6x^2 -10x - 15

Step-by-step explanation:

* means multiply

4x^3 + 6x^2 -10x - 15

2x * 2x^2 = 4x^3

2x * -5 = 10x

3 * 2x^2 = 6x^2

3 * -5 = -15

7 0

3 years ago

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