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2 years ago

Which quadratic equation is equivalent to (x - 4)2 – ( - 4) - 6 = 0?

Mathematics

1 answer:

zmey [24]2 years ago

7 0

Answer:

$u^2-u-6=0$

where

$u=(x-4)$

Step-by-step explanation:

we have

$(x-4)^2-(x-4)-6=0$

Let

$u=(x-4)$

substitute in the expression above

$(u)^2-(u)-6=0$

Solve for u

Complete the square

$(u^2-u+0.25)=6+0.25$

$(u^2-u+0.25)=6.25$

Rewrite as perfect squares

$(u-0.5)^2=6.25$

square root booth sides

$u-0.5=\pm2.5$

$u=0.5\pm2.5$

$u_1=0.5+2.5=3$

$u_2=0.5-2.5=-2$

Solve for x

Remember that

$u=(x-4)$

For u=3

$3=(x-4)$ ----> $x=7$

For u=-2

$-2=(x-4)$ ----> $x=2$

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What is 19% as a decimal and a fraction?

kondaur [170]

Answer:

Decimal - 0.19 Fraction - 19/100

Step-by-step explanation:

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2 years ago

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A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that

kondaur [170]

Answer:

Probability that the company wins project A or project B is 0.50.

Step-by-step explanation:

We are given that a company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25.

Also, Winning project A and winning project B are independent events.

Let the Probability of winning project A = P(A) = 0.40

Probability of winning project B = P(B) = 0.25

Now, as we know that ;

Probability that the company wins project A or project B = $P(A \bigcup B)$

$P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$

So, we have to find the value of Probability of winning project A and B, i.e;

$P(A \bigcap B)$

Since, we are given that Winning project A and winning project B are independent events which means when this condition is given then;

$P(A \bigcap B) = P(A) \times P(B)$

= 0.40 $\times$ 0.25 = 0.10

Now, Probability that the company wins project A or project B is given by;

$P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$

= 0.40 + 0.25 - 0.10

= 0.65 - 0.10 = 0.55

Hence, probability that the company wins project A or project B is 0.50.

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2 years ago

Hi. Please I need help with these questions.

ElenaW [278]

Answer:

Q 12 roots of the equation

$2x^{2} -6+1=0 \\= (x-\frac{\sqrt{10} }{2})(x+\frac{\sqrt{10} }{2})\\$

∝ = $\frac{\sqrt{10} }{2}$

β = $-\frac{\sqrt{10} }{2}$

no matter if u oppose the root

(i) 2( $\frac{\sqrt{10} }{2}$ ) $(-\frac{\sqrt{10} }{2} )^{2}$ +2 $(\frac{\sqrt{10} }{2} )^{2}$ ( $-\frac{\sqrt{10} }{2}$ )+2(

(ii)( $(\frac{\sqrt{10} }{2})^{2}$ - 3 ( $\frac{\sqrt{10} }{2}$ )( $-\frac{\sqrt{10} }{2}$ ) + ( $(-\frac{\sqrt{10} }{2})^{2}$ ) = $\frac{25}{2}$

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$4x^{2} -3x-4=0\\\alpha = -0.693\\\beta = 1.443$

the roots of the second equation are

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the equation is

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3 years ago

What are the two main purposes of all business

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Answer:

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2 years ago

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PLEASE HELP HYPERBOLAS What is the length of the transverse axis ? (x-1)^2/25-(y+3)^2/9=1

Sav [38]

Given equation of hyperbola is

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Given hyperbola is the horizontal hyperbola

The standard form of the horizontal hyperbola is

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When we compare these two equations, we get

h = 1, a = 5 , k = -3 and b = 3

Length of the transverse axis = 2a

Plug in the value of 'a' as 5

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3 years ago