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3 years ago

Which statement is true about the equation (x – 4)(x + 2) = 16?

Mathematics

2 answers:

BabaBlast [244]3 years ago

5 0

The factored form of the equation is (x + 4)(x – 6) = 0.

anyanavicka [17]3 years ago

3 0

we have

$(x-4)(x+2)=16$

Step 1

Find the standard form of the equation

$(x-4)(x+2)=16$

$x^{2}+2x-4x-8=16$

$x^{2}-2x-8-16=0$

$x^{2}-2x-24=0$

Step 2

Find the factored form

we have

$x^{2}-2x-24=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}-2x=24$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2}-2x+1=24+1$

$x^{2}-2x+1=25$

Rewrite as perfect squares

$(x-1)^{2}=25$

Square root both sides

$(x-1)=(+/-)5$

$x=1(+/-)5$

$x=1+5=6$

$x=1-5=-4$

therefore

the equation in factored form is equal to

$(x-6)(x+4)=0$

Step 3

Verify the statements

case A) The equation $x-4=16$ can be used to solve for a solution of the given equation

The statement is False

Because , If you solve the equation

$x-4=16\\x=16+4 \\x=20$

The value of $x=20$ is not a solution--------> see the procedure

case B) The standard form of the equation is $x^{2}-2x-8=0$

The statement is False

Because the standard form is equal to $x^{2}-2x-24=0$

See the procedure

case C) The factored form of the equation is $(x-6)(x+4)=0$

The statement is True

See the procedure

case D) One solution of the equation is $x=-6$

The statement is False

Because the solutions of the equation are $x=6$ and $x=-4$

See the procedure

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3 years ago

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Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

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Normal probability distribution

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When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$\mu = E(X) = np = 100*0.23 = 23$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21$

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

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3 years ago

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vladimir2022 [97]

The grocer wants to make a 10 pound mixture
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
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the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)

to solve for p and c lets use simultaneous equations
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture

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