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2 years ago

Solve for x in the equation x^2 + 10x + 12 = 36. x = –12 or x = 2 x = –11 or x = 1 x = –2 or x = 12 x = –1 or x = 11

Mathematics

2 answers:

lesya692 [45]2 years ago

8 0

Answer: x=2 or x=-12

Step-by-step explanation: Subtract 12 to both sides of the equation: x² + 10x = 24. Subtract 24 to both sides of the equation: x² + 10x -24. Next, find out which two numbers multiply to -24 and add up to 10: 12 and -2.

X² + 12x + -2x -24.

X(x - 2) and 12(x - 2)

Solve for x: (x+12) and (x-2) = 0

X = -12 or x=2

kolbaska11 [484]2 years ago

5 0

Answer: The correct option is

(A) x = -12 or x = 2.

Step-by-step explanation: We are given to solve the following quadratic equation for x :

$x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

From equation (i), we have

$x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0~~~~~~~[\textup{the sum of 12 and -2 is 10 and product is -24}]\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x+12)(x-2)=0\\\\\Rightarrow x+12=0,~~~~x-2=0\\\\\Rightarrow x=-12,2.$

Thus, the required solution of the given equation is x = -12 or x = 2.

Option (A) is CORRECT.

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tigry1 [53]

Answer:

(a) Brenda saved $23.50.

(b) The rate at which Brenda is saving money is 0.5 dollars per day.

(c) money saved on $J(14)$ is $27.

Step-by-step explanation:

Given:

Initial amount in the jar is, $J(0)=\$20$

Amount in the jar after a week or 7 days is, $J(7)=\$23.50$

Brenda is saving money at a linear rate.

(a)

Now, money at the end of the week is the total money saved by Brenda.

Therefore, total money saved by Brenda is equal to the money saved at the end of the week. So,

Total money saved by Brenda = $J(7)=\$23.50$

(b)

The rate of change of a function is given as:

$Rate=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

Here, $x_1=0,x_2=7, f(x_1)=J(0),f(x_2)=J(7)$

Therefore, the rate at which Brenda saves money is given as:

$Rate=\frac{J(7)-J(0)}{7-0}\\Rate=\frac{23.50-20}{7}\\Rate=\frac{3.5}{7}=0.5\ dollars/day$

Therefore, the rate at which Brenda is saving money is 0.5 dollars per day.

(c)

A linear function is of the form $f(x)=mx+b$ , where 'm' is the rate and 'b' is the initial value of the function.

Therefore, the linear function for the money saved by Brenda can be written as:

$J(x)=(Rate)x+J(0)\\J(x)=0.5x+20$

Now, $J(14)$ is given by plugging in 14 for 'x' in the above expression. So,

$J(14)=0.5\times 14+20\\J(14)=7+20=\$27$

Therefore, money saved on $J(14)$ is $27.

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2 years ago

Which is one of the solutions to the equation 2x^2 - x - 4 = 0

Alex73 [517]

Answer:

$x_{1}=\frac{1+\sqrt{33} }{4}\\x_{2}=\frac{1-\sqrt{33} }{4}$

Step-by-step explanation:

Using quadratic formula

$x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}$

we will have two solutions.

2x^2 - x - 4 = 0

So, a=2 b=-1 c=-4, we have:

$x_{1}=\frac{+1+\sqrt{-1^{2}-4*2*-4} }{2*2}\\\\x_{2}=\frac{+1-\sqrt{-1^{2}-4*2*-4} }{2*2}$

Finally, we have two solutions:

$x_{1}=\frac{1+\sqrt{33} }{4}\\\\x_{2}=\frac{1-\sqrt{33} }{4}$

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