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2 years ago

(2x+3)²=5.find the roots of the equation

Mathematics

1 answer:

bija089 [108]2 years ago

4 0

Answer:

-2.61803398875, -0.38196601125

(-3±√5)/2

Step-by-step explanation:

First, expand. (2x+3)² = 4x²+12x+9=5

4x²+12x+4 = 0

Quadratic equations take the form ax²+bx+c = 0

In this case,

a = 4

b = 12

c = 4

You can solve with the equation x=(-b±√b²-4ac)/2a

Plug in:

(-12±√144-64)/8

(-12±√80)/8

(-12±√2^4×5)/8

(-12±4√5)/8

(-3±√5)/2

Final answer x = (-3±√5)/2

If you want decimal form: -2.61803398875, -0.38196601125

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Answer:

True

Step-by-step explanation:

Parallel lines go straight on forever and ever without intersection

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3 years ago

Read 2 more answers

Cloud nine is having a sale on all shirts and pants in the store.Olivia purchased 8 shirts 4 pairs of pants for $176.Raheem purc

mihalych1998 [28]

Question is Incomplete; Complete question is given below;

Cloud Nine is having a sale on all shirts and pants in the store. Olivia purchased 8 shirts and 4 pairs of pants for $176. Raheem purchased 3 shirts and 4 pairs of pants for $116. Let x represent the price of a shirt and y represent the price of a pair of pants. Write a system of equations, and use the elimination method to find a reasonable price for a pair of pants.

Answer:

The system of equations are $\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.$

The reasonable price for pair of pants is $20.

Step-by-step explanation:

Let the price of shirt be 'x'.

Let price of pair of pants be 'y'.

Given:

Olivia purchased 8 shirts 4 pairs of pants for $176

So we can say that;

8 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 176.

framing in equation form we get;

$8x+4y=176 \ \ \ \ equation \ 1$

Also Given:

Raheem purchased 3 shirts and 4 pairs of pants for 116.

So we can say that;

3 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 116.

framing in equation form we get;

$3x+4y=116 \ \ \ \ equation \ 2$

Hence the system of equation are $\left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.$

Now by using elimination method we will subtract equation 2 from equation 1 we get;

$(8x+4y)-(3x+4y)=176-116\\\\8x+4y-3x-4y = 60\\\\5x =60\\\\x=\frac{60}{5}=\$12$

Now Substituting the value of x in equation 1 we get;

$8x+4y=176\\\\8\times 12+4y =176\\\\96+4y=176\\\\4y =176-96\\\\4y = 80\\\\y= \frac{80}{4} =\$ 20$

Hence The reasonable price for pair of pants is $20.

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3 years ago

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2 years ago

BAC ~ DEC what is the value of x?

Anna007 [38]

Answer: x = 37.8

Step-by-step explanation: We start with triangle ABC with two sides given as 15 and 18. We shall make angle C the reference angle and thereby calculate the third side, line BC.

Since we have the opposite side as 15, and the adjacent side (which lies between the reference angle and the right angle) as 18, we can use the tangent of the angle C

Tan C = Opp/Adj

Tan C = 15/18

Tan C = 0.8333

From our table of values/use of the calculator

Tan C = 39.8

Angle C in triangle ACB = Angle C in triangle ECD (Opposite angles are equal).

That takes us to triangle ECD, since the reference angle is known (39.8) and the opposite side is also given (31.5), we can now calculate the adjacent which is side x.

Tan C = Opp/Adj

Tan 39.8 = 31.5/x

when you cross multiply, x moves to the left hand side, while Tan 39.8 moves to the right hand side

x = 31.5/Tan 39.8

x = 31.5/0.8333

x = 37.8

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3 years ago

3 Which ordered pair is the solution of the system graphed below?

gayaneshka [121]

Answer:

C. (5, -3)

Step-by-step explanation:

Ordered pair just means the coordinate or the point at which both of the graphs intersect. On the x-axis, this is at point 5, and on the y-axis, this is at point -3. Since an ordered pair is in the form (x, y), the answer is therefore C.

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3 years ago

(2x+3)²=5.find the roots of the equation ​

(2x+3)²=5.find the roots of the equation