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3 years ago

2 (UHS)

Mathematics

1 answer:

Andrei [34K]3 years ago

3 0

Answer:

Both sides are equal.

Step-by-step explanation:

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Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –

Verdich [7]

Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

$(x+3)^2+(x+3)-2=0$

Let

$u=(x+3)$

Rewrite the equation

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

Complete the square

$u^2+u=2$

$u^2+u+1/4=2+1/4$

$u^2+u+1/4=9/4$

rewrite as perfect squares

$(u+1/2)^2=9/4$

square root both sides

$(u+1/2)=\pm\frac{3}{2}$

$u=(-1/2)\pm\frac{3}{2}$

$u=(-1/2)+\frac{3}{2}=1$

$u=(-1/2)-\frac{3}{2}=-2$

the solutions are

u=-2,u=1

<em>Alternative Method</em>

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

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

$a=1\\b=1\\c=-2$

substitute in the formula

$u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}$

$u=\frac{-1\pm\sqrt{9}} {2}$

$u=\frac{-1\pm3} {2}$

$u=\frac{-1+3} {2}=1$

$u=\frac{-1-3} {2}=-2$

the solutions are

u=-2,u=1

<em>Find the solutions of the original equation</em>

For u=-2

$-2=(x+3)$ ----> $x=-2-3=-5$

For u=1

$1=(x+3)$ ----> $x=1-3=-2$

therefore

The solutions of the original equation are

x=-5 and x=-2

4 0

4 years ago

Read 2 more answers

Yolanda filled 2liters bottles with water for a day at the park with her family. Her family drank 11.73 liters .How many liters

kotykmax [81]

Answer:

1.99 L

Step-by-step explanation:

In the question it is mentioned that

The total liters of the water filled is 2 liters

But the family drank 11.73 liters

How should it be possible that the family drank is more than the total liters

So here we assume that the family drunk water should be in milliliters

Now the number of liters left is

= 2,000 ML - 11.73 ML

= 1988.27 ML

Now convert into liters which is

= 1988.27 ÷ 1,000

= 1.99 L

7 0

3 years ago

How do I do this my hwk id due tomoorw

nexus9112 [7]

The perimeter of the given circle is 25.1 square cm.

Step-by-step explanation:

From the given diagram, the radius of the given circle is 4 cm.

The perimeter of any given circle is calculated by multiplying 2π with the radius. The radius of this circle is 4 cm and it says π = 3.142

The Perimeter for the given circle = 2π × r = 2 × 3.142 × 4 cm = 6.284 × 4 cm = 25.136 cm. Rounding this off to one decimal 25.136 square cm, the perimeter equals 25.1 square cm.

6 0

3 years ago

Is 5x-7y=2x-7 a linear equation?

Alexandra [31]

Yes. 5x-7y=2x-7
3x-7y=-7-3x
y=1+3/7x
y is the equation of the line where the y-intercept is (0,1) and the slope is 3/7.

3 0

3 years ago

1st question: Which TWO ratios below are equal? A) 3 to 8, C) 4 to 6, B) 6 to 9, D) 8 to 12 . Answer:___?

sineoko [7]

Answer:

Option B and C are equal ratios

15 pack of 8 pencils gives you more pencils

Step-by-step explanation:

8 0

3 years ago