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2 years ago

What value should be added to both sides for completing the square in this equation?

Mathematics

1 answer:

Mila [183]2 years ago

3 0

Hey there!

x^2 + 4x = 12

SUBTRACT 12 to BOTH SIDES

x^2 + 4x - 12 = 12 - 12

SIMPLIFY IT

x^2 + 4x - 12 = 0

FACTOR the LEFT SIDE of your EQUATION

(x - 2)(x + 6) = 0

• EQUATION #1: x - 2 = 0

• EQUATION #2: x + 6 = 0

SIMPLIFY IT

• EQUATION #1 answer: x = 2

• EQUATION #2 answer: x = -6

OVERALL ANSWER: x = 2 or x = -6

YOUR ANSWER: x = 2 (Option A.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

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En un triángulo rectángulo A es un ángulo agudo y Sen A = 4/5 ¿Cuál será el valor de Tan A?

Nonamiya [84]

Answer:

$\displaystyle \tan A=\frac{4}{3}$

Step-by-step explanation:

Funciones Trigonométricas

La identidad principal en trigonometría es:

$sen^2A+cos^2A=1$

Si sabemos que A es un ángulo agudo (que mide menos de 90°), su seno y coseno son positivos.

Dado que Sen A = 4/5, calculamos el coseno:

$cos^2A=1-sen^2A$

Sustituyendo:

$\displaystyle cos^2A=1-\left(\frac{4}{5}\right)^2$

$\displaystyle cos^2A=1-\frac{16}{25}$

$\displaystyle cos^2A=\frac{25-16}{25}$

$\displaystyle cos^2A=\frac{9}{25}$

Tomando raíz cuadrada:

$\displaystyle cos\ A=\sqrt{\frac{9}{25}}=\frac{3}{5}$

La tangente se define como:

$\displaystyle \tan A=\frac{sen\ A}{cos\ A}$

Substituyendo:

$\displaystyle \tan A=\frac{\frac{4}{5}}{\frac{3}{5}}$

$\displaystyle \tan A=\frac{4}{3}$

6 0

3 years ago

If A's income is 25% less than that of B, then how much percent is B's income more than that of A?

saul85 [17]

Let's say that B makes $100.

Then A makes $75.

So, your question then becomes 100 is what percent of 75?

This can be solved by setting up the proportion 100 / 75 = x / 100

75x = 10000

x = 133.3

So, B's income is 33.3% more than A's income.

7 0

3 years ago

What is the answer plzzzzzz help a kid out

Komok [63]

Answer:

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4 0

3 years ago

The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the

Naily [24]

Let r represent the radius of cylinder.

We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be $1.5r$ .

We will use lateral surface area of pyramid to solve our given problem.

$LSA=2\pi r h$ , where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

$LSA=2\pi r\cdot (1.5)r$

Now we will find the total surface area of cylinder.

$TSA=2\pi r(r+h)$

$TSA=2\pi r(r+1.5r)$

$TSA=2\pi r(2.5r)$

$\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}$

$\frac{TSA}{LSA}=\frac{2.5r}{1.5r}$

$\frac{TSA}{LSA}=\frac{25}{15}$

$\frac{TSA}{LSA}=\frac{5}{3}$

Therefore, the ratio of total surface area to lateral surface area is $5:3$ .

4 0

3 years ago

Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max's family spent $146 on 3 adults tic

Firdavs [7]

The price of 1 youth ticket is $ 22

Solution:

Let "y" be the price of 1 youth ticket

Let "a" be the price of 1 adult ticket

To find: price of 1 youth ticket

Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park

So we can frame a equation as:

2 adult tickets x price of 1 adult ticket + 3 youth tickets x price of 1 youth ticket = 134

$2 \times a + 3 \times y = 134$

2a + 3y = 134 ---- eqn 1

Max's family spent $146 on 3 adults tickets and 2 youth tickets

So we can frame a equation as:

3 adult tickets x price of 1 adult ticket + 2 youth tickets x price of 1 youth ticket = 146

$3 \times a + 2 \times y = 146$

3a + 2y = 146 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "y"

Multiply eqn 1 by 3

6a + 9y = 402 ---- eqn 3

Multiply eqn 2 by 2

6a + 4y = 292 ----- eqn 4

Subtract eqn 4 from eqn 3

6a + 9y = 402

6a + 4y = 292

( - ) -------------------

5y = 110

y = 22

Thus the price of 1 youth ticket is $ 22

3 0

3 years ago