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katovenus [111]3 years ago

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The standard form of the equation of a parabola is y = 5x2 + 20x + 14.

Irina-Kira [14]

The vertex form of quadratic equation is expressed as:

y = a (x - h)² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y- 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x +4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2)²

We can now manipulate further the equation above in the vertex form. Thus,

y= 5 [ x- (-2)]² - 6

8 0

2 years ago

Read 2 more answers

. Use the process outlined in the lesson to approximate the number 3√10. Use the approximation √10 ≈3162 277 7.

GaryK [48]

Answer:

sequence of five intervals

(1) 3³ < $3^{\sqrt{10} }$ < $3^{4}$

(2) $3^{3.1}$ < $3^{\sqrt{10} }$ < $3^{3.2}$

(3) $3^{3.16}$ < $3^{\sqrt{10} }$ < $3^{3.17}$

(4) $3^{3.162}$ < $3^{\sqrt{10} }$ < $3^{3.163}$

(5) $3^{3.1622}$ < $3^{\sqrt{10} }$ < $3^{3.1623}$

Step-by-step explanation:

as per question given data

√10 ≈ 3.162 277 7

to find out

sequence of five intervals

solution

as we have given that √10 value that is here

√10 ≈ 3.162 277 7 ........................1

so

when we find $3^{\sqrt{10} }$ ................2

put here √10 value in equation number 2

we get $3^{\sqrt{10} }$ that is 32.27

so

sequence of five intervals

(1) 3³ < $3^{\sqrt{10} }$ < $3^{4}$

(2) $3^{3.1}$ < $3^{\sqrt{10} }$ < $3^{3.2}$

(3) $3^{3.16}$ < $3^{\sqrt{10} }$ < $3^{3.17}$

(4) $3^{3.162}$ < $3^{\sqrt{10} }$ < $3^{3.163}$

(5) $3^{3.1622}$ < $3^{\sqrt{10} }$ < $3^{3.1623}$

5 0

2 years ago

You have to complete at least 10 physics problems and math problems within 2 hours before you playing video games. It will take

Ghella [55]

Answer:2

Step-by-step explanation:

Given

Physics problem requires 20 min

Math problem require 10 min

suppose x question of Physics and y questions of Math are done

so according to the question

$x+y\geq 10\ldots 1$

Time require for x Physics problem $=20 x$

Time require for y Math problem $=10 y$

so,

$20 x+10 y\leq 120\ldots 2$

On solving (1) and (2)

we get $x=2$ and $y=8$

Maximum no of Physics question which can be solved is 2

5 0

2 years ago

A surfboard that has a regular price of $150 is on sale at a 40% discount. What is the sale price with a 9% tax?

Ahat [919]

Answer:

$98.10

Step-by-step explanation:

150 decrease 40% =

150 × (1 - 40%) = 150 × (1 - 0.4) = 90

90 increase 9% =

90 × (1 + 9%) = 90 × (1 + 0.09) = 98.1

8 0

3 years ago

Solve the equation for all values of x in simplest form (x + 3)^2 = -16

Arlecino [84]

Answer:

x = -7 or x = 1

Step-by-step explanation:

Given expression:

(x + 3)² = -16

Problem;

Solve for x;

Solution:

To solve for x; we use the factorization method;

Take -16 to the left of the equation;

(x + 3)² = -16

(x + 3)² + 16 = 0

(x+ 3)² + 4² = 0

if x² + y² = (x + y)(x - y)

So;

(x + 3 + 4) (x + 3 - 4) = 0

(x + 7)(x - 1) = 0

x + 7 = 0 or x - 1 = 0

x = -7 or x = 1

6 0

2 years ago