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3 years ago

Complete the square to the problem X^2+6x-16=0

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

Answer:

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}$

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Which geometric object is defined as the set of all points in a plane at a given distance from a given point

hodyreva [135]

Answer:

Circle

Step-by-step explanation:

This object is what we call "circle". All the points in the circle are at the same distance from a given point which is the center of the circle. Moreover, the distance between the center and every point on the circle is called "radius". Higher values for the radius imply points at a higher distance from the center.

Additionally, we can calculate the perimeter of the circle, or the circumference, with the following formula:

circumference = 2*(radius) pi

Where pi is an irrational number usually used as 3.14.

If you have doubts, try to draw a circle and measure the distance between the center and any point on the circle.

8 0

3 years ago

Researchers working the mean weight of a random sample of 800 carry-on bags to e the airline. Which of the following best descri

Sphinxa [80]

Answer:

(E) The bias will decrease and the variance will decrease.

Step-by-step explanation:

Given that researchers working the mean weight of a random sample of 800 carry-on bags to e the airline.

We have to find out the effect of increasing the sample size on variance and bias.

We know as per central limit theorem, sample mean follows a normal distribution with mean = sample mean

and std deviation of sample mean = std error = $\frac{std dev}{\sqrt{n} }$

Thus std error the square root of variance is inversely proportional to the square root of sample size.

Also whenever we increase sample size the chances of bias would decrease as the sample size becomes larger

So correct answer is both bias and variation will decrease.

(E) The bias will decrease and the variance will decrease.

8 0

3 years ago

Use trigonometric identities to solve each equation within the given domain.

katrin [286]

Recall that the tangent function is defined by

tan(x) = sin(x)/cos(x)

Also recall the double angle identity for sine,

sin(2x) = 2 sin(x) cos(x)

Then the equation is the same as

3 sin(x)/cos(x) = 4 sin(x) cos(x)

Move everything to one side to prepare to factorize:

3 sin(x)/cos(x) - 4 sin(x) cos(x) = 0

sin(x)/cos(x) (3 - 4 cos²(x)) = 0

As long as cos(x) ≠ 0, we can omit the term in the denominator, so we're left with

sin(x) (3 - 4 cos²(x)) = 0

and so

sin(x) = 0 or 3 - 4 cos²(x) = 0

sin(x) = 0 or cos²(x) = 3/4

sin(x) = 0 or cos(x) = ±√3/2

On the interval [0, 2π),

• sin(x) = 0 for x = 0 and x = π

• cos(x) = √3/2 for x = π/6 and x = 11π/6

• cos(x) = -√3/2 for x = 5π/6 and x = 7π/6

(None of these x make cos(x) = 0, so we don't have to omit any extraneous solutions.)

6 0

3 years ago

Help on both of these pls also sry the lighting is weird

IRISSAK [1]

Answer:

see explanation

Step-by-step explanation:

The 2 angles form a right angle, thus their sum is 90°, hence

4x + 7 + 35 = 90

4x + 42 = 90 ( subtract 42 from both sides )

4x = 48 ( divide both sides by 4 )

x = 12

-----------------------------------------------------

To calculate the slope m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = $\frac{4-0}{1-0}$ = $\frac{4}{1}$ = 4

5 0

3 years ago

Find the complete factorization of

notsponge [240]

<h3>Option C is correct</h3>

<h3>Let us see the verification;</h3>

$6x {}^{3} - 15x {}^{2} - 9x \\ 3x(2x {}^{2} - 5x - 3) \\ 3x( 2x {}^{2} + x - 6x - 3) \\ 3x(x(2x + 1) - 3(2x - 1) \\ (2x + 1)$

<h2>Hence, Proved ✔︎</h2>

5 0

3 years ago