What is the mean absolute deviation of the following set of data?<br> 4<br> 6<br> 6<br> 2.

The solutions to a certain quadratic equation are x = -4 and x = 3. Write the equation in standard form below.

$y=a(x-x_1)(x-x_2)\\\\x_1=-4;\ x_2=3\ therefore\\\\y=a(x+4)(x-3)\\\\y=a(x^2+x-12)\\\\\boxed{y=ax^2+ax-12a}\ where\ a\in\mathbb{R}-\{0\}$

5 0

3 years ago

Read 2 more answers

3. A principal orders 2,592 pencils. She gives an equal amount to each of

AfilCa [17]

Each teacher should receive 108 pencils

3 0

3 years ago

Given the line y = − 2 5 x + 3, determine if the given line is parallel, perpendicular, or neither. Select the correct answer fo

stiks02 [169]

Answer:

(a) Neither

(a) Perpemdicular

Step-by-step explanation:

Required

Determine the relationship between given lines

(a)

$y = -\frac{2}{5}x + 3$

and

$y = \frac{2}{5}x + 7$

An equation written in form: $y=mx + b$ has the slope:

$m \to slope$

So, in both equations:

$m_1 = -\frac{2}{5}$

$m_2 = \frac{2}{5}$

For both lines to be parallel

$m_1 = m_2$

This is false in this case, because:

$-\frac{2}{5} \ne \frac{2}{5}$

For both lines to be perpendicular

$m_1 * m_2 = -1$

This is false in this case, because:

$-\frac{2}{5} * \frac{2}{5} \ne -1$

(b)

$5y + 2x = -10$

and

$-5x + 2y = 4$

Write equations in form: $y=mx + b$

$5y + 2x = -10$

$5y = -2x +10$

Divide by 5

$y = -\frac{2}{5}x +2$

$-5x + 2y = 4$

$2y = 5x + 4$

Divide by 2

$y = \frac{5}{2}x + 2$

In both equations:

$m_1 = -\frac{2}{5}$

$m_2 = \frac{5}{2}$

For both lines to be parallel

$m_1 = m_2$

This is false in this case, because:

$-\frac{2}{5} \ne \frac{5}{2}$

For both lines to be perpendicular

$m_1 * m_2 = -1$

This is true in this case, because:

$-\frac{2}{5} * \frac{5}{2} = -1$

Cancel out 2 and 5

$-1 = -1$

6 0

3 years ago

A B R and P are four points on a circle with centre 0. A O R and C are four points on a different circle. The two circles inters

Slav-nsk [51]

Answer:

x° = ∠OBR = ∠ABC (base angles of a cyclic isosceles trapezoid)

Step-by-step explanation:

APRB form a cyclic trapezoid

∠APO = x° (Base angle of an isosceles triangle)

∠OPR = ∠ORP (Base angle of an isosceles triangle)

∠ORB = ∠OBR (Base angle of an isosceles triangle)

∠APO + ∠OPR + ∠OBR = 180° (Sum of opposite angles in a cyclic quadrilateral)

Similarly;

∠ORB + ∠ORP + x° = 180°

Since ∠APO = x° ∠ORB = ∠OBR and ∠OPR = ∠ORP we put

We also have;

∠OPR = ∠AOP = ∠BOR (Alternate interior angles of parallel lines)

Hence 2·x° + ∠AOP = 180° (Sum of angles in a triangle) = 2·∠OBR + ∠BOR

Therefore, 2·x° = 2·∠OBR, x° = ∠OBR = ∠ABC.

6 0

3 years ago

A circle with circumference12 has an arc with a 330∘ degree central angle. What is the length of the arc?

posledela

The formula for arc length which is measured in units not degrees is $\frac{ \beta }{360} *2 \pi r$ , where 2 pi r is the circumference. We were given the circumference as 12 pi, so we can fill in the rest of the formula and the find the length of the arc that is intercepted by that 330° angle. $\frac{330}{360} *12 \pi$ gives us, after multiplying in the pi, an arc length of 34.56 units.

4 0

3 years ago

What is the mean absolute deviation of the following set of data? 4 6 6 2.