3. (1,-6) (-5,8)<br> What is the answer

Find the domain and range of the function graphed in the picture.

algol [13]

The domain is the set of allowed x inputs, or x coordinates of a function. In this case, any point on the curve has an x coordinate that is 4 or smaller.

Therefore, the domain is the set of numbers x such that $x \le 4$

To write this in interval notation, we would write $(-\infty, 4]$ This interval starts at negative infinity and stops at 4. We exclude infinity with the curved parenthesis and include 4 with the square bracket.

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The range is the set of possible y outputs. Every point on this curve has a y coordinate that is either 0 or it is larger than 0.

The range is the set of y values such that $y \ge 0$

In interval notation, it would be written as $[0, \infty)$ This time we start at 0 (including this endpoint) and "stop" at infinity

note: we always use curved parenthesis at positive or negative infinity because we cannot reach either infinity

7 0

3 years ago

A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

You must have 3 points lie on the parabola
Substitute the coordinates of each point in the equation to make system of equations of a , b and c
Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

6 0

3 years ago

Read 2 more answers

I have no idea what it is

amid [387]

Answer:

answer is option b

2x-3

3 0

2 years ago

PLEASE HELP ILL GIVE BRAINLIEST

dusya [7]

1)

$(-2+\sqrt{-5})^2\implies (-2+\sqrt{-1\cdot 5})^2\implies (-2+\sqrt{-1}\sqrt{5})^2\implies (-2+i\sqrt{5})^2 \\\\\\ (-2+i\sqrt{5})(-2+i\sqrt{5})\implies +4-2i\sqrt{5}-2i\sqrt{5}+(i\sqrt{5})^2 \\\\\\ 4-4i\sqrt{5}+[i^2(\sqrt{5})^2]\implies 4-4i\sqrt{5}+[-1\cdot 5] \\\\\\ 4-4i\sqrt{5}-5\implies -1-4i\sqrt{5}$

3)

let's recall that the conjugate of any pair a + b is simply the same pair with a different sign, namely a - b and the reverse is also true, let's also recall that i² = -1.

$\cfrac{6-7i}{1-2i}\implies \stackrel{\textit{multiplying both sides by the denominator's conjugate}}{\cfrac{6-7i}{1-2i}\cdot \cfrac{1+2i}{1+2i}\implies \cfrac{(6-7i)(1+2i)}{\underset{\textit{difference of squares}}{(1-2i)(1+2i)}}} \\\\\\ \cfrac{(6-7i)(1+2i)}{1^2-(2i)^2}\implies \cfrac{6-12i-7i-14i^2}{1-(2^2i^2)}\implies \cfrac{6-19i-14(-1)}{1-[4(-1)]} \\\\\\ \cfrac{6-19i+14}{1-(-4)}\implies \cfrac{20-19i}{1+4}\implies \cfrac{20-19i}{5}\implies \cfrac{20}{5}-\cfrac{19i}{5}\implies 4-\cfrac{19i}{5}$

7 0

2 years ago

Read 2 more answers

PLEASE HELP IM SERIOUSLY STUCK E

lara31 [8.8K]

Answer: 2.12 × $10^{-3}$

The coefficient (in green) will be 2.12

Step-by-step explanation:

Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.

Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.

To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.

To get back to the original value, we multiply this by $10^{-3}$ . This gives us our answer.

3 0

1 year ago

3. (1,-6) (-5,8) What is the answer