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3 years ago

What is the value of -2[3-11] divided by 3

Mathematics

1 answer:

faust18 [17]3 years ago

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Re-write the quadratic function below in Standard Form y = 3(x + 3)2 – 3

vivado [14]

Answer:

y=6x+15

Step-by-step explanation:

8 0

3 years ago

For a triangle $XYZ$, we use $[XYZ]$ to denote its area. Let $ABCD$ be a square with side length $1$. Points $E$ and $F$ lie on

nata0808 [166]

An algebraic equation enables the expression of equality between variable expressions

$\underline{The \ value \ of \ [AEF] \ is \ \dfrac{4}{9}}$

The reason the above value is correct is given as follows:

The given parameters are;

The symbol for the area of a triangle ΔXYZ = [XYZ]

The side length of the given square ABCD = 1

The location of point E = Side $\overline{BC}$ on square ABCD

The location of point F = Side $\overline{CD}$ on square ABCD

∠EAF = 45°

The area of ΔCEF, [CEF] = 1/9 (corrected by using a similar online question)

Required:

To find the value of [AEF]

Solution:

The area of a triangle = (1/2) × Base length × Height

Let x = EC, represent the base length of ΔCEF, and let y = CF represent the height of triangle ΔCEF

We get;

The area of a triangle ΔCEF, [CEF] = (1/2)·x·y = x·y/2

The area of ΔCEF, [CEF] = 1/9 (given)

∴ x·y/2 = 1/9

ΔABE:

$\overline{BE}$ = BC - EC = 1 - x

The area of ΔABE, [ABE] = (1/2)×AB ×BE

AB = 1 = The length of the side of the square

The area of ΔABE, [ABE] = (1/2)× 1 × (1 - x) = (1 - x)/2

ΔADF:

$\overline{DF}$ = CD - CF = 1 - y

The area of ΔADF, [ADF] = (1/2)×AD ×DF

AD = 1 = The length of the side of the square

The area of ΔADF, [ADF] = (1/2)× 1 × (1 - y) = (1 - y)/2

The area of ΔAEF, [AEF] = [ABCD] - [ADF] - [ABE] - [CEF]

[ABCD] = Area of the square = 1 × 1

$[AEF] = 1 - \dfrac{1 - x}{2} - \dfrac{1 - y}{2} - \dfrac{1}{19}= \dfrac{19 \cdot x + 19 \cdot y - 2}{38}$

From $\dfrac{x \cdot y}{2} = \dfrac{1}{9}$ , we have;

$x = \dfrac{2}{9 \cdot y}$ , which gives;

$[AEF] = \dfrac{9 \cdot x + 9 \cdot y - 2}{18}$

Area of a triangle = (1/2) × The product of the length of two sides × sin(included angle between the sides)

∴ [AEF] = (1/2) × $\overline{AE}$ × $\overline{FA}$ × sin(∠EAF)

$\overline{AE}$ = √((1 - x)² + 1), $\overline{FA}$ = √((1 - y)² + 1)

[AEF] = (1/2) × √((1 - x)² + 1) × √((1 - y)² + 1) × sin(45°)

Which by using a graphing calculator, gives;

$\dfrac{1}{2} \times \sqrt{(1 - x)^2 + 1} \times \sqrt{(1 - y)^2 + 1} \times \dfrac{\sqrt{2} }{2} = \dfrac{9 \cdot x + 9 \cdot y - 2}{18}$

Squaring both sides and plugging in $x = \dfrac{2}{9 \cdot y}$ , gives;

$\dfrac{(81 \cdot y^4-180 \cdot y^3 + 200 \cdot y^2 - 40\cdot y +4)\cdot y^2}{324\cdot y^4} = \dfrac{(81\cdot y^4-36\cdot y^3 + 40\cdot y^2 - 8\cdot y +4)\cdot y^2}{324\cdot y^2}$

Subtracting the right hand side from the equation from the left hand side gives;

$\dfrac{40\cdot y- 36\cdot y^2 + 8}{81\cdot y} = 0$

36·y² - 40·y + 8 = 0

$y = \dfrac{40 \pm \sqrt{(-40)^2-4 \times 36\times 8} }{2 \times 36} = \dfrac{5 \pm \sqrt{7} }{9}$

$[AEF] = \dfrac{9 \cdot x + 9 \cdot y - 2}{18} = \dfrac{9 \cdot y^2-2 \cdot y + 2}{18 \cdot y}$

Plugging in $y = \dfrac{5 + \sqrt{7} }{9}$ and rationalizing surds gives;

$[AEF] = \dfrac{9 \cdot \left(\dfrac{5 + \sqrt{7} }{9}\right) ^2-2 \cdot \left(\dfrac{5 + \sqrt{7} }{9}\right) + 2}{18 \cdot \left(\dfrac{5 + \sqrt{7} }{9}\right) } = \dfrac{\dfrac{40+8\cdot \sqrt{7} }{9} }{10+2\cdot \sqrt{7} } = \dfrac{32}{72} = \dfrac{4}{9}$

Therefore;

$\underline{[AEF]= \dfrac{4}{9}}$

Learn more about the use of algebraic equations here:

brainly.com/question/13345893

6 0

3 years ago

Dylan and Beatrice are working with the same function. Dylan input −8 into the function and got an output of 8.

kolbaska11 [484]

Answer:

Part A: If Beatrice inputs −8 into the function, she must get an output of 8.

Part B: (−4,8) , (4,−8) , (8,−4)

Step-by-step explanation:

Part A:

We know that a function is a relation that maps elements from one set (The domain, the set of the inputs) into elements from another set (the range, the set of the outputs)

Such that each input can be mapped into only one output.

Then if we know that our function maps the input -8 into the output 8.

Always that we use this function with the input -8. we will have the same output, 8.

Then we can conclude that the correct option to the first part is:

"If Beatrice inputs −8 into the function, she must get an output of 8. "

Part B:

Remember, -8 is mapped into 8, then the point (−8,4) (this says "-8 is mapped into 4) can never be on the graph of the function.

But the points:

(−4,8) , (4,−8) , (8,−4)

Could be on the graph of the function.

4 0

3 years ago

Which of the following is not the equation of the graphed line?

ehidna [41]

Answer:

well, we do not have the options here, but we can find the equation of the graph, so the equations that are different from that are the answer to this question:

in the graph, we can see that it goes through the points:

(0,1) and (2,0)

Remember that the slope of a line that goes through the points (x1, y1) and (x2, y2) is:

s = (y2 - y1)/(x2- x1)

then the slope for our line is:

s = (0 - 1)/(2 -0) = -1/2

Then our line is:

y = -(1/2)*x + b.

b is the y-intercept, and we know that when x = 0 y = 1, then:

1 = -(1/2)*0 + b

1 = b

then the equation is:

y = -(1/2)*x + 1

5 0

3 years ago

Isaac is on the 4th floor of a building. If he rides an elevator up 7 floors, what floor will he be on?

Lady_Fox [76]

An integer is a whole number.

1) if Isaac is on the 4th floor and goes up 7, that is 4 + 7= 11. So he is on the 11th floor.

2) the integer representing the floor he is starting on is 4 because that is the whole number associated with "4th."

3) the integer representing how many floors he will rise is 7.

4) the elevator will stop at 11.

Hope this helps! :)

6 0

3 years ago

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