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2 years ago

Does anyone know the answer to this one?

Mathematics

1 answer:

polet [3.4K]2 years ago

7 0

Answer:

$\large\boxed{a(x+4)(x-5)=0,\ a\in\mathbb{R}-\{0\}}\\\\\text{for}\ a=1\to\boxed{x^2-x-20=0}$

Step-by-step explanation:

$\text{If}\ x_1\ \text{and}\ x_2\ \text{are the roots of the quadratic equation}\ ax^2+bx+c=0,\\\text{then}\ ax^2+bx+c=a(x-x_1)(x-x_2).\\\\\text{If}\ x_1\ \text{and}\ x_2\ \text{, then they are the roots of the quadratic equation.}\\\\\text{We have}\ x_1=-4\ \text{and}\ x_2=5.\ \text{Therefore we have the equation:}\\\\a(x-(-4))(x-5)=0\\\\a(x+4)(x-5)=0\qquad\text{for any value of}\ a\ \text{except 0}.$

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WORTH 20 POINTS HELP

vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

$RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}$

$ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}$

$TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}$

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$QR = \frac{9 + 1}{2 + 3} = \frac{10}3$

$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

$ST = \frac{5+5}{-4 + 7} = \frac{10}3$

$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

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6 0

1 year ago

10 ft

Gnom [1K]

Answer:

105.12 feets

Step-by-step explanation:

From the figure x we can identify a rectangle and a semicircle :

Area of rectangle = Length * width

Area = 8 * 10 = 80 feet²

The Area of a semicircle = 1/2πr²

Radius, r = 8 /2 = 4 feets

A = 1/2 * 3.14 * 4²

A = 3.14 * 8

A = 25.12 feet²

Area of figure = 80 + 25.12 = 105.12 feets

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2 years ago

In a box there are two prizes that are worth $4, a single prize worth $20, and a single prize worth $200. A player will reach in

Ronch [10]

Answer:

Step-by-step explanation:

The player has a 1/4 chance of drawing any of the 4 prizes. This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $20 is 1/4 and the probability of drawing a prize of $200 is also 1/4. To find the fair price of the game, we have to calculate the expected value that the player will gain. This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all the obtained values togueter. Thus, the fair price of the game is

$4 * \frac{1}{2} + 20 * \frac{1}{4} + 200 * \frac{1}{4} = 57$

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2 years ago

Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about

Diano4ka-milaya [45]

Semi perimeter:-

$\\ \rm\rightarrowtail s=\dfrac{a+b+c}{2}$

$\\ \rm\rightarrowtail s=\dfrac{1.8+2.4+3}{2}$

$\\ \rm\rightarrowtail s=\dfrac{7.2}{2}=3.6cm$

Apply heron s formula

Area:-

$\\ \rm\rightarrowtail \sqrt{s(s-a)(s-b)(s-c)}$

$\\ \rm\rightarrowtail \sqrt{3.6(3.6-1.8)(3.6-3)(3.6-2.4)}$

$\\ \rm\rightarrowtail \sqrt{3.6(1.8)(0.6)(1.2)}$

$\\ \rm\rightarrowtail \sqrt{4.6656}$

$\\ \rm\rightarrowtail 2.16cm^2$

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1 year ago

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Solve the equation: 10 = -4 + x

Sonja [21]

10= -4 + x x=14 because you do the opposite of the sign you see in this case its a plus sign so you subtract -4 from ten and since the 4 is a negative and your subtracting you would add 4 I know this probably didn't help it sounds really confusing but I have hope that it did :)

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2 years ago

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