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3 years ago

X^2-x-6=0 Solve for X Show Work 10 Points Will Give branliest!

Mathematics

1 answer:

ss7ja [257]3 years ago

7 0

Answer:

there are two values for 'x'; one = 3 and the other is -2

Step-by-step explanation:

two answers because this is a quadratic equation which, when graphed, will produce a u-shaped curve which intersects the x-axis in the two coordinates listed above

x^2 - x - 6 = 0

use the 'foil' method backwards to find out two factors of 6 which will produce a -6 when multiplied and negative one when added; they are:

(x - 3)(x + 2)=0

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

An advertiser drops 10,000 leaflets on a city which has 2000 blocks. Assume that each leaflet has an equal chance of landing on

Ira Lisetskai [31]

Answer:

0.00673

Step-by-step explanation:

As each of the 10000 leaflets has equal chance on landing into 1 of the 2000 blocks, this means each leaflet has a probability of 1/2000 to land on the 1st block, 1/2000 to land on the 2nd lock, 1/2000 to land on the 3rd block, and so on.

The probability that a particular block will receive no leaflet is chance of each leaflets to land on the other 1999 blocks, which has a chance of 1999/2000. For all 10000 leaflets to happen like this independently, then the total probability is

$\left(\frac{1999}{2000}\right)^{10000} = 0.00673$

5 0

3 years ago

Is (0,3) a solution to the equation y = x + 3?

Anna11 [10]

Yes,
y=x+3
if x=0,
y=0+3
y=3
therefore (0,3) is a solution

3 0

3 years ago

Read 2 more answers

Think about converting 48% to an equivalent fraction in reduced form. If the denominator is 25, what is the numerator?

bulgar [2K]

Answer:

the numerator is 12

Step-by-step explanation:

since 48 is a percent, it would be put as 48/100 as a fraction. since both the numerator and denominator are divisible by 4, you can reduce the fraction into 12/25. Since the question is asking what the numerator was when the denominator was 25, the answer is 12.

8 0

4 years ago

Each crate holds 25 reusable water bottles. Each crate costs $45. How much should the track team charge for each water bottle to

Reptile [31]

Answer:

$ 9 each bottle

Step-by-step explanation:

1 crate = $45

1 crate = 25 bottles

if we want to earn $180 per crate , we have to add this value to the $45

45 + 180 = 225

if the value of the box to win $180 is $225, we have to divide the new value by 25 (number of bottles) and we will have what we will have to charge each bottle

225/25 = 9

we have to charge $ 9 each bottle to earn $ 180 per crate

7 0

3 years ago