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3 years ago

7

use factoring solve x^3-9x=0, then using the quadratic formula sole 49/2 - 1/4 x^2, explain how you solved and use the vocab wor

ds quadratic formula, factoring, completing the square and discriminant

1 answer:

Simora [160]3 years ago

4 0

Answer:don’t

Step-by-step explanation:

Know

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Please help me urgent!!

arsen [322]

<h3>Hey! </h3>

$\sf \longmapsto S_{ 20} = \dfrac{n}{2} \times 2a + (n - 1)d \\ \\ \sf\longmapsto S_{20}= \dfrac{20}{2} \times 2(2) + (20 - 1)6 \\ \\ \sf\longmapsto S_{20} = 10 \{ 4 + 114 \} \\ \\ \sf \longmapsto \boxed{\bf{S_{20} = 1180}}$

Hope it helps :)

8 0

3 years ago

mr. ken's class is collecting empty water bottles. they started with 17 water bottles on day 1. on day 3, they had 30 water bott

Oxana [17]

They had 23 and 38 water bottles on day 2 and day 4 respectively. Also, there will be 68 water bottles on day 7.

<u><em>Explanation</em></u>

Suppose, the equation representing the number of bottles is $y= ax^2 +bx+c$ , where $x$ is the number of days.

There are 17 water bottles on day 1, 30 water bottles on day 3 and 47 water bottles on day 5

So, the three points in the form of (x, y) are: (1, 17) , (3, 30) and (5, 47)

Plugging these three points into the above equation, we will get .....

$17=a(1)^2 + b(1) +c\\ a+b+c=17 ............................ (1)\\ \\ 30=a(3)^2+b(3)+c\\ 9a+3b+c=30 ......................... (2) \\ \\ 47=a(5)^2+b(5)+c\\ 25a+5b+c=47 ......................... (3)$

Subtracting equation (1) from equation (2) , we will get .....

$8a+2b=13 ..................... (4)$

Subtracting equation (2) from equation (3) , we will get .....

$16a+2b=17 ...................... (5)$

Now, subtracting equation (4) from equation (5) , we will get ......

$16a -8a = 17-13\\ \\ 8a= 4\\ \\ a=\frac{4}{8}= 0.5$

Substituting this $a= 0.5$ into equation (4) ........

$8(0.5)+2b=13\\ \\ 4+2b=13\\ \\ 2b=9\\ \\ b=\frac{9}{2}=4.5$

Again, substituting $a=0.5$ and $b=4.5$ into equation (1) , we will get ......

$0.5+4.5+c=17\\ \\ 5+c=17\\ \\ c=17-5 =12$

So, <u>the equation will be now</u>: $y= 0.5x^2 +4.5x+12$

For finding the number of bottles on day 2 , day 4 and day 7 , we need to plug $x=2 , 4, 7$ respectively into the above equation.

For $x= 2$ , $y= 0.5(2)^2 +4.5(2)+12 = 2+9+12= 23$

For $x= 4$ , $y= 0.5(4)^2 +4.5(4)+12 = 8+18+12= 38$

For $x= 7$ , $y= 0.5(7)^2 +4.5(7)+12 = 24.5+31.5+12= 68$

So, they had 23 water bottles on day 2 and 38 water bottles on day 4

Also, there will be 68 water bottles on day 7

6 0

3 years ago

The price of a cup of coffee was $2.20 yesterday. Today, the price rose to $2.55 Find the percentage increase. Round your answer

mrs_skeptik [129]

Answer:

%15.9 increase

Step-by-step explanation:

8 0

2 years ago

GEOMETRY HELP! <br><br> This is my last question and I don’t know what the answer is! Please help!

Angelina_Jolie [31]

Temporarily subdivide the given area into two parts: a large rectangle and a parallelogram. Find the areas of these two shapes separately and then combine them for the total area of the figure.

By counting squares on the graph, we see that the longest side of the rectangle is the hypotenuse of a triangle whose legs are 8 and 2. Applying the Pyth. Thm., we find that this length is √(8^2+2^2), or √68. Similarly, we find the the width of this rectangle is √(17). Thus, the area of the rectangle is √(17*68), or 34 square units.

This leaves the area of the parallelogram to be found. The length of one of the longer sides of the parallelogram is 6 and the width of the parallelogram is 1. Thus, the area of the parallelogram is A = 6(1) = 6 square units.

The total area of the given figure is then 34+6, or 40, square units.

7 0

4 years ago

Solve the following.

never [62]

Answer:

b. x = 11/8, x = 59/72.

Step-by-step explanation:

4|8x - 6| = 5|-8x + 7|

square both sides:

16(64x^2 - 96x + 36) = 25( 64x^2 - 112x + 49)

1600x^2 - 1024x^2 - 2800x + 1536x + 1225 - 576 = 0

576x^2 - 1264x + 649 = 0

x = [1264 +/- √(1264^2 - 4 * 576* 649)] / (2*576)

x = 11/8, x = 59/72.

3 0

3 years ago