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3 years ago

Which are the solutions to the quadratic equation x^2=9x+6

1 answer:

5 0

I will use a quadratic formula:

$x^2=9x+6\ \ \ \ |-9x-6\\\\x^2-9x-6=0\\\\a=1;\ b=-9;\ c=-6\\\\b^2-4ac=(-9)^2-4\cdot1\cdot(-6)=81+24=105\\\\\sqrt{b^2-4ac}=\sqrt{105}\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_1=\dfrac{-(-9)-\sqrt{105}}{2\cdot1}=\dfrac{9-\sqrt{105}}{2}\\\\x_2=\dfrac{-(-9)+\sqrt{105}}{2\cdot1}=\dfrac{9+\sqrt{105}}{2}$

You might be interested in

The length and width of a rectangle are in a 3:5 ratio. The perimeter of the rectangle is 64. What are the length and width of t

Levart [38]

Hey there! I'm happy to help!

We know that the perimeter is 2L+2W. Le'ts plug in the values 3 and 5 from our ratio and see what our perimeter would be with that.

2(3)+2(5)

6+10

How can we get this 16 to 64?

64/16=4

So, we need to multiply this length and width by four to get 64 as our perimeter!

3*4=12

5*4=20

We can plug this into our perimeter equation

2(12)+2(20)

24+40

Therefore, our length is 12 and our width is 20.

Have a wonderful day! :D

5 0

3 years ago

An online furniture store sells chairs for $200 each and tables for $800 each. Every day, the store can ship at most 19 pieces o

HACTEHA [7]

Answer:

9 tables (see below)

Step-by-step explanation:

Let t represent the number of table sales required to meet revenue requirements. The total of sales for the day must be ...

7(200) +t(800) ≥ 8000

800t ≥ 6600 . . . . . . . . . . subtract 1400

t ≥ 8.25

If additional sales are limited to tables, the store must sell at least 9 tables. The revenue goal can also be met by selling 1 chair and 8 tables. (A chair brings in 0.25 times the revenue of a table.)

If the store sells 5 more chairs, it only needs to sell 7 tables. (This combination will result in 19 pieces being sold.)

3 0

3 years ago

Read 2 more answers

A ball is thrown in the air from a height of 3 m with an initial velocity of 12 m/s. To the nearest tenth of a second, how long

stepladder [879]

Answer: 1.4 seconds

<u>Step-by-step explanation:</u>

The equation is: h(t) = at² + v₀t + h₀ where

a is the acceleration (in this case it is gravity)
v₀ is the initial velocity
h₀ is the initial height

Given:

a = -9.81 (if it wasn't given in your textbook, you can look it up)
v₀ = 12
h₀ = 3

Since we are trying to find out when it lands on the ground, h(t) = 0

EQUATION: 0 = 9.81t² + 12t + 3

Use the quadratic equation to find the x-intercepts

a=-9.81, b=12, c=3

$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(12)\pm \sqrt{(12)^2-4(-9.81)(3)}}{2(-9.81)}\\\\\\x=\dfrac{-12\pm 16.2}{-19.62}\\\\\\x=\dfrac{-12+ 16.2}{-19.62}=-0.2\qquad x=\dfrac{-12- 16.2}{-19.62}=\large\boxed{1.4}\\$

Note: Negative time (-0.2) is not valid

4 0

3 years ago

1. is 9 1/10 closer to 9 or 10?

Bumek [7]

Answer:

1. 9 1/10 is closer to 9

2. 6 7/10 is closer to 7

3. 7 5/8 is closer to 8

4. 2 1/7 is closer to 2

5 0

2 years ago

Read 2 more answers

I need a real answer to this problem and if you can't answer then please don't answer this. Just give me the answer for the blan

Harlamova29_29 [7]

To divide the triangles into these regions, you should construct the <u>perpendicular bisector</u> of each segment.
These perpendicular bisectors intersect and divide each triangle into three regions.
The points in each region are those closest to the vertex in that <u>region</u>.

<h3>What is a triangle?</h3>

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

<h3>What is a line segment?</h3>

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

<h3>What is a perpendicular bisector?</h3>

A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.

In this scenario, we can reasonably infer that to divide the triangles into these regions, you should construct the <u>perpendicular bisector</u> of each segment. These perpendicular bisectors intersect and divide each triangle into three regions. The points in each region are those closest to the vertex in that <u>region</u>.

Read more on perpendicular bisectors here: brainly.com/question/27948960

#SPJ1

5 0

2 years ago