Mathematics, 27.01.2022 07:30 Powerhickory1313

I need help figuring out what to do with this problem, please help if you can :))

Answers: 1

Show answers

Answers

Answer from: bbysl15

x = 3; y = 3/2; z = -1

Step-by-step explanation:

The diameter of the circle is 41, so the radius is 41/2.

DA, DB, and DC are radii of the circle, so their lengths are equal and they are half of the diameter.

DA = DB = DC = 41/2

Set each expression equal to 41/2.

Then you have a system of 3 equations in 3 variables.

8x + 2z - 3/2 = 41/2

6x + y + 1 = 41/2

11y - 2z + 2 = 41/2

Multiply both sides of all equations by 2 to get rid of the fractions.

16x + 4z - 3 = 41

12x + 2y + 2 = 41

22y - 4z + 4 = 41

Move all constants to the right side.

16x + 4z = 44 (I'll name this equation Equation 1.)

12x + 2y = 39 (This is Equation 2.)

22y - 4z = 37

Line up the variables.

16x + 4z = 44

12x + 2y = 39

22y - 4z = 37

We will use the elimination method.

Add the first and third equations to eliminate z.

Write the second equation below it.

16x + 22y = 81

12x + 2y = 39

Now you have a system of 2 equations in 2 unknowns.

We will now eliminate y. Multiply he second equation by -11 and write it below the first equation. Then add them.

16x + 22y = 81

(+) -132x - 22y = -429

-116x = -348

Divide both sides by -116.

x = 3

Plug in 3 for x in Eq. 1 and solve for z.

16x + 4z = 44 Eq. 1

16(3) + 4z = 44

48 + 4z = 44

4z = -4

z = -1

Plug in 3 for x in Eq. 2 and solve for y.

12x + 2y = 39 Eq. 2

12(3) + 2y = 39

36 + 2y = 39

2y = 3

y = 3/2

x = 3; y = 3/2; z = -1

Answer from: Quest

are you an artist's daughter? cuz dang you a fine piece of art, girl.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Which functions are even? check all of the boxes that apply. f(x) = x4 – x? f(x) = x2 – 3x + 2 f(x) = (x - 2) f(x) = x done

Answers: 3

Answer

Mathematics, 21.06.2019 16:00

What is the value of x in the diagram below?

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

You eat $0.85 for every cup of hot chocolate you sell. how many cups do you need to sell to earn $55.25

Answers: 2

Answer

Mathematics, 22.06.2019 02:00

Hurry!me out! m c 8 10 12 gracie's art box has 5 less crayons, c, than three times the number of markers, m. function: c = 3m - 5 complete the table to show how the number of crayons depends on the number of markers. enter answers in order from top to bottom.

Answers: 2

Answer

You know the right answer?

I need help figuring out what to do with this problem, please help if you can :))
...

Questions