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Kitty [74]
3 years ago
5

What is the solution to the following system?​

Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0

Answer:

(2,1,0)

Step-by-step explanation:

3x+3y+6z=9

3(2)+3(1)+6(0)=9

6+3+0=9

6+3=9

9=9

x+3y+2z=5

x(2)+3(1)+2(0)=5

2+3+0=5

2+3=5

5=5

3x+12y+12z=18

3(2)+12(1)+12(0)=18

6+12+0=18

6+12=18

18=18

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What is the area of a circle whose equation is (x-3)² + (y + 1) ² =81?
kupik [55]
Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle: 

\frac{(x-x_{1})^2}{r^2}+ \frac{(y-y_{1})_^2}{r^2}=1

Where (x_{1}, y_{1}) is the centre of the circle. In this case, we don't need to know the centre. Just the radius. 

Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81. 

\frac{(x-3)^2}{81}+ \frac{(y+1)^2}{81}=1

Great! We now know the radius of the circle. It is \sqrt{81} because it is the bottom fraction. Now we know that the radius is 9. 

So now lets input this into the area of circle formula: 

A=πr^2 

Now we insert our radius. 

A=9^2π 

=A=81π 

You can convert that into a decimal if you wish. 

Hope this helped!

~Cam943, Moderator
4 0
3 years ago
Word problem with time....find the answer pleaseee
topjm [15]

Answer:

10.35 am

Step-by-step explanation:

Find the LCM

LCM = 275 minutes ÷ 60 minutes to change into hours

= 4hrs 35 min

6.00am + 4hrs 35min

= 10.35 am

8 0
3 years ago
Using the net below, find the surface area
polet [3.4K]

Answer:

56 cm^2

Step-by-step explanation:

Surface area is just finding the areas of each face in a figure. As we are given a net of a figure, it is much easier for us to calculate it.

Area of square base (side^2)

4^2 = 16 cm^2

Area of ONE triangular face (1/2 x b x h):

1/2 x 4 x 5 = 10 cm^2

Multiply that by 4 because we have 4 triangular faces: 10 cm^2 x 4 = 40 cm^2

ADD all the areas of triangles and square:

16 cm^2 + 40 cm^2 = 56 cm^2

HOPE THIS HELPS

Have a nice day!

4 0
2 years ago
Cot^2x csc^2x + 2 csc^2x –cot^2 = 2
kow [346]

Answer:

x = π/2 + πk

Step-by-step explanation:

cot² x csc² x + 2 csc² x − cot² x = 2

Multiply both sides by sin² x:

cot² x + 2 − cos² x = 2 sin² x

Add cos² x to both sides:

cot² x + 2 = 2 sin² x + cos² x

Pythagorean identity:

cot² x + 2 = sin² x + 1

Subtract 1 from both sides:

cot² x + 1 = sin² x

Pythagorean identity:

csc² x = sin² x

Multiply both sides by sin² x:

1 = sin⁴ x

Take the fourth root:

sin x = ±1

Solve for x:

x = π/2 + 2πk, 3π/2 + 2πk

Which simplifies to:

x = π/2 + πk

4 0
3 years ago
Joe spends 18.75% of his working day washing cars. He spends 1.5 hours washing cars. How many total hours does he work per day?
insens350 [35]

Answer:

8 hours

Step-by-step explanation:

Joe spends 18.75% of his working day washing cars.

Joe spends 1.5 hours washing car.

Therefore 18.75% is equal to 1.5 hour.

18.75% = 1.5 hour

1% = 1.5 ÷ 18.75 = 0.08 hour

100% = 0.08 x 100 = 8 hours

4 0
3 years ago
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