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svet-max [94.6K]
3 years ago
7

Given that g(x) = 2 x + 7 + 1, write an expression for f(x) in terms of z.

Mathematics
1 answer:
Oduvanchick [21]3 years ago
8 0

Answer:

so the answer is 10

Step-by-step explanation:

g(x)=×+7+1

2+7+1

10

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Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic
Marina86 [1]

Answer:

Equation of Sphere =  x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

(PA)^{2} = (2PB)^{2}

(PA)^{2} = 4 (PB)^{2}

(x - (-3))^{2} + (y - 6)^{2} + (z-3)^{2} = 4 x (x-6)^{2} + (y-2)^{2} + (z-(-3))^{2}

Solving the above equation:

(x + 3))^{2} + (y - 6)^{2} + (z-3)^{2} = 4 x {(x-6)^{2} + (y-2)^{2} + (z + 3))^{2}}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4 { x^{2} + 36 - 12x + y^{2} + 4 - 4y + z^{2} + 9 + 6z}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4x^{2} + 144 - 48x +4y^{2} + 16 - 16y + 4z^{2} + 36 + 24z

Putting the right hand side = 0 and solving the equation:

x^{2} - 4x^{2} + y^{2} - 4y^{2} + z^{2} - 4z^{2} + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3x^{2} - 3y^{2}  -3z^{2}  + 54x + 4y -30z -142  = 0

Taking (-) common

- ( 3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142) = 0

3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

7 0
3 years ago
Need full answer explaining please
Gnesinka [82]
A straight angle is equal to 180 degrees. 180-80=100. 100-60=40. so y=40. vertical angles are congruent so x=40 degrees.
5 0
3 years ago
Read 2 more answers
The first term of an arithmetic sequence is 7 and the sixth term is 22. Find(a)the common difference;(2)(b)the twelfth term;(2)(
SVEN [57.7K]

d = 3 , a₁₂ = 40 and Sx_{100} = 7775

In an arithmetic sequence the nth term and sum to n terms are

<h3>• an = a₁ + (n-1)d</h3><h3>• S_n = \frac{n}{2}[2a + (n-1)d]</h3><h3>where d is the common difference</h3><h3>a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3</h3><h3>a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40</h3><h3>S₁₀₀ = \frac{50}{2}[(2×7) +(99×3)</h3><h3>       = 25(14 + 297) = 25(311)= 7775</h3>
7 0
3 years ago
Can someone answer this plssss
Tpy6a [65]

Answer:

AB : Y= 4  CB: Y= -1

Step-by-step explanation:

I think?? I'm so so sorry I didn't really pay attention to these shape figures in math :(((

3 0
3 years ago
50 POINTS
exis [7]
This is the answer (4,3) x=4, y=3
6 0
3 years ago
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