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elixir [45]
3 years ago
10

Which equation has the same solution

Mathematics
1 answer:
Temka [501]3 years ago
8 0
4x^2+48x=20
4x^2+48x+144=164
(2x+12).(2x+12)= + 59rt(164)
                                -
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Someone please help me with this question
mrs_skeptik [129]

Answer:

10x

Step-by-step explanation:

By definition

(f\codt g)(x)=f(x)\cdot g(x)

So we just need to multiply the two functions

(f\cdot g)(x)= f(x)\cdot g(x)\\=\sqrt{2x}\cdot \sqrt{50x}\\=\sqrt{(2x)\cdot (50x)}=\sqrt{100x^2}\\=10\sqrt{x^2}\\=10x \text{ since x is non negative}

8 0
2 years ago
The center of a circle is at (-5 12) and it has a radius of 16. what is the equation of the circle?
Naya [18.7K]

Answer:

(x+5)^2+(y-12)^2=256

Step-by-step explanation:

Comparing the given (x+5)^2+(y-12)^2=256

to                                   (x - h)^2 + (y - k)^2 = r^2,  

we see that h must be -5, k must be 12 and r must be 16.  This is the desired equation of the circle with center at (-5, 12) and radius 16.

4 0
3 years ago
2z-18-4z=-8 what is the value of z
zmey [24]

The z is 5

−2⋅<em>z</em>=−8+18

-

2

⋅

z

=

-

8

+

18

Simplify :

−2⋅<em>z</em>=10

-

2

⋅

z

=

10

Dividing by the variable coefficient :

<em>z</em>=−

10

2

z

=

-

10

2

Simplify :

<em>z</em>=−5

z

=

-

5

The solution of equation

2⋅<em>z</em>−18−4⋅<em>z</em>=−8

2

⋅

z

-

18

-

4

⋅

z

=

-

8

is

[−5]

7 0
3 years ago
Find the area of the triangle described.
Artemon [7]

Answer:

28

Step-by-step explanation:

You multiply 7 and 8, and then divide it by two.

8 0
3 years ago
Read 2 more answers
Classify each conic section and write its equations in standard form. Show work.
svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0
2 years ago
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