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3 years ago

determine if the sequence is geometric or arithmetic and find the ratio or difference. -1, 6, -36, 216

1 answer:

4 0

The sequence is an geometric progression;
Nth=a₁r^(n-1)
a₁ is the first term=-1
r=ratio=a₂/a₁=6/-1=-6

Nth=-1(-6^(n-1)

NTh=an

a₁=-1(-6⁰)=-1
a₂=-1(-6¹)=6
a₃=-1(-6²)=-36
a₄=-1(-6³)=216

therefore this serie is rising at an increasing fast speed, it is an geometric progression.

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Solve. 3x2 + 4x = –5 using quadratic equation ...?

cupoosta [38]

3x^2 + 4x - 5 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 3
b = 4
c = -5

x = [-4 ±√(16 + 60)]/6
x = [-4 ±√76]/6
x = [-4 ±√(2^2 * 19)]/6
x = [-4 ±2√19]/6
x = [-2 ±√19]/3

x = [-2 + √19]/3
x = [-2 + 4.35]/3
x = 2.35/3
x = 0.78 (rounded to the nearest hundredth)

x = [-2 - ±√19]/3
x = [-2 - 4.35]/3
x = -6.35/3
x = -2.12 (rounded to the nearest hundredth)

∴ x = -2.12 , 0.78 (rounded to the nearest hundredth)

6 0

3 years ago

If a polygon has six sides, then it is a hexagon. true or false.

slava [35]

If a polygon does not have six sides, then it is not a hexagon.

8 0

3 years ago

Write the product using exponents. 2⋅2⋅2⋅n⋅n Using exponents, the product is ?

Blababa [14]

The answer is 8n^2

2x2 is 4 x 2 is 8 two n variables so multiple it by 2 and you get your answer

3 0

2 years ago

I need help please.

Ivan

1. It is given that f(x) is 16 times the square root of x.

Putting that in mathematical terms we have,

f(x) = 16 * $\sqrt{x}$

also, y = f(x)

So, we have the function

y= 16 $\sqrt{x}$

4. We need to solve the inequality equation : 4x + 2y ≤ 6

Let us take the equation,

4x+2y ≤ 6

2y ≤ 6-4x

y ≤ $\frac{6-4x}{2}$

y ≤ 3-2x

So, any point (x,y) lies on the given inequality region, where y≤ 3-2x

5. Solving system of equations using addition method

Given:

-5x-y =38 ------> a

-6x-3y =60 -------> b

Divide the equation b by no. 3

(-6x-3y)/3 = 60/3

-2x-y = 20 -------> c

Subtracting equation c from a we have,

-5x-y - (-2x-y) = 38 - 20

-5x-y+2x+y = 18

-3x = 18

x = -6

Now, substituting the value of x in equation a, we get

-5(-6) - y =38

30-y =38

y= 30-38 = -8

y=-8

∴ x = -6 and y = -8

6. Finding composition of functions

Given : f(x) =15x + 7 ; g(x) = x² - 5x

To find : (f+g)(x)

(f+g) (x) = f(g(x))

So, replace the value of x in f(x) by g(x), where g(x)= x² - 5x

(f+g)(x) = 15(x²-5x) +7 =15x²-75x+7

∴ (f + g)(x) = 15x²-75x+7

7. System of 3 equations must be solved to find the solution

-8x-8y-5z=-6

7x-8y-9z =17

9x+2y+6z =-1

Solving by substitution method.

Isolate x from first equation :

x= (-6+8y+5z)/(-8)

Substitute this value of x in 2nd and 3rd equations.

$7 (- \frac{-6+8y+5z}{8})-8y -9z = 17$

$9(- \frac{-6+8y+5z}{8}) + 2y + 6z = -1$

Now, isolating y from the 2nd equation rewritten above, we have

y= - $\frac{107 z + 94}{120}$

Now substituting this value of y in the 3rd equation rewritten above, we have

$9(- \frac{-6+8(-\frac{107 z + 94}{120})+5z}{8}) + 2(-\frac{107 z + 94}{120}) + 6z = -1$

Isolating z from above equation, we have

z = -2

Substitute z= -2 in the equation of y, we have

y= - $\frac{107 (-2) + 94}{120}$ = 1

y = 1

Substituting the value of y and z, in the equation of x, we have

x= (-6+8(1)+5(-2))/(-8) = 1

x = 1

∴ x=1 ; y = 1 ; z = -2

8. 5x ≤ 7

Solving the above equation, we have

x ≤ 7/5

Please see attachment for the graph.

9. The given function is : g(y) = $\sqrt{y}$ -6

The domain is the set of values of y for which there can be a value of g(y).

Here g(y) can be real only if y is greater than or equal to 0.

∴ The domain of the given function is [0,∞) .

10. Given : y is a function of x.

Definition of function : A function is a relation that associates each element in the domain to one element of another set, the co-domain of the function.

∴ For each element x, in the domain, there is only one value of y in the range.