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3 years ago

Simple 9th grade math

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

5 0

Answer:

-1078

Step-by-step explanation:

To find the nth term in an arithmetic sequence we use the following formula

aₙ=a₁+(n-1)*d

Where a₁ is the first time, and d is the common difference (in this case -20)

So we have

2+(55-1)*-20

2+(54)*-20

2-1080

-1078

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Which exponential function goes through the points (1, 16) and (4, 128)?

djyliett [7]

Answer:

Here is the complete question (attachment).

The function which represent the given points are $f(x)=8(2)^{x}$

Step-by-step explanation:

We know that a general exponential function is like, $y=a(b)^{x}$

We can find the answer by hit and trial method by plugging the values of $(x,y)$ coordinates.

Here we are going to solve this with the above general formula.

So as the points are $(1,16)$ then for $x=1,\ y=16$

Can be arranged in terms of the general equation.

$ab^1=16$ ...equation(1) and $ab^4=128$ ...equation(2)

$a\times b=16, then\ a=\frac{16}{a}$

Plugging the values in equation 2.

We have

$\frac{16}{b} b^4=128,16\times b^3=128,b=\sqrt[3]{\frac{128}{16}} =\sqrt[3]{8}=2$

Plugging $b=2$ in equation 1.

We have $a=\frac{16}{b} =\frac{16}{2} =8$

Comparing with the general equation of exponential $a=8$ and $b=2$

So the function which depicts the above points = $y=8(2)^x$

From theoption we have B as the correct answer.

7 0

3 years ago

500kg sack of sugar mass on moon

JulsSmile [24]

Answer:

82.67 Kilograms

4 0

3 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y , 8 z>

Δf = λ Δh

< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>

8 = 8 λ x -------------1

8 = 8 λ y ---- ------2

4 = 8 λ z ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

$4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36$

$\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36$

So the value of λ is

$\lambda =\pm \dfrac{1}{2}$

When λ = 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= 2 , y = 2 , z=1

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= - 2 , y = - 2 , z= - 1

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0

3 years ago

Read 2 more answers

What is (x − 3)(x − 5) = 35

JulijaS [17]

Answer:

x=10 x=-2

Step-by-step explanation:

(x − 3)(x − 5) = 35

FOIL

x^2 -5x-3x+15 = 35

Combine like terms

x^2 -8x+15 = 35

Subtract 35 from each side

x^2 -8x+15-35 = 35-35

x^2 -8x-20 =0

Factor

What 2 numbers multiply to -20 and add to -8

-10*2 = -20

-10 +2 = -8

(x-10)(x+2) =0

Using the zero product property

x-10 =0 x+2 = 0

x=10 x=-2

6 0

3 years ago

Select the expression that represents a rational function.

Sati [7]

Answer:

y = (x +2)/(x -3)

Step-by-step explanation:

A rational function is a function (y = ...) that has a definition that is the ratio of two polynomials.

Of the choices listed, the one attached is the rational function.

8 0

3 years ago