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3 years ago

Which expression has an equivalent value to x2 + 9x + 8 for all values of x?

Mathematics

2 answers:

Sindrei [870]3 years ago

7 0

The first one! hope it helps

guapka [62]3 years ago

5 0

First One

If you distribute this
(x*x) + (x*8) + (x*1) + (8*1)
x^2 + 8x + 1x + 8
x^2 + 9x + 8

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Suppose a population is growing by 8% each year. How many years will it take the population to double?

Doss [256]

ANSWER

$\text{9 years}$

EXPLANATION

We want to find the number of years that it will take the population to double.

To do this, we have to apply the exponential growth function:

$y=a(1+r)^t$

where y = final value

a = initial value

r = rate of growth

t = time (in years)

For the population to double, it means that the final value must be 2 times the initial value:

$y=2a$

Substitute the given values into the function above:

$\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}$

To solve further, convert the function from an exponential function to a logarithmic function as follows:

$\log _{1.08}2=t$

Solve for t:

$\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}$

It will take 9 years for the population to double.

4 0

1 year ago

Carlos drunk 2740 milliliters after football practice how much liters does he drink

Anni [7]

2.74 liters since 1000mL is a liter.

7 0

3 years ago

Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4 On a coordinate plane, 2 straight lines are shown.

Katen [24]

Answer:

(4,0)

Step-by-step explanation:

we have

$y< 3x-1$ ----> inequality A

$y \geq -x+4$ ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each ordered pair

case 1) (4,0)

Inequality A

$0< 3(4)-1$

$0< 11$ ----> is true

Inequality B

$0 \geq -(4)+4$

$0 \geq 0$ ----> is true

the ordered pair makes both inequalities true

case 2) (1,2)

Inequality A

$2< 3(1)-1$

$2< 2$ ----> is not true

the ordered pair not makes both inequalities true

case 3) (0,4)

Inequality A

$4< 3(0)-1$

$4< -1$ ----> is not true

the ordered pair not makes both inequalities true

case 4) (2,1)

Inequality A

$1< 3(2)-1$

$1< 5$ ----> is true

Inequality B

$1 \geq -(2)+4$

$1 \geq 2$ ----> is not true

the ordered pair not makes both inequalities true

5 0

3 years ago

Read 2 more answers

The function f(x) = x2 + 10x – 3 written in vertex form is f(x) = (x + 5)2 – 28. What are the coordinates of the vertex?

Alexxandr [17]

Vertex form uses the following formula:

$y = a(x-h)^2 + k$

Identify the values of h and k in your function:

$(x+5)^2 - 28$
$h = -5, k = -28$

The vertex is found with the following point:

$(h,k)$
$\text{Vertex: (-5, -28)}$

The vertex will be found at (-5, -28).

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3 years ago

3 cm 4 cm Find the area. A = 1/2 (a*P)

ss7ja [257]

The answer would be 3:33333

3 0

2 years ago