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bogdanovich [222]

3 years ago

7

Find out for what value of the variable:

1 answer:

Burka [1]3 years ago

5 0

Answer:

$a=-1,\ a=-5$

$x=-2+i,\ -2-i$

Step-by-step explanation:

<u>Equations</u>

We have two cases where some variable is required to be found such that some condition is met. The first case is about finding the value of a that complies:

$a^2+7a+6=a+1$

Rearranging

$a^2+6a+5=0$

Factoring:

$(a+1)(a+5)=0$

There are two solutions:

$a=-1,\ a=-5$

The second case requires us to find the value of x such that

$3x^2-x+1 =2x^2+5x-4$

Rearranging

$x^2+4x+5=0$

This second-degree equation has no real roots. We'll offer the imaginary (complex) solutions:

$x=-2+i,\ -2-i$

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What is the factored form of 125a^6-64?

Afina-wow [57]

Answer:

It's B. on EtDtGtE

Step-by-step explanation:

8 0

3 years ago

30 treadmills to 36 elliptical machines write the ratio in simplest form

coldgirl [10]

Answer:30:36

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

I'm stuck on this question, any ideas? thanks

True [87]

Answer:

$\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}=-1/36$

Step-by-step explanation:

So we have the limit:

$\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}$

Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:

$\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}\cdot (\frac{(6+x)(6)}{(6+x)(6)})$

Distribute:

$=\lim_{x \to 0} \frac{(6)-(6+x)}{x(6+x)(6)}$

Simplify the numerator:

$=\lim_{x \to 0} \frac{6-6-x}{x(6+x)(6)}\\=\lim_{x \to 0} \frac{-x}{x(6+x)(6)}$

Both the numerator and the denominator have an x. Cancel:

$=\lim_{x \to 0} \frac{-1}{(6+x)(6)}$

Direct substitution:

$= \frac{-1}{(6+0)(6)}$

Simplify:

$=-1/36$

And that's our answer.

And we're done!

8 0

3 years ago

Read 2 more answers

If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fo

amm1812

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

$(f \circ g)(x) = f(g(x))$

In this case:

$f(x) = 4x^2 - 8x - 20$

$g(x) = 2x + a$

So

$(f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20$

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when $x = 0, f(g(x)) = 25$ . So

$4a^2 - 8a - 20 = 25$

$4a^2 - 8a - 45 = 0$

Solving a quadratic equation, by Bhaskara:

$\Delta = (-8)^2 - 4(4)(-45) = 784$

$x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5$

$x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5$

The possible values are a = -2.5 or a = 4.5.

5 0

3 years ago

If represents the number of bacteria in a culture at time t, how many will there be at time

Crazy boy [7]

Answer:

Population of bacteria at time $t = 6$ is $2441$

Step-by-step explanation:

The complete question is

If $y = 10 (2.5)^t$ represents the number of bacteria in a culture at time t, how many will there be at time $t = 6$

Solution

Given

The population of bacteria after time t is equal to $y = 10 (2.5)^t$

Population when at time $t = 6$

We will substitute the value of time in above equation.

$y = 10 (2.5)^6\\y = 10 *244.14\\y = 2441.4 = 2441$

6 0

3 years ago