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3 years ago

Solve for equation x. 3In(x)+2In(4)=In(128)

1 answer:

3 0

$Domain:\ x > 0\\\\3\ln(x)+2\ln(4)=\ln(128)\qquad\text{use}\ \lag_ab^n=n\log_ab\\\\\ln(x^3)+\ln(4^2)=\ln(128)\qquad\text{use}\ \log_ab+\ln_ac=\ln_a(bc)\\\\\ln(16x^3)=\ln(128)\iff16x^3=128\qquad\text{divide both sides by 16}\\\\x^3=8\to x=\sqrt[3]8\\\\\boxed{x=2}\in D$

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$25,000 $45,000 $55,000 $25,000 $35,000 $1,000,000 $35,000 $45,000 $55,000 $25,000 Which of these is the MOST reasonable represe

MaRussiya [10]

45,000 would be the normal pay for a typical employee

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3 years ago

Help me with this one problem please :( <br> Find the following arc measures.

r-ruslan [8.4K]

Answer:

Arc KL $=23$

Arc OM $=113$

Step-by-step explanation:

We know that Angle NPM is equal to 90 degrees.

Therefore, Angle KPM is also equal to 90 degrees.

We are told that Arc LM is equal to 67.

Thus, the measure for Arc KL is equal to $90-67=23$

We also know that Angle OPN is equal to Angle KPL.

Therefore, the measure of Arc ON $=23$

Using that information, we know that Arc OM is equal to $90+23=113$

Hope I helped!

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3 years ago

ASAP BRAINLIEST !! Luis is given the fraction 4/5. He is told to create an equivalent fraction with a numerator of 32. Explain t

solniwko [45]

Answer: answer 40.

Step-by-step explanation:

Note : lets make x the missing denominator.

I would take the 4/5 and set it equals to 32/x

we then cross multiply

where it would be 4 * x = 32 * 5

it would then be 4x = 160

we would then divide 160 by 4

x = 160/ 4

and x would be 40

.... therefore the missing denominator is 40.

8 0

3 years ago

Read 2 more answers

8+0=8 describe the number sentence

Wittaler [7]

Whatever is adding with 0 its that number its like mulitipulcation with 1 because whatever is times by one like 25x1= 25

8 0

3 years ago

Read 2 more answers

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago