Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. Please explain how you got the answer. e^x=3.4

2^x+6=3

Answers

Answer 1

Answer: $e^x=3.4\n\nlne^x=ln3.4\n\nx=ln3.4\n\nx\approx1.22$

$2^(x+6)=3\n\nlog_22^(x+6)=log_23\n\nx+6=log_23\n\nx=log_23-6\n\nx\approx1.58-3\n\nx\approx-1.42$

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A conference room is in the shape of a rectangle. Its floor has a length of (x − 4) meters and a width of (3x − 1) meters. The expression below represents the area of the floor of the room in square meters:(x − 4)(3x − 1)

Which of the following simplified expressions represents the area of the floor of the conference room in square meters? (5 points)

A.x2 − 13x + 4
B.3x2 − 13x + 4
C.3x2 − 11x + 4
D.x2 − 12x + 4

Answers

B. 3x^2 - 13x + 4 because you have to foil

What is the mixed number of 4/3

Answers

To find the mixed number:-

4/3 is an improper fraction.

How many times can 4 go into 3?

once, so the whole number is 1.

4-3 = 1

1 remainder, so 1 is the numerator.

1 1/3

Final answer: 1 1/3

4/3= 1 1/3

The final answer is 1 1/3~

Which of the following graphs represent functions Circle your answers. If it is a function, state the domainand range. If the graph is not included, make a table and graph the function by hand.

Answers

Answer:

Step-by-step explanation:

A). y = |2x - 3| + 1

Domain of function is defined by the x-values (Input values) and Range by the y-values(Output values).

From the graph,

Domain : (-∞, ∞)

Range : [1, ∞)

B). Table of the input-output values of the function,

y = x² - 2x + 1

x -2 -1 0 1 2

y 9 4 1 0 1

By graphing the function as attached,

Domain of the function : (-∞, ∞)

Range of the function : [0, ∞)

C). x² + y² = 3²

Domain of the function : [-3, 3]

Range of the function : [-3, 3]

D). x = 5

Domain of the line : [5, 5]

Range of the line : (-∞, ∞)

Evaluate the cube of a fraction number (4/7)3

Answers

Answer:

$(64)/(343)$

Step-by-step explanation:

$((4)/(7)) ^(3)$

= $(4^3)/(7^3)$

= $(64)/(343)$

What is the solution set for x in log4(x+5)+log4x=log4 14

Answers

$log_ {4} (x+5) + log_4(x) = log_4(14)$

For logs with same base :

$log_b(f(x)) + log_b(g(x)) = log_b(f(x)*g(x))$

$Log_4(x+5) + log_4(x) =log_4((x+5)x)$

$log_4((x+5) = log_4(14)$

When the logs have the same base :

$log_b(f(x)) = log_b(g(x))$

$F(x) = g(x)$

For $log_4((x+5)x) = log_4(14)$

Solve $(x+5)x = 14$

expand

$(x+5)x = x^2 + 5x$

$x^2+5x+14$

$(x-2)(x+7) = 0$

$x = 2 , x = - 7$

Therefore, the final solution : $x = 2$

hope this helps!

The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10Find d when v=70